Structural glass flexural strengthening with CFRP composites and Fe-SMA based on passive, active and hybrid techniques

Universidade do Minho Escola de Engenharia Jorge de Araújo Rocha Structural glass flexural strengthening with CFRP composites and Fe-SMA based on passive, active and hybrid techniques October, 2022 Structural glass flexural strengthening with CFRP composites and Fe-SMA based on passive, active and hybrid techniques Jorge de Araújo Rocha UMinho | 2022 Universidade do Minho Escola de Engenharia October, 2022 Jorge de Araújo Rocha Structural glass flexural strengthening with CFRP composites and Fe-SMA based on passive, active and hybrid techniques Doctoral Thesis Civil Engineering Work conducted under supervision of Professor Eduardo Nuno Borges Pereira Professor José Manuel de Sena Cruz ii COPYRIGHT AND TERMS OF USE OF THIS WORK BY A THIRD PARTY This is academic work that can be used by third parties as long as internationally accepted rules and good practices regarding copyright and related rights are respected. Accordingly, this work may be used under the license provided below. If the user needs permission to make use of the work under conditions not provided for in the indicated licensing, they should contact the author through the RepositoriUM of Universidade do Minho. License granted to the users of this work Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International CC BY-NC-SA https://creativecommons.org/licenses/by-nc-sa/4.0/ iii ACKNOWLEDGMENTS This research has been carried out at the Civil Engineering Department of University of Minho, Portugal, under the supervision of Professor Eduardo Nuno Borges Pereira and co-supervision of Professor José Manuel de Sena Cruz. This work was financially supported by the Portuguese Foundation for the Science and Technology (Fundação para a Ciência e a Tecnologia, FCT) under the grant number SFRH/BD/122428/2016, which is gratefully acknowledged. This study would not have existed without the financial support of this institution. I’d like to start by saying “thank you so much!” to Professors Eduardo Pereira and José Sena Cruz. This sentence is clearly too short to express my deepest gratitude for their guidance, constant encouragement, confidence and enthusiasm throughout the development of this work, as well as for their profuse wisdom and knowledge. In addition, I would also like to highlight their human qualities and friendship. This work would not be the same without the inspiration, interesting discussions and careful reading of my supervisors. I can never thank them for how much I learned from them. I would like to thank all the staff of the Civil Engineering Department of University of Minho. I am especially grateful to all laboratory technicians of the Structural Laboratory of University of Minho, especially António Matos and Marco Peixoto. Also, I would like to acknowledge the Institute for Sustainability and Innovation in Structural Engineering (ISISE) for providing the facilities and resources to develop this thesis. I could not forget to thank the contribution of all the companies that have been involved for the development of this work: (i) COVIPOR – Companhia Vidreira do Porto Lda., especially Francisco Ferreira and Mauricio Sousa; (ii) S&P Clever Reinforcement Iberica Lda.; (iii) Sika AG Company; and (iv) re-fer AG Company. I would like to thank my peers and friends from the Civil Engineering Department of University of Minho, for the hours we spent together discussing the most varied topics with each other. I could not forget all my close friends, which supported and encouraged me throughout this work. Finally, I would like to dedicate this work to my grandparents, parents, sister and girlfriend. To my grandparents Maria and Manuel, to my parents Eugénia and Carlos and to my sister Filipa, “obrigado” for your constant presence and unconditional love. Now, in particular to Filipa, my soulmate, thank you for your love, kindness, support, dedication and strength. I am grateful to have your company every day of my life. Thank you all, you are the best!!! iv STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. University of Minho, October 31, 2022 Jorge de Araújo Rocha Assinado por: Jorge de Araújo Rocha Num. de Identificação: 14193031 Data: 2022.10.31 17:10:58+00'00' v “NOTHING IN LIFE IS TO BE FEARED, IT IS ONLY TO BE UNDERSTOOD. NOW IS THE TIME TO UNDERSTAND MORE, SO THAT WE MAY FEAR LESS.” Marie Curie vi ABSTRACT Contemporary architecture encourages the use of glass in structural applications. Glass industry has developed the thermal toughening to increase its tensile strength and lamination to prevent brittle failure. However, glass can still fail unexpectedly due to the growth of surface flaws. Recent studies have focused on glass composite systems, mainly using steel as reinforcement. Other reinforcement materials (e.g. CFRP and Fe-SMA) and application techniques (e.g. prestressing) need also to be explored, given their promising features to face the growing structural challenges. This thesis aimed at covering two main topics related to structural glass: (i) post-cracking performance and (ii) mechanical post-tensioning. Its main objective was to evaluate the feasibility of using CFRP and Fe-SMA as reinforcement in flexure to obtain ductile failure modes, as well as the application of post-tensioning to reduce the unpredictability of the glass fracture strength. The experimental programs included (i) tensile tests on double-lap joints to assess the bond performance of glass-toCFRP adhesive connections, (ii) flexural tests on small-scale monolithic glass beams with externally bonded CFRP or Fe-SMA reinforcements, and (iii) flexural tests on large-scale laminated glass beams with hybrid (EBR + NSM) strengthening. It was possible to obtain ductile failure modes when glass was strengthened with CFRP and Fe-SMA. The post-cracking performance was sensitive to the adhesive type, reinforcement material, strengthening system and, in the case of Fe-SMA reinforced glass, the activation temperature. Hybrid strengthening systems prevented premature debonding of the reinforcement and made better use of its tensile capacity. NSM-CFRP composite systems were safely prestressed and FRP peeling-off failure was avoided during load releasing. Considering the importance of design rules for practitioners, numerical modelling was carried out to assess (i) the efficiency of different constitutive models to simulate the non-linear behaviour of glass in tension and (ii) the influence of design parameters on the numerical response of glass composite systems. Further numerical simulations were performed to better understand the structural performance of CFRP reinforced glass elements, including at the level of the glass-to-CFRP adhesive joint. The results obtained were promising, and although additional studies are needed, new perspectives were opened for a future safer and widespread use of glass as a structural material. KEYWORDS: CFRP; Fe-SMA; Glass composite systems; Flexural response; Prestressing; Numerical modelling vii RESUMO A arquitetura contemporânea tem encorajado a aplicação estrutural do vidro. A indústria do vidro desenvolveu os processos de têmpera, de modo a aumentar a sua resistência à tração, e de laminação, com o propósito de evitar roturas frágeis. O vidro pode, ainda assim, romper inesperadamente devido à propagação de defeitos superficiais. Recentemente, os sistemas compósitos de vidro têm sido estudados como uma alternativa para prevenir roturas inesperadas, usando principalmente aço. Outros tipos de reforço recentes (ex: CFRP e Fe-SMA) e técnicas de aplicação (por exemplo, protensão) apresentam também características promissoras. Esta tese aborda dois tópicos cruciais no contexto do vidro estrutural: (i) o comportamento pósfissuração e (ii) o pré-esforço mecânico. A obtenção de modos de rotura dúcteis por via do reforço com CFRP e Fe-SMA e a redução da imprevisibilidade da resistência à tração do vidro por via da aplicação de pré-esforço foram os principais objetivos deste estudo. Os programas experimentais incluíram (i) ensaios em juntas de sobreposição dupla para caracterizar o desempenho de ligações adesivas vidro-CFRP, (ii) ensaios de flexão em vigas de vidro monolítico de pequena dimensão, reforçadas externamente com CFRP e Fe-SMA, e (iii) ensaios de flexão em vigas de vidro laminado de grande dimensão com sistemas de reforço híbridos (EBR + NSM). Foi possível obter roturas dúcteis em elementos estruturais de vidro reforçados com CFRP e Fe-SMA. O desempenho pós-fissuração mostrou ser sensível ao tipo de adesivo, ao material de reforço, ao sistema de reforço e, no caso de vidro reforçado com Fe-SMA, à temperatura de ativação. Os sistemas de reforço híbridos mostraram bons resultados na prevenção do destacamento prematuro do reforço. Considerando a importância das regras de projeto para os sistemas em estudo, realizaram-se simulações numéricas para avaliar (i) a eficácia de diferentes modelos constitutivos para simular o comportamento não-linear do vidro e (ii) a influência de parâmetros de projeto na resposta numérica de sistemas compósitos de vidro. Posteriormente realizaram-se ainda simulações numéricas adicionais para aprofundar o conhecimento sobre o desempenho estrutural de elementos de vidro reforçados com CFRP, incluindo simulações ao nível das juntas adesivas entre vidro e CFRP. Os resultados obtidos foram promissores e, embora sejam necessários estudos adicionais, abriram-se novas perspetivas para que a aplicação estrutural do vidro seja mais segura e generalizada no futuro. PALAVRAS-CHAVE: CFRP; Fe-SMA; Pré-esforço; Reposta à flexão; Simulação numérica; Sistemas compósitos de vidro xiv LIST OF FIGURES Figure 1.1: Research methodology ................................................................................................. 8 Figure 2.1: Schematic representation of the production process of float glass. Adapted from Henriques [4]. .............................................................................................................................................. 16 Figure 2.2: Comparison between the distributions of residual stress in (a) thermally toughened glass and (b) chemically toughened glass. Adapted from Huveners [1]. .................................................. 20 Figure 2.3: Comparison between the fracture patterns of (a) annealed glass, (b) heat-strengthened glass and (c) fully tempered glass. Adapted from Haldimann [2]. .................................................. 21 Figure 2.4: Evolution of the initial fracture strength and post-failure performance of glass as a function of the tempering level. Adapted from Sedlacek et al . [5] ................................................................ 23 Figure 2.5: Redistribution of normal strains during the cracking process of two-layer laminated glass panel: (a) uncracked stage; (b) cracking stage; and (c) post-cracking stage. Adapted from Molnár et al. [25]. ....................................................................................................................................... 23 Figure 2.6: Distribution of normal strains over the cross-section of a two-layer laminated glass: (a) monolithic limit; (b) intermediate stage; and (c) layered limit. Adapted from Molnár et al. [25]. ...... 24 Figure 2.7: Evolution of the shear modulus of the interlayers PVB Butacite [43] and SGP SentryGlass [44] for a reference temperature of 20 ºC. .................................................................................... 26 Figure 2.8: Structural glass applications: (a) pedestrian bridge designed by China Railway Major Bridge Reconnaissance & Design Institute Co Ltd. for Zhangjiajie Natural Park, China; (b) glazed floor at Apple Store in Paris, France [54]; (c) glazed roof at British Museum in London, UK [55]; and (d) glazed façade at 111 Main building in Salt Lake City, USA [54]. ............................................................... 29 Figure 2.9: Types of glass beams: (a) continuous beams applied in a historic house in Ireland [54]; and (b) segmented-bolted beams designed by Arup for the Medical School building in Glasgow, UK [14]. ............................................................................................................................................ 30 Figure 2.10: Examples of all-glazed structures: (a) glazed staircase at Apple Leidseplain in Amsterdam, Netherlands [54]; (b) Apple Pudong in Shanghai, China [54]; (c) Apple Story on 5 th Avenue in New York, USA [56]; and (d) glass bridge at CORE Shopping Centre in Calgary, Canada [57]. ............... 31 Figure 2.11: Difference between the transparency levels of (a) the original glass cube and (b) the glass cube rebuild in 2011 [56]. ........................................................................................................... 32 Figure 3.1: Structural behaviour of composite glass systems: (a) load vs. deflection diagram; and distribution of normal strains over the cross-section at the (b) elastic phase, (c) cracking phase and xv (d) yielding phase, as well as the crack growth. Note: the neutral axis (n.a.) is displayed as a horizontal dotted line. ................................................................................................................................... 39 Figure 3.2: Fully transparent pavilion built at Delft University using steel-reinforced glass beams [30]. ................................................................................................................................................... 42 Figure 3.3: Cross-section geometry of steel-reinforced glass beams manufactured and tested as part of research projects developed at Delft University of Technology: (a) Veer et al . [27]; (b) and (c) Bos et al . [6]; (d) Louter et al . [30]; (e) Louter [36]; and (f) Louter et al . [35]. Note: units in [mm]. ....... 43 Figure 3.4: Cross-section geometry of steel-glass composite beams tested by (a-c) Louter et al . [38] – (a) geometry 1 F ; (b) geometry 2 F ; and (c) geometry 3 F – and (d) Louter et al . [7]. Note: units in [mm]. ................................................................................................................................................... 44 Figure 3.5: Anchorage of the reinforcement element at the beam ends studied by Louter and Veer [35]: (a) system #1; (b) system #2; and (c) system #3. ................................................................. 45 Figure 3.6: Embedded reinforcement system: (a) assemblage of the laminated glass panel; and (b) embedded reinforcement acting as a connecting element. ....................................................... 47 Figure 3.7: Steel-framed glass beam developed by Belis et al . [5]: (a) cross-section-geometry and schematic representation of the connection between beam segments; and (b-c) Dutch Ministry of Finance in The Hague. Note: units in [mm]. .................................................................................. 48 Figure 3.8: Cross-section geometry of glass-timber composite beams tested by (a) Hamm [50], (b) Kreher [54] and (c) Kozlowski [52]. Note: units in [mm]. ......................................................... 49 Figure 3.9: SG-laminated glass beams with embedded GFRP reinforcement tested by Louter et al . [59]: (a) cross-section geometry; and (b) specimen. Note: units in [mm]. ...................................... 51 Figure 3.10: Cross-section geometry of GFRP-reinforced glass beams tested by (a) Correia et al . [11] and (b) Valarinho et al . [12]. Note: units in [mm]. ......................................................................... 53 Figure 3.11: Crack patterns of GFRP-reinforced glass beams tested by Valarinho et al . [12]: (a) SFlex beams; and (b) SDur beams. ........................................................................................................ 53 Figure 3.12: Glass-CFRP composite beams: (a) roof structure of the Loggia dei Vicari, in Italy [10]; and cross-section geometry of specimens tested by (b) Palumbo et al . [10], (c) Louter et al . [65] and (d) Cagnacci et al . [64,66]. Note: units in [mm]. ................................................................................ 55 Figure 3.13: Post-tensioned glass beams tested by (a and b) Louter et al . [9], (c and d) Cupác et al . [40], (e) Weller and Engelmann [71], (f) Jordão et al . [70] and (g) Louter et al . [9]. Note: units in [mm]. ................................................................................................................................................... 59 xvi Figure 3.14: Different anchoring systems studied by Louter et al . [33] for transferring the posttensioning force from the reinforcement to the glass. .................................................................... 62 Figure 3.15: Schematic phase diagram of Ni-Ti alloys, adapted from Rojob and El-Hacha [104]. .... 64 Figure 3.16: Behaviour of Fe-SMAs: (a) phase diagram [104] and (b) schematic activation procedure [92]. ............................................................................................................................................ 65 Figure I.1: Four-point bending tests of the glass-GFRP composite beams: (a) schematic representation; (b) experimental setup [19]. Note: units in [mm]. .......................................................................... 98 Figure I.2: Load vs . relative displacement obtained from tensile tests on double-lap joints with (a) polyurethane and (b) epoxy adhesives [19]. .................................................................................. 98 Figure I.3: Structural responses (load vs . deflection) obtained from the experimental tests: (a) S Dur beams; (b) S Flex beams [19]. ...................................................................................................... 99 Figure I.4: Experimental crack patterns: (a) S Dur beams; (b) S Flex beams [19]. ............................ 99 Figure I.5: Axial strains vs . load measured at different depths of the S Flex -1 beam mid-span section. ................................................................................................................................................. 100 Figure I.6: Damage law adopted for simulating glass behaviour. .................................................. 110 Figure I.7: Load vs . deflection curves of the S Dur and S Flex beams obtained from the SCM-FEMIX, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). .................................... 113 Figure I.8: Load vs . deflection curves of the S Dur and S Flex beams obtained from the SCM-ABAQUS, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). .................................... 114 Figure I.9: Load vs . deflection curves of the S Dur and S Flex beams obtained from the DPM-ABAQUS, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). .................................... 115 Figure I.10: Load vs . deflection curves obtained from the experimental tests and distinct numerical models: (a) S Dur beams; (b) S Flex beams. ................................................................................. 116 Figure I.11: Ratio between the slope of the load vs . deflection curves and the elastic stiffness for the S Dur beams obtained from the ABAQUS models. ....................................................................... 117 Figure I.12: Ratio Ev / Ew along the tangent line of the load vs . displacement curves of the DPMABAQUS. ................................................................................................................................... 117 Figure I.13: Load vs . deflection curves of the S Dur beams obtained from SCM-FEMIX and SCM-FEMIX 90º, and corresponding crack pattern at different phases, (i), (ii), (iii), (iv), (v) and (vi). ................ 120 Figure I.14: Load vs. displacement curves of S Dur beams obtained from the three initial material models and the SCM-FEMIX 90º. ................................................................................................ 120 Figure I.15: Sensitivity of both ABAQUS material models in relation to the mesh pattern. ............. 121 xvii Figure I.16: Sensitivity of both ABAQUS model in relation to the fracture energy. ......................... 123 Figure I.17: Sensitivity of DPM-ABAQUS in relation to the dilation angle. ...................................... 124 Figure I.18: Sensitivity of DPM-ABAQUS in relation to the shape of the yield surface. ................... 124 Figure I.19: Ek / Et ratio along the load vs . deflection curves of the (a) SCM-ABAQUS and (b) DPMABAQUS. ................................................................................................................................... 125 Figure I.20: Load vs. deflection curves of the S Flex beams obtained from SCM-FEMIX and SCM-FEMIXA, and corresponding crack pattern at different phases, (i) and (ii). ............................................. 126 Figure I.21: Load vs . deflection curves of the S Flex beams obtained from the three material models and the SCM-FEMIX A. ............................................................................................................... 126 Figure I.22: Elastic stiffness vs . deflection diagrams of the S Flex beams. ..................................... 127 Figure I.23: Load vs . deflection curves of the S Flex beams obtained from SCM-FEMIX and SCM-FEMIX A/90º, and corresponding crack pattern at different phases, (i) and (ii). ...................................... 128 Figure I.24: Load vs . deflection curves of the S Flex beams obtained from the three material models and the SCM-FEMIX A/90º. ........................................................................................................ 128 Figure I.25: Comparison between the numerical and experimental normal strains obtained at the midspan section of the SFlex-1 beam corresponding to (a) cracking load Fcr and (b) ultimate load Fult. ................................................................................................................................................. 130 Figure I.26: Localized bending effect at the GFRP reinforcement caused by the formation and propagations of a nearby ............................................................................................................ 131 Figure I.27: Ek / Et ratio along the load vs . deflection curves of the (a) SCM-ABAQUS and (b) DPMABAQUS. ................................................................................................................................... 132 Figure II.1: Double-lap joint tests: (a) specimen’s geometry, (b) studied connection and (c) connection cross-section. Units in [mm]. ...................................................................................................... 145 Figure II.2: Double-lap joint tests: (a) schematic representation and (b) image showing the measuring systems adopted. Units in [mm]. ................................................................................................ 147 Figure II.3: Region of interest defined to the DIC analysis of the double-lap joints. ........................ 148 Figure II.4: Typical tensile stress-strain curves of the tested adhesives: (a) SikaForce; (b) SikaDur; and (c) 3M. ....................................................................................................................................... 149 Figure II.5: Experimental and numerical load ( F ) – loaded end slip ( sle ) responses obtained from the series of double-lap joints (a) SF-L25 and (b) SF-L50 with the SikaForce adhesive, (c) SD-L25 and (d) SD-L50 with the SikaDur adhesive, and (e) 3M-L25 and (f) 3M-L50 with the 3M adhesive. Note: ‘Bond xviii Model’ is the analytical F – sle response obtained from the local τ – s laws calibrated in Section 4 for each type of adhesive. ................................................................................................................ 151 Figure II.6: Longitudinal strain in glass measured by strain gauges placed on the outer faces of both glass sheets,  , and tensile load, F , versus the loaded end slip, sle , for (a) SF-L25-I, (b) SF-L50-I, (c) SD-L25-I and (d) SD-L50-I. .......................................................................................................... 153 Figure II.7: Bond test region after collapse of double-lap joints, indicating the typical failure modes observed in each series, as well as the direction of load application. ........................................... 153 Figure II.8: Debonding at the glass/adhesive interface (a) in SF-L25 specimens and cohesive shear debonding in adherends (b) in SD-L25 specimens. In each case both images show the two opposite faces of the bonded connection after failure. ............................................................................... 154 Figure II.9: Comparison between F – sle curves extracted from the LVDTs and the DIC technique for (a) SF-L25-I, (b) SF-L50-I, (c) SD-L25-I and (d) SD-L50-I. ............................................................. 155 Figure II.10: Slip between the CFRP laminate and the glass sheets along Lb in (a) SF-L25-I and (b) SDL25-I, extracted from the DIC method for the last image captured before the failure. Note: all values in millimetres. ............................................................................................................................ 155 Figure II.11: Slip between the CFRP laminate and the glass sheets along Lb in (a) SF-L50-I and (b) SDL50-I, extracted from the DIC method for the last image captured before the failure. Note: all values in millimetres. ............................................................................................................................ 156 Figure II.12: Load ( F ) vs . slip ( sle ) response obtained for the SD-L50-I specimen, together with the maximum principal strain fields obtained with DIC at the ROI, showing the cracks formed at stages (a), (b), (c) and (d). .................................................................................................................... 158 Figure II.13: Cleavage effect in SF-L25-I (a) showing the lateral deflection of the glass sheet I (b) and in the glass sheet II (c) in relation to the CFRP laminate. Note: nomenclature presented in Figure II.1 and all values in mm. ................................................................................................................. 162 Figure II.14: Parameters involved in the analytical model [41]: (a) slip; (b) bond stress; (c) CFRP strain and (d) CFRP axial force. ............................................................................................................ 164 Figure II.15: Distribution of (a) maximum principal stress and (b) shear stress along the bond length obtained for the 3M adhesive from numerical simulations, at the instant when the tensile strength of the 3M adhesive at the loaded end section was reached and the adhesive failure was initiated. Note: values of stress in MPa. ............................................................................................................. 166 Figure II.16: Comparison of the experimentally obtained Maximum load ( Fmax ) for each bonded length ( Lb ) with the expected one using the analytical model for (a) SikaForce and (b) 3M adhesives. .... 167 xix Figure II.17: Geometry, boundary conditions and load configuration used in the numerical simulation of the behaviour of double-lap joints (a), and detail of the bond test region showing the studied connection including the mesh and the boundary conditions (b). ................................................. 169 Figure II.18: Numerical model used in the iterative procedure applied to the SF-L25 series, showing the points where the displacements were measured (a) for the initial τ – s relationship (b) and for the numerically fitted τ – seff law. ..................................................................................................... 171 Figure II.19: Numerical and experimental load ( F ) vs. free end slip ( sle ) responses for each series of double-lap joints: (a) SF-L25, (b) SF-L50, (c) SD-L25, (d) SD-L50, (e) 3M-L25 and (f) 3M-L50. ..... 172 Figure II.20: Distribution of slip, CFRP strain and bond stress along the bond length obtained from DIC method (DIC) and numerical simulations (NS) for (a) SF-L25-I, (b) SD-L25-I and (c) 3M-L25-I specimens. Note: values extracted when the maximum load was reached in each of the specimens. ................................................................................................................................................. 174 Figure II.21: Evolution of shear stress to shear strength ratio (horizontal axis) at different distances to the loaded end (vertical axis) along the ligament for both bond lengths of each adhesive: (a) SF, (b) SD and (c) 3M specimens. Note: values extracted from the numerical models for the average maximum load of the corresponding L25 series. ......................................................................... 175 Figure III.1: Typical tensile stress-strain curves of the adhesives used in this investigation ............ 187 Figure III.2: Double-lap joint tests: (a) specimen’s geometry; and (b) loaded end section. Units in [mm]. ................................................................................................................................................. 188 Figure III.3: Experimental load ( F ) vs . loaded end slip ( sle ) responses obtained from tensile tests on double-lap joints with (a) soft, (b) intermediate and (c) stiff adhesives. Adapted from Rocha et al. [26]. ................................................................................................................................................. 189 Figure III.4: Failure modes observed in double-lap joint tests: (a) debonding at the glass/adhesive interface in SF specimens; (b) tensile glass failure in 3M specimens; and (c) glass substrate failure and fibre-tear failure in CFRP in SD specimens. .......................................................................... 190 Figure III.5: Four point bending tests on glass-CFRP composite beams: (a) geometry and test configuration, including the lateral guides and the support frames used to guarantee the adequate support conditions; (b) cross-section of the beam specimens; and (c) experimental setup, including the region of interest defined to the DIC analysis of the specimens and detailing the speckle pattern. All units in [mm]. ....................................................................................................................... 191 xx Figure III.6: Strategies adopted to mitigate undesirable affects during the tests: (a) metallic frame to prevent torsional rotations at the supports sections; and (b) PTFE plates to avoid metal-glass contact. ................................................................................................................................................. 193 Figure III.7: Flexural behaviour of the S Force series: (a) load versus mid-span deflection curves; (b) illustration of the crack patterns observed in the S Force -I; and (c) DIC crack patterns of the S Force -II beam at different stages. ............................................................................................................ 195 Figure III.8: Flexural behaviour of the 3M series: (a) load versus mid-span deflection curves; and DIC crack patterns of the beams (b) 3M-I and (c) 3M-II at different stages. ......................................... 196 Figure III.9: Flexural behaviour of the S Dur series: (a) load versus mid-span deflection curves; and DIC crack patterns of the beams (b) S Dur -I and (c) S Dur -II at different stages. ................................... 197 Figure III.10: Failure modes observed in the composite beams after four-point bending tests: (a) debonding at the adhesive/glass interface in S Force beams, (b) fibre-tear failure in CFRP in 3M beams; and (c) fibre-tear failure in CFRP and (d) glass substrate failure in S Dur beams. .......................... 198 Figure III.11: Finite element model to simulate the glass-CFRP composite beams, including supports, symmetry conditions and mesh pattern. Notes: t may be non-existent ( PB hypothesis), zero ( IB hypothesis) or equal to the layer thickness ( EB hypothesis), depending on the hypothesis adopted to simulate the adhesive joint. All units in [mm]. ............................................................................. 208 Figure III.12: Comparison between the experimental and numerical responses of the (a) S Force , (b) S Dur and (c) 3M series, considering the three hypotheses adopted to simulate the glass-to-CFRP adhesive connection. .................................................................................................................. 210 Figure IV.1: Tensile tests on Fe-SMA strips: (a) experimental setup and DIC pattern; and (b) stressstrain response obtained from both measurements methods, as well as evolution of the Poisson’s ratio. .......................................................................................................................................... 226 Figure IV.2: Schematic representation of the activation procedure of Fe-SMAs under strain recovery constraint (red colour) adapted from Shahverdi et al . [31]. .......................................................... 229 Figure IV.3: Glass-SMA composite beams: (a) beam geometry and instrumentation adopted for the bending tests; (b) cross-section geometry; (c) metallic frames placed at the support sections; (d) lateral guides to prevent lateral instability; and (e) experimental setup. All units in [mm]. ....................... 230 Figure IV.4: Pre-straining of Fe-SMAs: (a) schematic diagram (b) stress-strain diagram retrieved from the experiments. ........................................................................................................................ 231 xxi Figure IV.5: Activation of the Fe-SMA strips: (a) activated region and adopted strategy; (b) welding machine used to supply electrical power for the activation process; and (c) and (d) connection between the welding machine clamps and the Fe-SMA reinforcement. All units in [mm]. ........................... 233 Figure IV.6: Preliminary experiments conducted to determine the user-defined variables required by the thermographic camera. ........................................................................................................ 234 Figure IV.7: Images retrieved by the infrared camera corresponding to T = Ta in each of the posttensioned beams: (a) P_T120-I, (b) P_T120-II, (c) P_T140 and (d) P_T160. ............................... 234 Figure IV.8: Activation process of the externally bonded Fe-SMA strips: displacement at mid-span ( dexp ), strain at the top edge of the glass panel (ε g,t ) and temperature in the Fe-SMA ( T ). ........... 237 Figure IV.9: Finite element model used to determine the recovery stress in the Fe-SMA strips, identifying the length (red colour) that was subjected to temperature variation. All units in [mm]. . 239 Figure IV.10: Results of the flexural tests with the reference beams: (a) structural responses and crack pattern of the beams (b) R_T0-I and (c) R_T0-II at different stages. ............................................. 242 Figure IV.11: Results of the flexural tests with the post-tensioned beams: (a) comparison between the structural responses of both P_T120 beams with those of the reference series, as well as the crack pattern of the beams (c) P_T120-I (c) and (d) P_T120-II at different stages. ................................ 243 Figure IV.12: Results of the flexural tests with the post-tensioned beams: comparison between the structural responses of the beams (a) P_T140 and (b) P_T160 and those obtained from the reference series, as well as the crack pattern of the beams (c) P_T140 and (d) P_T160 at different stages. 244 Figure IV.13: Failure modes: (a) debonding of the Fe-SMA strip at the adhesive/reinforcement interface observed in the beams R_T0-II and P_T140; and (b) cohesive failure of the 3M adhesive due to the appearance of shear cracks........................................................................................................ 246 Figure IV.14: Stress distribution over the cross-section due to the post-tensioning: (a) compression and flexural forces; (b) compression stress distribution; (c) flexural stress distribution; and (d) final stress distribution. ................................................................................................................................ 248 Figure IV.15: Resistant mechanism after glass cracking: (a) and (b) cracked cross-section and (c) strain and (d) stress distributions. ............................................................................................... 250 Figure V.1: Schematic representation of the cross section of the laminated glass beams: (a) exploited view; (b) assembled view after the lamination process; and (c) detailing the glass groove for inserting the reinforcement. Units in [mm]. ............................................................................................... 269 xxii Figure V.2: Overview of the experimental setup used for prestressing the CFRP laminates: (a) prestressing bed; and (b) external reaction frame, hydraulic jack and metal clamps used to fix the CFRP laminates. ........................................................................................................................ 271 Figure V.3: Schematic activation procedure of Fe-SMAs under constraint strain recovery, also including the phase behaviour. Adapted from Michels et al. [30]. ............................................................... 275 Figure V.4: Activation of the Fe-SMA reinforcement: (a) schematic representation of the experimental procedure; (b) overview of the experimental setup adopted; and connection between the power supply clamps and the (c) NSM-SMA and (d) EBR-SMA strips, respectively. ............................................ 276 Figure V.5: Four-point bending tests carried out in this study: (a) general layout; and (b) experimental setup. ........................................................................................................................................ 278 Figure V.6: Post-tensioning of the P_CFRP_CFRP beam, namely the evolution of the pre-strain in the CFRP laminate, of the compressive pre-stress at the bottom glass edge and the temperature over the time. .......................................................................................................................................... 280 Figure V.7: Experimental measurements recorded during the activation of the NSM-SMA strips in the SMA_SMA and SMA_CFRP beams: (a) displacement at the mid-span section ( dexp ), (b) axial strain at the top edge of the glass panel (ε g,t ) and (c) temperature in the Fe-SMA ( T ). .............................. 281 Figure V.8: Experimental measurements recorded during the activation of the EBR-SMA strips in the CFRP_SMA and SMA_SMA beams: (a) displacement at the mid-span section ( dexp ), (b) axial strain at the top edge of the glass panel (ε g,t ) and (c) temperature in the Fe-SMA ( T ). .............................. 282 Figure V.9: Phased analysis adopted in numerical simulation to model the post-tensioning procedure and determine the recovery stress in the Fe-SMA strips, including the finite element model and the FeSMA strip length (red colour) that was subjected to temperature variation. .................................. 283 Figure V.10: Flexural behaviour of the beams R_CFRP_CFRP and P_CFRP_CFRP: (a) load deflection curves; and (b-c) DIC crack patterns at different stages. .............................................................. 285 Figure V.11: Flexural behaviour of the beams CFRP_SMA and SMA_CFRP: (a) load deflection curves; and (b-c) DIC crack patterns at different stages. .......................................................................... 286 Figure V.12: Flexural behaviour of the SMA_SMA beam: (a) load deflection curves; and (b) DIC crack patterns at different stages. ........................................................................................................ 287 Figure V.13: Flexural responses and crack patterns at failure of monolithic glass beams reinforced with (a) CFRP and (b) Fe-SMA. ................................................................................................... 289 Figure V.14: Typical failure modes observed in (a) SMA_SMA beam and (b) in all other glass composite beams. ...................................................................................................................................... 296 xxiii LIST OF ABBREVIATIONS AND SYMBOLS Abbreviations AB Adhesively bonded reinforcement AFRP Aramid fibre reinforced polymers Al2O3 Aluminium oxide B2O3 Boron trioxide BSG Borosilicate glass CaO Calcium oxide CC Consequence class Cd-Au Cadmium-Gold (alloy) CEN European Committee for Standardization CFRP Carbon fibre reinforced polymers C-G Cohesive failure in glass CLS Collapse limit state CNR Italian National Research Council CoV Coefficient of variation CS-G Glass substrate failure Cu-SMA Copper-based shape memory alloy DCB Double Cantilever Beam Di Ductility index DIC Digital image correlation DMA Dynamic mechanical analysis DPM Damage plasticity model EB Elastic behaviour (approach) Empa Swiss Federal Laboratories for Materials Science and Technology EBR Externally bonded reinforcement EN European Norm ENF End Notched Flexure EVA Ethylene Vinyl Acetate xxx ε y Yield strain λ  ; μ Lamé’s constants ρ Density ρ r Reinforcement percentage σ g,b Axial stress at the glass bottom edge σ g,t Axial stress at the glass top edge σ m Normal strength σ n Stress in the normal direction to the interface σ pre Axial stress corresponding to the Fe-SMA pre-strain σ rec,cr Recovery stresses developed in Fe-SMA from cracking loads σ rec,max Maximum recovery stress σ rec,sg Recovery stress developed in Fe-SMA from strain gauge measurements σ y Yield stress τ m Bond strength τ s; τ t Stress in both tangential directions to the interface τ s,max; τ t,max Shear strengths τ ( s ) Shear stress at the bonded interfaces τ ( x ) Shear stress curve on the bond length υ Poisson's ratio υ CFRP Poisson's ratio of CFRP υ g Poisson's ratio of glass υ GFRP Poisson's ratio of GFRP ψ Dilation angle ω 1 Angular frequency of the fundamental vibration mode ω j Angular frequency ω max Highest angular frequency 1 CHAPTER 1 INTRODUCTION MOTIVATION The development of new materials has always been responsible for great advancements throughout the history of Humanity. Some of them were even used to name time periods, such as the Stone Age, Bronze Age and Iron Age [1]. Although glass has never named any period in the history, it has been used by humans for centuries. Today, glass is a symbol of the contemporary architecture due to its transparency, which is a unique characteristic that other traditional building materials (e.g. concrete, steel and timber) do not have. Due to its versatility, glass has been widely used throughout history for a variety of purposes, from fibres to large-scale structures, from decorative elements to structural applications and from the automotive industry to construction and communications [1]. In the construction industry, glass was used for centuries as a non-structural material in windows and building envelopes to create interior spaces without blocking the entrance of visible light into the buildings [2]. Nowadays there is an increasing demand for transparency. Thus, glass has been increasingly used as a load-bearing material to produce structural elements (e.g. beams and even columns) for roof and façade structures, footbridges and staircases. Furthermore, glass can take countless aesthetical possibilities and, taking into account the concerns related to building sustainability and the use of resources, it may be 100 % recyclable. As an example, improved delamination techniques, such as the wet method, are being developed to separate the glass from the interlayer and in turn recycle both materials [3–5]. CHAPTER 1 2 Although glass has interesting properties for structural applications (e.g. very high compression strength), like concrete its behaviour in tension is brittle and unpredictable due to the unavoidable mechanical flaws induced during the production and handling operations. These small mechanical flaws grow when the glass is subjected to long-term loads and moisture. Consequently, even if glass does not break at load application, it may break after a certain period of time which is a function of the loading history, surface characteristics and environmental conditions [6]. Glass industry has introduced several technological innovations in the glass production process, namely the thermal toughening and the lamination. While the former reduces the unpredictability of glass and increases its tensile strength due to the residual stress state generated after being reheated, the latter introduces relatively safe failure mechanisms, guaranteeing the structural integrity of the glass element after cracking due to the interlayer action. Both processing methods have contributed to promote the use of glass as a load-bearing material in a wide spectrum of structural applications. On the other hand, glass industry has developed new manufacturing plants with the aim of extending the maximum size of glass elements, hitherto limited to the standard size of 6.00 × 3.21 [m] [7]. Given the increasing structural relevance of glass elements, stiffer interlayers (e.g. ionomers) have also been developed to enhance the preand post-failure performance of the laminated glass, as well as its resistance to moisture and UV radiation [8]. The latest technological advances in the glass industry have attracted the interest of the international research community, which has been addressing numerous concerns about glass structural applications. This investigation has been translated into the development and improvement of existing guidelines and standards (e.g. [9–13]). Nonetheless, the most challenging structural applications (e.g. beams) are not covered by existing standards. Most design methodologies for structural glass mainly focus on (i) the shear interaction at the bonded interfaces of laminated glass panes, (ii) the flexural behaviour of glass panels subjected to out-of-plane loads, (iii) the buckling behaviour of glass elements under compression (e.g. glass fins) and in-plane shear stresses, as well as on (iv) the connection technologies between glass elements. Adopting the design methodologies commonly used in the aeronautics, glass structural systems have been designed according to the concepts of hierarchy, robustness and redundancy [11]. However, these methodologies are certainly not economical and, whatever the type of glass, laminated glass breaks without showing warning signs. Furthermore, whatever the interlayer material, laminated glass does not have sufficient post-fracture strength and ductility for structural applications [14,15]. A INTRODUCTION 3 secondary load carrying mechanism is therefore essential to comply with the structural redundancy requirements. Following the philosophy employed in reinforced concrete, safety concepts have been developed combining glass with reinforcement materials, such as concrete, timber, steel and Carbon (CFRP) and Glass (GFRP) Fibre Reinforced Polymers [15–18]. When glass breaks, collapse is avoided by transferring tensile stress from the glass to the reinforcement through shear stresses in the adhesive joint. Subsequently, the applied load is transferred to the supports by means of a resisting mechanism formed by an uncracked glass zone in compression and the reinforcement element in tension. As a result, composite glass systems can still carry load after the first glass cracking. Besides the reinforcement material, the post-failure performance is a function of several aspects, and some of them have been addressed in recent investigations, such as (i) the reinforcement percentage (e.g. [19]), (ii) the cross-section geometry (e.g. [20]), (iii) the type of bonding agent (e.g. [20,21]) and (iv) the type of glass (e.g. [22]). Multiple aesthetical possibilities can be obtained by assembling individual glass sheets through interlayers and transparent adhesives. Hence, besides the traditional rectangular sections, box-, Iand T-sections have also been investigated to prevent lateral-torsional buckling, since glass structural elements are typically slender compared to reinforced concrete [23,24]. Like in concrete structures strengthened with composite materials, epoxy adhesives are commonly used as bonding agent because these ensure superior bond performance compared with other types of adhesive (e.g. polyurethane and acrylate). However, soft adhesives have also been used to increase ductility [20]. Glass composite systems manufactured with annealed glass sheets have shown better post-failure performance than those with thermally toughened glass [22]. Although the latter shows much higher tensile strength than annealed glass, the former is better at providing residual strength because it breaks into larger fragments than fully tempered glass and heat-strengthened glass. On the other hand, glass composite systems with passive reinforcement have successfully achieved sufficient robustness and safety after cracking, but the tensile strength of glass is still unreliable. In recent years, as an alternative to the thermal toughening, mechanical post-tensioning has been investigated with the aim of improving the fracture strength of glass. Unlike tempering, mechanical post-tensioning does not modify the nature of the glass fracture and, in addition, it can be adjusted as a function of the glass element. Steel, CFRP and GFRP have been used as prestressed reinforcement materials in post-tensioned glass systems [18]. The principle of such systems is similar to prestressed CHAPTER 1 4 concrete. Different systems are used to introduce prestress in concrete elements, such as (i) the cambered prestressing systems; (ii) the prestressing against an external support; and (iii) the prestressing against the target element [25,26]. The last two strategies have been used for posttensioning of glass (e.g. [27–31]), but the prestressing against an external support is the most prominent. The second method consists of prestressing the reinforcement against an independent and external reaction steel frame before bonding it to the target element [25]. When the adhesive is fully cured, the reinforcement is released and the prestress is transferred to the glass, thus introducing a compression pre-stress state in tensile glass zones to prevent the growth of small surface flaws under service loading. On the other hand, the last method requires the use of anchorages. These are fixed at the ends of the target element, providing reaction force while the prestress is applied by pulling the reinforcement with hydraulic jacks [25]. When the adhesive is fully cured, all temporary elements are removed [26]. CFRPs have been widely used in recent decades for the strengthening of existing concrete structures, mainly due to their relatively high stiffness and tensile strength, low relaxation, lightness and high resistance to corrosion [32]. However, few works are found in the literature focusing on CFRPs as reinforcement material for glass composite systems, both experimentally (e.g. [30,33–35]) and numerically (e.g. [34,36]). Two strengthening techniques are commonly used for the application of CFRPs [26,37–40]: (i) the Externally Bonded Reinforcement (EBR) technique, which consists of bonding the CFRP laminate on the tensile surfaces of the structural element to be strengthened; and (ii) the Near Surface Mounted (NSM) technique, which consists of introducing the CFRP laminate or bar inside pre-opened grooves located in the tensile region of the target structural element. In glass elements, the reinforcement is typically applied according the EBR technique (e.g. [27,31,41]). However, its performance strongly depends on the resistance of the substrate material [42]. As a consequence, over the last decades, the NSM technique has been increasingly used as an effective alternative to the classical approach of applying externally bonded CFRPs [40]. Compared to EBR, the NSM technique is less prone to premature debonding due to the larger bonding surface area between the adherends, as well as the confinement effect created by the grooves, thus allowing a more efficient use of the tensile capacity of the reinforcement material. Furthermore, the surrounding glass protects the reinforcement against corrosion, fire, vandalism actions, mechanical damage and aging [43]. As a result, an increasing number of investigations have been addressing the feasibility of strengthening glass elements according to the NSM technique (i) by laminating the reinforcement together with the INTRODUCTION 5 glass sheets and using the interlayer as a bonding agent (e.g. [22,44]) or (ii) by designing recessed grooves on the glass edges for the subsequent insertion of the reinforcement element (e.g. [33,45]). Lately, Shape Memory Alloys (SMA) have been used for the strengthening of existing concrete structures. Unlike traditional materials (e.g. steel and FRPs), (i) mechanically deformed SMAs can recover their initial shape by heating, the well-known shape memory effect; and, (ii) under certain temperature conditions, they can also recover from high imposed mechanical deformations after unloading and without heating, the so-called superelasticity [46,47]. SMAs have been employed in different engineering fields due to their unique properties, such as (i) the post-tensioning of structural elements (e.g. [48–53]) and (ii) the energy dissipation in structures subjected to dynamic loads (e.g. [54,55]). When the SMA reinforcement is properly anchored to the target element prior to its activation (e.g. adhesively bonded and mechanically anchored), post-tensioning forces are generated by heating the SMA. This simple procedure has encouraged the application of SMAs in the construction industry, whose conventional procedure of prestressing with hydraulic jacks is often difficult to implement due to the lack of space [47,56]. Among the other SMAs, iron-based alloys (Fe-SMA) present essential characteristics for the construction industry, such as: (i) reasonably low cost, (ii) relatively high modulus of elasticity and low activation temperature, as well as (iii) good workability, (iv) machinability and (v) weldability [47,57]. Due to the novelty of the glass as a load-bearing material and SMAs as a reinforcement material, to the best of the author’s knowledge only four studies (e.g. [58–61]) are found in the literature addressing this topic. Glass contains mechanical flaws randomly distributed on its surfaces and edges and, therefore, high stress concentrations should be avoided to prevent these flaws from growing over time [62,63]. If relatively high prestressing levels are adopted, glass breakage may be an unavoidable event while loading starts (e.g. [64]). On the other hand, the use of mechanical anchorages can be technically and aesthetically inappropriate, as they cannot be fastened to the substrate material like in concrete or metallic structures. In this context, SMAs may be a promising candidate to be used as reinforcement material for the fabrication of post-tensioning glass systems that are safer than those produced with traditional reinforcement materials. If SMAs are adhesively bonded to the glass, their activation damages the adhesive joint, mobilizing longer bond lengths and creating damage gradients that smoothen the transfer of the post-tensioning force from the reinforcement to the glass. Furthermore, the shape memory effect could be used in two different contexts: (i) before glass rupture, to improve the tensile strength of glass by creating favourable stresses in the glass tensile zone; and (ii) after CHAPTER 1 6 glass rupture, to enhance the post-failure performance until the glass element is replaced, reducing the deformation, preventing the crack progression and, eventually, closing existing cracks. OBJECTIVES AND RESEARCH METHODOLOGY Despite the most recent developments, there are still significant gaps in the glass composite systems knowledge for structural applications, namely on the following topics: (i) the post-failure behaviour of reinforced glass systems; and, (ii) the mechanical post-tensioning of glass. The present work aims at contributing to the existing knowledge on glass composite systems. Thus, the main objectives of this PhD thesis are two-fold: (i) to develop strengthening systems capable of guaranteeing safe failure modes in glass structures; and (ii) to develop reliable post-tensioning methodologies to reduce the unpredictability of the glass fracture strength. It is expected that this research work contributes to the existing knowledge on the composite glass systems, providing analytical and numerical methodologies for predicting the post-failure performance. The development of post-tensioning methodologies capable of increasing the fracture strength of glass and reducing the risk of peeling-off failure due to stress concentrations is also expected. Finally, and due to its importance, this work contributes for the definition and development of design guidelines, as to better accounting for the robustness of glass composite systems. Therefore, the first objective set for this thesis, related to the development of strengthening systems to introduce ductile failure modes in structural glass elements, was achieved by addressing the following tasks:  The assessment of the influence of the type of adhesive on the bond behaviour of glass-toCFRP adhesively bonded connections. It includes tensile tests on double-lap joint specimens to characterize the shear interaction at the bonded interfaces, calibration of local bond stressslip relationships by using an existing computational tool and numerical modelling to better understand the observed phenomena in the experiments, using the derived local bond stressslip relationships as input;  The assessment of the post-failure performance of annealed glass beams reinforced with externally bonded CFRP laminates, and to study the influence of the adhesive type by testing small-scale specimens until failure in a four-point-bending configuration;  The development of finite element models to simulate the experimental results obtained from experiments, and to evaluate the efficiency of different mechanical constitutive models to INTRODUCTION 7 simulate the non-linear behaviour of glass in tension. These are important for a better understanding the observed phenomena in the tests, as well as to extend the studies carried out and to assess the applicability and efficiency of different modelling strategies to simulate the bond behaviour of glass-to-CFRP adhesively bonded joints. The second objective set for this thesis, related to the development of reliable methodologies for posttensioning glass, was achieved by carrying out the following topics:  The fabrication of post-tensioned glass beams by prestressing CFRP laminates and by activating Fe-SMA strips, both externally bonded to the glass substrate. It includes a study about the influence of different types of adhesive on the transfer of prestressing force from the reinforcement to the glass, in case of CFRP-reinforced specimens;  The assessment of the post-failure performance of annealed glass beams reinforced with externally bonded Fe-SMA strips and study the benefits of activating Fe-SMA strips on the fracture strength of glass and post-failure performance of such systems, as well as the study of the influence of the Fe-SMA activation temperature on the post-tensioning level and adhesive damage propagation. It includes four-point bending tests until failure with passive and post-tensioned small-scale specimens, as well as an analytical model to determine the maximum post-tensioning level to ensure a relatively safe failure;  The development and assessment of the feasibility of a hybrid strengthening system capable of preventing premature debonding of the reinforcement element due to critical shear crack and, in case of post-tensioning of the glass, peeling-off at load introduction (release of the prestressed reinforcement), in order to take advantage of the full tensile capacity of the reinforcement material. Large-scale specimens were tested until failure adopting a four-point bending configuration. Based on the above-mentioned objectives, the overall research methodology that was followed is schematically depicted in Figure 1.1. CHAPTER 1 8 Figure 1.1: Research methodology Four-point bending tests Numerical simulation Double-lap joint tests Analytical modelling  s sm  m Production / activation Four-point bending tests Hybrid strengthening Design recommendations Glass-CFRP composite systems Fe-SMA reinforcement Literature review Bond behaviour of adhesive joints with glass Flexural performance of glass composite systems Numerical simulation of the tensile behaviour of glass Strategies for post-tensioning the glass composite systems Use of Fe-SMA materials for post-tensioning of structural elements INTRODUCTION 9 OUTLINE OF THE DISSERTATION The content of this work, which is presented as a collection of five papers published or submitted to peer-review international journals, is organized in five chapters as follows:  Chapter 1 provides a general introduction to the research topic, describes the general objectives and overall methodology and, finally, presents the outline of the present work;  Chapter 2 focuses on the fundamental aspects of glass as a building material, such as the production process and the main material properties, the processing methods developed by the glass industry to improve its overall performance and the current requirements and methodologies for the design of glass structures. Few examples of glass structures are presented in this chapter, providing a general overview of the most common glass structural applications;  Chapter 3 concerns the premises behind the reinforced glass concept and gives an overview of the available literature on glass composite systems with passive or post-tensioned steel, timber, GFRP and CFRP reinforcements, covering aspects such as the bond behaviour of adhesively bonded connections and the post-failure performance of composite elements. A critical discussion on the feasibility of using SMAs as reinforcement in glass composite systems is carried out at the end of the chapter, as well as a brief description of the phase behaviour of the most important SMAs for civil engineering applications;  Chapter 4 presents a brief summary of the papers that constitute this PhD thesis. Four of these papers have been already published in scientific journals (Q1), while fifth has been submitted;  Chapter 5 summarizes the main conclusions of the developed work and presents recommendations for future work. REFERENCES [1] Soler X. Structural glass in buildings : study of the deflection, durability, and breakage of laminated glass elements and polymeric interlayers. PhD thesis. University of Lleida, Spain, 220AD. [2] Ritchie I. Aesthetics in glass structures. Structural Engineering International: Journal of the International Association for Bridge and Structural Engineering (IABSE) 2004;14:73–5. https://doi.org/10.2749/101686604777964062. [3] Dyer T. Glass Recycling. Elsevier Inc.; 2014. https://doi.org/10.1016/B978-0-12-3964595.00014-3. CHAPTER 2 16 for 90 % of the world’s flat glass production [2,3]. Compared to previous production methods of flat glass (e.g. Fourcault and Pittsburgh), this method (i) is less expensive, (ii) allows to obtain glass panels with constant thickness and (iii) allows to produce of larger glass panels under safe conditions [2]. The production of float glass is schematically presented in Figure 2.1, being possible to distinguish three main stages: (i) melting, (ii) forming and (iii) cooling. Initially, the raw materials are introduced in a furnace at a temperature of 1500 ºC. Subsequently, at a temperature of 1200 ºC, the molten glass is poured into an enclosed box where it floats on a bath of molten tin. This is the phase responsible for providing glass panels with very smooth surfaces, eliminating the need for any polishing to obtain satisfactory transparency. The thickness of the glass sheet is assigned at this phase and, depending on the speed of the rollers of the annealing lehr (next phase), it can vary between 2.0 and 25.0 mm. After that, at a temperature of approximately 600 ºC, the glass sheet enters an oven called annealing lehr , where it is slowly cooled up to approximately 100 °C in order to avoid residual stresses. Finally, the glass is inspected and subsequently cut into panels of 6.00  3.21 [m]. The glass obtained from the float process is commonly called as annealed glass because the last stage of the manufacturing process occurs in an annealing lehr [2,3]. Figure 2.1: Schematic representation of the production process of float glass. Adapted from Henriques [4]. The float production process is not perfect and induces small deficiencies in glass during its manufacture. As a result, the surfaces of glass panels are not completely identical due to (i) the diffusion of tin atoms into the bottom surface, which influences the bond behaviour of adhesive joints applied to this surface; and, (ii) the superficial defects caused by the transport rolls of the annealing lehr on the bottom surface, which decrease its mechanical strength [2,5]. It should be noted that the glass surface in contact with the molten tin can be identified when exposed to ultraviolet radiation. Melter Tin bath float Annealing lehr 1500 ºC 1200 ºC 600 ºC 500 ºC 100 ºC Raw Material Inspection Cutting GLASS AS A BUILDING MATERIAL 17 MATERIAL PROPERTIES 2.2.1. Chemical composition In the production of glass, the fusion of the chemical ingredients is followed by its rapid cooling, which occurs without crystallization of the minerals. Depending on the chemical composition, the glass can be classified into two different categories: (i) the soda lime silicate glass (SLSG) and (ii) borosilicate glass (BSG). The borosilicate glass offers very high resistance to temperature changes, as well as a very high hydrolytic and acid resistance. This is only used in special applications (e.g. fire protection glazing, heat resistant glazing and chemical laboratory devices) because of its high cost [2]. Table 2.1 shows the chemical composition of both glass types previously mentioned. Table 2.1: Chemical composition of the soda lime silicate glass and borosilicate glass according to standards EN 572-1:2004 [6] and EN 1748-1-1:2004 [7], respectively. Components Soda lime silica glass [%] Borosilicate glass [%] Silica sand SiO2 69 - 74 70 - 87 Lime (calcium oxide) CaO 5 - 14 - Soda Na2O 10 - 16 0 - 8 Boron trioxide B2O3 - 7 - 15 Potassium oxide K2O - 0 - 8 Magnesia Mg 0 - 6 - Aluminium oxide Al2O3 0 - 3 0 - 8 others - 0 - 5 0 - 8 The chemical composition of glass has an important influence on its viscosity, melting temperature and thermal expansion. The glass transition temperature of the soda lime silicate glass is about 530 ºC. According to Haldimann [8], the solidification of the glass (transition between liquid and solid states) does not occur for a precise temperature but over a temperature range, in contrast to crystalline materials. The best performance of the borosilicate glass in some applications comes from boron (B2O3) and potassium (K2O) oxides. Besides the chemical composition listed in Table 2.1, these two glass types also have other components, such as iron, cobalt and titanium oxides and others, which are responsible for their coloration. 2.2.2. Physical and mechanical properties For the contemporary architecture, the transparency within the visible spectrum (wavelengths between 380 and 750 nm) is the most important physical property of glass. The optical properties of glass (e.g. CHAPTER 2 18 absorbed and transmitted radiation spectrum) depend on its thickness, chemical composition and applied coatings. The infrared radiation with a wavelength exceeding 5000 nm is absorbed by the glass, as well as the ultraviolet radiation [2]. Glass is an isotropic material with elastic behaviour until failure. Such as concrete, glass presents a brittle failure, without plastic deformation. At molecular level, the tensile strength of glass is exceptionally high, ranging from 6000 to 10000 MPa [1,2]. However, due to the manufacturing process and handling of glass sheets, flaws are always present at the glass surfaces and its effective tensile strength is therefore much lower than the theoretical value [3]. The tensile strength of annealed glass for structural applications (macroscopic scale) varies between 30 and 80 MPa [9]. It is influenced by several aspects, namely (i) the size of the glass element, (ii) the loading history (intensity and duration), (iii) the residual stress and (iv) the environmental conditions, as well as the conditions of the glass surfaces (size and depth of flaws) [2]. Loading history directly influences the conservation of glass surfaces. The deterioration of surfaces flaws occurs when glass is subjected to long-term loads under humidity conditions [1,2]. Consequently, the higher the load and the severity of environmental conditions, longer the load duration and deeper the initial surface flaws, the lower the effective tensile strength of the glass. In general, the literature indicates values of tensile strength between 45 and 55 MPa [2,10]. According to EN 16612:2020 [11], both soda lime silicate glass and borosilicate glass have a characteristic flexural strength of 45 MPa. Table 2.2 shows the other mechanical properties of these glass types. TYPES OF GLASS After production, annealed glass can undergo secondary processing methods (e.g. edge treatment, coatings and thermal treatment) depending on the purpose of the glass product. Among these processing methods, thermal treatment (tempering) stands out. The structural application of annealed glass has been limited by the uncertainty involving its tensile strength, due to the growth of surface flaws over time. In addition, in the construction industry, the annealed glass is seen as an extremely dangerous material. When it breaks, it creates large, irregular and sharp fragments, compromising the people's safety [1]. In this context, tempering is clearly the most important processing method to meet the current structural requirements. GLASS AS A BUILDING MATERIAL 19 Table 2.2: Physical and mechanical properties of the soda lime silicate glass and borosilicate glass according to standards EN 572-1:2004 [6] and EN 1748-1-1:2004 [7], respectively. Properties Units Soda lime silica glass Borosilicate glass Density kg m3 ⁄ 2500 2200 - 2500 Knoop hardness GPa 6.0 4.5 - 6.0 Thermal conductivity Wm-1K-1 1 1 Specific thermal capacity Jkg-1K-1 720 800 Coefficient of thermal expansion K-1 910-6 Glass 1: 3.1 - 4.0 Glass 2: 4.1 - 5.0 Glass 3: 5.1 - 6.0 Average refractive index within the visible spectrum -- 1.52 a) 1.50 Modulus of elasticity MPa 70000 60000 - 70000 Shear Modulus MPa 28455 b) -- Poisson ratio -- 0.23 c) 0.20 Characteristic bending strength MPa 45 -- Notes: a) A value of 1.52 is commonly used in studies on structural glass, although the standard EN 572-1:2004 indicates 1.50 b) This value is proposed by Huveners [1] c) The standard EN 572-1:2004 indicates a values of 0.20: however, 0.23 is the most commonly used value in studies on structural glass Tempering is widely used in the glass industry to improve its resistance against mechanical loads and changes in temperature. It creates a residual stress field in the glass consisting of tensile stresses in the core and compression stresses on the external surfaces and edges. As the glass core does not contain flaws, it can still withstand a significant tensile stress and hence the tensile strength of the glass increases due to the favourable compressive pre-stress on the outer surfaces and surroundings. On the other hand, the undesirable flaws can only grow when a tensile stress higher than the residual compressive pre-stress is induced by external loading, thus reducing the unpredictability of the glass. As long as the applied tensile stress is lower than the residual compressive pre-stress, there is no effective tensile stress and consequently no crack growth [2]. Thermal toughened glass is obtained by reintroducing the float glass into a furnace and by heating it above the glass transition temperature ( Tg = 650 ºC). Subsequently, jets of cold air are used to cool the heated float glass, first solidifying the outer glass regions while the core region remains soft [3]. When the glass core cools, thermal contraction is prevented by the solidified outer surfaces, generating tensile stresses in the core region and, by internal equilibrium reasons, compression stresses in the outer regions. Thereby, the residual stress level depends on the cooling speed rate. Typically, the residual stress field presents an approximately parabolic distribution over the glass thickness. The CHAPTER 2 20 ratio between the maximum tensile (core) and compression (surface) stresses is approximately 1:2 (see Figure 2.2). (a) (b) Figure 2.2: Comparison between the distributions of residual stress in (a) thermally toughened glass and (b) chemically toughened glass. Adapted from Huveners [1]. Two types of thermally toughened glass are commonly mentioned in the literature: the heatstrengthened glass and the fully tempered glass. The latter has a higher cooling rate than the former. Typically, the residual compressive pre-stress in fully tempered glass varies between 80 and 150 MPa while in heat-strengthened glass it ranges from 40 to 80 MPa [2,10]. According to the European standard EN 16612:2013 [11], the characteristic values of bending strength for heat-strengthened and fully tempered glass are respectively equal to 70 and 120 MPa, much higher than the 45 MPa found for annealed glass. After the tempering process, the glass cannot be cut or drilled because the stress state (energy balance) would be disturbed and the glass would crack immediately. Chemical tempering can be an alternative to increase the tensile strength of glass. Residual stresses are induced through a chemical reaction in which sodium ions are exchanged by potassium ions (approximately 30 % larger in volume) [2]. This chemical process occurs only in a very thin glass zone near the surfaces and edges (see Figure 2.2). In contrast to thermally toughened glass, chemically tempered glass can be cut and/or drilled after tempering. Even so, its structural application is rare because this tempering process is expensive and time-consuming and, on the other hand, surface flaws can be deeper than the thin compression glass zone, causing spontaneous failure without external loading. The fracture pattern depends on the amount of strain energy stored in the glass, i.e. the level of residual stress derived from the thermal treatment and the tensile stresses induced by external loads [12]. While annealed glass (negligible residual stress) usually breaks into relatively large fragments, heat-strengthened glass breaks into medium-to-small fragments and fully tempered glass (with the Fully tempered glass Heat-strengthened glass Compression stress Tensile stress - + - Chemically toughened - + - Compression stress Tensile stress Glass thickness (tg) ~ 2 3 tg -+ Compression glass zone - outer glass regions Tensile glass zone - glass core Fully tempered glass Heat-strengthened glass Compression stress Tensile stress - + - Chemically toughened - + - Compression stress Tensile stress Glass thickness (tg) ~ 2 3 tg -+ Compression glass zone - outer glass regions Tensile glass zone - glass core GLASS AS A BUILDING MATERIAL 21 highest residual stress among the glass types) breaks into even smaller and generally harmless fragments (e.g. dice), minimizing the risk of injury of loss of human life when they fall (see Figure 2.3). Given the above, fully tempered glass is commonly known as “safety glass” and is therefore used for a wide range of applications. However, due to the high amounts of strain energy, fully tempered glass shatters in an explosive manner when the residual stress equilibrium is disturbed. (a) (b) (c) Figure 2.3: Comparison between the fracture patterns of (a) annealed glass, (b) heat-strengthened glass and (c) fully tempered glass. Adapted from Haldimann [2]. The fracture pattern influences both the post-failure safety and the post-failure performance [13]. Although fully tempered glass is the safest and has the highest tensile strength of all types of glass, it shows the poorest post-failure performance due to the lack of integrity of the tiny fragments as well. Concerning the heat-strengthened glass, it provides an interesting compromise between relatively high tensile strength and sufficiently large fragmentation for good post-failure performance [2]. Fully tempered glass can spontaneously break due to nickel-sulfite (NiS) inclusions, which penetrate the glass during its manufacturing process [14]. NiS particles expand in volume due to temperature variations, inducing high stress concentrations. As the core of fully tempered glass is subjected to a relatively high residual tensile pre-stress, the volume expansion of the NiS particles can cause spontaneous breakage [1–3]. Different topics have been focused in some studies addressing the glass tempering, namely (i) the fragmentation mechanism (e.g. [15–17]), (i) the residual stress state, either performing numerical simulations (e.g. [18,19]) or applying the principle of the photo-elasticity (e.g. [20]), and (iii) the influence of NiS inclusions (e.g. [21]). CHAPTER 2 22 LAMINATED GLASS Although the thermal toughening of the annealed glass improves its mechanical performance and reduces its unpredictability, monolithic glass panels still exhibit brittle behaviour, with no plastic deformation before collapse and no load carrying capacity after glass cracking. Like annealed glass, thermally toughened glass fails suddenly and without any warning sign, posing a significant safety risk when applied as a structural material [13]. In this sense, the lamination process was developed in 1909 by Edouard Benedictus [22] to overcome this challenge, since it provides stability to the fragments after glass cracking. The lamination process consists of joining at least two glass plies by means of a transparent and polymeric interlayer. It should be noted that laminated glass can comprise glass plies with the same thickness, or not, and with different residual stress levels – from annealed glass to fully tempered glass. Based on the concept of redundancy, when one of the glass plies breaks, the interlayer holds the fragments in place, preventing injury and damage property, and the external load is transferred for the surviving glass sheets through shear stresses in the interlayer [23]. As the fragments remain bonded to the interlayer after cracking, the interlocking effect between them results in residual structural capacity. This capacity depends on the fragmentation level. The larger the fragments the better the post-failure performance of the laminated glass (see Figure 2.4). As depicted in Figure 2.5, after glass cracking, the interlayer can carry tensile stress while the glass fragments can still carry compression stress, creating a resisting mechanism capable of providing a certain level of residual strength and ductility, mainly for out-of-plane loads [24]. The cracking mechanism in laminated glass panes is schematically represented in Figure 2.5 and can be divided into three stages: (i) the uncracked stage, without glass cracking; (ii) the cracking stage, in which the load carrying capacity is provided by the surviving glass sheets; and (iii) the post-cracking stage, with all glass plies cracked. For this reason, laminated glass is used for structural applications rather than monolithic glass. The interlayer can be either an adhesive foil or an adhesive resin, but the former is the most used to produce laminated glass. Adhesive resins are commonly applied to join glass sheets at the construction site and the polymerization requires UV-radiation [14], e.g. acrylate adhesives. According to Callewaert [22], the lamination process involves three main stages: (i) first, the glass sheets are washed and introduced in a clean room; (ii) then, the glass sheets are stacked onto each other and adhesive foils are inserted between them, creating a “sandwich” panel; and (iii) finally, laminated glass GLASS AS A BUILDING MATERIAL 23 is produced by moving the glass sheets to an autoclave at a temperature between 130 and 150 ºC, where they remain under a pressure of 14 bar for 2 to 3 hours. Figure 2.4: Evolution of the initial fracture strength and post-failure performance of glass as a function of the tempering level. Adapted from Sedlacek et al . [5] (a) (b) (c) Figure 2.5: Redistribution of normal strains during the cracking process of two-layer laminated glass panel: (a) uncracked stage; (b) cracking stage; and (c) post-cracking stage. Adapted from Molnár et al. [25]. The interlayer (e.g. stiffness and strength properties) plays a key role in the post-failure performance of laminated glass, as well as the type of glass (e.g. size of the broken glass fragments) [26]. As mentioned, the interlayer is a polymeric material with a non-linear and viscoelastic response. As a consequence, laminated glass presents a time-dependent response, i.e. its flexural stiffness is a function of the loading history (duration and intensity) and temperature [27]. Therefore, the flexural stiffness of laminated glass can vary between two distinct scenarios: (i) the layered limit, with shear stiffness (G) → 0, in which the composite panel behaves like superimposed glass sheets without any composite action between them; and, (ii) the monolithic limit, with G → ∞, in which the interlayer ensures perfect bond between the glass sheets without relative displacement between them [28,29]. The stiffer and thinner the interlayer, the higher the shear interaction at the bonded interfaces and the more the laminated glass resembles the monolithic glass [24] (see Figure 2.6). - ++ - - + - + - + Compression strains Tensile strains Crack Crack Glass sheets Glass sheet Interlayer - ++ - - + - + - + Compression strains Tensile strains Crack Crack Glass sheets Glass sheet Interlayer - ++ - - + - + - + Compression strains Tensile strains Crack Crack Glass sheets Glass sheet Interlayer Higher tensile strength and impact resistance Better post-failure performance CHAPTER 2 24 Polyvinyl Butyral (PVB), Ionoplast (e.g. SentryGlass - SGP) and Ethylene Vinyl Acetate (EVA) are the most suitable interlayers for structural glass applications. Table 2.2 presents the main material properties of these interlayers. PVB has been the most used interlayer in the construction industry since the 1960s. This is based on several reasons: (i) firstly, PVB has high transmittance within the visible spectrum, similar to that of glass; (ii) secondly, it filters most of the UV radiation; (iii) thirdly, there are many manufacturers producing PVB, making it an economical interlayer for large-scale applications; and (iv) finally, it shows a good acoustic performance [30,31]. However, it has low shear stiffness and is highly viscoelastic even at room temperature [2,9]. Lately, stiffer interlayers (e.g. ionomer polymers and thermoplastic polyurethane) have been applied with the aim of increasing the structural application of glass by improving the shear interaction between the bonded interfaces. (a) (b) (c) Figure 2.6: Distribution of normal strains over the cross-section of a two-layer laminated glass: (a) monolithic limit; (b) intermediate stage; and (c) layered limit. Adapted from Molnár et al. [25]. Focusing on the PVB and on the Ionoplasts, the most used interlayers in the construction industry today, the application of interlayer materials is briefly described next. PVB was first used as an interlayer to produce laminated glass for windshields, which took place in the 1930s [24]. After its great success in the automotive industry, the PVB has been widely used for the last 40 years in the construction industry [22]. Its chemical composition has been modified over time to meet new requirements, improving physical and aesthetic characteristics. To increase the load carrying capacity of glass facades, the SGP was developed in the 1990s by DuPont. It features high stiffness over a wide temperature range, making it suitable for structural applications. Like PVB, the chemical composition of SentryGlass has also been modified in recent decades to improve its performance. Glass structures can be subjected to various load conditions, whose duration varies from few seconds to several years, as well as to various thermal conditions. Depending on these aspects, a polymer can - + - + - + - +Compression strains Tensile strains - + - + Glass sheet Glass sheet Interlayer - + - + - + - +Compression strains Tensile strains - + - + Glass sheet Glass sheet Interlayer - + - + - + - +Compression strains Tensile strains - + - + Glass sheet Glass sheet Interlayer Lower shear stiffness + higher temperature + thicker interlayer GLASS AS A BUILDING MATERIAL 25 show an elastic, viscoelastic or viscous response. Hence, the mechanical properties of interlayers are usually presented as a reduction master curve, which is commonly derived by applying the timetemperature superposition principle. Each curve describes the evolution of a material property over time at a reference temperature. Based on the Maxwell-Weichert viscoelastic model, the reduction master curves are analytically represented using Prony series. The number of terms in the Prony series depends on the time period of interest and on the experimental data available for curve fitting. In general, such curves are extracted using different experimental setups, such as uniaxial tensile tests (e.g. [32]), dynamic mechanical analysis (DMA) tests on interlayer samples (e.g.[28]), pull-out tests (e.g. [33]) or torsional and flexural creep/relaxation tests on small-scale laminated glass specimens ([34]). Giovanna et al . [27] provide an overview of the test methods used to determine interlayer properties in laminated glass. Table 2.3: Physical and mechanical properties of the most popular interlayer materials for structural glass applications [22]. Properties Units PVB PVB Structural Ionoplast EVA Density kg m3 ⁄ 1070 1080 950 930 Tensile strength MPa 25 to 27 33 34.5 9 to 31 Elongation at failure % 200 to 250 190 > 500 > 415 Glass transition temperature K 28 to 32 40 to 45 50 to 55 -60 to -31 Coefficient of thermal expansion ºC 468 155 100 to 150 98 Note: These mechanical and physical properties may slightly change depending on the producer Based on DMA tests, Figure 2.7 illustrates, for a reference temperature of 20 ºC, the shear modulus of the commercial interlayers PVB Butacite and SGP SentryGlass , both produced by Kuraray Co. Ltd. [35]. As expected, both interlayers present similar shear modulus for short-term loads (e.g. shock loads) due to its viscoelastic behaviour. However, great differences between them are observed for mediumand long-term loads, the most of the applied loads in common structures. Both PVB and SGP exhibit viscoelastic response within the temperature range for common structural applications, from -20 to 80 ºC [36], as well as a similar shear modulus at low temperatures (< 0 ºC). However, these interlayers present significantly different glass transition temperatures, which for PVB is 20 ºC while for SGP it is 55 ºC [37]. The structural response of laminated glass has attracted the interest of several authors, either by simulating it numerically (e.g. [25,38]) and analytically (e.g. [29,39]) or performing experimental tests (e.g. [22,26,34,40–42]). In this context, the influence of the interlayer on the flexural stiffness (e.g. CHAPTER 2 32 (b) (c) Figure 2.11: Difference between the transparency levels of (a) the original glass cube and (b) the glass cube rebuild in 2011 [56]. FINAL CONSIDERATIONS One of the main challenges when glass is used as a structural material is its brittle behaviour. Its tensile strength is unreliable and time-dependent. Failure can occur without any warning in a catastrophic manner once the critical fracture toughness is attained. Thermal toughening is an effective solution to prevent the growth of surface flaws over time, but both fully tempered glass and heat-strengthened glass exhibit undesirable fragmentation patterns for structural applications. The tensile strength of glass and its fragmentation pattern seem to be two incompatible properties by applying tempering. Glass lamination was developed based on the redundancy concept, but the collapse of entire glass structures can never be overlooked. Although the interlayer action is successful in preventing injuries or even loss of human life due to the fall of glass shards, laminated glass can barely support its own self-weight after cracking. 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Challenging Glass 3: Conference on Architectural and Structural Applications of Glass, CGC 2012, 2012, p. 57–65. https://doi.org/10.3233/978-1-61499-061-1-57. [57] Wellershoff F, Sendelbach M, Schmitt F. Glass Bridges and Blass Walls. Challenging Glass 2 - Conference on Architectural and Structural Applications of Glass, CGC 2010 2010:217–26. 38 CHAPTER 3 STRENGTHENING OF GLASS Glass is still an extremely fragile material. Therefore, based on the philosophy employed in reinforced concrete, glass has been combined with other materials in order to improve its post-failure performance. Furthermore, different concepts have been studied with respect to (i) type of glass, (ii) type of adhesive, (iii) reinforcement percentage; (iv) relative position of the reinforcement element, and (v) post-tensioning level. As a consequence, further investigations are focusing (i) on the bond behaviour of glass-to-reinforcement adhesive joints, which plays a crucial role in the overall response of glass composite systems; and (ii) on the numerical modelling of glass composite systems, which is essential to use this new technology at an industrial level for large scale applications. Reinforcement materials recently applied in civil engineering, such as SMAs, seem to be a promising alternative for the post-tensioning of glass structures. In addition, SMAs have self-sensing attributes that can be exploited to develop continuous monitoring techniques for glass structures. The present chapter presents and discusses some of the most important investigations on glass composite beams strengthened with steel, timber, GFRP and CFRP reinforcement materials, ranging from the bond behaviour of adhesive joints to the structural behaviour of composite systems and its numerical simulation, as well as the phase behaviour of SMAs. STRUCTURAL AND SAFETY CONCEPT Despite the improvements introduced by glass industry in the last decades (e.g. production and lamination processes), the behaviour of glass is still fragile regardless of its residual stress level, interlayer properties and structural options adopted. As a consequence, the safety of glass structures STRENGTHENING OF GLASS 39 is commonly ensured by adopting over-designing techniques, either by adding sacrificial glass sheets (e.g. glass floors) and/or by adopting thicker glass panes [1]. However, over-designed glass structures are certainly not cost-effective and the failure of the entire structure cannot be ruled out (e.g. unexpected loads – vandalism and accidental loads). Like concrete, glass combines high compression strength with relatively low tensile strength. Therefore, it is reasonable to adapt the commonly accepted design philosophy of reinforced concrete to the glass, by bonding and/or anchoring reinforcement at the tensile region of the glass elements [2], thus creating glass composite systems. Even if glass is broken, they can still carry load due to the transfer of tensile stress from the cracked glass to the reinforcement element through shear stresses in the adhesive joint, creating a resisting mechanism formed by a compression force in the uncracked glass zone and a tensile force in the reinforcement (see Figure 3.1). The reinforcement acts as a crack bridge, thus preventing uncontrolled crack propagation and transferring the tensile force over the crack to the supports/foundations. (a) (b) (c) (d) Figure 3.1: Structural behaviour of composite glass systems: (a) load vs. deflection diagram; and distribution of normal strains over the cross-section at the (b) elastic phase, (c) cracking phase and (d) yielding phase, as well as the crack growth. Note: the neutral axis (n.a.) is displayed as a horizontal dotted line. Deflection Load (i) (ii) (iii) Elastic phase Glass Reinforcement Cracking phase Yielding phase (i) (ii) (iii) Elastic phase Cracking phase Yielding phase n.a. n.a. n.a. Deflection Load (i) (ii) (iii) Elastic phase Glass Reinforcement Cracking phase Yielding phase (i) (ii) (iii) Elastic phase Cracking phase Yielding phase n.a. n.a. n.a. Deflection Load (i) (ii) (iii) Elastic phase Glass Reinforcement Cracking phase Yielding phase (i) (ii) (iii) Elastic phase Cracking phase Yielding phase n.a. n.a. n.a. Deflection Load (i) (ii) (iii) Elastic phase Glass Reinforcement Cracking phase Yielding phase (i) (ii) (iii) Elastic phase Cracking phase Yielding phase n.a. n.a. n.a. CHAPTER 3 40 Glass composite systems with timber (e.g. [3,4]), steel (e.g. [5–8]), CFRP (e.g. [9,10]) and GFRP (e.g. [11–16]) have been investigated as an alternative means of ensuring post-failure strength capacity and ductility in glass structures. Timber, GFRP and CFRP show brittle behaviour until failure, such as glass. However, the sequential failure of these materials and/or connections allows the glass composite systems to exhibit non-linear inelastic behaviour, with progressive decrease in stiffness with increasing load [17]. On the other hand, the ductility in glass-steel composite systems is a consequence of the yielding of the reinforcement material, which causes an increase in deformation under an approximately constant load. BOND BEHAVIOUR OF GLASS JOINTS Bolted connections are still extensively used by glass industry. However, they lack structural efficiency and reliability, as the drilling/cutting required may introduce flaws and discontinuities on the glass surfaces [18]. In contrast, adhesively bonded joints seem to minimize the development of stress concentrations and, consequently, avoid the formation of additional surface flaws, besides the clear aesthetic advantages compared to mechanic connections [18]. Soft gap-filling adhesives have been widely used in glazing systems. However, they are not able to transfer significant stress due to their low tensile strength. Lately, stiffer and stronger adhesives, based on epoxy and acrylate resins, are being study for this purpose. The composite action between adherends, materialized by an adhesive joint, is crucial for the structural behaviour of composite systems. The bond behaviour of adhesive connections depends strongly on the adhesive type. This aspect is particularly relevant in glass structures because they do not have the ability to redistribute stress concentrations due to the yielding. Thus, it is particularly important to characterize the bond behaviour of adhesive connections, with respect to the substrate materials, the thickness of the adhesive layer, the effect of environmental conditions and the duration and rate of the load [19]. Some studies are found addressing the bond behaviour of glass composite systems. Glass-to-steel (e.g. [19–21]), glass-to-GFRP (e.g. [15,22]), glass-to-timber (e.g. [3,23]) and, very recently, glass-toSMA (e.g. [24,25]) adhesively bonded connections have been investigated, using different types of adhesive (e.g. epoxy, acrylate, structural polyurethane and polyurethane gap-filing) to assess their influence on the shear interaction between adherends. Moreover, the interlayer has also been studied as a bonding agent when the reinforcement is introduced within the laminated glass panel before the lamination process (e.g. [20]). Different test setups have been adopted, such as single lap joint tests STRENGTHENING OF GLASS 41 (e.g. [21]), double-lap joint tests (e.g. [15]) and pull-out tests (e.g. [20]), as well as interface characterization tests such as Double Cantilever Beam (DCB) for mode-I fracture and End Notched Flexure (ENF) for mode-II fracture (e.g. [26]). Although most studies have focused on the experimental characterization of glass composite systems, the development of analytical (e.g. [22]) or numerical (e.g. [27]) tools have also been addressed. Local bond stress – slip laws are calibrated to match experimental responses and are used as an input in numerical models, where adhesive damage is typically modelled using interface models, which in turn use energetic criteria (e.g. traction-separation laws) to govern the crack growth. GLASS COMPOSITE SYSTEMS IN LITERATURE 3.3.1. Glass-steel composite systems Glass-steel composite systems have been investigated since 2003 (e.g. [28–30]). Besides the experimental validation of the structural concept, these studies have focused on the influence of additional aspects on the structural response, such as the cross-section geometry, the bonding strategy for joining the reinforcement and the glass, the reinforcement percentage, the type of glass and the adhesive stiffness. One of the largest investigations focusing on glass-steel composite systems was carried out at Delft University of Technology (TU Delft), as part of a wide research project to build a fully transparent pavilion using glass as a load-bearing material [31], as shown in Figure 3.2. The production of an 18 m long steel-reinforced glass beam capable of supporting load after glass cracking and, in turn, presenting a relatively safe and ductile failure mechanism [6,32–36] was a major milestone of this project. Before that, small scale models were manufactured and tested, assessing the influence of different cross-section geometries (see Figure 3.3) on the overall response of glass-steel composite systems [31,37]. Beams with most complex geometries were obtained by assembling the glass panels using an interlayer or a transparent structural adhesive. Based on the results, boxIand T-section beams are better at preventing the lateral-torsional buckling of the compression glass zone [32]. Isection beams were extensively studied as a part of another large research project on glass-steel composite systems: the European project Innovative Steel-Glass-Structures (INNOGLAST) [38]. As glass composite systems are a relatively recent development in the construction industry and there are no specific design guidelines, a general design guidance was created by summarizing the main results of INNOGLAST [38]. This beam geometry is relatively easy to produce in comparison with box- CHAPTER 3 48 (a) (b) (c) Figure 3.7: Steel-framed glass beam developed by Belis et al . [5]: (a) cross-section-geometry and schematic representation of the connection between beam segments; and (b-c) Dutch Ministry of Finance in The Hague. Note: units in [mm]. 3.3.2. Glass-timber composite systems Solutions including glass and timber are used for a long time (e.g. windows), but glass is mostly applied as an infill. Since the 2000s, some studies have addressed the possibility of strengthening glass with timber (e.g. [4,50–55]). Like glass, timber is one of the most important materials in contemporary architecture due to its mechanical and aesthetical features. Timber is a natural and environmentally friendly material. Its high strength-to-weight ratio and relatively low thermal conductivity make it an attractive alternative compared to other construction materials [53]. I-section beams formed by a glass web and timber flanges (see Figure 3.8a) were the first concept studied using both materials together [51]. It was concluded that timber reinforcement can be successful in providing load carrying capacity after glass breakage. After that, for the application of glass-timber composite beams at the Palafitte hotel, in Switzerland, Kreher [55] carried out an 12 Glass Glass Steel plate 30 10 Connection block Bolts STRENGTHENING OF GLASS 49 extensive experimental campaign on I-section beams (see Figure 3.8b), varying both the glass type and the cross-section geometry. As expected, the higher the tempering level, the poorer the post-failure response, since thermally toughened glass has higher tensile strength and lower integrity after cracking in comparison with annealed glass. Moreover, the authors highlighted that such concept is aesthetically advantageous and capable of fulfilling the most recent design requirements, namely those regarding the structural performance under fire. (a) (b) (c) Figure 3.8: Cross-section geometry of glass-timber composite beams tested by (a) Hamm [51], (b) Kreher [55] and (c) Kozlowski [53]. Note: units in [mm]. In these mentioned studies, I-section beams were always manufactured by bonding timber bars on the side faces of the glass panel, similar to the EBR technique. However, in order to increase the bonding area between the adherends, Kozlowski [53] investigated another concept in which the glass pane was introduced into pre-cut groves in the timber flanges (see Figure 3.8c). First, adopting this novel concept, the influence of the adhesive layer thickness on the post-cracking behaviour of timberreinforced glass beams was assessed by Hulimka and Kozlowski [52]. Then, Kozlowski et al . [54] tested I-section beams manufactured with three types of adhesive (silicone, acrylate and epoxy) and heat-strengthened glass panes. Probably due to the high amounts of strain energy released after glass rupture, none of the specimens showed post-cracking response. Notwithstanding, specimens with stiffer adhesives presented almost full composite action, in contrast to the softer silicone ones. 250 30 to 50 50 to 60 10 587 160 100 65 65 12 300 200 55 75 8 30 12 to 15 250 30 to 50 50 to 60 10 587 160 100 65 65 12 300 200 55 75 8 30 12 to 15 250 30 to 50 50 to 60 10 587 160 100 65 65 12 300 200 55 75 8 30 12 to 15 CHAPTER 3 50 3.3.3. Glass-GFRP composite systems In the last few decades, FRPs have been widely used in the construction industry, mainly as a reinforcement material in new structures or for the strengthening of existing concrete structures [56,57]. FRPs are available as unidirectional strips made by pultrusion or as sheets or fabrics with unidirectional or multidirectional fibres. The former, which are the FRPs commonly used as reinforcement in civil engineering applications, consist of long, unidirectional and continuous fibres embedded in a resin matrix. In this sense, FRPs are a heterogeneous and anisotropic material. While fibres govern the mechanical response of FRPs, which usually present a linear elastic response until failure, the matrix protects them from environmental agents (e.g. moisture) and redistributes stresses along the fibres. FRPs are commonly manufactured using thermosetting resins, such as polyester, vinylester and epoxy resins [56]. FRPs produced with carbon (CFRP), glass (GFRP), and aramid (AFRP) fibres are the most used for structural applications [58]. In construction, GFRPs are commonly used due to their low-cost [58]. This material presents high strength/weight and stiffness/weight ratios, as well as high durability. Like glass, GFRPs present a brittle failure and although they have high strength, commonly ranging from 200 to 500 MPa, their modulus of elasticity is relatively low compared to steel, CFRP or even glass. Furthermore, GFRP profiles can assume a variety of forms and shapes [59]. GFRP-reinforced glass beams are one of the most investigated glass composite concepts (e.g. [11,12,14,15,60–63]). Research on this topic have mainly focused on the influence of the adhesive type (e.g. [12,15]) and cross-section geometry (e.g. [15]), as well as the efficiency of different application alternatives for the GFRP reinforcement, such as (i) GFRP rods embedded within the interlayer (e.g. [60]), (ii) GFRP pultruded profiles externally bonded (e.g. [11]) and (iii) GFRP plates introduced between glass sheets in laminated glass (e.g. [62]). Louter et al . [60] evaluated the feasibility of producing SG-laminated glass beams reinforced with embedded round (series #1) or flat (series #2) GFRP rods (see Figure 3.10). Promising results were obtained from both series through four-point bending tests. For short-term loading and at room temperature, the interlayer was able to provide sufficient shear interaction between both adherends. Furthermore, specimens with flat GFRP rods presented a stiffer post-fracture response than those reinforced with round GFRP rods, with a smaller GFRP-to-glass contact area than the first ones (see Table 3.2). Therefore, the series #1 were unloaded after significant slippage of the reinforcement, while the series #2 failed explosively by lateral-torsional buckling. Despite slight differences between STRENGTHENING OF GLASS 51 both specimen series (e.g. tensile capacity, modulus of elasticity and geometry), it was concluded that the reinforcement-to-glass bonding area plays an important role in the post-failure response, even when embedded reinforcement systems are adopted. (a) (b) Figure 3.9: SG-laminated glass beams with embedded GFRP reinforcement tested by Louter et al . [60]: (a) cross-section geometry; and (b) specimen. Note: units in [mm]. Later, I-section beams formed by a glass web and GFRP flanges (series I ) were tested by Correia et al . [12], as well as reference beams reinforced at the bottom edge with an externally bonded GFRP laminate (series R ), as shown in Figure 3.10a. For bonding both components, an elastic gap-filling polyurethane adhesive ( PU ) and an epoxy adhesive ( EP ) were used. Based on four-point bending tests, I-section beams exhibited a higher residual strength capacity than those from the R series, in part because a much higher reinforcement percentage was adopted in the former (see Table 3.2). On the other hand, L-shaped GFRP plates were also used to join the GFRP flanges to the glass web, significantly increasing the bonding area between adherends. As a result and taking the R series as a reference, the I-section beams were able to (i) avoid premature detachment of the reinforcement by preventing high interfacial stresses at the tip of delamination cracks when the stiff adhesive was used and (ii) produce superior residual strength capacity by promoting greater shear interaction between adherends when the flexible adhesive was used. As observed in steel-reinforced glass beams, the reinforcement percentage and the bonding surface area were also important here. Like in glass-steel composite systems (see Section 3.3.1), the type of adhesive remains a key parameter when GFRP replaces steel as reinforcement material. In this sense, Valarinho et al . [15] tested I-section GFRP-reinforced glass beams (cross-section geometry depicted in Figure 3.10b), adopting both isostatic and hyperstatic test configurations. In order to cover a wide range of shear 115 GFRP round rods 2 2 11 1Glass sheets 2Interlayer 5 2 11 GFRP flat rods 0.8  6 8 CHAPTER 3 52 stiffness, three different adhesives were used to join the components: (i) an elastic gap-filling polyurethane adhesive ( SFlex series), with the lowest modulus of elasticity; (ii) an epoxy adhesive ( SDur series), the stiffest one; and (iii) a structural polyurethane adhesive ( SForce series), with a moderate modulus of elasticity. With a focus on the isostatic tests, the stiffest adhesive was the best in providing residual strength, as expected, while SFlex series showed the highest values of deflection at failure, as well as the lowest values of residual strength and post-failure stiffness (see Table 3.2). The high post-cracking deformation observed in the SFlex series derived from a significant slip between the adherends due to the high deformability and low stiffness of the gap-filling polyurethane adhesive. Accordingly, the SForce and SDur series showed much denser crack patterns than the SFlex series, whose post-failure response was mainly governed by the damage propagation towards the supports at the adhesive joint level and the consequent horizontal crack propagation, i.e. crack branching, in the glass panel, as shown in Figure 3.11. Table 3.2: Overview of investigated concepts of GFRP-reinforced glass beams, indicating the most relevant parameters related to the specimen geometry and its post-failure performance. Reference: Louter et al . [60] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] #1 SG-interlayer 0.85 2.00 82.14 119 > 1250 #2 0.78 2.83 213 > 2349 Reference: Correia et al . [12] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] R-PU Polyurethane 10.00 0.10 74.00 < 100 438 R-EP Epoxy 104 394 I-PU Polyurethane 139.5 a) 0.04 82.67 153 883 I-EP Epoxy 199 426 Reference: Valarinho et al . [15] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] SDur Epoxy 90.32 a) 0.06 85.71 282 569 SForce Polyurethane 224 297 SFlex Non-structural 165 1825 Notes: ρr = tensile reinforcement percentage; Pb = reinforcement-to-glass bonding perimeter; Ar = reinforcement cross-section area; ht = total height of the specimen; Ls = span length; Fmax = peak load registered after glass cracking; Fcr = cracking load; δult = mid-span deflection at failure; and δcr = mid-span deflection correponding to Fcr. a) These values were determined considering the total amount of reinforcement. However, tensile forces were only supported by the bottom GFRP flange. STRENGTHENING OF GLASS 53 (a) (b) Figure 3.10: Cross-section geometry of GFRP-reinforced glass beams tested by (a) Correia et al . [12] and (b) Valarinho et al . [15]. Note: units in [mm]. (a) (b) Figure 3.11: Crack patterns of GFRP-reinforced glass beams tested by Valarinho et al . [15]: (a) SFlex beams; and (b) SDur beams. 3.3.4. Glass-CFRP composite systems Today, CFRPs are one of the first choices for the strengthening of existing concrete structures [58]. Compared to steel, they are a lighter material and have higher stiffness and tensile strength, lower relaxation, no creep deformation and longer fatigue life, as well as higher resistance to chemical, thermal and aggressive environmental effects. With advance in technology, the cost of CFRPs is 112 12 GFRP profile 12  10 124 2 76 12 30 20 GFRP profile 76  10 5 124 50 12 17 GFRP profile 50  10 5 112 12 GFRP profile 12  10 124 2 76 12 30 20 GFRP profile 76  10 5 124 50 12 17 GFRP profile 50  10 5 CHAPTER 3 54 decreasing and nowadays they are a viable and competitive solution for structural applications as a reinforcement material [58,64]. The structural behaviour of glass beams reinforced with CFRP has been addressed by few studies (e.g. [9,65,66,10]). In a general analysis, different strategies for applying CFRP reinforcement are found in the literature, such as: (i) CFRP laminates externally bonded to the glass [10]; (ii) CFRP rods embedded into the interlayer [66]; and (iii) CFRP rods introduced into previously designed grooves in laminated glass [65], resembling the NSM technique. For the application of large CFRP-reinforced glass beams in the roof structure of the Loggia dei Vicari in Italy (see Figure 3.12a), Palumbo et al . [10] carried out the first study on glass-CFRP composite beams to the best of the author’s knowledge. A small-scale prototype was tested adopting a threepoint bending configuration. The specimen was manufactured by bonding a CFRP laminate to the bottom edge of an SG-laminated glass panel (see Figure 3.12b). Experimental results showed the ability of the CFRP reinforcement to generate stress distribution mechanisms after glass cracking, providing a significant post-cracking load carrying capacity (see Table 3.3). Table 3.3: Overview of investigated concepts of CFRP-reinforced glass beams, indicating the most relevant parameters related to the specimen geometry and its post-failure performance. Reference: Palumbo et al . [10] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] - Epoxy - - 100 179 - Reference: Louter et al . [66] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] - SG-interlayer 0.26 2.67 82.1 96 > 3061 Reference: Cagnacci et al . [65,67] Series Adhesive ρr [%] Pb/Ar [mm-1] ht/Ls [mm/m] Fmax/Fcr [%] δult/δcr [%] S-EP Epoxy 1.15 a) 0.50 107.1 22 - S-PO Polyester 21 - H-EP Epoxy 55 - H-PO Polyester 80 - Notes: ρr = tensile reinforcement percentage; Pb = reinforcement-to-glass bonding perimeter; Ar = reinforcement cross-section area; ht = total height of the specimen; Ls = span length; Fmax = peak load registered after glass cracking; Fcr = cracking load; δult = mid-span deflection at failure; and δcr = mid-span deflection correponding to Fcr. a) This value was determined considering the total amount of reinforcement. However, tensile forces were only supported by the bottom CFRP bar after glass rupture. STRENGTHENING OF GLASS 55 (a) (b) (c) (d) Figure 3.12: Glass-CFRP composite beams: (a) roof structure of the Loggia dei Vicari, in Italy [10]; and crosssection geometry of specimens tested by (b) Palumbo et al . [10], (c) Louter et al . [66] and (d) Cagnacci et al . [65,67]. Note: units in [mm]. Following the philosophy employed in glass-GFRP composite beams (see Section 3.3.3), Louter et al . [66] introduced round CFRP rods into the interlayer of two-layer laminated glass panels during the lamination process, as schematized in Figure 3.12c. On the other hand, Cagnacci et al . [65,67] developed a novel concept of CFRP-reinforced glass beams which consists of inserting round CFRP rods into U-shaped recessed grooves on both longitudinal edges of a three-layer laminated glass panel (see Figure 3.12d). The specimens were manufactured with CFRP bars with smooth ( S ) and helical wrapped ( H ) surfaces, as well as epoxy ( EP ) and polyester ( PO ) adhesives for bonding the components. As observed in concrete structures (e.g. [68]), the surface properties of CFRP bars strongly influenced the shear interaction level at the reinforcement/adhesive interface. Higher residual strength was achieved replacing smooth CFRP bars by helical wrapped ones (see Table 3.3). As a result, the specimen failure was no longer governed by adhesive failure at the CFRP/adhesive interface, but by tensile failure in CFRP (specimens with polyester adhesive) or damage propagation at the adhesive joint and glass substrate (specimens with epoxy adhesive). This difference between 100 CFRP rods 1.5 5 100 50 12 300 32 10 GFRP bars 8 CFRP laminate 100 CFRP rods 1.5 5 100 50 12 300 32 10 GFRP bars 8 CFRP laminate 100 CFRP rods 1.5 5 100 50 12 300 32 10 GFRP bars 8 CFRP laminate CHAPTER 3 56 failure modes was probably a result of the shear stiffness provided by each adhesive. In contrast to the polyester adhesive, the epoxy adhesive was not able to mobilize long bond lengths to transfer the shear stresses between adherends, thus inducing high interfacial stresses at the tip of delamination cracks. Given the above, some improvements would be necessary to achieve greater post-failure strength, such as the adoption of a higher reinforcement percentage. POST-TENSIONING OF GLASS As noticed in passively reinforced glass beams, the annealed glass is better at providing structural integrity after cracking due to the interlocking between the resulting large shards. However, its tensile strength is time-dependent because surface flaws grow when subjected to tensile stress and humidity. Tempering has been successful in avoiding this unpredictability, but when fully tempered glass breaks, it results in small shards, compromising the structural integrity of glass elements and, consequently, the post-failure load-carrying capacity and ductility of composite systems [12,15,69]. Heatstrengthened glass provides an interesting compromise between fairly tensile strength and sufficiently large fragmentation patterns, but annealed glass has obvious economic and structural benefits for the construction industry [1]. In addition, heat-strengthened glass subjected to in-plane loads can break into tiny fragments, like fully tempered glass. Resembling the prestressing methodologies employed to concrete structures, post-tensioned composite systems have been recently investigated with the aim of improving the performance of glass structural elements, both before and after glass cracking. Like tempering, post-tensioning induces beneficial compressive stress in the glass to prevent existing flaws from growing under service load, making it safer for large-scale applications. Compared to tempering, the mechanical prestressing of glass can be advantageous in several aspects, such as: (i) the post-failure performance of glass remains virtually unchanged after post-tensioning; (ii) the glass can theoretically be drilled and/or cut after post-tensioning to overcome unexpected geometric challenges; (iii) both the prestressing level and the layout can be adapted to each structural element and its loading conditions, unlike the thermally toughened glass available on the market; and (iv) after glass rupture, the reinforcement acts as a crack bridge, transferring the tensile force to the supports and providing residual load carrying capacity. A limited number of researches have addressed the post-tensioning of glass composite systems. Steel (e.g. [6,8,41,70]) is the most commonly used material as prestressed reinforcement, and recently CFRP (e.g. [9]) and GFRP (e.g. [62]) as well. These exploratory studies have mainly focused on the STRENGTHENING OF GLASS 57 post-tensioning setup and on the anchorage system to transfer the post-tensioning force from the reinforcement to the glass. Regarding the first aspect, the reinforcement can be introduced within the laminated glass panel (e.g. [6,8]) or placed externally (e.g. [9,71]) and, on the one hand, can be positioned as a straight line along the glass element (e.g. [9]) or adopting a layout similar to the shape of the bending moment diagram (e.g. [71]), on the other hand. Concerning the anchorage strategy, the reinforcement can be mechanically anchored at the beam ends (e.g. [8]) and/or adhesively bonded to the glass (e.g. [9]). One of the first studies on post-tensioned glass systems was performed by Bos et al . [6]. A T-section beam was post-tensioned using a steel tendon mechanically anchored at the beam ends (see Figure 3.3c). After that, it was bonded to the glass using a UV-curing acrylate adhesive. The glass web consisted of a SG-laminated glass panel with three glass layers and the steel tendon was introduced between the outer glass layers, adopting a parabolic layout. Based on the experimental results, the initial failure strength of glass can be significantly increased by applying prestress. Post-tensioning reduces the tensile strength reserve of the reinforcement material, wherefore safety measures must be taken to ensure sufficient residual strength after glass cracking. Furthermore, prestressing can triggers or magnifies the torsional-lateral buckling in the compression glass zone, and therefore changes in cross-section geometry may be necessary to prevent or delay it. Louter et al . [9] developed and tested two post-tensioning setups. One of the specimen series (MECHPT) consisted of post-tensioning SG-laminated glass beams by stretching steel tendons placed in recessed grooves on the top and bottom sides (see Figure 3.13a). These steel tendons were not bonded to the glass. They were mechanically anchored at the beam ends. In addition, the posttensioning force was approximately the same in both tendons, thus imposing a uniform compressive pre-stress on the cross-section. Another series ( ADH-PT ) consisted of prestressing a steel plate before bonding it to the bottom edge of the glass panel (see cross-section geometry in Figure 3.13b). In this case, the post-tensioning force generated an axial force ( P ) and a bending moment ( P  e ) due to the eccentricity of the steel reinforcement in relation to the neutral axis. Compared to unreinforced reference series, both post-tensioning setups were successful in increasing the failure strength of glass, between 47.5 ( MECH-PT series) and 128.4 % ( ADH-PT series), as presented in Table 3.4. Regarding the post-cracking response, ADH-PT beams exhibited much higher ductility values than the MECH-PT beams. Furthermore, while the former failed by detachment of the steel plate after extensive crack propagation towards the supports, the latter failed explosively due to lateral instability of the CHAPTER 3 64 When SMAs are first subjected to load-unload cycles, in a process called “training”, unrecoverable plastic strains are generated [108]. However, they stabilize after sufficient cycling and the hysteresis response of the SMA becomes consistent. Depending on the training process, SMAs can show a oneway or two-way shape memory effect. The former is the SMA’s capability to memorize its original shape in austenite phase (higher temperatures), while the latter is the SMA’s capability to memorize the original shape in both austenite and martensitic phases [109]. The phase diagram of the Ni-Ti alloy is schematized in Figure 3.15. In the absence of mechanical loading, the martensite phase is called twinned martensite. For temperatures below Mf (martensite finish temperature), the detwinned martensite phase is induced by external loading, causing a macroscopic deformation that remains after unloading. In the absence of mechanical loading, the reverse transformation is induced by heating the material above As (austenite start temperature) and the detwinned martensite material starts to recover the permanent deformation previously induced, in a process called shape memory effect, which is entirely completed when the material is heated to Af (austenite finish temperature). Figure 3.15: Schematic phase diagram of Ni-Ti alloys, adapted from Rojob and El-Hacha [105]. The main difference between the Ni-Ti alloy and Fe-SMAs is associated to the mechanism of martensitic transformation. As shown in Figure 3.16a, the detwinning process in Fe-SMAs takes place at temperatures between Ms (martensite start temperature) and As , while in Ni-Ti alloys takes place at temperatures below Mf . Furthermore, unlike the Ni-Ti alloys, the superelasticity effect is not exhibited by Fe-SMAs because they deform irreversibly when they are mechanically loaded under temperatures above Af [96]. At low temperatures, the austenite-martensite transformation occurs before plastic deformation, while at high temperatures, only irreversible deformation occurs. The procedure for postDetwinned Martensite Twinned Martensite Austenite Temperature Mf Stress MsAsAf Forward Transformation Reverse Transformation Detwinning STRENGTHENING OF GLASS 65 tensioned strengthening by activation Fe-SMA materials can be summarized into three main steps: (i) pre-straining; (ii) activation; and, (iii) service loading [101]. Figure 3.16b illustrates the stress-strain and stress-temperature relationships during the two first steps required for the post-tensioning of FeSMA reinforcement. Based on Figure 3.16, the Fe-SMA strip is first mechanically loaded at room temperature – phase (1) – and, after the transformation phase from austenite to detwinned mastensite is reached, it is completely unloaded – phase (2). Then, the Fe-SMA strip is mechanically anchored or adhesively bonded to the structural element to be strengthened. Subsequently, the Fe-SMA strip is activated through resistive heating – phase (3). When the temperature reaches As , the reverse transformation from the detwinned martensite phase to austenite phase begins and the Fe-SMA tends to shrink. As the longitudinal deformation of the Fe-SMA strip is previously restrained, recovery stresses are developed due to the reverse transformation from martensite to austenite – phase (3.1) – and thermal contraction of the Fe-SMA reinforcement – phase (3.2). (a) (b) Figure 3.16: Behaviour of Fe-SMAs: (a) phase diagram [105] and (b) schematic activation procedure [93]. Temperature Mf Stress MsAsAf Austenite Detwinned Martensite Detwinned Martensite Irreversible Plastic Deformation Austenite 3 1 2 Stress Strain Stress Af 1 2 3.1 3.2 4 Pre-straining 1 2Unloading Activation Temperature 3 Thermal expansion 3.1 4 Service load 3.2 Cooling Heating Recovery stress Plastic strain Recovery strain 3 3 CHAPTER 3 66 If SMA reinforcement is adhesively bonded to the glass and a proper activation strategy is adopted, then its activation could ensure a smooth and safe transfer of post-tensioning force from the reinforcement to the glass due to the adhesive damage caused by heating. Given the above, SMA materials can be a promising solution for the post-tensioned strengthening of glass structural elements. In addition, their shape memory effect could be used in two distinct contexts: (i) before glass rupture, to improve the tensile strength of glass by creating favourable pre-stresses in the tensile zone; or (ii) after glass rupture, to enhance the post-failure performance until the glass element to be replaced, reducing the deformation, preventing the crack progression and, eventually, closing existing cracks. On the other hand, SMAs can still be used for structural health monitoring (e.g. [110,111]). Their selfsensing properties provide automated damage detection capabilities for civil engineering structures without external sensors, resulting in less complex systems. Structural health monitoring is typically based on the relationship between the electrical resistivity of the SMA and their deformability. As the tensile strength of glass is unpredictable, the risk of catastrophic collapses can be significantly reduced using the self-sensing functionality of the SMAs for identifying stress concentrations. One of the most important properties in SMA materials is the temperature hysteresis, which measures the difference between the transition temperatures for martensitic and reverse transformations. Depending on the chemical composition of the SMAs, they may have narrow or wide hysteresis. Accordingly, for a wide range of engineering applications, the hysteresis must require careful consideration during the SMA material selection. SMAs with a wide hysteresis are required for posttensioning, in order to maintain the pre-defined shape within a large temperature range. In other words, in order to avoid significant losses in post-tensioning force after activation and during the structure lifetime, Ms must always be lower than the ambient temperature in any case [96]. Glass-SMA composite systems have been addressed by few studies (e.g. [25,112,24,113]). Deng et al . [25] and Silvestru et al . [24] developed an extensive experimental campaign to characterize the influence of different adhesives on the bond behaviour of glass-to-SMA adhesive connections. In a later stage, aiming to develop SMA reinforced glass elements for structural applications, Silvestru et al . [112] conducted an exploratory study to assess the feasibility of strengthening laminated glass beams with externally bonded Fe-SMA strips. Results showed that the Fe-SMA reinforcement is able to prevent the glass brittleness and, when activated, to increase its initial fracture strength. Furthermore, Bedon et al . [113] performed an exploratory investigation on the flexural behaviour of laminated glass panels STRENGTHENING OF GLASS 67 reinforced with Ni-Ti wires embedded in the interlayer. The numerical study was based on two premises: (i) at lower temperatures, the Ni-Ti wires would provide further flexural stiffness because the interlayer would be able to guarantee sufficient shear interaction between the glass plies, while (ii) at higher temperatures, with the decrease in shear stiffness of the interlayer, the Ni-Ti wires would be activated, preventing out-of-plane deformations in the laminated glass panel. FINAL CONSIDERATIONS Current research is mainly focused on the experimental validation of the structural concept of glass composite systems, addressing aspects such as the reinforcement material, the type of glass and the bonding strategy. As a consequence, further topics for understanding the structural behaviour of glass composite systems are still insufficiently studied, such as the bond behaviour of glass-reinforcement adhesively bonded connections. However, in both cases, most studies have focused on the experimental characterization of glass composite systems, neglecting the development of reliable analysis and design tools. Although CFRPs are widely used in the construction industry for strengthening existing concrete structures, the experimental research on glass composite systems has been mostly devoted to the flexural behaviour of steel-reinforced and GFRP-reinforced glass beams. Compared to other reinforcement materials (e.g. steel), CFRPs present higher tensile stiffness and tensile strength. Thus, they can be adopted to reduce the reinforcement percentage and improve the aesthetic characteristics of glass composite systems. Post-tensioning is an effective strategy to solve the mismatch between glass fragmentation and tensile strength created by thermal tempering. However, post-tensioning force transfer mechanisms should be carefully designed to prevent high stress concentrations because glass has time-dependent strength. 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LABSE - Lanka Association of Building Services Engineers; 2008. [75] Teh Y. Fast , Accurate Force and Position Control of Shape Memory Alloy Actuators. PhD thesis. Australian National University, 2008. [76] Hartl D, Lagoudas D. Aerospace applications of shape memory alloys. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 221, 2007, p. 535–52. https://doi.org/10.1243/09544100JAERO211. CHAPTER 4 80 instead of the values reported in the literature after experimental testing, to avoid convergence problems (e.g. snap-back instabilities) and reduce deleterious dynamic effects. PAPER II  Rocha J, Sena-Cruz J, Pereira E. Tensile behaviour of CFRP-glass adhesively bonded connections: double-lap joint tests and numerical modelling. Engineering Structures 2022; 260:114212. https://doi.org/10.1016/j.engstruct.2022.114212 Impact factor: 5.582 This paper first presents and discusses the results of an experimental study involving tensile tests on double-lap joint specimens, in order to characterize the bond behaviour of glass-to-CFRP adhesive connections. For this purpose, three different adhesives were selected to assess the influence of the adhesive’s nature on the behaviour of glass-to-CFRP adhesive connections. Furthermore, two overlap lengths were tested, the second being twice as long as the first. Based on the experimental results, flexible adhesives seem to be better at promoting stress redistribution mechanisms, mobilizing longer bond lengths to transfer shear stresses between adherends. Adhesives showing an extremely stiff response induce high stress concentrations in the glass substrate, promoting premature failure of bonding systems due to cohesive shear debonding at the glass substrate. In the second part of this paper, local bond stress – slip laws were derived for each of the adhesive types used to manufacture glass-to-CFRP adhesive connections. Using a second order differential equation in terms of slip, this analytical study was performed based on a computational application developed by Sena-Cruz and Barros [4]. It finds the parameters required by the chosen local bond stress – slip laws using an inverse analysis strategy complemented with numerical fitting tools. Furthermore, in order to determine the effective bond length for each adhesive type, the maximum load was plotted as a function of the anchorage length of the CFRP laminate. Compared to stiff, the flexible adhesives require longer bond lengths to mobilize the full load-carrying capacity of glass-toCFRP adhesive connections. Finally, a numerical study was also carried out to show how the response of glass-to-CFRP adhesively bonded connections can be accurately simulated by applying the analytically derived bond stress – slip laws. SUMMARY OF APPENDED PAPERS 81 PAPER III  Rocha J, Sena-Cruz J, Pereira E. Influence of adhesive stiffness on the post-cracking behaviour of CFRP-reinforced structural glass beams. Composites Part B Engineering 2022; 247:110293. https://doi.org/10.1016/j.compositesb.2022.110293 Impact factor: 11.322 This paper was aimed at assessing the influence of the adhesive type on the post-cracking performance of glass-CFRP composite beams under flexure. The three adhesives previously used for double-lap joint specimens were also used in this case. The CFRP reinforcement was adhesively bonded to the bottom edge of annealed glass elements. In the first part of this paper, the experimental procedures are detailed and the experimental results obtained from four-point bending tests are presented and discussed. They show that CFRP-reinforced glass beams can exhibit ductile failure modes. Furthermore, depending on the type of adhesive, the cracking load can be sometimes attained or surpassed during the post-cracking phase, improving significantly the structural safety. Adhesives with high toughness and moderate stiffness seem to be the best for manufacturing glass-CFRP composite systems because they prevent high stress concentrations at the glass substrate while being sufficiently stiff. Reliable approaches for the modelling of reinforced glass structures are investigated in the second part of this paper, which focuses on the best approach to numerically simulate the glass-to-CFRP adhesive connections depending on the adhesive type. They were well simulated assuming (i) perfect bond between components, neglecting the physical existence of the adhesive layer, for the stiffest adhesive; (ii) perfect bond at the glass/adhesive/CFRP interfaces, simulating the adhesive as a linear elastic material, for the moderate stiffness adhesive; and (iii) non-linear behaviour of the adhesive connection, adopting interface elements governed by the local bond stress – slip laws derived from double-lap joint tests, for the softest adhesive. PAPER IV  Rocha J, Pereira E, Sena-Cruz J. Feasibility of mechanical post-tensioning of annealed glass beams by activating externally bonded Fe-SMA reinforcement. Construction and Building Materials 2022; 365:129953. https://doi.org/10.1016/j.conbuildmat.2022.129953 Impact factor: 7.693 CHAPTER 4 82 This paper investigates for the first time, to the best of the author’s knowledge, the feasibility of posttensioning annealed glass beams by activating Fe-SMA strips adhesively bonded to the bottom edge. To estimate the benefits of the post-tensioning on the flexural response of such glass composite beams, post-tensioned glass beams are compared to reference ones (with passive Fe-SMA reinforcement). Fe-SMA strips were activated by heating them to temperatures between 120 and 160 ºC. In order to prevent premature debonding of the Fe-SMA strips due to the inevitable adhesive damage caused by heating, these were not activated throughout their full extension. Fe-SMA strips zones near the beam ends were left without being activated in order to act as anchorage zones during the heating phase, while composite action is partially lost. Based on four-point bending tests, it has been shown that Fe-SMA reinforced glass beams were observed to exhibit a significant load-carrying capacity after glass cracking, as well as extremely ductile failure modes due to the Fe-SMA yielding. Post-tensioning reduced the possibility of an unexpected glass breakage due to the growth of initial surface flaws, and post-tensioned beams showed up to 30 % higher cracking loads than reference beams. The activation strategy proved to be appropriate to avoid both the premature debonding of the reinforcement element and high stress concentrations at the glass substrate. In general, the Fe-SMA can be a promising reinforcement material to be used in glass composite systems, either passive or post-tensioned. PAPER V  Rocha J, Pereira E, Sena-Cruz J. Flexural behvaiour of post-tensioned laminated glass beams with hybrid strengthening systems using CFRP and Fe-SMA reinforcements. In subimition to Construction and Building Materials. Impact factor: 7.693 The feasibility of strengthening glass structural elements with hybrid strengthening systems is assessed in this paper. Tailored Laminated glass beams were fabricated by joining three annealed glass layers using PVB interlayers. Each specimen was strengthened with CFRP and/or Fe-SMA reinforcements applied according to the EBR and NSM techniques. It should be noted that (i) two epoxy adhesives were used to bond both reinforcement materials to the glass; (ii) CFRP laminates were prestressed when inserted into the groove pre-designed before the glass lamination, according to the NSM technique; and (iii) Fe-SMA strips were always activated regardless of their position. FeSMA strips were not activated near the beam ends to preserve the full mechanical characteristics of the adhesive near the supports and act as anchorage zones. The experimental results showed that SUMMARY OF APPENDED PAPERS 83 NSM CFRP composite systems can be safely prestressed, preventing the premature FRP peeling-off failure during the prestress application. In addition, hybrid strengthening systems are more efficient than the EBR systems in preventing the premature debonding of the reinforcement element due to a critical shear crack, taking better advantage from the tensile capacity of the reinforcement materials. In general, hybrid strengthening systems are good for improving the overall flexural behaviour of glass beams because the Fe-SMA reinforcement can always be activated and the CFRP reinforcement remains providing post-cracking stiffness after the yielding of the Fe-SMA. REFERENCES [1] Sena-Cruz J, Barros J, Azevedo A, Ventura-Gouveia A. Numerical Simulation of the Nonlinear Behavior of RC Beams Strengthened With NSM CFRP Strips. CMNE 2007 - Congress on Numerical Methods in Engineering and XXVIII CILAMCE - Iberian Latin-American Congress on Computational Methods in Engineering, Porto: 2007, p. 13–5. [2] Simulia. ABAQUS computer software and Online Documentation. v6.12. 2012. [3] Valarinho L, Sena-Cruz J, Correia J, Branco F. Numerical simulation of the flexural behaviour of composite glass-GFRP beams using smeared crack models. Composites Part B: Engineering 2017;110:336–50. https://doi.org/10.1016/j.compositesb.2016.10.035. [4] Sena-Cruz J, Barros J. Modeling of bond between near-surface mounted CFRP laminate strips and concrete. Computers and Structures 2004;82:1513–21. https://doi.org/10.1016/j.compstruc.2004.03.047. 84 CHAPTER 5 CONCLUSIONS AND FUTURE WORK CONCLUSIONS Recently, the structural glass applications are among the most prominent breakthroughs in civil engineering. Glass is currently seen as the greatest symbol of the contemporary architecture. Following the philosophy behind reinforced concrete, glass composite systems emerge as the main approach to overcome the glass brittleness and, in turn, boost its structural application. However, (i) the bond behaviour of glass-to-reinforcement adhesive connections, (ii) the structural performance of glass composite systems, (iii) the unpredictability of the glass tensile strength and (iv) the numerical simulation of glass composite systems are still open topics, and their development is essential for the acceptance and recognition by the construction industry. The main objective of the research conducted in this PhD thesis was, on the one hand, to develop, test, analyse and evaluate appropriate strengthening strategies for preventing catastrophic failures in glass structures and, on the other hand, to reduce the unpredictability of the glass fracture strength. Annealed glass was used in all experiments due to its obvious benefits after cracking, as mentioned before. Two different reinforcement materials were studied: (i) CFRP, which is widely used in the construction industry for the strengthening of existing concrete structures; and, (ii) Fe-SMA, which is emerging as a competitive alternative to CFRP in the post-tensioned strengthening of existing concrete structures. Monolithic glass elements (a single glass sheet) were firstly tested to measure the effective contribution of the reinforcement on the postcracking performance, while laminated glass elements were then selected with the aim of developing and applying a hybrid strengthening system capable of delaying the premature debonding of the CONCLUSIONS AND FUTURE WORK 85 reinforcement element and preventing peeling-off failure during the release of the prestressed reinforcement. After the completion of this work, the objectives initially defined for this PhD thesis were fully accomplished. Specific conclusions related to the research carried out and the recommendations for future developments are presented in the following sections. 5.1.1. Glass-CFRP composite systems In this first research domain, experimental, analytical and numerical studies were performed about the structural performance of glass-CFRP composite systems. It was assessed by means of an extensive experimental campaign aiming at the characterization of (i) the bond behaviour of glass-toCFRP adhesive connections by carrying out tensile tests on double-lap joint specimens and (ii) the overall behaviour of CFRP reinforced glass beams. 5.1.1.1. Preliminary numerical study on FRP reinforced glass beams Based on previous experimental results found in the literature (glass-GFRP composite beams), a preliminary numerical study was carried out to assess the efficiency of different constitutive models commonly used for glass modelling, namely the smeared crack models (SCM) available in the finite elements software FEMIX and ABAQUS and the damage plasticity model (DPM) from ABAQUS. Furthermore, the influence of some parameters required by material models on the numerical responses were assessed through a parametric study. Preliminary numerical simulations on glass-GFRP composite beams showed that all mechanical constitutive models were adequate to simulate the non-linear behaviour of glass in tension. Unlike FEMIX, ABAQUS/Explicit requires a dynamic-based numerical approach to obtain convergence, which implies a much higher computational effort. Even performing quasi-static analyses, through a proper prescription of the loading time, mass scaling factor, loading scheme and the damping ratio, the undesirable dynamic effects seem to have influenced the cracking load, since in a dynamic-based numerical approach, the force – deflection curve does not depend only on stiffness (displacement), but also on mass (acceleration) and damping (velocity) properties. The damping ratio played a key role in reducing the significant of the dynamic response, but experimental calibration is very difficult. On the other hand, both ABAQUS models showed great ability to capture in greater detail all the effects of cracking on the structural response because, as opposed to FEMIX model, much smaller load steps were easily implemented without compromising stability during crack formation. CHAPTER 5 86 Focusing on ABAQUS models, the SCM was more efficient than the DPM at simulating the postcracking behaviour of glass, as the latter does not allow considering a maximum absolute damage factor of 1.0, with residual stress in cracks. In addition, the DPM required as input parameters the dilation angle and the shape of the yield surface, which are two parameters typically used for simulating concrete but not so much in glass. The DPM showed greater difficulties in capturing the mode-II fracture at the glass-to-GFRP interfaces due to the assumptions inherent to this constitutive model. ABAQUS models required finer mesh patterns to capture phenomena (e.g. cracking at the glass bottom edge) than SCM-FEMIX. On the other hand, numerical results showed that a minimum modeI fracture energy should adopted, which are typically higher than the experimental values found in the literature, in order to avoid convergence problems (e.g. snap-back instabilities). Other deleterious effects may be excessive dynamic effects or lack of convergence, 5.1.1.2. Bond behaviour of glass-to-CFRP adhesively bonded connections Concerning the bond behaviour of glass-to-CFRP adhesive connections, double-lap joint specimens with bond lengths of 25 mm (L25 series) and 50 mm (L50 series) were produced using three different adhesives: (i) SikaForce L100 7100 (SF series), a flexible polyurethane adhesive with non-linear behaviour; (ii) SikaDur 330 (SD series), a stiff epoxy adhesive with linear elastic behaviour; and (iii) 3M DP490 (3M series), an epoxy adhesive with moderate stiffness and non-linear behaviour. Double-lap joint tests showed that the bond behaviour and failure mode of glass-to-CFRP adhesive connections strongly depend on the adhesive type. Unlike the SD series, which presented linear behaviour until failure, a remarkable loss of shear stiffness occurred in SF series due to the highly non-linear behaviour of the SikaForce adhesive. On the other hand, 3M series exhibited an intermediate performance. Unlike the SF and 3M series, in which the maximum load increased respectively 54.9 % and 11.6 % when the bond length was extended from 25 mm to 50 mm, this did not occur in the SD series. This reflects the inability of stiffer/brittle adhesives to mobilize relatively long bond lengths and smoothen stress concentrations at the substrates. Such behaviour promoted premature glass breakage due to the growth of existing surface flaws. Furthermore, the 3M series presented 23.5 % – 42.8 % higher cracking loads than those obtained from the corresponding SD series. Unlike the SikaDur, the 3M and SikaForce adhesives developed an extended plastic zone capable of smoothening local stress concentrations, confirmed with higher values of slip at maximum load in the corresponding series, varying between 1.25 – 8.33 times for L25 series and 1.04 – 4.26 CONCLUSIONS AND FUTURE WORK 87 times for L50 series. The adhesive ductility played a critical role in the failure mode of double-lap joint specimens, with SD series exhibiting distinct failure modes from the other specimen series, mainly dominated by fibre-tear failure in CFRP and glass substrate failure When using stiffer adhesives, the maximum load may not be a function of the tensile strength of glass or the shear strength of the adhesive because local mechanical properties become more relevant (e.g. edge treatment quality, density of surface flaws) on the performance of glass-CFRP composite systems. In this case, the maximum load and the failure mechanism is mainly governed by a dynamic phenomenon related to the sudden release of strain energy when initial cracks appeared in the substrate. Such behaviour mainly depends on the load level at crack initiation. This is very important in glass structures, as glass contains countless flaws randomly distributed on its surfaces. The performance observed in each series fundaments this idea: among the adhesives that meet the required specifications (e.g. shear strength), the one with the greatest deformation capacity should be adopted. To solve the 2nd order equation of bond, the local bond stress (τ) – slip ( s ) laws were derived for each specimen series. A linear τ – s law was adopted for SD series due to the absence of any adhesive damage propagation before failure. To account for the non-linear behaviour exhibited by the SF and 3M series, the Dimande’s exponential τ – s relationship was adopted in both cases. Taking SF joints as a reference, 3M joints are up to 3.0 times stronger and, theoretically, SD joints have no bond strength limit. Then, additional numerical simulations were performed to assess the efficiency of using the τ – s relationships to simulate glass-to-CFRP adhesive connections. The results showed that mixed-mode I+II occurred due to the lateral deflection of glass plates. Numerical simulations were successfully used to recalibrate the τ – s relationships to account for this unanticipated effect. While the shear stress distribution along the bond length was almost constant in SF joints, it presented a quadratic distribution in SD joints, with shear stress at the loaded end 2 times higher than at the free end. 5.1.1.3. Post-cracking performance of glass-CFRP composite beams Following the premises of the EBR technique, a CFRP laminate was bonded to the bottom edge of monolithic glass panels using the three adhesives previously adopted for manufacturing double-lap joint specimens. The specimens produced with SikaForce L100 7100, SikaDur 330 and 3M DP490, CHAPTER 5 88 respectively identified as the S Force , S Dur and 3M series, were tested until failure adopting a fourpoint bending configuration. The experimental campaign showed the advantages and feasibility of using CFRP to produce glass composite systems. It was shown that glass structures can exhibit safe and relatively ductile failure mechanisms when CFRP materials are bonded to the glass using structural adhesives. Before cracking, the flexural behaviour was clearly linear elastic. Since the glass panel has a much higher flexural stiffness than any other component, all series exhibited similar values of initial stiffness and cracking load, with differences between series of less than 6.7 %. After crack initiation, all composite beams maintained their integrity due to the contribution of reinforcement, exhibiting a post-cracking stage that was strongly influenced by the adhesive type. Excluding the S Dur series, all the others presented residual strength ratios above 100 %. This occurred due to the brittle behaviour of SikaDur and its low strain energy release (i.e. damping capacity). In S Dur beams, the crack propagation was mainly governed by mode-II fracture and dynamic effects (e.g. sudden load drops), which seem to have contributed for the growth of existing surface flaws at the glass substrate, reducing the tensile stress required for the formation of new cracks and promoting an asymmetric progression of cracks towards the supports. Although the residual strength reached in S Force series is 1.35 times higher than that obtained from S Dur series due to the SikaForce’s ability to smoothen stress concentrations, both presented similar ductility ratios due to the low toughness of the SikaForce adhesive, as a result of its reduced capacity to withstand the shock loads induced by new cracks. Consequently, the flexural cracks in S Force beams were predominantly V-shaped, which apparently provided additional load-bearing capacity and flexural stiffness at the beginning of the postcracking stage. Due to the brittle nature of the glass, the elastic strain energy absorption capacity of the adhesive plays a key role. While the SikaForce adhesive showed insufficient resistance to withstand shock loads, the SikaDur adhesive showed insufficient sufficient ductility and damping capacity to smoothen stress concentrations, the 3M adhesive seemed to be able to meet these requirements simultaneously. Accordingly, compared to the S Force and S Dur series, 3M series presented a much better postcracking performance, with a 17.9 % – 58.6 % higher residual strength index and a 51.1 % – 61.2 % higher ductility index. Numerical modelling was performed and aimed at finding the best approach to simulate the adhesive joint (shear interaction level) in glass-CFRP composite systems. The adhesive joint was simulated CONCLUSIONS AND FUTURE WORK 89 considering (i) perfect bond ( PB hypothesis), (ii) linear elastic behaviour ( EB hypothesis) and (iii) adhesive damage propagation ( IB hypothesis). Numerical simulations captured well the overall performance and crack patterns of glass-CFRP composite beams. Material properties obtained from simple mechanical characterization tests ( PB and EB hypotheses) or adhesion tests ( IB hypothesis) were shows to be sufficient to successfully predict the behaviour of complex glass structural systems. The IB hypothesis was better at capturing the flexural behaviour of the S Force series, while the S Dur and 3M series were better simulated using the PB and EB hypotheses, respectively. 5.1.2. Mechanical post-tensioning of Fe-SMA reinforced glass beams Fe-SMA strips were bonded to the bottom edge of monolithic glass panels using the 3M DP490 adhesive. Excluding the reference beams (R_T0 series), all Fe-SMA strips were pre-strained before bonding. After the adhesive cured, they were heated at 120 ºC (P_T120 series), 140 ºC (P_T140 beam) and 160 ºC (P_T160 beam) to create post-tensioning. As the polymeric adhesives do not perform well at high temperatures, only the middle region of Fe-SMA strips was heated, in order to preserve the properties near the beam ends. Then, the specimens were tested until failure in a fourpoint bending configuration. Relatively safe and ductile failure mechanisms were observed in all specimens, showing the efficiency of strengthening glass beams with Fe-SMA to avoid catastrophic failures. Moreover, the experimental program also demonstrated the great potential of post-tensioning glass elements by activating externally bonded Fe-SMA reinforcement. Mechanical post-tensioning with Fe-SMA materials may be a promising strategy to prevent the growth of existing surface flaws under service load. The pre-cracking stage was dominated by a linear elastic behaviour. All specimens were able to maintain their integrity during the cracking process, exhibiting a post-cracking response that was strongly influenced by the activation temperature. The R_T0 series showed a post-cracking response significantly distinct from that observed in glass-CFRP composite beams (3M series). Due to the nonlinear behaviour of the Fe-SMA, the R_T0 series presented a ductility capacity at least 1.75 times higher than the one of the 3M series. On the other hand, the yielding of the Fe-SMA prevented the R_T0 series from reaching residual strength ratio higher than the one in the 3M series, which was approximately 20.0 % lower. The activation strategy adopted, which consisted on heating only the middle region of the Fe-SMA strips, proved to be a suitable as an alternative to avoid the use of metallic elements (e.g. mechanical PAPER I 96 Numerical simulations are essential to investigate the structural behaviour of hybrid glass systems, or to design more complex or structurally demanding cases. However, the brittle behaviour of glass poses great challenges to the numerical simulations of structures comprising glass components, as well as the calibration of the material constitutive models adopted. Different authors have shown that the major challenges associated to the numerical simulation of structural glass behaviour, besides the calibration of the non-linear constitutive models used for glass simulation, are (i) the realistic definition of the structural interaction between materials and (ii) the assessment of the post-cracking behaviour [19,21]. Several approaches have been used to study critical aspects related to laminated glass and/or hybrid glass structural elements: (i) the type of interlayer representation and factors that influence its stiffness, such as temperature and load duration; (ii) the type of interaction between materials, mainly glass and reinforcement; and (iii) the type of constitutive models used to describe the non-linear behaviour of the glass and interlayer, as well as the behaviour of the reinforcement. Different constitutive models suitable for representing brittle or quasi-brittle behaviour have been used to simulate the non-linear behaviour of glass. While Neto et al . [18] have used a discrete crack approach, Valarinho et al. [19], Bedon and Louter [21–24] and Louter et al. [25] have used a smeared crack approach. Damaged plasticity approach was also used by Bedon and Louter [26]. The numerical simulations in Bedon and Louter [21–24] were performed in the ABAQUS finite elements software, by employing the Rankine failure criterion for cracks detection. The “brittle failure” option was adopted to model cracking evolution in Bedon and Louter [21,22], while the “brittle shear” option was adopted in Bedon and Louter [23,24]. Finally, the study performed by Bedon and Louter [26] included the numerical simulation of post-tensioned glass beams using ABAQUS, by means of the “concrete damaged plasticity” model, commonly used for modelling concrete. Because glass is an extremely fragile material, which has low fracture energy, some studies have adopted strategies to overcome problems related to the convergence of numerical models, such as linear sequential elastic analysis. The aim was to avoid a possibly negative tangential stiffness, which is the main cause for convergence problems found in non-linear analysis [25]. However, all these strategies require additional regularization procedures to obtain mesh objective results [18]. Considering the importance of developing accurate approaches for the simulation of glass structures, and the challenges that normally are associated to the simulation of the behaviour of brittle materials such as glass, this study is aimed at assessing the in-depth details associated to the numerical simulation of reinforced structural glass, including both the force-deflection response and the cracking PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 97 evolution. This work presents a numerical study of the structural behaviour of glass beams reinforced with GFRP laminates, which were simulated using different Smeared Crack (SCM) and Damaged Plasticity (DPM) models, available in FEMIX [27] and ABAQUS 6.14 [28], as well as different static and dynamic numerical approaches. In order to evaluate the efficiency of these models for the simulation of the post-cracking behaviour, the different numerical responses were analysed and compared considering the following factors: initial stiffness, cracking load, post-cracking stiffness, crack pattern and progressive failure. For this purpose, the material parameters derived by Valarinho et al . [19], based on experimental tests of glass-GFRP composite beams, were used. In this context, the present work addresses two main novel aspects, (i) concerning the comparison of different approaches for the numerical simulation of reinforced structural glass, since existing literature is absent in such critical analysis; (ii) on the other hand, literature often refers ABAQUS/Explicit analyses without addressing the influence of dynamic effects; both factors are critical for accurate simulations. The paper identifies the most critical factors and possible strategies to obtain quasi-static analysis without excessive computational effort. 2 TESTS ON GLASS-GFRP COMPOSITE SYSTEMS The numerical simulations of glass-GFRP composite beams were based on an exploratory experimental study carried out by Valarinho et al. [19]. These beams were tested following the fourpoint bending setup. The glass-GFRP composite beam specimens, as shown in Figure I.1, consisted of annealed glass panels, with cross-section of 12  100 [mm], reinforced at the bottom face with a GFRP pultruded laminate with a cross-section of 12  8 [mm]. These materials were joined using two different adhesives, with a 2.0 mm thick layer: (i) a polyurethane adhesive, Sikaflex 265, with low Young’s modulus and considered as a flexible adhesive, and (ii) an epoxy adhesive, SikaDur 31-fc, with high Young’s modulus and considered as a stiff adhesive. Double-lap joint specimens were also tested in tension by Valarinho et al . [19], in order to characterize the bond behaviour between GFRP and glass. From these tests the following main conclusions were obtained: (i) in the specimens with flexible adhesive, which exhibited an initial linear behaviour, a significant loss of stiffness before collapse was observed (see Figure I.2a), with failure characterized by debonding at the glass-adhesive interface; (ii) the specimens with stiff adhesive exhibited a practically linear behaviour until the collapse (see Figure I.2b), eventually with glass failure. PAPER I 98 (a) (b) Figure I.1: Four-point bending tests of the glass-GFRP composite beams: (a) schematic representation; (b) experimental setup [19]. Note: units in [mm]. (a) (b) Figure I.2: Load vs . relative displacement obtained from tensile tests on double-lap joints with (a) polyurethane and (b) epoxy adhesives [19]. Figure I.3 presents the structural behaviour of the glass-GFRP composite beams with polyurethane (S Flex beams) and epoxy (S Dur beams) adhesives obtained from four-point bending tests [19]. These composite beams presented linear elastic behaviour until the first crack appeared in the glass panel. Due to the brittle nature of glass failure and the inherent variability of its tensile strength, the cracking loads reached during testing have shown some scatter, as well as the post-cracking responses. This variability is associated to the numerous flaws contained by glass, which are randomly distributed in the material – such flaws, which are very small in size (not distinguishable by the naked eye) result F/2 50 470 230 Glass Adhesive GFRP 8 100 y x PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 99 mainly from the production process, and also from cutting and handling operations [29]. This inherent characteristic of glass explains not only the relatively high scatter of its tensile strength (e.g. Veer and Rodichev [30]), but also the occurrence of relevant size effects [31]. In the post-crack phase, a progressive loss of stiffness was observed after the development of a single crack in the case of the glass-GFRP composite beams made with polyurethane adhesive (see Figure I.4b). In the case of the composite beams made with epoxy adhesive, several cracks have developed, propagating towards the supports (see Figure I.4a). According to Valarinho et al . [19], the deflection increment before cracking (pre-cracking stage) ranged from 0.95 mm/min to 1.52 mm/min and then, during the post-cracking stage, between 1.70 mm/min and 3.21 mm/min. In these tests, both the applied load and the midspan deflection were measured at an average acquisition frequency of 5 Hz. All glass-GFRP beams were tested at an average temperature of 24 °C and 60 % of relative humidity. (a) (b) Figure I.3: Structural responses (load vs . deflection) obtained from the experimental tests: (a) S Dur beams; (b) S Flex beams [19]. (a) (b) Figure I.4: Experimental crack patterns: (a) S Dur beams; (b) S Flex beams [19]. The double-lap joint specimens have shown significant relative displacements between the glass pane and the GFRP laminate when flexible adhesives were used (about 20 times higher than for the stiff 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] SDur-1 SDur-2 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] SFlex-1 SFlex-2 PAPER I 100 adhesives). For this reason, four strain gauges (SG1 to SG4) were installed at different locations of the S Flex -1 beam at its mid-span section: (i) SG1 was placed at the top edge of the glass panel; (ii) SG2 was placed at the bottom/bonded edge of the glass panel; (iii) SG3 was placed at the top/bonded edge of the GFRP laminate; and (iv) SG4 was placed at the bottom edge of the GFRP laminate. As depicted in Figure I.5, a significant slippage occurred at the bonded interfaces of S Flex -1, both before and after the first crack was formed. Therefore, Bernoulli’s hypothesis was not observed for these beams. Figure I.5: Axial strains vs . load measured at different depths of the S Flex -1 beam mid-span section. 3 NUMERICAL SIMULATON Based on an initial estimation of the material non-linear parameters derived in Valarinho et al . [19], different material models, based in smeared crack and damaged plasticity approaches, were studied to simulate the non-linear behaviour of glass, as detailed in the following sections. 3.1. Smeared crack approach The smeared crack approach has been used by different researchers to describe the non-linear behaviour of brittle and quasi-brittle materials, e.g. concrete, masonry and glass. This approach can be categorized into fixed and rotating [32]. With the fixed concept, the orientation of the cracks is fixed during the entire computational process, whereas the rotating concept allows the orientation of the cracks to co-rotate with the axes of principal stress [32]. The multi-fixed crack concept provides an intermediate option. The multi-fixed concept, used by FEMIX [27], is suitable for tension-shear conditions, which is typical of fracture propagation problems [32]. The cracks start only under tension conditions, in mode-I, and subsequently propagate in tension-shear conditions. In the described behaviour, the maximum principal stress directions rotate after crack formation, which leads to increasing discrepancy relatively 0 1 2 3 4 -2.0 -1.0 0.0 1.0 2.0 Load, F [kN] Strain, ε[‰] SG1 SG2 SG3 SG4 SG1 SG2 SG3 SG4 PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 101 to the fixed crack directions. After the first crack, a new crack may appear when: (i) the maximum principal stress of an integration point exceeds the defined tensile strength, and (ii) the angle between the direction of the existing cracks and the direction of the maximum principal stress exceeds the value of a predefined threshold angle. The smeared crack approach contributes to describe the structural behaviour of the material when the maximum principal stress exceeds the uniaxial tensile strength. The main assumptions of this numerical approach are: (i) the damaged area is distributed by a specific crack band width, h , and (ii) the constitutive law of the damaged material is characterized by a tension-softening diagram, which, together with the fracture energy, Gf , are considered as material properties [33]. The type of tensionsoftening diagram and the number of cracks in each integration point are parameters required by the multi-fixed smeared crack approach [34]. Bazant and Oh [33], Sena-Cruz [34] and Rots et al. [35] proposed different ways to estimate the crack band width: (i) equal to the square root of the area of the finite element, (ii) equal to the square root of the area of the integration point, and (iii) equal to a constant value. The mesh objectivity must be ensured by the relationship between the crack band width and mesh size [32,34]. According to de Borst [36], the computational instabilities and convergence problems (e.g. snap-back instabilities) are avoided when the Eq. (I.1) is fulfilled. Therefore, the crack band width must be controlled to guarantee the stability and convergence of the smeared crack models. The other parameters are assumed to be constant properties of the material. The minimum facture energy required for a stable numerical process is given by Eq. (I.2), obtained from the manipulation of Eq. (I.1). ℎ ≤𝐺𝑓𝐸 𝑓𝑡2𝑏 (I.1) 𝐺𝑓 ≥𝑓𝑡2𝑏ℎ 𝐸 (I.2) The smeared crack approach was formulated in such a way that not only tension-softening but also crack shear can be taken into account through the shear retention factor, β [35]. This can be defined in two different ways [32,34]: (i) a constant value, and (ii) a non-constant value using the Eq. (I.3), where p is a constant value (e.g. 1, 2 or 3), ε n cr and ε n,ult cr are the crack normal strain and the ultimate crack normal strain, respectively. PAPER I 102 𝛽 =(1− 𝜀𝑛 𝑐𝑟 𝜀𝑛,𝑢𝑙𝑡 𝑐𝑟 )𝑝 (I.3) The constant shear retention factor implies a linear ascending relation between shear stress and shear strain across the crack, as well as a constant crack shear modulus [32]. In addition to the arbitrariness in choosing this value, the shear stress can increase indefinitely with a constant shear retention factor and, consequently, the maximum principal stress directions in cracked elements rotate ceaselessly [32]. The ABAQUS uses a smeared crack approach with fixed concept (orthogonal cracks). Therefore, the maximum number of cracks at an integration point is limited by the number of stress components, e.g. 3 cracks in 3D models and 2 cracks in 2D models. According to ABAQUS [28], although the fixed concept has the orthogonally limitation, it is considered superior to the rotating concept when the effect of multiple cracks is important, since the last concept is restricted to a single crack at each integration point. The shear retention factor is defined as a non-constant value through the Eq. (I.3). 3.2. FEMIX smeared crack model (SCM-FEMIX) This Section presents the assumptions adopted in the numerical simulation of the glass, GFRP and adhesives for the simulation of the beams with the FEMIX software. Three different strategies were considered to simulate the adhesive joint of composite beams: (i) the Perfect Bond ( PB ) between the glass and GFRP laminate, neglecting the physical existence of the adhesive; (ii) the Linear Elastic Behaviour ( LEB ) of the adhesive, using plane stress elements for 2D models or solid elements for 3D models, and assuming perfect bond at the GFRP/adhesive and adhesive/glass interfaces; and (iii) the Non-Linear Behaviour ( NLB ) of the joint, using interface elements, simulating the non-linear behaviour of the interfaces (GFRP/adhesive and adhesive/glass) and the adhesive itself. 3.2.1. Annealed glass According to the Guideline for European Structural Design of Glass Components [37], in the simulation the linear elastic behaviour of annealed glass a Young’s modulus, Eg , of 70 GPa, a Poisson’s ratio, υ g , of 0.23 and a tensile strength, fg,t , which ranges from 30 MPa to 80 MPa, were adopted. In composite beams models, the glass was simulated by linear elastic behaviour in compression and in tension, before cracking. Rankine failure criterion was used for the crack detection. After the cracking, non-linear behaviour of the glass was simulated by the smeared crack model. PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 103 After a parametric study, in which the experimental and the numerical results were compared in terms of initial stiffness, cracking load, post-cracking stiffness, crack pattern and progressive failure of the composite beams, Valarinho et al . [19] defined the glass linear features required by this mechanical constitutive model. The following properties were adopted: (i) tensile strength of 50 MPa, (ii) tensionsoftening diagram with linear shape, (iii) quadratic shear retention factor law, (iv) minimum mode-I fracture energy, Gf , to avoid snap-back instabilities, according to Eq. (I.2), and (v) crack band width equal to the square root of the finite elements area. A threshold angle of 30º was also defined for the development of new cracks, as well as the maximum number of two and three cracks in each element in 2D and 3D models, respectively. 3.2.2. GFRP The GFRP was modelled as linear elastic material, for both compression and tension, assuming the following mechanical properties (obtained from tests): Young’s modulus, EGFRP , of 28.7 GPa, Poisson’s ratio, υ GFRP , of 0.28. 3.2.3. Interface Based on the parametric study described in Valarinho et al . [19], where three strategies were tested for the numerical modelling of the adhesive bonded joint, the perfect bond ( PB ) strategy was adopted to simulate the composite beam with epoxy adhesive (stiff adhesive). Previous numerical simulations showed that the two alternative strategies ( LEB and NLB ) did not accurately capture the experimental response after cracking, in terms of stiffness and ultimate load. The polyurethane adhesive of the S Flex beam was described by the non-linear behaviour ( NLB ) strategy using a non-linear bond-slip relationship, as suggested in Valarinho et al . [19]. The PB strategy was initially excluded because it neglected the physical existence of the adhesive layer. On the other hand, previous simulations using the LEB strategy showed higher post-cracking stiffness than the one observed in the experimental responses, since it was not able to simulate the adhesive failure. Assuming a bilinear bond-slip relationship, Table I.1 presents the used properties: (i) the linear elastic tangential stiffness, Kt , (ii) the shear strength, τ m , and (iii) the mode-II fracture energy, Gm . The linear elastic tangential stiffness was assumed to be the same in both directions of the adhesive layer. Finally, according to Sena-Cruz [34], a high value of the linear elastic normal stiffness, Kn , was adopted in order to avoid any influence on the shear behaviour of the interface elements. PAPER I 104 Table I.1: Mechanical properties used to simulate the polyurethane adhesive using the bilinear bond-slip relationship ( NLB strategy). Kn [MPa/mm] Kt [MPa/mm] τ m [MPa] Gm [N/mm] 106 0.4048 1.70 3.50 The non-linear bond-slip relationship used in Valarinho et al . [19] is governed by the Eq. (I.4), where τ m and sm are the maximum shear stress and the corresponding maximum slip, respectively, and the shape of the preand post-peak curves are defined respectively by the parameters α and α ’ [34]. The mechanical properties used to model the polyurethane adhesive are presented in Table I.2. The modeII fracture energy, Gm , was calculated as the integral of the post-peak curve, according to Eq. (I.5). 𝜏(𝑠)= { 𝜏𝑚(𝑠 𝑠𝑚)𝛼 𝑖𝑓 𝑠 ≤ 𝑠𝑚 𝜏𝑚(𝑠 𝑠𝑚)−𝛼′ 𝑖𝑓 𝑠 ≥ 𝑠𝑚 (I.4) 𝐺𝑚=∫ 𝜏𝑚(𝑠 𝑠𝑚)−𝛼′𝑑𝑠 ∞ 𝑠𝑚 (I.5) Table I.2: Mechanical properties used in [19] to describe the polyurethane adhesive joint of the S Flex beam. Kn [N m3 ⁄] τ m [MPa] sm [mm] α [-] α ’ [-] 106 1.70 4.20 0.90 3.00 3.2.4. Mesh strategy Taking into account the real geometry and the symmetry conditions of the glass-GFRP composite beams (see Figure I.1), only half span was numerically simulated ( l = 700 mm). In the S Dur beams, 8-node plane stress elements, with 2  2 Gauss-Legendre integration scheme, were used to simulate the glass panel and GFRP laminate (2D models). However, to compare the results obtained in the three material models (reasons are given in Section 3.3.3), 20-node solid elements were also used to simulate the different structural materials (GFRP laminate and glass panel) of the S Flex beams (3D models). In the NLB strategy, in agreement with the previously presented assumptions, the adhesive layer was simulated by 16-node interface elements with 3 (height)  2 (thickness) using Gauss-Lobatto integration rule. The thickness of the adhesive joint was reproduced by positioning the glass panel at a distance of 2 mm from the GFRP laminate, which was then filled by the interface elements. PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 105 Based on the sensitivity of mesh analysis carried out in Valarinho et al . [19], elements of 10  10 [mm] yield sufficiently accurate simulations. In the 3D models, only one layer of finite elements was used to describe the beam thickness (10 (width)  10 (height)  12 (thickness) [mm]). In order to avoid out-plane displacements, the z-direction displacements of the nodes located at the middle-thickness were prevented. 3.3. ABAQUS smeared crack model (SCM-ABAQUS) As for the FEMIX smeared crack model (see Section 3.2), similar assumptions and mechanical properties were adopted when using ABAQUS commercial package. The GFRP laminate was modelled as a linear elastic material with the same mechanical properties presented in Section 3.2.2. In the case of the simulation of the annealed glass, the smeared crack model available in ABAQUS/Explicit is suitable for quasi-static and dynamic analyses [28]. The computational effort required by ABAQUS/Explicit depends on the density of the materials [28]. Thus, a density of 2500 kg m3 ⁄ and 1600 kg m3 ⁄ was adopted for the annealed glass and GFRP, respectively. By default, ABAQUS/Explicit considers the geometric non-linearity through the “Nlgeom” setting. However, this option was ignored for the sake of simplicity because the influence of the geometric non-linearity on the structural responses would be very small. 3.3.1. Annealed glass The compressive behaviour of annealed glass was assumed as linear elastic. The brittle failure in tension was properly considered by adopting the “Brittle Cracking” mechanical model, using the “Brittle Shear” option to model crack evolution. This constitutive model is suitable for concrete brittle and quasi-brittle materials, and it was also adopted for glass [19,21–23,25,26]. Before the tensile strength is reached, the linear elastic behaviour was assumed. In the “Brittle Cracking” model, a Rankine failure criterion is used for the crack detection. The main parameters introduced in this material model are: (i) the tensile strength, (ii) the mode-I facture energy, and (iii) shear retention factor law (in “Brittle Shear” option). Similarly to the FEMIX models (see Section 3.2), the following properties were adopted: the tensile strength, fg,t , of 50 MPa, minimum mode-I facture energy, Gf , and the quadratic shear retention law. The ABAQUS approach adopts, by default, a crack band width, h , equal to the square root of the finite elements area, as well as a linear tension-softening diagram when the “ GFI ” option (facture energy cracking criterion) is selected [28]. PAPER I 112 of 3 J m2 ⁄ (0.003 N/mm) [44] has been used to define the fracture energy of annealed glass, regardless of the mesh size. Therefore, this value was also considered in this parametric study. On the other hand, the dilatancy is the physical phenomenon that describes the increase in volume of the material microstructure caused by shear stresses. This phenomenon is mainly associated with soils and quasi-brittle materials (heterogeneous materials). Compared to concrete, smooth surfaces are created when the glass breaks. Therefore, the dilation angle in glass is likely lower than in concrete, which is usually greater than 30º, according to Coronado and Lopez [41]. Values of 1º, 10º and 20º were considered. As the S Dur beams were numerically simulated neglecting the physical existence of the adhesive layer, according to PB strategy (see Section 3.2.3), considerable shear stresses were expected near the bottom edge of the glass panel. Thereby, the influence of the yield surface shape was considered in this parametric study. Values of 0.5 (Rankine yield surface), 0.67 (recommended value in ABAQUS [28]), and 1.0 (Von Mises yield surface) were considered for the crack detection criteria. In addition to the material parameters required by the constitutive models, the post-cracking behaviour of glass-GFRP composite systems is influenced by the mesh pattern, which determines whether a numerical model is capable of capturing in detail all the failure processes that were observed experimentally. Thus, the ability to capture localized phenomena, such as the progressive detachment of the GFRP laminate towards the supports, can be substantially influenced by the mesh pattern adopted, both the mesh size and the number of integration points per finite element. In the present research 8-node plane stress elements of 10  10 [mm] with 2  2 Gauss-Legendre integration scheme were used in SCM-FEMIX, while 4-node plane stress elements of 5  5 [mm] with reduced integration (CPS4R) were used in ABAQUS models to simulate S Dur beams. In order to assess the influence of the mesh pattern on each ABAQUS model, a sensitivity analysis was carried out considering two additional mesh sizes: 2.5  2.5 and 10  10 [mm]. 4 RESULTS AND DISCUSSION Figure I.7, Figure I.8 and Figure I.9 show the load ( F ) vs. deflection at mid-span (δ ) responses of S Dur and S Flex beams obtained from the numerical simulations, as well as the crack patterns obtained at relevant phases: (i) onset and end of the post-cracking stage of S Dur beams, and (ii) after cracking for the S Flex beams. In S Dur beams, the crack patterns are also presented at an intermediate stage of the post-cracking response to show the evolution of the cracking processes. The S Dur beam analysis PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 113 was stopped when the initial cracking load was fully recovered. On the other hand, in the simulation of S Flex beam, the analysis was stopped when the deflection of 12 mm was attained, since the postcracking stage of these composite beams showed an almost linear steady recovery of the load carrying capacity. Additionally, the further computation was difficult due to pronounced numerical instabilities after this displacement was attained, most likely due to the large opening of the cracks already formed. Figure I.10 shows the load vs . deflection responses obtained by using the three numerical models, as well as the experimental results obtained for the composite beams made with epoxy (S Dur ) and polyurethane (S Flex ) adhesives (two test results are presented for each type of beam). Table I.3 summarizes, for the simulated beams, the main parameters characterizing their structural behaviour: elastic stiffness, Kel , cracking load, Fcr , and corresponding deflection, δ cr . (i) (ii) (iii) S Dur beam (iv) S Flex beam Figure I.7: Load vs . deflection curves of the S Dur and S Flex beams obtained from the SCM-FEMIX, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (ii) (iii)(i) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (iv) PAPER I 114 (i) (ii) (iii) S Dur beam (iv) S Flex beam Figure I.8: Load vs . deflection curves of the S Dur and S Flex beams obtained from the SCM-ABAQUS, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). Table I.3: Elastic properties of the S Dur and S Flex beams defined from the experimental and numerical responses, as well as the difference of the numerically obtained properties in relation to the respective experimental values. S Dur beams S Flex beams Kel [kN/mm] Fcr [kN] δ cr [mm] Kel [kN/mm] Fcr [kN] δ cr [mm] S Dur -1 1.63 6.28 3.85 - - - S Dur -2 1.70 5.45 3.20 - - - S Flex -1 - - - 1.55 3.80 2.45 S Flex -2 - - - 1.66 4.60 2.77 SCM-FEMIX 1.57 (-5.7%) 5.02 (-14.4%) 3.20 (-9.2%) 1.38 (-14.0%) 4.40 (4.8%) 3.18 (21.8%) SCM-ABAQUS 1.55 (-6.9%) 5.04 (-14.1%) 3.25 (-7.8%) 1.41 (-12.1%) 4.76 (13.3%) 3.33 (27.6%) DPM-ABAQUS 1.56 (-6.3%) 5.11 (-12.9%) 3.27 (-7.2%) 1.43 (-10.9%) 4.79 (14.0%) 3.36 (28.7%) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (i) (ii) (iii) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (vi) PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 115 (i) (ii) (iii) S Dur beam (iv) S Flex beam Figure I.9: Load vs . deflection curves of the S Dur and S Flex beams obtained from the DPM-ABAQUS, and corresponding crack pattern at different phases, (i), (ii), (iii) and (iv). 4.1. S Dur beams 4.1.1. Pre-cracking stage In the pre-cracking stage, the assumptions of the PB strategy (perfect bond between the GFRP laminate and the glass) resulted in a slight difference between the numerical and the experimental stiffness of the response in the elastic domain, since the physical absence of the epoxy adhesive layer caused a small decrease in the section height (108 mm) and, consequently, in its flexural stiffness. While the load vs. deflection curve obtained from the SCM-FEMIX (static analysis) remains perfectly linear during the pre-cracking stage, in the ABAQUS models this does not occur. The equation of motion of a dynamic structural problem is described by Eq. (I.15), where: (i) F is the applied external force; (ii) M , C and K are the mass, damping and stiffness matrix of the structural element, respectively; and (iii) d , d 󰇗 and d 󰇘 are, respectively, the displacement, velocity and acceleration vectors. 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (i) (ii) (iii) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (iv) PAPER I 116 𝐹=𝑀𝑑󰇘+𝐶𝑑󰇗+𝐾𝑑 (I.15) (a) (b) Figure I.10: Load vs . deflection curves obtained from the experimental tests and distinct numerical models: (a) S Dur beams; (b) S Flex beams. In order to evaluate the influence of the dynamic effects on the structural responses, Figure I.11 presents, step-by-step (0.05 s), the relationship between the slope of the tangent line of the load vs . deflection curves obtained from the ABAQUS models and elastic stiffness derived from the SCM-FEMIX (1.566 kN/mm). This relation, later designated Rk , is represented against the mid-span deflection in Figure I.11. The dynamic effects (inertial forces) are clearly visible at the beginning of the load vs. deflection curves obtained from the ABAQUS models, as shown by the rapid growth observed in Rk . The small perturbations of Rk caused by the high frequency vibration modes could be avoided by adopting stiffness-proportional damping, but the computational effort of the numerical models would increase and its accuracy would not significantly improve, namely regarding the cracking load. 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] R-SDur-1 R-SDur-2 SCM-FEMIX SCM-ABAQUS DMP-ABAQUS 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] R-SFlex-1 R-SFlex-2 SCM-FEMIX SCM-ABAQUS DPM-ABAQUS PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 117 Figure I.11: Ratio between the slope of the load vs . deflection curves and the elastic stiffness for the S Dur beams obtained from the ABAQUS models. In all numerical models the same mechanical properties of the materials have been adopted, but Rk is generally less than 1.0 throughout the pre-cracking stage (see Figure I.11). This was expectable, because while the equation of motion of a static structural problem depends only on the displacement, in a dynamic structural problem it depends also on the velocity and acceleration, as defined by Eq. (I.15). The tangent line to the load vs. deflection curve obtained from the DMP-ABAQUS increases unexpectedly before cracking. In order to evaluate the influence of the dynamic effects in this artefact, Figure I.12 presents the ratio between the viscous energy, Ev , and work of the external forces, Ew , being the viscous energy the energy dissipated by damping mechanisms, including bulk viscosity damping and material damping. The Ev Ew ⁄ ratio shows that dynamic effects are not responsible for the oscillations in the Rk ratio of the DPM-ABAQUS. Figure I.12: Ratio Ev Ew ⁄ along the tangent line of the load vs . displacement curves of the DPM-ABAQUS. The first crack appears in the central region of the beam between the loading points in all models, inside the pure bending area. Taking into account this information, for the S Dur beams, which were modelled assuming the perfect bond between glass and GFRP laminate ( PB strategy), the analytical 0.950 0.975 1.000 1.025 1.050 0.0 1.0 2.0 3.0 4.0 Rk Deflection, δ[mm] SCM-FEMIX SCM-ABAQUS DPM-ABAQUS 0.0 1.0 2.0 3.0 4.0 0.950 0.975 1.000 1.025 1.050 0.0 12.5 25.0 37.5 50.0 Rk Deflection, δ[mm] Ev/Ew[%] Ev/Ew Rk PAPER I 118 cracking load, Fcr,a , is given by Eq. (I.16), where Iel = 1.111  106 mm4 (homogenized cross-section), yel = 56.285 mm, l1 = 470 mm and hGFRP = 8.0 mm. On the other hand, considering the elastic integration method and neglecting the shear effects, the analytical deflection at mid-span corresponding to the cracking load, 𝛿 cr,a , is provided by Eq. (I.17), where l2 = 230 mm and EIel = 7.779  1010 N.mm2. In the numerical modelling the crack initiation occurs when the stress at the integration points located right above the bottom edge of the glass sheet reach the tensile strength. Table I.4 shows the elastic properties of S Dur beams, computed from Eq. (I.16) and Eq. (I.17), considering the assumptions mentioned previously. 𝐹𝑐𝑟,𝑎=2𝑓𝑔,𝑡∙𝐼𝑒𝑙 (𝑦𝑒𝑙−ℎ𝐺𝐹𝑅𝑃)∙𝑙1 (I.16) 𝛿𝑐𝑟,𝑎=1 𝐸𝐼𝑒𝑙(𝐹𝑐𝑟𝑙1 4𝑙22−𝐹𝑐𝑟𝑙1𝑙2 2𝑙2+𝐹𝑐𝑟 12𝑙13−(𝐹𝑐𝑟𝑙12 4+𝐹𝑐𝑟𝑙1𝑙2 2)𝑙1) (I.17) Table I.4: Mechanical properties of the elastic behaviour of S Dur beams analytically calculated. Kel,a [kN/mm] Fcr,a [kN] δ cr,a [mm] 1.59 4.90 3.08 In general, the numerical and analytical results have shown a good agreement. The small differences observed may be due to: (i) the analytical approach, which omits the shear deformation effects and, consequently, may slightly underestimate the vertical deformations; and (ii) the distance between the first integration point at which cracking occurs and the surface between the glass and the laminate, where cracking initiates. Additionally, the deflection immediately before and immediately after cracking, which should be approximately similar as captured by the numerical models, were observed to be different in the experimental responses. However, in this case this was probably due to the relatively low rate of the data acquisition system used during the experiments (mean value of 5 Hz) when compared to the very rapid development of cracking (not captured by the transducers readings), as well as the difficulty usually associated with the control of tests where abrupt losses of stiffness or load carrying capacity occur. 4.1.2. Post-cracking stage Comparing the numerical and experimental results, it is generally observed that all the numerical models captured reasonably well the post-cracking behaviour of S Dur beams. However, the final crack patterns of the three models show significant differences. The failure caused by the excessive damage PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 119 on the bottom edge of the glass panel was satisfactorily represented by SCM-FEMIX, through the formation of several cracks at the glass/GFRP interface, starting at the loading points and propagating towards the supports. However, these cracks, which eventually lead to the laminate detachment, are not clearly visible in the case of ABAQUS models, resulting in higher stiffness of the load vs . deflection responses during the entire post-cracking stage when compared to SCM-FEMIX (see Figure I.10). The type of smeared crack approach may justify this difference. While the SCM-FEMIX uses a multi-fixed concept, with a maximum of two cracks in each integration point and a threshold angle of 30º (see Section 3.2.1), the SCM-ABAQUS uses, by default, a fixed crack concept (orthogonal cracks), which in general leads to a stiffer response. The final crack pattern of SCM-FEMIX-90º (see Figure I.13), with predominantly vertical and more distributed cracks, resembles better the SCM-ABAQUS crack patterns and the experimental results (see Figure I.4a). As shown in Figure I.14, the smeared crack approach mainly influences the propagation of cracks and, consequently, the post-cracking behaviour. SCM-FEMIX 90º and SCMABAQUS correctly simulated the distribution of cracks between loading points, although they were unable to reproduce the increasing slope of the cracks towards the supports, as was the case with DPM-ABAQUS (see Figure I.9). Considering the higher stiffness of the epoxy adhesive, the GFRP/glass interface induces high shear stresses in the integration points near the interface. Consequently, the maximum principal stresses experience large rotations. As result, SCM-FEMIX 90º shows higher postcracking stiffness than SCM-FEMIX. PAPER I 120 (i) (ii) (iii) SCM-FEMIX (see Figure I.7) (iv) (v) (vi) SCM-FEMIX 90º Figure I.13: Load vs . deflection curves of the S Dur beams obtained from SCM-FEMIX and SCM-FEMIX 90º, and corresponding crack pattern at different phases, (i), (ii), (iii), (iv), (v) and (vi). Figure I.14: Load vs. displacement curves of S Dur beams obtained from the three initial material models and the SCM-FEMIX 90º. Figure I.15 presents the structural response and the final crack pattern obtained from different mesh patterns (see Section 3.5). Like in SCM-FEMIX, SCM-ABAQUS with a fine mesh was able to capture the cracking at the GFRP/glass interface towards the support, resulting in lower stiffness during the 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (ii) (iii) (i) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] (iv) (v) (vi) 0 2 4 6 8 04812 16 Load, F [kN] Deflection, δ[mm] SDur-1 SDur-2 SCM-FEMIX SCM-ABAQUS DMP-ABAQUS SCM-FEMIX-90º PRELIMINARY NUMERICAL STUDY ON FRP REINFORCED GLASS BEAMS 121 post-cracking stage compared to the models with coarse meshes (5  5 and 10  10 [mm]). Therefore, the post-cracking behaviour of S Dur beams obtained from SCM-ABAQUS is mesh dependent. According to ABAQUS [28], the smeared crack models inherently induce mesh sensitivity in the results. In opposition to SCM-FEMIX, SCM-ABAQUS requires an extremely fine mesh to obtain similar post-cracking behaviour, due to the lower sensitivity of the finite elements with reduced integration and the fixed smeared crack approach (orthogonal cracks). On the other hand, unlike SCMABAQUS, similar post-cracking responses were obtained from DPM-ABAQUS with different mesh patterns. As the maximum damage factor recommended by ABAQUS is 0.99 (see Section 3.4), all cracks retained a residual stress roughly corresponding to 1.0 % of the glass’s tensile strength. However, regardless of that, DPM-ABAQUS was unable to capture the cracking at the GFRP/glass interface, possibly due to the limitations previously discussed, which are inherent to the constitutive model adopted. 2.5  2.5 5  5 10  10 SCM-ABAQUS 2.5  2.5 5  5 10  10 DPM-ABAQUS Figure I.15: Sensitivity of both ABAQUS material models in relation to the mesh pattern. While in DMP-ABAQUS the cracked behaviour of glass is simulated through the progressive loss of material stiffness, in SCM-ABAQUS the cracked behaviour of glass is divided into two components: (i) 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] 2.5 × 2.5 5 × 5 10 × 10 0 2 4 6 8 0 4 8 12 16 Load, F [kN] Deflection, δ[mm] 2.5 × 2.5 5 × 5 10 × 10 PAPER IV 224 (e.g. adhesively bonded and/or mechanically anchored) to the structural element prior to its activation, recovery stresses (post-tensioning forces) are developed by heating and subsequent cooling of the SMA material. The simplicity of this post-tensioning technique has enhanced the applicability of SMAs for the post-tensioned strengthening of existing structures, where the conventional procedure with hydraulic jacks is often difficult to implement due to lack of space [25,34]. The most recognized SMA is the nickel-titanium (Ni-Ti) alloy, which has been used in the automotive, aerospace, robotic, biomedical and construction industries for both sensory and structural (e.g. damper and reinforcement) purposes [24]. However, the Ni-Ti alloy may hardly be considered as a sustainable solution for generalized applications in the construction industry [31]. In construction, the material usage is several orders of magnitude larger when compared to other industries and, therefore, low-cost and less resource-intensive SMAs have been applied in this case, namely the iron-based (FeSMAs) and the copper-based (Cu-SMAs) alloys. Fe-SMAs are relatively low cost and easy to process, machine and weld, thus making them the most promising candidates for the application in the construction industry, whether for repairing existing structures or for reinforcing new ones [25,35]. In 1982, Sato et al . [36] discovered shape memory effect in Fe-Mn-Si alloys. Since then, the chemical composition of Fe-SMAs has been improved to increase their corrosion resistance, training effect, cyclic deformation and strength [37]. In this context, a new Fe-SMA, suitable for the construction industry, was developed in 2009 by Dong et al . [38] at the Swiss Federal Laboratories for Materials Science and Technology (Empa), Switzerland. This Fe-SMA, which can be activated by resistive heating, was especially developed for the post-tensioned strengthening of existing concrete structures. In addition, it is produced at atmospheric conditions, without the need for expensive high-vacuum processing facilities and thermomechanical training, making the large-scale production feasible [31,39]. Research studies have shown the potential of this Fe-SMA for the post-tensioned strengthening of concrete, using strips (e.g. [30,31,40,41]) or ribbed bars (e.g. [42,43]), and metallic (e.g. [28,29,34]) structural elements. Further research studies have been conducted to show the potential of the developed Fe-SMA for structural engineering applications, investigating aspects related to the fatigue behaviour (e.g. [39]), phase transformation (e.g. [41]), creep and stress relaxation (e.g. [44]), electrochemical and corrosion behaviour (e.g. [45]) and recovery stress (e.g. [46]). The application of SMAs as reinforcement material in glass composite systems is a very recent research field and, consequently, very few studies are found in the literature addressing this topic. They have focused on the bond behaviour of glass-to-SMA adhesively bonded joints (e.g. [47,48]). In MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 225 addition, Silvestru el at . [22] proved, for the first time, the feasibility of activating Fe-SMA reinforcement to introduce an initial compressive pre-stress in laminated glass beams. Furthermore, the results showed that SMA reinforced glass elements can exhibit ductile failure modes. 1.3. Research significance This study investigates the feasibility of the post-tensioning of monolithic glass beams by activating FeSMA strips previously bonded to the bottom edge, according to the External Bonded Reinforcement (EBR) technique, as well as the influence of the activation temperature on their post-cracking performance. After being bonded with an epoxy adhesive to glass structural elements, Fe-SMA strips were heated at temperatures ranging between 120 ºC and 160 ºC to activate them and introduce post-tensioning in the glass elements. The experimental programme comprised (i) mechanical characterization tests and (ii) full-scale bending tests. This study also addresses the opportunity to adapt the Fe-SMA reinforcement activation procedure in order to take advantage of initially deleterious effects, such as the degradation of the adhesive due to temperature exposure, in favour of an optimized anchorage and the gradual stress transfer from the reinforcement to the glass substrate. 2 EXPERIMENTAL PROGRAMME Two different types of experimental tests were carried out in the scope of this work: (i) first, material characterization tests were conducted to determine the mechanical properties of the Fe-SMA material and (ii) second, four-point bending tests were carried out to assess the flexural behaviour of annealed glass beams strengthened with passive Fe-SMA strips (reference beams) and activated Fe-SMA strips (post-tensioned beams). 2.1. Materials 2.1.1. Iron-based shape memory alloy (Fe-SMA) In this research, the Fe-17Mn-5Si-10Cr-4Ni-1(V,C) (mass%) alloy with shape memory effect, developed by Dong et al . [38], was used as a reinforcement material for glass beams. Its detailed production procedure is described by Leinenbach et al. [49]. The industrial production of this Fe-SMA is ensured by re-fer AG Company, which offers two distinct products: (i) ribbed bars; and (ii) plates with thicknesses of 0.5 and 1.5 mm and widths of 50 and 100 mm. In this study, Fe-SMA plates of 100 (width)  1.5 (thickness) [mm] were used to extract strips of 1500 (length)  10 (width)  1.5 (thickness) [mm]. The Fe-SMA strips were cut using the water jet technique to avoid overheating the Fe-SMA material. Specimens were also extracted to characterize the Fe-SMA’s tensile behaviour. PAPER IV 226 Five specimens of 250 (length)  10 (width) [mm] were tested in tension at ambient temperature and at a constant displacement rate of 1.0 mm/min until failure. Prior to testing, 50 mm long tabs were glued to the edges of the Fe-SMA strips to avoid premature failure of the specimen due to stress concentrations introduced by the clamping equipment. The longitudinal deformation of each specimen was measured using a clip gauge (type: MFA 12; linearity: 0.1 %; sensitivity: 2.0 mV/V; resolution: 1.0 p.m.; precision: ±1.5 μm) with stroke of 50 mm, which was placed at the central region of the specimens (see Figure IV.1a). A universal testing machine and a load cell with a maximum capacity of 200 kN (precision of 0.01 kN) were used to record the load. Furthermore, some specimens were monitored with the Digital Image Correlation (DIC) technique and using the GOM Correlate 2019 software [50] for processing the images. A thin spray of white matt paint was applied over a region of interest, followed by a spray of black dots using black paint. The camera used to capture the images included a full frame CMOS sensor (7360  4912 pixels). The images of the ROI were collected at an acquisition frequency of 0.1 Hz. (a) (b) Figure IV.1: Tensile tests on Fe-SMA strips: (a) experimental setup and DIC pattern; and (b) stress-strain response obtained from both measurements methods, as well as evolution of the Poisson’s ratio. Table IV.1 includes the average values obtained for the modulus of elasticity ( Er ), tensile strength ( fr,t ) and ultimate strain (ε r,ult ). As the Fe-SMA shows a highly non-linear behaviour, Er was determined from the linear portion of the stress-strain response between stress values of 0 MPa and 200 MPa. The mechanical properties indicated in Table IV.1 compare very well with values found in the literature for this Fe-SMA. The modulus of elasticity of 172 GPa is in the range of previously published values, from 160 GPa [46] to 175 GPa [39]. With respect to the tensile strength, 948.1 MPa is also an 0 7 14 21 28 35 0 0.5 1 1.5 2 2.5 0 200 400 600 800 1000 Poisson's ratio, υ[-] Tensile stress, σ[MPa] Axial strain, ε[%] Clip gauge DIC analysis Poisson's ratio MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 227 intermediate value between 939.3 MPa by Silvestru et al . [48] and 1015 MPa by Ghafoori et al . [39]. However, the ultimate strain of 31.0 % is lower when compared to the values reported in the literature, usually higher than 40 %. The main reason for this difference seems to be displacement speed between clamps, which in this study was set to 1.0 mm/s while literature values range from 0.012 mm/s [48] and 0.075 mm/s [39]. Table IV.1: Mechanical properties of the Fe-SMA material, annealed glass and 3M adhesive (average values). Material Er [GPa] fr,t [MPa] ε r,ult [%] υ [-] Fe-SMA 172.0 (1.7%) 948.1 (0.6%) 32.5 (2.3%) 0.39 Material Eg [GPa] fg,t [MPa] υ [-] Annealed glass 1) 74.0 (2.6%) 40 0.23 Material Eadh [MPa] fadh [MPa] ε adh,ult [‰] υ [-] Adhesive 1) 1728.1 (3.3%) 32.8 (4.2%) 30.7 (2.8%) 0.38 Notes: 1) Results collected from Rocha et al . [51] Coefficients of variation (CoV) are indicated in parenthesis Figure IV.1b shows the typical stress – strain experimental response obtained from both measurement methods. Given the good agreement between the DIC and clip gauge measurements, the Poisson’s ratio was determined from the deformation fields at the surface of the specimens and assuming plane stress state. Figure IV.1b shows the obtained Poisson’s ratio as a function of the axial strain. Unexpectedly, at the beginning of loading, the Poisson’s ratio reached values of approximately 2.0, which gradually decreased to 0.39 at the end of the stress – strain response. Such response seems to be related to the phase change behaviour of the SMA materials. During the martensitic transformation, at the beginning of the stress – strain response, axial deformation is associated to the lattice detwinning. On the other hand, after martensitic transformation, at the end of the stress – strain response, further axial deformation is associated to the permanent and irreversible slip between atomic planes (yielding). Hence, at this final stage, the Fe-SMA Poisson’s ratio converges to values exhibited by traditional materials (e.g. steel). 2.1.2. Glass and adhesive All specimens used in the experimental programme were made of annealed glass. Laminated glass was not considered at this stage of the research because the interlayer may be significantly damaged during the heating of Fe-SMA strips, leading to layering of the glass plies. This effect, which is difficult to measure experimentally, may introduce uncertainty in the structural response of post-tensioned beams. The edges of the annealed glass panels were polished to minimize the flaws resulting from PAPER IV 228 the cutting process and to prevent accidents during handling. The mechanical properties of the annealed glass shown in Table IV.1 were previously assessed by Rocha et al . [51], with the tensile strength ( fg,t ) and the modulus of elasticity ( Eg ) equal to 40 MPa and 74.0 GPa, respectively. An epoxy adhesive, the two-component adhesive 3M Scotch-Weld DP490, suitable for glass-to-steel bonded connections was used in these experiments. The tensile behaviour of this adhesive was previously characterized by Rocha et al . [51]. Its mechanical properties are presented in Table IV.1, including the Poisson’s ratio determined by Nhamoinesu and Overend [52]. The adhesive presents a non-linear behaviour in tension until failure, combining a high tensile strength ( fadh ) of 32.8 MPa with a relatively low modulus of elasticity ( Eadh ) of 1728.1 MPa, as well as an ultimate strain (ε adh,ult ) of 30.7 ‰. 2.2. Production and testing of the specimens As schematically shown in Figure IV.2, the application of Fe-SMA strips for post-tensioning of structural elements consists of three main phases: (i) pre-straining; (ii) activation; and (iii) service loading. The post-tensioning procedure will be briefly explained in this section. First, the Fe-SMA strip is mechanically loaded (path (1) in Figure IV.2) at room temperature, between Ms (martensite start temperature) and As (austenite start temperature), modifying the lattice from austenite to detwinned martensite (i.e., martensitic transformation). When the target strain is attained, the Fe-SMA is then completely unloaded (path (2) in Figure IV.2), then presenting a permanent macroscopic deformation. Second, the Fe-SMA strip is mechanically anchored and/or adhesively bonded to the structural element. Third, the Fe-SMA strip is activated through resistive heating (path (3) in Figure IV.2) and, when As is surpassed, the restrained Fe-SMA strip tends to shrink due to the reverse transformation from detwinned martensite to austenite. Consequently, tensile stresses (i.e., recovery stresses) are developed in the Fe-SMA strip, recovering the thermal expansion observed at the beginning of the thermal cycle. When the target temperature is attained, heating of the Fe-SMA strip is stopped and the recovery stress gradually increases during the cooling phase, until the ambient temperature is reached again (path (4) in Figure IV.2). Further details related to the behaviour of Fe-SMA during the activation can be found in the literature (e.g. [39,53]). Taking into account the procedure mentioned above, the post-tensioned glass beams were prepared considering the following steps: (i) cutting the Fe-SMA strips; (ii) pre-straining the Fe-SMA strips; (iii) bonding the Fe-SMA strips to the bottom edge of the glass panels; and (iv) activating the Fe-SMA strips using a resistive heating device. The reference beams were manufactured considering only the first MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 229 and third steps. On the other hand, the bonding of Fe-SMA strips – the third step of the general procedure – involved additional paths. First, the bonding surfaces were carefully degreased and cleaned with acetone. Subsequently, the adhesive was prepared and applied according to the requirements included in the manufacturer specifications. After that, both adherends were assembled and then slightly pressed against each other in order to reach a pre-defined adhesive layer thickness. Finally, all specimens were placed in a climatic chamber at 30 ºC during 7 days. Figure IV.2: Schematic representation of the activation procedure of Fe-SMAs under strain recovery constraint (red colour) adapted from Shahverdi et al . [31]. The glass-SMA composite beams were manufactured considering the geometry shown in Figure IV.3, which consisted of an annealed glass panel of 100 (height)  12 (thickness) [mm] reinforced at the bottom edge with a Fe-SMA strip of 10 (width)  1.5 (thickness) [mm]. The components were joined using the epoxy adhesive presented in Section 2.1. The thickness of the adhesive joint ( ta in Figure IV.3) was set to 0.3 mm. A total of 6 glass-SMA composite beams were produced, namely two reference beams with passive Fe-SMA strips and four post-tensioned beams with activated Fe-SMA strips. They were identified following the nomenclature i-j-z , where i was adopted to distinguish reference beams (R) from post-tensioned beams (P), j refers to the activation temperature (T0 for reference beams and T120, T140 and T160 for post-tensioned beams – further details in Section 2.2.2) and z identifies the specimens of each series with the same activation temperature (I and II). ε rev 𝜎 rec Temperature Stress Strain Stress Thermal expansion 1 2 3 4 5Pre-straining 1 2 3 4 5 Unloading Cooling Ms AsAf 4 12 Ms - Martensite start temperature Irreversible Plastic Deformation 3 As - Austenite start temperature Af - Austenite finish temperature Ta Heating Service load ε pre ε rem 𝜎 pre PAPER IV 230 (a) (b) (c) (d) (e) Figure IV.3: Glass-SMA composite beams: (a) beam geometry and instrumentation adopted for the bending tests; (b) cross-section geometry; (c) metallic frames placed at the support sections; (d) lateral guides to prevent lateral instability; and (e) experimental setup. All units in [mm]. Ø40 50 275 Glass-SMA composite beam 100 F 50 50 470 470 460 [mm] 600 LVDT_1 LVDT_2 LVDT_3 SG Metallic lateral guides Special metallic frame A A' 15 B B' Annealed glass panel Fe-SMA strip 100 1.5 12 10 ta Annealed glass panel Fe-SMA strip 50 25 100 120 10 15 180 10 10 Metallic frame Support (roller) Glass-SMA composite beam Metallic Screws Teflon plates A-A' 150 10 B-B' 5100 Metallic lateral guides Glass-SMA composite bem Threaded rod 100 1.5 12 10 ta Annealed glass panel Fe-SMA strip 50 25 100 120 10 15 180 10 10 Metallic frame Support (roller) Glass-SMA composite beam Metallic Screws Teflon plates A-A' 150 10 B-B' 5100 Metallic lateral guides Glass-SMA composite bem Threaded rod 100 1.5 12 10 ta Annealed glass panel Fe-SMA strip 50 25 100 120 10 15 180 10 10 Metallic frame Support (roller) Glass-SMA composite beam Metallic Screws Teflon plates A-A' 150 10 B-B' 5100 Metallic lateral guides Glass-SMA composite bem Threaded rod MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 231 2.2.1. Pre-straining of Fe-SMA strips The amount of recovery stress depends on the amount of martensite in the Fe-SMA. Investigations conducted by Shahverdi et al . [31] on the Fe-SMA used in this study showed that a pre-strain (ε pre ) of 2.0 % is sufficient to achieve the maximum possible recovery stress. Therefore, before bonding the FeSMA strips to the glass substrate, these were pre-strained up to 2.25 % at room temperature. After unloading, the Fe-SMA strips showed a permanent remaining deformation (ε rem ) of approximately 1.25 %. Only a portion of the ε rem could be recovered by activation (recovery strain) since the nonlinear behaviour exhibited during pre-straining was a consequence of the phase transformation from austenite to martensite, as well as the plastic deformation (irreversible slippage between atoms) [46]. As shown in Figure IV.4, the deviation from the linear elastic unloading is called pseudo-elastic strain, indicating that the reverse transformation from martensite to austenite occurred partially during unloading [46]. The longitudinal deformation in the Fe-SMA strips was measured using a clip gauge (the same used for the characterization of the Fe-SMA described in Section 2.1.1) with a gauge length of 100 mm. A universal testing machine was used to apply the load. (a) (b) Figure IV.4: Pre-straining of Fe-SMAs: (a) schematic diagram (b) stress-strain diagram retrieved from the experiments. 2.2.2. Activation procedure Glass contains numerous surface flaws that result from the production, cutting, polishing and handling processes [1]. In addition, glass edges typically have lower tensile strength than glass surfaces [54]. Accordingly, a smooth transfer of the post-tensioning force from the reinforcement to the glass panel must be guaranteed to avoid the growth of existing surface flaws over time, especially near the glass corners, which are usually weaker than the glass surfaces due to the handling operations. In addition, Stress Unloading Strain a - recovery strain + plastic strain c - elastic strain b - pseudo-elastic strain Loading abc 0 200 400 600 800 0 5 10 15 20 25 30 Stress, σ[MPa] Strain, ε[‰] Loading Unloading E = 172 GPa PAPER IV 232 based on previous studies on the activation of adhesively bonded SMA reinforcement (e.g. [48,55]), an undamaged bond region (anchorage zone) should be guaranteed on both sides of the activated FeSMA strip zone to transfer the post-tensioning force from the reinforcement to the glass substrate. These anchorage zones prevent premature debonding of the Fe-SMA strip during activation due to the loss of shear interaction at the bonded interfaces caused by heating. Accordingly, the Fe-SMA strips should not be activated throughout its entire length. As shown in Figure IV.5a, the activated length ( la ) was set to 700 mm (half of the beam span), creating an undamaged bond length of 400 mm at both beam ends (non-activated Fe-SMA strip zones). A welding machine was used to supply the electrical power (see Figure IV.5b). Two metallic pieces were symmetrically positioned at 350 mm from the mid-span section and subsequently pressed against the bottom edge of the Fe-SMA strip by means of metal clamps (see Figure IV.5c and Figure IV.5d). After that, the electrode holder and the ground clamp were connected to these metallic pieces, creating a circuit where the electrical current flowed from the former to the latter. Polytetrafluoroethylene (teflon) plates were positioned between the metallic pieces and the metal clamps, for safety. A relatively high current density of ≈ 4.0 A/mm2 was adopted to shorten the heating phase as much as possible, in order to reduce the heat flow into the non-activated Fe-SMA strip zones. Different activation temperatures ( Ta ) were adopted to activate the Fe-SMA: (i) 120 ºC for the P_T120 beams, (ii) 140 ºC for the P_T140 beam, and (iii) 160 ºC for the P_T160 beam. The power supply was interrupted when the target temperature was attained. The activation process was assumed complete when the temperature on the Fe-SMA strip reached the room temperature again. Figure IV.5a shows the instrumentation adopted for the activation process. The deflection at mid-span section of the Fe-SMA reinforced glass beams was measured using a displacement transducer – Linear Variable Differential Transformer (LVDT) – with stroke of 50 mm and precision of 0.01 mm. Furthermore, a strain gauge (type: BFLA-5-3-3L by TML; gauge length: 5 mm; gauge factor: 2.08 ± 1 %) was placed at the top edge of the glass panel. On the other hand, an infrared camera (Type: FLIR T420; temperature range: -20 ºC to 650 ºC; spectral range: 7.5 μ m to 13 μ m) was used to monitor the temperature evolution in the Fe-SMA strip during the activation process. User-defined parameters required by the infrared camera (e.g. emissivity) were previously calibrated using a type K thermocouple (see Figure IV.6). For the sake of simplicity, only a small part of the Fe-SMA strips (≈ 20 mm in length) was monitored by the infrared camera (control region), therefore assuming a constant temperature along the activated length. The infrared camera was positioned so that only the MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 233 Fe-SMA strip was captured by the control region (see Figure IV.7), in order to avoid de influence of the emissivity of other components on the maximum temperature registered within the control region, which was taken as the effective activation temperature. (a) (b) (c) (d) Figure IV.5: Activation of the Fe-SMA strips: (a) activated region and adopted strategy; (b) welding machine used to supply electrical power for the activation process; and (c) and (d) connection between the welding machine clamps and the Fe-SMA reinforcement. All units in [mm]. 50 50 350 350700 LVDT SG Activated length (la) Non-activated Fe-SMA strip zones 1500 Electrical Power Supply Annealed glass Panel Fe-SMA strip Non-activated Fe-SMA strip zones Metallic clamp Metallic piece Electrode holder Teflon plate Fe-SMA reinforcement PAPER IV 240 loaded end sections of the non-activated Fe-SMA strip zones. As expected, the dnum – dexp relationship suggests that the adhesive damage propagation into the non-activated region was significantly influenced by the activation temperature. The application of higher Ta extended the heating phase, increasing the heat flow into the non-activated zone, and developed greater σ rec,sg , increasing the stress concentrations in the anchorage zones. The combination of these two effects increased the lb,d and, as a consequence, the stress transfer zone between adherends shifted towards the beam ends. In practical terms, a similar effect would be obtained if a longer length of the beam was activated and post-tensioned ( lb,d > la ), thus promoting dexp slightly larger than dnum . The recovery strain – recovery stress ratio depends on the restraint conditions of the anchorage zone. When assuming that the glass panel behaves as an infinitely rigid substrate, the maximum recovery stress (σ rec,max ) can be fully mobilized if the anchorage zones do not allow any deformation (e.g. slip at the bonded interfaces). Nevertheless, in reality, elastic deformation of the adhesive joint along the stress transfer length, as well as the adhesive damage propagation into the non-activated region (softening and debonding stages), both occur. As a consequence, the non-activated Fe-SMA strip zones located between lb,d and la were tensioned (σ ≈ σ rec,sg ) and elongated. Therefore the activated FeSMA strip zone was allowed to contract slightly (recovery strain) and, consequently, the potential recovery stress was reduced (σ rec,sg ≤ σ rec,max ). Nevertheless, due to the heat flow into the nonactivated region, these Fe-SMA strip zones were to some extent activated ( T < Ta ), reducing the shrinkage of the activated Fe-SMA strip zone. Therefore, it is reasonable to assume that the experimental σ rec,sg were not significantly affected by the adhesive damage propagation and resemble well the numerical ones. The activation process was well captured when assuming no composite action between adherends within the activated region. Furthermore, it should be noted that the recovery stresses are a function of the activation temperature, the substrate stiffness and the anchorage restraint conditions. If the glass panel and the adhesive joint were infinitely stiff in flexure and shear, respectively, the σ rec,sg would have varied between 231.1 MPa ( Ta = 120 ºC) and 379.2 MPa ( Ta = 160 ºC), which compares very well with the values commonly found in the literature for this Fe-SMA material (e.g. [31]). Assuming fg,t = 40 MPa (see Table IV.1) and neglecting its inherent variability, it would be expected that the first cracking load of the post-tensioned beams would be 1.25 to 1.42 times higher than that obtained from R_T0 beams (increment of cracking load – Δ Fcr ). It is noteworthy that these values do MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 241 not consider any influence of the activation procedure on the mechanical properties of the Fe-SMA reinforcement. 4 RESULTS AND DISCUSSION Figure IV.10 and Figure IV.11 and Figure IV.12 show the applied load ( F ) versus mid-span deflection (δ ) experimental responses of the reference and post-tensioned beams, respectively, as well as the crack patterns obtained using the DIC technique at different stages. On the other hand, Table IV.3 summarizes the experimental responses in terms of initial stiffness ( K ), cracking load ( Fcr ) and corresponding deflection (δ cr ), maximum load ( Fmax ), and ultimate deflection (δ ult ). Table IV.3 lists two additional parameters: (i) the residual strength index ( RSi ), which was defined as the Fmax / Fcr ratio, quantifying the load carrying capacity after crack initiation; and (ii) the ductility index at failure ( Di ), which was defined as the δ ult / δ cr ratio, quantifying the capacity of the beams to deform after the appearance of the first crack. 4.1. Reference beams As shown in Figure IV.10, both reference beams presented similar structural responses, exhibiting linear behaviour during the pre-cracking stage with K = 1.53 kN/mm. Thereafter, successive sudden load drops occurred due to the appearance of cracks appearing from the mid-span section towards the supports, creating non-linear branches with progressive loss of stiffness due to the yielding of the Fe-SMA. The large crack openings attained and the extensive horizontal crack propagation generated crack branching (V-shaped cracks). The high deformation capacity of the reinforcement material delayed the appearance of shear cracks, as well as the debonding of the Fe-SMA strip. The R_T0-I beam failed due to debonding of the Fe-SMA strip at the reinforcement/adhesive interface (see Figure IV.13) due to cracks that formed in the shear span (failure mode: critical shear crack). In contrast, the R_T0-II beam was unloaded prior to collapse because the maximum deflection allowed by the experimental setup was reached. In general, both R_T0 beams showed the ability to recover the load carrying capacity after initial cracking, exceeding Fcr during the post-cracking stage. These results show that glass structural elements can present safe and ductile responses when Fe-SMA is used as reinforcement, as previously observed by Silvestru et al . [22]. PAPER IV 242 (a) δ = δ cr δ = 10 mm δ = 20 mm δ = 30 mm / δ = δ ult δ = δ cr δ = 10 mm δ = 20 mm / δ = δ ult (b) (c) Figure IV.10: Results of the flexural tests with the reference beams: (a) structural responses and crack pattern of the beams (b) R_T0-I and (c) R_T0-II at different stages. 0.0 1.5 3.0 4.5 6.0 010 20 30 40 50 Load, F [kN] Deflection, δ[mm] R_T0-I R_T0-II MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 243 (a) δ = δ cr δ = 10 mm δ = 20 mm δ = 30 mm δ = 40 mm / δ = δ ult δ = δ cr δ = 10 mm δ = 20 mm δ = 30 mm δ = 40 mm / δ = δ ult (b) (c) Figure IV.11: Results of the flexural tests with the post-tensioned beams: (a) comparison between the structural responses of both P_T120 beams with those of the reference series, as well as the crack pattern of the beams (c) P_T120-I (c) and (d) P_T120-II at different stages. 0.0 1.5 3.0 4.5 6.0 010 20 30 40 50 Load, F [kN] Deflection, δ[mm] P_T120-I P_T120-II R_T0-I R_T0-II PAPER IV 244 (a) (b) δ = δ cr δ = 10 mm δ = 20 mm δ = 30 mm δ = δ ult δ = δ cr δ = 10 mm δ = 20 mm δ = 30 mm δ = 40 mm / δ = δ ult (c) (d) Figure IV.12: Results of the flexural tests with the post-tensioned beams: comparison between the structural responses of the beams (a) P_T140 and (b) P_T160 and those obtained from the reference series, as well as the crack pattern of the beams (c) P_T140 and (d) P_T160 at different stages. 0.0 1.5 3.0 4.5 6.0 010 20 30 40 50 Load, F [kN] Deflection, δ[mm] P_T140 R_T0-I R_T0-II 0.0 1.5 3.0 4.5 6.0 010 20 30 40 50 Load, F [kN] Deflection, δ[mm] P_T160 R_T0-I R_T0-II MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 245 Table IV.3: Main properties of the reference (R_T0) and post-tensioned (P_T120, P_T140 and P_T160) SMA reinforced glass beams extracted from the flexural tests. Reference beams Property R_T0-I R_T0-II R_T0 series K [kN/mm] 1.53 1.53 1.53 Fcr [kN] 3.67 3.63 3.65 δ cr [mm] 2.40 2.38 2.39 Fmax [kN] 4.22 3.86 4.04 δ ult [mm] 32.9 22.1 27.5 Di [%] 1370 931 1151 RSi [%] 115 106 111 Post-tensioned beams Property P_T120-I P_T120-II P_T140 P_T160 Ta [ºC] 122 124 142 161 K [kN/mm] 1.50 (-1.8%) 1.50 (-1.9%) 1.49 (-2.7%) 1.54 (0.7%) Fcr [kN] 4.26 (16.8%) 4.28 (17.2%) 4.44 (21.8%) 4.75 (30.3%) δ cr [mm] 2.84 (19.0%) 2.86 (19.5%) 2.99 (25.2%) 3.09 (29.5%) Fmax [kN] 4.74 (17.2%) 4.69 (16.2%) 4.89 (21.1%) 4.92 (21.7%) δ ult [mm] 43.2 (56.8%) 47.1 (71.0%) 32.5 (17.8%) 46.8 (70.0%) Di [%] 1519 (31.9%) 1648 (43.2%) 1085 (-5.7%) 1512 (31.5%) RSi [%] 111 (0.4%) 110 (-0.8%) 110 (-0.6%) 103 (-6.6%) Notes: The values indicated in parentheses represents the difference between the property of the post-tensioned beams with the one of the reference beams 4.2. Post-tensioned beams 4.2.1. Initial stiffness Similarly to the reference beams, all post-tensioned beams exhibited linear behaviour during the precracking stage. Excluding the P_T160 beam, all post-tensioned beams showed lower initial stiffness than the reference beams, between 1.8 % (P_T120-I beam) and 2.7 % (P_T140 beam). This reduction is explained by two main aspects: (i) first, heating the Fe-SMA strips partially damaged the adhesive joint of post-tensioned beams, reducing the composite action between adherends; and (ii) second, the tensile stiffness of the Fe-SMA strips decreased after activation [31]. Thereby, the reduction of the initial stiffness of post-tensioned beams showed to be proportional to Ta . Unexpectedly, the P_T160 beam showed the highest initial stiffness among the post-tensioned beams, being 0.7 % higher than the one obtained from the R_T0 series. This can be explained by minor geometric deviations, as well as residual frictional forces between the glass panel and the lateral guides. PAPER IV 246 (a) (b) Figure IV.13: Failure modes: (a) debonding of the Fe-SMA strip at the adhesive/reinforcement interface observed in the beams R_T0-II and P_T140; and (b) cohesive failure of the 3M adhesive due to the appearance of shear cracks. Critical shear crack Adhesive Fe-SMA strip Load point Shear crack Fe-SMA strip Cohesive failure of the adhesive MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 247 4.2.2. First cracking load When comparing the post-tensioned beams with the R_T0 series, it is possible to observe that the activation of the Fe-SMA reinforcement increased the glass fracture strength between 16.8 % – in the P_T120-I beam (with the lowest Ta ) – and 30.3 % – in the P_T160 beam (with the highest Ta ). According to Table IV.3, the first cracking loads obtained from bending tests ( Fcr (P_T120-I beam) < Fcr (P_T120-II beam) < Fcr (P_T140 beam) < Fcr (P_T160 beam) are consistent with the results obtained from the activation process. However, the estimated values of Δ Fcr for post-tensioned beams (see Section 3.2) were not reached, being the experimental Δ Fcr (see Table IV.3) between 6.8 % (P_T120-I beam) and 8.4 % (P_T140 beam) lower than the former. Despite the inherent variability of the tensile strength of glass, as well as the decrease in tensile stiffness of the Fe-SMA material after activation (see Section 4.2.1), the loss of post-tensioning force (stress relaxation in Fe-SMA) seems to be the main explanation for this difference, as observed in previous studies on the long term-behaviour of activated Fe-SMA reinforcement (e.g. [31,42]). Based on the Fcr obtained from flexural tests, the analytical model presented in APPENDIX A was used to determine the decrease in post-tensioning force over time, assuming linear elastic behaviour for all components, as well as the strain distribution shown in Figure IV.14. Based on previous studies (e.g. [29,30]), the stress – strain curve shown by activated Fe-SMA strips resembles the one shown by passive Fe-SMA strips after the former achieve an increase in axial strain (ε rev ) of ≈ 1.0 % (see Figure IV.2). Thus, the reversal stress (σ rev ) was assumed equal to σ (ε pre ) = 638.5 MPa (maximum stress reached during the pre-straining process). Table IV.4 compares the recovery stresses obtained from cracking loads (σ rec,cr ) and strain gauges measurements (σ rec,sg ). Values of σ rec,cr lower than σ rec,sg were obtained in all beams, varying between 4.9 % (P_T120-I beam) and 10.1 % (P_T140 beam). It is noteworthy to mention that, for the sake of simplicity, the analytical procedure did not take into account several aspects that obviously influenced the first cracking load of post-tensioned beams, mainly the permanent adhesive damage after the activation of the Fe-SMA strips and its effect on the composite action reduction. According to Eq. (IV.8) in APPENDIX A, lower values of Iel would result in higher recovery stresses. Therefore, if the adhesive damage would have been introduced in the analytical procedure, the difference between σ rec,cr and σ rec,sg would be smaller, mainly in the beams whose Fe-SMA strips were activated at higher temperatures. PAPER IV 248 (a) (b) (c) (d) Figure IV.14: Stress distribution over the cross-section due to the post-tensioning: (a) compression and flexural forces; (b) compression stress distribution; (c) flexural stress distribution; and (d) final stress distribution. Table IV.4: Parameters used to determine the recovery stresses from cracking loads and comparison with the ones derived from the strain gauges measurements. Beam Iel [mm4] Ia [mm4] σ rec,sg [MPa] 1) σ rec,cr [MPa] P_T120-I 973645.3 951294.1 201.7 191.8 (-4.9%) P_T120-II 973386.9 207.0 195.3 (-5.6%) P_T140 970587.7 263.8 237.3 (-10.1%) P_T160 967071.0 335.2 313.4 (-6.5%) Notes: 1) Values retrieved from Table IV.2 considering no composite action between adherends Post-tensioning force loss is indicated in parentheses and represents the difference between σ rec,cr and σ rec,sg Disregarding small temperature variations, which may have slightly reduced the post-tensioning force due to the thermal expansion of the Fe-SMA reinforcement, the stress relaxation of Fe-SMA material is the main explanation for why the σ rec,cr were consistently lower than the σ rec,sg . The post-tensioned beams were tested up to 48 hours after activation of the Fe-SMA strips. According to the tensile relaxation tests conducted by Shahverdi et al . [31], activated Fe-SMA strips with an initial recovery stress of 350 MPa (≈ σ rec,sg for the P_T160 beam) experienced a relaxation of ≈ 6.0 % during this time period. It should be noted that the relaxation behaviour depends on the amount of recovery stress and, in line with the experimental results, stress relaxation in Fe-SMA increases for increasing recovery stress. Nevertheless, according to Hosseini et al . [53], a significant part of the losses in the recovery stress can be retrieved by reactivating the Fe-SMA reinforcement, providing a possible solution to restore the initial recovery stresses in practical applications. P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P σ( P ) P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P σ( P ∙ e ) P P e (-) (-) (+) += (-) Neutral axis Glass panel Fe-SMA reinforcement e P 𝜎𝑔,𝑡 𝜎𝑔,𝑏 MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 249 4.2.3. Post-cracking behaviour In general, the post-cracking behaviour is characterized by a series of sudden load drops which create non-linear branches, with progressive loss of stiffness due to the martensitic transformation in the FeSMA reinforcement (see Figure IV.11 and Figure IV.12). Like in the R_T0 series, crack propagation towards the supports was delayed by the extremely ductile behaviour of the Fe-SMA after the martensitic transformation. The post-tensioned beams presented high deformation capacity, reaching ductility values above 1000 %. In terms of residual strength, all post-tensioned beams were able to exceed the first cracking load during the post-cracking stage. Compared to the R_T0 series, the post-tensioned beams achieved higher values of Fmax , between 16.2 % (P_T120-I beam) and 21.7 % (P_T160 beam). However, in general, the post-tensioned beams showed lower RSi values than the reference ones. The activation of the Fe-SMA reinforcement reduced its tensile strength reserve (difference between σ rev and σ rec,sg ) before the forward transformation, thus reducing significantly the post-cracking stiffness of the post-tensioned beams, as well as their load carrying capacity. Therefore, as experimentally observed, the residual strength tended to be lower in beams with higher Ta . Nevertheless, the P_T140 beam displayed an unexpectedly high RSi value among the post-tensioned beams. The high scatter of the tensile strength of glass seems to be the main reason for this result, having produced a lower Fcr than expected. This also justifies why the P_T140 beam showed a greater difference between σ rec,cr and σ rec,sg (see Section 4.2.2) than the P_T160 beam. Glass structures are safe only when the resisting mechanism generated after the initial glass cracking is capable of assuring a load carrying capacity that is higher than the Fcr . Therefore, a maximum recovery stress (σ rec,max ) should be estimated to ensure Fult > Fcr . After cracking, the load carrying mechanism is formed by a compression force in the uncracked glass zone and a tensile force in the reinforcement element, identified as Fc,g and Fr,t in Figure IV.15, respectively. Two failure mechanism were considered: (i) tensile failure in the Fe-SMA reinforcement and (ii) crushing of the cross-section area where compression stresses are maximum. Lateral instability and debonding of the Fe-SMA strip were neglected because they can be postponed or avoided by changing the beam geometry and choosing adhesives with greater shear resistance, respectively. The compression strength of glass ( fg,c ) was not experimentally characterized in this investigation. A fg,c = 500 MPa was adopted in this study [57]. PAPER IV 256 based shape memory alloy strips. Structural Concrete 2017;19:876–91. https://doi.org/10.1002/suco.201700120. [31] Shahverdi M, Michels J, Czaderski C, Motavalli M. Iron-based shape memory alloy strips for strengthening RC members: Material behavior and characterization. Construction and Building Materials 2018;173:586–99. https://doi.org/10.1016/j.conbuildmat.2018.04.057. [32] Shin M, Andrawes B. Experimental investigation of actively confined concrete using shape memory alloys. Engineering Structures 2010;32:656–64. https://doi.org/10.1016/j.engstruct.2009.11.012. [33] Rojob H, El-Hacha R. Self-prestressing using iron-based shape memory alloy for flexural strengthening of reinforced concrete beams. ACI Materials Journal 2017;114:523–32. https://doi.org/10.14359/51689455. [34] Izadi MR, Ghafoori E, Shahverdi M, Motavalli M, Maalek S. Development of an iron-based shape memory alloy (Fe-SMA) strengthening system for steel plates. Engineering Structures 2018;174:433–46. https://doi.org/10.1016/j.engstruct.2018.07.073. [35] Kajiwara S. Characteristic features of shape memory effect and related transformation behavior in Fe-based alloys. Materials Science and Engineering A 1999;273–275:67–88. https://doi.org/10.1016/s0921-5093(99)00290-7. [36] Sato A, Chishima E, Soma K, Mori T. Shape memory effect in γ⇄ϵ transformation in Fe-30Mn1Si alloy single crystals. Acta Metallurgica 1982;30:1177–83. https://doi.org/10.1016/0001-6160(82)90011-6. [37] Sato A, Kubo H, Maruyama T. Mechanical properties of Fe-Mn-Si based SMA and the application. Materials Transactions 2006;47:571–9. https://doi.org/10.2320/matertrans.47.571. [38] Dong Z, Klotz UE, Leinenbach C, Bergamini A, Czaderski C, Motavalli M. A novel Fe-Mn-Si shape memory alloy with improved shape recovery properties by VC precipitation. Advanced Engineering Materials 2009;11:40–4. https://doi.org/10.1002/adem.200800312. [39] Ghafoori E, Hosseini E, Leinenbach C, Michels J, Motavalli M. Fatigue behavior of a Fe-Mn-Si shape memory alloy used for prestressed strengthening. Materials and Design 2017;133:349– 62. https://doi.org/10.1016/j.matdes.2017.07.055. [40] Shahverdi M, Czaderski C, Motavalli M. Iron-based shape memory alloys for prestressed nearsurface mounted strengthening of reinforced concrete beams. Construction and Building Materials 2016;112:28–38. https://doi.org/10.1016/j.conbuildmat.2016.02.174. [41] Czaderski C, Shahverdi M, Brönnimann R, Leinenbach C, Motavalli M. Feasibility of iron-based shape memory alloy strips for prestressed strengthening of concrete structures. Construction and Building Materials 2014;56:94–105. https://doi.org/10.1016/j.conbuildmat.2014.01.069. MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 257 [42] Michels J, Shahverdi M, Czaderski C, El-Hacha R. Mechanical performance of iron-based shape-memory alloy ribbed bars for concrete prestressing. ACI Materials Journal 2018;115:877–86. https://doi.org/10.14359/51710959. [43] Shahverdi M, Czaderski C, Annen P, Motavalli M. Strengthening of RC beams by iron-based shape memory alloy bars embedded in a shotcrete layer. Engineering Structures 2016;117:263–73. https://doi.org/10.1016/j.engstruct.2016.03.023. [44] Leinenbach C, Lee WJ, Lis A, Arabi-Hashemi A, Cayron C, Weber B. Creep and stress relaxation of a FeMnSi-based shape memory alloy at low temperatures. Materials Science and Engineering A 2016;677:106–15. https://doi.org/10.1016/j.msea.2016.09.042. [45] Lee WJ, Partovi-Nia R, Suter T, Leinenbach C. Electrochemical characterization and corrosion behavior of an Fe-Mn-Si shape memory alloy in simulated concrete pore solutions. Materials and Corrosion 2016;67:839–46. https://doi.org/10.1002/maco.201508701. [46] Lee WJ, Weber B, Feltrin G, Czaderski C, Motavalli M, Leinenbach C. Stress recovery behaviour of an Fe–Mn–Si–Cr–Ni–VC shape memory alloy used for prestressing. Smart Materials and Structures 2013;22:125037. https://doi.org/10.1088/0964-1726/22/12/125037. [47] Deng Z, Silvestru V, Michels J, Li L, Ghafoori E, Taras A. Performance of Glass to Iron-based Shape Memory Alloy Adhesive Shear Joints with Different Geometry. In: Belis B& L (Eds. ., editor. Challenging Glass Conference Proceedings, vol. 8, Ghent, Belgium: 2022, p. 1–12. https://doi.org/10.47982/cgc.8.397. [48] Silvestru V, Deng Z, Michels J, Li L, Ghafoori E, Taras A. Application of an iron-based shape memory alloy for post-tensioning glass elements. Glass Structures and Engineering 2022;7:187–210. https://doi.org/10.1007/s40940-022-00183-z. [49] Leinenbach C, Kramer H, Bernhard C, Eifler D. Thermo-mechanical properties of an Fe-Mn-SiCr-Ni-VC shape memory alloy with low transformation temperature. Advanced Engineering Materials 2012;14:62–7. https://doi.org/10.1002/adem.201100129. [50] GOM. Correlate Software and Online Documentation. Rev.121188. 2019. [51] Rocha J, Sena-Cruz J, Pereira E. Tensile behaviour of CFRP-glass adhesively bonded connections: double-lap joint tests and numerical modelling. Engineering Structures 2022;260:114212. https://doi.org/10.1016/j.engstruct.2022.114212. [52] Nhamoinesu S, Overend M. The mechanical performance of adhesives for a steel-glass composite façade system. Challenging Glass 3: Conference on Architectural and Structural Applications of Glass, CGC 2012, Delft, Netherlands: 2012, p. 293–306. https://doi.org/10.3233/978-1-61499-061-1-293. 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APPENDIX A The recovery stress (σ rec,cr ) can be derived from the first cracking load. For the sake of simplicity, the tensile behaviour of activated Fe-SMA strips was assumed to be bilinear (see Figure IV.2), with the first branch including ε ≤ ε rev and the second ε > ε rev . An equivalent modulus of elasticity ( Er , rec ), defined as the slope of the first linear branch (see Eq. (IV.1)), was conservatively used in these calculations. 𝐸𝑟,𝑟𝑒𝑐=(𝜎𝑟𝑒𝑣−𝜎𝑟𝑒𝑐)𝜀𝑟𝑒𝑣 ⁄ (IV.1) Neglecting the adhesive damage, the moment of inertia ( Iel ) is given by Eq. (IV.2), in which bi , hi and Ei correspond to the width, height and modulus of elasticity of each component, and zi determines the distance between the centroid and the neutral axis. In turn, the position of neutral axis ( yel ) can be determined by means of Eq. (IV.3), where zi,t represents the distance between the centroid of each component and the beam’s top edge. 𝐼𝑒𝑙=∑(𝑏𝑖ℎ𝑖3 12 ∙𝐸𝑖 𝐸𝑔+𝑏𝑖ℎ𝑖𝑧𝑖2∙𝐸𝑖 𝐸𝑔) (IV.2) 𝑦𝑒𝑙=∑𝑏𝑖ℎ𝑖𝑧𝑖,𝑡∙𝐸𝑖𝐸𝑔 ⁄ ∑𝑏𝑖ℎ𝑖∙𝐸𝑖𝐸𝑔 ⁄ (IV.3) Cracking initiates when fg , t is attained at the bottom edge of the glass panel. Therefore, the initial compression stress at the bottom edge of the glass panel (σ g , b ) can be determined from Eq. (IV.4), where Fcr is the cracking load, l1 is the length of the shear span and hg is the height of the glass panel. MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 259 𝜎𝑔,𝑏=𝐹𝑐𝑟𝑙1 2𝐼𝑒𝑙 ∙(ℎ𝑔−𝑦𝑒𝑙)−𝑓𝑔,𝑡 (IV.4) Considering Figure IV.14, σ g , b can be written as a function of σ rec,cr using Eq. (IV.5), in which Ar is the cross-section area of the Fe-SMA strip, d is the distance between the intermediate fibre of the Fe-SMA strip and the top glass edge, and Aa is the cross-section area of the composite beam. Ia and Aa are given by Eq. (IV.6) and Eq. (IV.7), respectively while ya can be determined through Eq. (IV.3), like yel , but in this case considering only the contribution of the glass panel and the Fe-SMA strip (no composite action). According to Section 3.2, these parameters were calculated assuming Er,a = 95 GPa and Eadh = 0. 𝜎𝑔,𝑏=𝜎𝑟𝑒𝑐,𝑐𝑟∙𝐴𝑟 𝐴𝑎+𝜎𝑟𝑒𝑐,𝑐𝑟∙𝐴𝑟∙(𝑑−𝑦𝑎) 𝐼𝑎∙(ℎ𝑔−𝑦𝑎) (IV.5) 𝐼𝑎=∑(𝑏𝑖ℎ𝑖3 12 ∙𝐸𝑖 𝐸𝑔) (IV.6) 𝐴𝑎=∑𝑏𝑖ℎ𝑖∙𝐸𝑖𝐸𝑔 ⁄ (IV.7) Finally, equating Eq. (IV.4) and Eq. (IV.5), σ rec,cr can be determined as a function of Fcr using the following expression: 𝜎𝑟𝑒𝑐,𝑐𝑟=(𝐹𝑐𝑟.𝑙1 2𝐼𝑒𝑙 ∙(ℎ𝑔−𝑦𝑒𝑙)−𝑓𝑔,𝑡) 𝐽⁄ (IV.8) Where, 𝐽 =(𝐴𝑟 𝐴𝑎+𝐴𝑟∙(𝑑−𝑦𝑎) 𝐼𝑎∙(ℎ𝑔−𝑦𝑎)) PAPER IV 260 APPENDIX B Tensile failure in Fe-SMA Considering the strain distribution shown in Figure IV.15, the beam collapse is governed by Eq. (IV.9) in which ε g,t is the axial strain at the top edge of glass and yult represents the position of the neutral axis at failure. 𝜀𝑔,𝑡=(𝜀𝑟,𝑢𝑙𝑡−𝜀𝑟𝑒𝑚)∙𝑦𝑢𝑙𝑡 (𝑑−𝑦𝑢𝑙𝑡) ≤𝑓𝑔,𝑐 𝐸𝑔 (IV.9) With, 𝑦𝑢𝑙𝑡=2𝐴𝑟∙𝑓𝑟,𝑡 𝑡∙𝜀𝑔,𝑡∙𝐸𝑔 By enforcing the equilibrium of internal forces, the ultimate load ( Fult ) is provided by Eq. (IV.10). 𝐹𝑢𝑙𝑡=2∙𝐴𝑟∙𝑓𝑟,𝑡∙(𝑑− 𝑦𝑢𝑙𝑡 3 ⁄ ) 𝑙1 (IV.10) From the rearrangement of Eq. (IV.8), Fcr can be determined from Eq. (IV.11). 𝐹𝑐𝑟=2𝐼𝑒𝑙 (ℎ𝑔−𝑦𝑒𝑙)∙𝑙1∙(𝐽∙𝜎𝑟𝑒𝑐,𝑚𝑎𝑥+𝑓𝑔,𝑡) (IV.11) No composite action between the adherends was considered to determine Ia , and Aa (see Section 3.2). Thereby, equating Eq. (IV.10) and Eq. (IV.11), σ rec,max can be calculated through the following expression: 𝜎𝑟𝑒𝑐,𝑚𝑎𝑥≤𝐴𝑟∙𝑓𝑟,𝑡∙(𝑑− 𝑦𝑢𝑙𝑡 3 ⁄ )∙(ℎ𝑔−𝑦𝑒𝑙) 𝐽∙𝐼𝑒𝑙 −𝑓𝑔,𝑡 𝐽 (IV.12) Glass crushing Assuming glass crushing, the tensile strain in the Fe-SMA strip (𝜀𝑟) at failure is given by Eq. (IV.13), considering by default 𝜀𝑟 > ε rem + ε rev . 𝜀𝑟=𝑓𝑔,𝑐∙(𝑑−𝑦𝑢𝑙𝑡) 𝐸𝑔∙𝑦𝑢𝑙𝑡 +𝜀𝑟𝑒𝑚≤𝜀𝑟,𝑢𝑙𝑡 (IV.13) With, MECHANICAL POST-TENSIONING OF FE-SMA REINFORCED GLASS BEAMS 261 𝑦𝑢𝑙=2𝐴𝑟∙(𝜎𝑟𝑒𝑣+(𝜀𝑟−𝜀𝑟𝑒𝑚−𝜀𝑟𝑒𝑣)∙𝐸𝑟,𝑟𝑒𝑣) 𝑡∙𝑓𝑔,𝑐 Fult is given by the following expression: 𝐹𝑢𝑙𝑡=𝑡∙𝑓𝑔,𝑐∙𝑦𝑢𝑙𝑡∙(𝑑− 𝑦𝑢𝑙𝑡 3 ⁄ ) 𝑙1 (IV.14) In order to determine σ rec,max corresponding to the glass crushing, Eq. (IV.11) and Eq. (IV.14) were equated and Eq. (IV.15) was obtained. 𝜎𝑟𝑒𝑐,𝑚𝑎𝑥≤𝑡∙𝑓𝑔,𝑐∙𝑦𝑢𝑙𝑡∙(𝑑− 𝑦𝑢𝑙𝑡 3 ⁄ )∙(ℎ𝑔−𝑦𝑒𝑙) 2𝐼𝑒𝑙∙𝐽 −𝑓𝑔,𝑡 𝐽 (IV.15) 262 PAPER V HYBRID STRENGTHENING SYSTEMS REFERENCE: Rocha J, Pereira E, Sena-Cruz J. Flexural behvaiour of post-tensioned laminated glass beams with hybrid strengthening systems using CFRP and Fe-SMA reinforcements. In Submition to Construction and Building Materials. ABSTRACT: The fracture strength of glass is often an unreliable parameter and post-tensioning strategies have been investigated to mitigate this uncertainty. Glass composite systems with EBR strengthening systems often fail due to premature debonding. In concrete structures, the NSM technique has been successful in preventing peeling-off failure due to the crack propagation. CFRP and Fe-SMA reinforcement have been explored for the post-tensioned strengthening of existing structures. By combining NSM and EBR techniques, this study explores the benefits of applying hybrid strengthening systems to glass structures. Thus, five large-scale laminated glass beams were tested in flexure. Different strengthening systems (reinforcement material versus application technique) were adopted in each specimen, using CFRP and/or Fe-SMA as reinforcement. Flexural tests showed that hybrid strengthening systems are better than EBR systems at preventing crack-induced debonding. The best strengthening system includes NSM-CFRP and EBR-SMA reinforcements. Both can be safely post-tensioned, preventing stress concentrations in the glass substrate, and the NSM-CFRP reinforcement can still carry load after the possible debonding of the EBR-SMA reinforcement. HYBRID STRENGTHENING SYSTEMS 263 KEYWORDS: CFRP laminate; Fe-SMA strips; Hybrid strengthening system; Laminated glass; Posttensioning; Recovery stress 1 INTRODUCTION However, in recent decades, glass has also been used with structural functions (e.g. floors, beams and frames), being generally designed to withstand flexural loads. Unlike other building materials (e.g. reinforced concrete, steel and timber), the glass brittleness and the lack of appropriate European standardization – Eurocodes – makes the design and application of glass structural elements very challenging. Following the design methodologies used in the aeronautic industry, glass structures have been designed according to the concepts of hierarchy, robustness and redundancy [1]. For structural applications, laminated glass is preferred because it satisfies the concept of redundancy by dividing the glass panel into thinner glass plies joined by transparent interlayers. 1.1. Post-tensioned glass systems The design of glass structural elements consists of verifying whether the tensile strength of glass is sufficient to withstand the anticipated actions. However, its long-term tensile strength is unreliable due to the growth of surface flaws under humidity conditions [2]. Hence, glass requires sufficient redundancy after breakage to accomplish the robustness requirements. However, glass lamination is not sufficient to provide the desirable robustness for unpredictable actions (e.g. vandalism and earthquakes) and/or imperfections derived from design, fabrication and assembly procedures (e.g. stress concentrations). A secondary load carrying mechanism is therefore essential to provide ductility and residual strength capacity after glass cracking. Several reinforcement materials, such as timber (e.g. [3,4]), steel (e.g. [5–8]), Carbon Fibre Reinforced Polymers, CFRP (e.g. [9–11]), and Glass Fibre Reinforced Polymers, GFRP (e.g. [12–17]), have been used with the aim of enhancing the post-failure structural redundancy of glass structural elements. However, the tensile strength of annealed glass is still unpredictable. Although the glass industry has successfully developed thermal toughening to improve its fracture strength, annealed glass presents obvious economic, structural and technical benefits for the construction industry [18]. In analogy to prestressed concrete, post-tensioned strategies have been recently tested to improve the overall performance of glass structural elements, both before and after glass cracking. Like tempering, the mechanical post-tensioning introduces beneficial compressive pre-stress in the glass tensile zones that avoid existing flaws from growing under service loading. However, the latter does not affect the nature of glass fragmentation. A limited number of studies have tested post-tensioning methodologies PAPER V 264 using steel (e.g. [6,8,19,20]) and CFRP (e.g. [9]). In these studies, the reinforcement has been mechanically anchored (e.g. [8]) and/or adhesively bonded (e.g. [19]) to the glass. A reinforcement layout resembling the bending moment diagram has also been adopted to decrease the deformation of glass elements under service loading (e.g. [6,20]). 1.2. CFRP in glass industry CFRP materials have been widely used to strengthen existing concrete structures adopting two distinct techniques. While the Externally Bonded Reinforcement (EBR) technique is based on adhesively bonding the reinforcement to the tensile face of the structural element to be strengthened, the Near Surface Mounted (NSM) technique consists of inserting the reinforcement inside pre-opened grooves in the tensile zone. The premature debonding of the CFRP reinforcement triggered by a critical shear crack has often been observed in EBR systems, both in reinforced concrete (e.g. [21]) and glass (e.g. [22]). Compared to the EBR, the NSM system is less prone to premature debonding due to the larger bonded surface area between adherends, as well as the confinement effect provided by the grooves [23]. Furthermore, the groove is completely filled with adhesive, thus protecting the reinforcement against corrosion, fire, vandalism actions, mechanical damage and aging [24]. Some studies have addressed the structural behaviour of CFRP reinforced glass structural elements, both experimentally (e.g. [9–11,25]) and numerically (e.g. [11,26]). These have shown that such reinforcement is efficient in producing glass composite systems showing relatively ductile failure modes due to the sequential failure of materials and/or connections, the so-called pseudo-ductility behaviour [27]. CFRP has been applied according to the EBR technique (e.g. [22,25]), embedded into the interlayer (e.g. [11]) or introduced inside recessed grooves designed during the glass lamination (e.g. [10]). It is noteworthy to mention that the feasibility of prestressing CFRP reinforcement before bonding it to the glass has also been addressed (e.g. [9]). 1.3. SMA in glass industry Unlike the traditional reinforcement materials, Shape Memory Alloys (SMA) exhibit (i) shape memory effect, which is the ability to retrieve its initial shape by heating after mechanical deformation, and (ii) superelasticity, which is the ability to fully retrieve its initial shape after unloading under certain temperature conditions. Due to the shape memory effect, SMAs have been used for post-tensioning existing structural elements (e.g. [28–33]). In opposition to the traditional materials, whose posttensioning procedure is often difficult due to the lack of space to install hydraulic jacks for prestressing the reinforcement, activation of SMA materials is simple [34,35]. In the case of glass structures, the HYBRID STRENGTHENING SYSTEMS 265 shape memory effect of SMAs can be used in two distinct scenarios: (i) before glass rupture, to increase the initial fracture strength by inducing favourable compressive pre-stresses in the tensile zones, or (ii) after glass rupture, to temporarily enhance the post-failure performance until the cracked glass element is replaced, reducing the deformation, preventing the crack progression and, ultimately, restraining or partially closing existing cracks. Nickel-titanium (Ni-Ti) alloy is the most recognized SMA, but it is not considered suitable for the construction industry due to its expensive nature [31]. Hence, low-cost SMAs were recently developed and investigated, with emphases on iron-based alloys (Fe-SMA). Compared to the Ni-Ti alloy, Fe-SMAs show (i) lower cost, (ii) easier manufacturing process, (iii) higher modulus of elasticity, and (iv) lower activation temperature [36]. They are suitable for a wide range of applications in the construction industry. In this context, the Fe-17Mn-5Si-10Cr-4Ni-1(V, C) alloy, a promising Fe-SMA for the construction industry, was developed by Dong et al . [37] at the Swiss Federal Laboratories for Materials Science and Technology (Empa), Switzerland. This novel Fe-SMA is produced at atmospheric conditions and without expensive high-vacuum processing facilities and thermomechanical training [31,38]. Some studies have focused on the post-tensioned strengthening of concrete (e.g. [30,33,39– 41]) and steel (e.g. [28,29,35]) structural elements using this Fe-SMA. Few studies (e.g. [42–46]) have addressed the structural behaviour of SMA reinforced glass elements, probably due to the relative novelty of both materials in the civil engineering. Bedon et al . [42] performed an exploratory numerical study on the feasibility of activating embedded Ni-Ti wires to reduce out-of-plane deformations in laminated glass panels. Rocha et al . [44] and Silvestru et al . [46] investigated the feasibility of activating externally bonded Fe-SMA strips to increase the initial fracture strength of annealed glass beams and improve its post-failure performance. Compared to traditional prestressing methodologies, the activation of Fe-SMA strips is advantageous for smoothing the transfer of post-tensioning force to the glass substrate because heating the Fe-SMA induces a favourable adhesive damage gradient within the activation region and nearby regions [44]. Recently, the bond behaviour of glass-to-SMA adhesively bonded joints has also been investigated (e.g. [47,45]). 1.4. Research significance Taking into account the challenges associated to the long-term tensile strength, lack of ductility and reliability of glass as a structural material, as well as the scarcity of research works focusing on the feasibility of strengthening glass elements with CFRP and Fe-SMA reinforcements, this research is aimed at investigating the post-tensioning of laminated glass beams by prestressing CFRP laminates PAPER V 272 Table V.3: Characteristics of the laminated glass beams tested in this study, including geometry, reinforcement materials and respective application technique, adhesives and respective thickness, and post-tensioning level adopted in each beam. Property Units Beam designation R_CFRP_CFRP P_CFRP_CFRP CFRP_SMA SMA_CFRP SMA_SMA Glass panel Type of glass - Annealed Annealed Annealed Annealed Annealed Cross-section Outer layers [mm] 220  10 220  10 220  10 220  10 220  10 Inner layer [mm] 198  3 198  3 198  3 198  3 198  3 Length [mm] 2900 2900 2900 2900 2900 Interlayer Material - PVB PVB PVB PVB PVB Thickness [mm] 0.76 0.76 0.76 0.76 0.76 Strengthening system NSM reinforcement Material - CFRP CFRP CFRP Fe-SMA Fe-SMA Cross-section [mm] 20  1.2 20  1.2 20  1.2 20  1.5 20  1.5 EBR reinforcement Material - CFRP CFRP Fe-SMA CFRP Fe-SMA Cross-section [mm] 20  1.2 20  1.2 20  1.5 20  1.2 20  1.5 Reinforcement ratio [%] 0.96 0.96 1.08 1.08 1.20 HYBRID STRENGTHENING SYSTEMS 273 Table V.3 (Cont.): Characteristics of the laminated glass beams tested in this study, including geometry, reinforcement materials and respective application technique, adhesives and respective thickness, and post-tensioning level adopted in each beam. Property Units Beam designation R_CFRP_CFRP P_CFRP_CFRP CFRP_SMA SMA_CFRP SMA_SMA Adhesively bonded connections NSM reinforcement Adhesive - SD SD SD 3M 3M Layer thickness ( ta ) [mm] 1.65 1.65 1.65 1.50 1.50 EBR reinforcement Adhesive - SD SD 3M SD 3M Layer thickness ( ta ) [mm] 1.0 1.0 0.5 1.0 0.5 Post-tensioning NSM reinforcement Target temperature [ºC] - - - 200 200 Initial pre-strain [‰] - 2.0 2.0 - - EBR reinforcement Target temperature [ºC] - - 120 - 120 Initial pre-strain [‰] - - - - - PAPER V 274 In the specimens R_CFRP_CFRP and P_CFRP_CFRP, the two reinforcement elements were simultaneously bonded to the glass, since only the SD adhesive was used for this purpose. Regarding the R_CFRP_CFRP beam, it was prepared by executing only the first and third steps. For the remaining specimens, each reinforcement element was bonded individually and in a separate stage, either because different adhesives were used to bond each reinforcement, or because in the case of the FeSMA strips these were not entirely activated, as further explained in Section 3.3. Therefore, all specimens strengthened with Fe-SMA were manufactured by applying twice the general procedure described above, for each of the reinforcement elements individually. 3.2. Prestressing of CFRP Glass edges show lower apparent tensile strength than the glass surfaces, because the former contain deeper surface flaws induced during the production, cutting, polishing and handling operations [51,52]. In addition, it is reasonable to assume that the glass corners show an even lower tensile strength, as they are typically the most unprotected zones when glass pieces are handled. As a result, preliminary studies (e.g. [53]) have shown that prestressing externally bonded reinforcement is often unsuccessful because the glass fails due to the stress concentration at the loaded end sections. Accordingly, in this case, only the NSM-CFRP laminates were prestressed. After being mechanically anchored at both ends using metal clamps (see Figure V.2b), the NSM-CFRP laminates were prestressed up to an average strain of 2.0 ‰ (σ ≈ 367.7 MPa) using a hydraulic jack. The axial strain was recorded by means of a strain gauge (type: PFL-10-11-3LJC-F by TML; measuring length: 10 mm; gauge factor: 2.12 ± 1 %) previously installed in the middle of the CFRP laminate. The prestressing level was continuously monitored until the NSM-CFRP laminate was released. 3.3. Activation of Fe-SMA Fe-SMAs have two distinct crystal structures, called (i) austenite phase, which is stable at higher temperatures, and (ii) martensite phase, which is stable at lower temperatures. The martensitic transformation consists of modifying the lattice from austenite to detwinned martensite through mechanical deformation or temperature variation. As schematized in Figure V.3, the martensitic transformation does not involve any slippage between atoms (neighbors remain neighbors). It takes place at temperatures between Ms (martensite start temperature) and As (austenite start temperature). When the Fe-SMA is heated at temperatures above As , the detwinned martensite is reversed to austenite and its initial shape is retrieved. HYBRID STRENGTHENING SYSTEMS 275 Post-tensioning of structural elements with Fe-SMAs involves three phases: (i) pre-straining, (ii) activation and (iii) service loading (see Figure V.3). In the first phase, the Fe-SMA is mechanically loaded at room temperature ( Ms < T < As ) until reaching a target strain. Once unloaded, the Fe-SMA shows a permanent deformation that can be partially recovered through heating ( T > As ). When the Fe-SMA is adhesively bonded to the target structural element, recovery stress is generated during the activation (rise in temperature to a specific peak value) and, as a result, the target structural element is post-tensioned. Stress recovery ends when the Fe-SMA reaches the room temperature again. Figure V.3: Schematic activation procedure of Fe-SMAs under constraint strain recovery, also including the phase behaviour. Adapted from Michels et al. [30]. According to the technical specifications provided by the producer, Fe-SMA strips were pre-strained to 2.0 % at room temperature. A hydraulic jack was used to apply the load and a clip gauge (technical specifications described in Section 2.1.1) to measure the longitudinal deformation. Adhesive damage is an inevitable consequence of activating the Fe-SMA reinforcement. However, this apparently deleterious effect can be used to prevent stress concentrations in the glass substrate. A favourable damage gradient is produced along the adhesive connection, on both sides of the activated Fe-SMA strip zone, which helps to smooth the stress transfer between adherends. Desirably, the adhesive bond regions closest the beam ends should remain undamaged to efficiently transfer the post-tensioning force between the adherends. Following the recommendations proposed by Rocha et al . [44], the Fe-SMA strips were heated symmetrically with respect to the mid-span section and the activated length ( la ) was set to 1400 mm, as schematized in Figure V.4a. Stress Strain Stress Af 1 2 3.1 3.2 4 Temperature Thermal expansion Recovery stress 3 Austenite Martensite Austenite 1 2 3 4 Ms < T < AsT > As Pre-straining 1 2Unloading Activation 3.1 4 Service load 3.2 Cooling Heating 3 PAPER V 276 (a) (b) (c) (d) Figure V.4: Activation of the Fe-SMA reinforcement: (a) schematic representation of the experimental procedure; (b) overview of the experimental setup adopted; and connection between the power supply clamps and the (c) NSM-SMA and (d) EBR-SMA strips, respectively. Glass composite beam 50 50 2900 700 700 1400 LVDT SG Metal lateral guides 222 Laminated glass Fe-SMA reinforcement Activated length ( la ) Non-activated region Non-activated region 1600 Electrical power supply Electrical cables Glass composite beam Ground clamp Electrode holder Metal pieces Welding machine Thermocouple type K Undamaged bond length Activation zone Strain gauge & LDVT HYBRID STRENGTHENING SYSTEMS 277 Accordingly, the non-activated NSM-SMA strip zones were first bonded to the glass. After that, the unbonded Fe-SMA zone ( l = la ) was activated. Then, the unbonded groove zone was filled with adhesive and, finally, the EBR reinforcement was bonded to the glass and subsequently activated in some of the specimens. Electric power was supplied to the Fe-SMA reinforcement using two small metal pieces placed 700 mm apart from the mid-span section, in order to connect the electrode holder and the ground clamp (see Figure V.4) and induce a current at the Fe-SMA. To activate the NSM-SMA strip, the metal pieces were inserted into the groove, between the reinforcement and the outer glass sheets (see Figure V.4b). Metal clamps were used to press the metal pieces against the EBR-SMA strip (see Figure V.4c). A relatively high current density of approximately ≈ 4.0 A/mm2 was applied. The Fe-SMA strips were heated at different temperatures: (i) 200 ºC for NSM-SMA strips; and (ii) 120 ºC for EBRSMA strips (see Table V.3). Due to a brief power outage during the activation process, in the SMA_CFRP beam, the NSM-SMA strip was only heated at ≈ 180 ºC. Figure V.4b shows the instrumentation adopted during the activation of the Fe-SMA strips, which included the measurement of (i) the mid-span deflection by means of a displacement transducer – linear variable differential transformer (LVDT) – with stroke of 25 mm and precision of 0.01 mm; (ii) the axial strain at the top edge of the glass panel using a strain gauge (technical specifications indicated in Section 3.2) and (iii) the temperature in the Fe-SMA through a type K thermocouple. All measurements were recorded at an average frequency of 5 Hz. 3.4. Four-point bending tests As shown in Figure V.5, five laminated glass beams with a span of 2.8 m were tested adopting a symmetrical four-point bending configuration, with two central load points 700 mm apart. In these tests, the ratio between the shear span length and the beam height (≈ 4.8 times) was the same as that one adopted for the monolithic glass beams previously tested [22,44]. To prevent lateral-buckling, two pairs of vertical metal guides were symmetrically positioned at 700 mm from the mid-span section and metal frames were placed at the beams supports. In these supports, threaded screws were inserted into the holes and carefully pressed against the glass to maintain the alignment of the specimens during the test. Furthermore, polytetrafluoroethylene (teflon) was placed between the threaded screws and the glass beams to prevent premature failure by direct metal-glass contact due to stress concentrations. Lateral guides were also wrapped with a thin teflon film to avoid frictional forces during the test. PAPER V 278 (a) (b) Figure V.5: Four-point bending tests carried out in this study: (a) general layout; and (b) experimental setup. As shown in Figure V.5, displacement transducers with stroke of 50 mm (linearity of 0.15 %) were used to measure the deflection at the load point (LVDT1 and LVDT3) and mid-span (LVDT2) sections. Axial strains were recorded by placing strain gauges on the top edge of the glass (SG1) and on the bottom edge of the EBR reinforcement (SG2). Their technical specifications were indicated above, in Section 3.2. A load cell with a maximum capacity of 200 kN and precision of 0.01 kN was used to measure the applied load. The beams were loaded monotonically under displacement control at a displacement rate of 1.0 mm/min (internal LVDT control of the actuator). A relatively high acquisition frequency of 25 Hz was adopted for all experimental measurements. Finally, the tests were conducted in laboratory environment at an average temperature of 24 ºC and relative humidity of 65 %. All experimental tests were monitored also adopting the Digital Image Correlation (DIC) technique, in order to document the crack evolution and complement the understanding of the structural behaviour Ø40 50 275 Ø10 F 1400 Ø8 Glass composite beam 50 50 2800 1050 1050 700 LVDT1 LVDT2 LVDT3 SG1 SG2 Metal lateral guides Support metal frames Metal profile Metal rollers 222 Laminated glass EBR reinforcement HYBRID STRENGTHENING SYSTEMS 279 obtained from flexural tests until failure. The camera used to capture the images was equipped with a full frame CMOS (7360  4912 pixels), and the focal distance of the lens was 35 mm. The GOM Correlate 2019 software [54] was used for image processing. Images were recorded at 10-second intervals. Due to the large dimension of the specimens tested (length of 2900 mm), the region of interest (ROI) included only half of the span, in order to optimize resolution. 4 RESULTS 4.1. Post-tensioning Table V.4 presents the pre-strain (ε r,p ) and the corresponding post-tensioning force ( Fp ) measured after the NSM-CFRP laminates were released by the hydraulic jacks. Figure V.6 shows the evolution of the pre-strain and temperature over time for the P_CFRP_CFRP beam. In the beams P_CFRP_CFRP and CFRP_SMA, the ε r,p recorded by strain gauges decreased about 4.5 % and 4.9 % when the NSMCFRP laminate was released, respectively. The eccentricity of the post-tensioning force in relation to the neutral axis generated camber in the laminated glass beams, which slightly reduced the prestress. Table V.4: Results obtained during the prestressing procedure of the NSM-CFRP reinforcement in the P_CFRP_CFRP and CFRP_SMA beams. Beam Reinforcement ε r,p [‰] Fp [kN] P_CFRP_CFRP NSM 1.926 8.50 CFRP_SMA NSM 1.923 8.49 Figure V.7 and Figure V.8 show the evolution of the vertical displacement at the mid-span section ( dexp ), the tensile strain at the top edge of the glass panel (ε g,t ) and the temperature in the FeSMA strip ( T ) during the activation process. It should be noted that the positive values correspond to downward displacements and tensile strains. Table V.5 summarizes the values of dexp and ε g,t registered at the end of the cooling phase, as well as the maximum temperature ( Ta ) attained in the Fe-SMA strip. At the beginning of the heating phase, for temperatures below As (≈ 60 ºC), all specimens deformed downwards due to the thermal expansion of the Fe-SMA. Since the Fe-SMA strips were restrained by the glass, the beams deformed upwards between 0.413 mm (CFRP_SMA beam) and 1.058 mm (SMA_SMA beam), depending on the activation temperature and number of activated Fe-SMA strips in each specimen. PAPER V 280 Figure V.6: Post-tensioning of the P_CFRP_CFRP beam, namely the evolution of the pre-strain in the CFRP laminate, of the compressive pre-stress at the bottom glass edge and the temperature over the time. 4.1.1. Numerical modelling The recovery stress (σ rec ). developed in the Fe-SMA strips was determined based on the experimental measurements (see Table V.5) by performing numerical simulations using the finite elements software ABAQUS 6.14 [48]. They were carried out based on the recommendations proposed by Rocha et al . [44]. All components were simulated as an isotropic material with linear elastic behaviour. The activated Fe-SMA strip zone was simulated by adopting a modulus of elasticity ( Er,a ) equal to 95 GPa. In addition, the absence of shear interaction along la was considered by setting Eadh to zero. Finally, in the non-activated beam regions, all components, including the adhesive, were simulated using the mechanical properties indicated in Table V.1. In the beams CFRP_SMA and SMA_SMA, the post-tensioning procedure entailed two phases (see Section 3) that were precisely reflected in the numerical simulations. A phased analysis with an incremental-iterative procedure was employed in the calculations. The first phase simulated the prestressing/activation of the NSM reinforcement involving the following components: (i) the laminated glass panel; (ii) the NSM reinforcement; (iii) the adhesive bonding of the non-activated Fe-SMA strip zones to the glass; and (iv) the boundary conditions. The second phase consisted of activating the EBR-SMA reinforcement. In this phase, the EBR reinforcement and corresponding adhesive layer were added to the numerical model from the first phase. Figure IV.9 schematizes the numerical simulation of these specimens. 020 40 60 80 100 120 140 160 180 200 0.0 5.0 10.0 15.0 20.0 25.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 Temperature, T [ºC] Strain, ε[‰] Time, t [h] NSM-CFRP strain Glass top edge strain Temperature Bonding Unloading HYBRID STRENGTHENING SYSTEMS 281 Figure V.7: Experimental measurements recorded during the activation of the NSM-SMA strips in the SMA_SMA and SMA_CFRP beams: (a) displacement at the mid-span section ( dexp ), (b) axial strain at the top edge of the glass panel (ε g,t ) and (c) temperature in the Fe-SMA ( T ). Three-dimensional simulations were carried out using 8-node cubic elements (C3D8) of 10  10 [mm]. Figure IV.9 shows the geometry, boundary conditions, load configuration and the mesh pattern. Adhesive damage propagation into the non-activated region was neglected and the “tie” constraint was assigned to the Fe-SMA/adhesive and adhesive/glass interfaces. The recovery stress was simulated as a temperature variation along the la and was extracted when the numerical axial stress at the top edge of glass attained ε g,t (see Table V.5). In specimens where the prestressing of the CFRP laminate was also included in the numerical simulations (e.g. CFRP_SMA beam), a temperature 0 1000 2000 3000 4000 5000 6000 7000 8000 -0.75 -0.50 -0.25 0.00 0.25 0.50 0 1000 2000 3000 4000 5000 6000 7000 8000 Displacement, dexp [mm] Time, t [s] Downward Upward 0 1000 2000 3000 4000 5000 6000 7000 8000 -0.05 -0.03 0.00 0.03 0.05 0.08 Strain, ε g,t [‰] Compression Tension 0 50 100 150 200 250 0 1000 2000 3000 4000 5000 6000 7000 8000 Temperature, T [ºC] Time, t [s] SMA_CFRP SMA_SMA 0 50 100 150 200 250 0 200 400 600 800 PAPER V 288 As expected, the structural response of the glass composite beams was composed of two different stages: (i) the pre-cracking stage, during which the glass panel was the main responsible for withstanding the applied bending load; and (ii) the post-cracking stage, starting with the appearance of the first crack, which involved the appearance of new cracks towards the support, as well as the propagation of existing ones. During the second stage, additional load carrying capacity was provided by the resisting mechanism formed by the compression force in the upper uncracked glass zone and the tensile force in the reinforcement element. As a consequence, all specimens presented a relatively ductile failure. Crack propagation towards the supports resulted in successive load drops during the post-cracking stage, leading to a progressive loss of stiffness of the beams. At the end of the postcracking stage, all specimens ruptured when explosive failure occurred at the compression zone of glass beams. Table V.7: Summary of the main properties extracted from the F – δ experimental responses of laminated glass beams, as well as the failure mode observed and the strain gauge measurements when F = Fult . Property Units Beam designation R_CFRP_CFRP P_CFRP_CFRP CFRP_SMA SMA_CFRP SMA_SMA Structural response K [kN/mm] 3.49 3.53 3.63 3.57 3.47 Fcr [kN] 11.31 13.88 15.48 14.02 22.02 δ cr [mm] 3.24 3.93 4.26 3.93 6.34 Fmax [kN] 18.19 20.27 18.95 17.79 19.30 Fult [kN] 17.65 20.27 18.95 17.79 18.13 δ ult [mm] 31.45 26.54 22.24 34.59 35.21 Di [%] 971.2 675.3 521.7 881.2 555.0 RSi [%] 160.8 146.0 122.4 126.9 87.6 Failure modes - - GC GC GC GC GC Strain gauge measurements ε g,t [‰] -1.09 -1.43 -1.22 -1.25 -2.65 ε r [‰] 4.45 4.35 4.72 4.71 48.72 For comparison, Figure V.13 presents the F – δ responses of monolithic glass beams previously tested, namely the S Dur [22] and P_T120 series [44], as well as the crack patterns observed in each series before collapse. In order to assess the efficiency of the hybrid strengthening systems tested, Table V.8 summarizes the RSi , Di and ε r obtained from these specimen series, as well as the observed failure modes. [Document text truncated for crawler view.]