Damage and failure mechanisms under fatigue in long fibre composites with ultra-thin plies

Grupo de Elasticidad y Resistencia de Materiales Departamento de Mecánica de Medios Continuos y Teoría de Estructuras Damage and failure mechanisms under fatigue in long fibre composites with ultra-thin plies PhD Thesis Dissertation of: Serafín Sánchez Carmona Supervisors: Elena Correa Montoto Alberto Barroso Caro Advisor: Federico París Carballo Sevilla, 2023 Acknowledgements In this predoctoral period I have learnt to deal with different aspects of the college career: from conducting research to giving lectures as well as collaborating on organisation tasks and interacting with delightful people. All the knowledge that I have taken is impossible to express it in the following lines. Thus, this manuscript only covers the research work developed during this thesis. Fortunately, I have received much more from those who taught, helped, or advised me in this life period. First, I would like to thank my supervisors Elena Correa and Alberto Barroso for their untiring support and endless motivation, being always so close when I needed their advice. Our continuous discussions have always inspired me to reflect on different points of view, which have perfected my knowledge. Particularly, I am greatly indebted to Elena Correa for her meticulous revisions of the papers, allowing me to improve my English skills, and to Alberto Barroso for his productive meetings, conveying to me the importance of time. Second, I want to thank my advisor Federico París for his guidance, providing and inspiring me during this period. His enthusiasm and enjoyment have always been an essential part of my motivation to come back to college career. I also wish to extend my thanks to all my colleagues of the Group of Elasticity and Strength of Materials for helping me whenever I needed it; especially to José Cañas, Vladislav Mantič, Antonio Blázquez, Enrique Graciani, Jesús Justo, Israel García, Alejandro Estefani and Isabel del Príncipe. A special mention is deserved for the colleagues who have supported me every day, from having coffee every morning up to the night hours invested in this period: María Luisa Velasco, María de los Ángeles Herrera y Carlos Sandino. Although they are not visible in the work developed in my thesis, they have been essential for its development daily. I would also like to acknowledge my colleagues of the Laboratory of Elasticity and Strength of Materials: Antonio Cañas, José Ramón Rodríguez, Miguel Muñoz, Patricia Zumaquero and Teresa Aranda. All of them have helped and guided me through the facilities to perform my experimental tasks. Also, I want to thank Roberto Prieto, Jorge Marín and Julio Gil for their collaboration. During these last two years, I had the opportunity of collaborating with the group of Marino Quaresimin from the Università degli Studi di Padova. Despite continuing the collaboration, it was mainly developed during two stays of a total of 3 months in Vicenza (Italy), where I was working together with Paolo Andrea Carraro, Lucio Maragoni, Federico Lamon and Mirko Simonetto. There, I was able to discover the importance of knowing and understanding the results of other research groups to enrich your own investigation. I would also like to extend my sincere appreciation to Ozen Gursoy, Niloofar Katiraee and Giulia Scampone to share marvellous moments during my stays. I would like to acknowledge the Universidad de Sevilla because this thesis has been mainly supported by the predoctoral fellowship “Personal Investigador en Formación” (VIPPIT-2018-II.2). It has also been partially funded by Consejería de Economía y Conocimiento Junta de Andalucía (P18-FR-3360). My sincere thanks to my close friends, Inmaculada, Alejandro and Ana, who have encouraged and supported me whatever my decision was, as long as it made me happy. A special mention to my family. I owe them all the required efforts that they have carried out to give me the opportunity to study at the university, being able to aspire to my dream career. I love you. Last but not least, my very special thanks to Sandra, my dear fiancé. I have shared both achievements and frustrations with her while she has accompanied me throughout this whole period, taking care of me more than I myself. Contents Acronyms ......................................................................................................................... 9 1. Introduction ............................................................................................................ 11 1.1. Research background ...................................................................................... 11 1.2. Objectives ....................................................................................................... 16 1.3. Contents .......................................................................................................... 17 2. Characterisation of ultra-thin composites ............................................................... 25 2.1. Determination of low-grammage material properties .................................... 25 2.2. Fatigue life of 90º unidirectional laminates .................................................... 33 3. Fatigue damage mechanisms in composite laminates with UTPs .......................... 37 3.1. Transverse damages in the ultra-thin 90º ply block ....................................... 42 3.2. Longitudinal damages in the ultra-thin 90º ply block .................................... 44 3.3. Influence of the ultra-thin 90º ply block thickness ......................................... 47 4. Analysis of the edge effect in cross-ply laminates .................................................. 51 4.1. Alteration of the stress state along free edge .................................................. 51 4.2. Numerical predictions associated with the edge effect ................................... 54 4.3. Experimental evidence ................................................................................... 57 5. Discussion of the results ......................................................................................... 59 5.1. Considerations about UTP’s characterisation................................................. 59 5.2. Considerations about fatigue damage mechanisms using UTPs .................... 60 5.3. Considerations about the edge effect in UTPs ................................................ 62 6. Conclusions, on-going developments and future work .......................................... 65 6.1. Conclusions .................................................................................................... 65 6.2. On-going developments .................................................................................. 67 6.2.1. Numerical predictions of the onset of transverse damages .................... 67 6.2.2. Flexural behaviour of cycled cross-ply samples..................................... 69 6.2.3. Inter-fibre failure analysis under biaxial loads using BEM .................... 70 6.3. Future work .................................................................................................... 71 6.3.1. Through-the-width propagation of the different fatigue damages.......... 71 6.3.2. Damage mechanisms under Tension-Compression and Compression- Compression cyclic loading ................................................................................... 71 6.3.3. Comparison between development of damages on ultra-thin and ultrathick 90º ply blocks ................................................................................................ 71 Bibliography ................................................................................................................... 73 APPENDED PUBLICATIONS PAPER A: Thermomechanical characterisation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy tape prepreg TP 402/T700S PAPER B: Fatigue life of unidirectional 90° carbon/epoxy laminates made of conventional and ultra‐thin plies varying manufacturing and testing conditions PAPER C: Experimental observations of fatigue damage in cross-ply laminates using carbon/epoxy ultra-thin plies PAPER D: Non-conventional failures caused by the edge effect in cross-ply laminates made of ultra-thin plies 9 Acronyms BEM: Boundary Element Method C-C: Compression-Compression CFRP: Carbon-Fibre Reinforced Plastic CLT: Classical Lamination Theory CTE: Coefficient of Thermal Expansion DL: Delamination DT: Delamination Trace ERV: Elementary Representative Volume GTD: Generalised Transverse Damage ID: Isolated Debond I-CD: Isolated-Continued Debonds LD: Longitudinal Debonds LHS: Local Hydrostatic Stress T-T: Tension-Tension T-C: Tension-Compression UTP: Ultra-Thin Ply 16 an existent free edge. Pipes and Pagano [54] dealt with this phenomenon as originally was considered for finite-width angle-ply laminates subjected to tension. Interlaminar stresses (obtained using finite-differences) were added to the solution from CLT, altering the stress state along the free edges and only affecting a characteristic length equal to the laminate thickness in the width direction. Some years later, the phenomenon was presented for cross-ply laminates using different closed form solutions for the interlaminar stresses. Kassapoglou and Lagace [55] used the Force Balance Method and the Principle of Minimum Complementary Energy, Becker [56] used a higher-order plate theory and Pagano et al. [57] used again finite-differences considering mechanical as well as thermal loading. All these studies were comprehensively reviewed in two articles by Mittelstedt and Becker [58] and Mittelstedt et al. [59]. This PhD Thesis has covered a comprehensive study in which the phenomena of scale effect and edge effect have been considered to deeply understand how damage and failure mechanisms appear and progress in CFRP cross-ply laminates with ultra-thin 90º ply block under cyclic loading. Most of the work has been related to experimental tasks in order to micromechanically highlight the difference on the appearance of fatigue damages due to the so-called scale effect. Nevertheless, numerical tasks have been developed to mainly analyse the edge effect. 1.2. Objectives After considering all the previously mentioned issues in CFRP cross-ply laminates, the main objective of this PhD Thesis is the comprehension of fatigue damage mechanisms in cross-ply laminates when ultra-thin plies are used in the 90º ply block to clarify how scale effect impairs in the fatigue behaviour of composite materials. The achievement of this main objective has required accomplishing the following analyses: • To characterise the thermo-mechanical properties of the low grammages prepreg materials in order to analyse the effect of the different ply’s thicknesses on the properties of a ply block. • To exhaustively identify the micromechanical damage that appear under fatigue loading when ultra-thin thicknesses are used for the 90º ply block, connecting it with the so-called scale effect under quasi-static loading. 17 • To comprehend the different fatigue damage mechanisms encountered in the 90º ply block, analysing the phenomenon of the edge effect when ultra-thin 90º ply block thicknesses are involved. It is worth mentioning that this Thesis does intend to provide fatigue damage trends more than quantitative predictions, observing exhaustively the different typologies of damage, in order to understand the differences on the appearance of the damage mechanisms when UTP is used instead of conventional ones under fatigue loading. 1.3. Contents The following chapters deal with the content detailed next. Obviously, this first chapter has focused on the introductory research background of the topic under study and the definition of the objectives. Chapter 2 covers two different experimental characterisations. First, the material properties are measured for the different cured prepreg grammages, and second, the fatigue life of 90º unidirectional laminates is experimentally obtained. Chapter 3 deals with an exhaustive observation of the fatigue damages encountered in cross-ply laminates when an ultra-thin 90º ply block is used. This chapter is the main part of this Thesis due to the fact that the microscopic revision of CFRP laminates is highly time-consuming and the meticulous detection of the different typologies of damages needs to be carefully done to avoid misleading conclusions. Chapter 4 is about the edge effect phenomenon which acquires more relevance when an ultra-thin 90º ply block is involved, and due to the fact that visual inspection is carried out at the free edge of the samples, where this effect takes place. In this study, a profound analysis of the singularity that appears at the 0/90 bimaterial corner is performed to ensure the real stresses that arise from the so-called edge effect. All results from Chapter 2 to Chapter 4 are discussed in Chapter 5. The summary of the main conclusions, the on-going works that are being developed after the results obtained in this Thesis and the future works are included in Chapter 6. After this last chapter, the employed bibliographic references are detailed, and a list of publications derived from this PhD Thesis work is also included. The publications invoked in the compendium, and detailed in the following pages, are shown 18 chronologically with respect to the work developed during the Thesis, indicating the name of the paper, the authors and the data of the Journal as well as the abstract. It is worth highlighting that all experimental tasks, from the purchase and the reception of the prepreg materials to inspecting the damages in samples, have been developed in the facilities of the Laboratory of Elasticity and Strength of Materials by the author of this Thesis. 19 PAPER A [60] • Name of the publication: Thermomechanical characterisation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy tape prepreg TP 402/T700S. • Authors: Serafín Sánchez-Carmona, María Luisa Velasco, Alberto Barroso, Elena Correa. • Data of the journal: Data in Brief, volume 47, number 108966, April 2023. • Abstract: With the aim to calculate through the Classical Laminate Theory the most reliable stress value generated in the 90° layer of cross-ply laminates tested under fatigue loading, the mechanical and thermal properties were measured for a novel composite material TP402/T700S 12K/35% using two different unidirectional tape prepregs, 30 and 150 g/m2. 0° unidirectional (UD-0), 90° unidirectional (UD-90), ±45°, 10° off-axis and samples for thermal properties measurements were manufactured in an autoclave. Tensile and thermal tests were performed in an Instron 4482 and in an oven, respectively, using strain gauges for all of them. Data collected was analysed following technical standards. The values of the mechanical properties, i.e., elastic and shear stiffness and strength, and the coefficients of thermal expansion (CTEs), α1 and α2, were calculated also obtaining the corresponding statistics. 20 PAPER B [61] • Name of the publication: Fatigue life of unidirectional 90° carbon/epoxy laminates made of conventional and ultra-thin plies varying manufacturing and testing conditions. • Authors: Serafín Sánchez-Carmona, Elena Correa, Alberto Barroso, Federico París. • Data of the journal: Fatigue & Fracture of Engineering Materials & Structures, number 13966, February 2023 • Abstract: Unidirectional 90° laminates (UD-90) have been tested under tension– tension loading (R = 0.1) to comprehend the effect of different conditions on their fatigue life. Four different case studies have been evaluated: the existence of porosity using two different UD-90 laminates cured at different pressures in an autoclave, the importance of the surface finishing when a pressure plate is used, the effect of load frequency, and the relevance of the prepreg thickness comparing 190 and 50 g/m2 prepregs while keeping the total thickness of the laminates constant. All these case studies have been analyzed employing S–N curves as the starting point of the authors' current research for the prediction of the onset of transverse damages in ultra-thin plies in the assessment of different cross-ply laminates under cyclic loading. 21 PAPER C [62] • Name of the publication: Experimental observations of fatigue damage in crossply laminates using carbon/epoxy ultra-thin plies. • Authors: Serafín Sánchez-Carmona, Elena Correa, Alberto Barroso, Federico París. • Data of the journal: Composite Structures, volume 306, number 116564, February 2023. • Abstract: The damage mechanisms of cross-ply laminates under fatigue loading have been deeply studied during last years. In the case of quasi-static loads the so-called scale effect has recently acquired renewed importance after the appearance of ultra-thin plies. In this work, the experimental observation of the onset of transverse damage and its progression in two different cross-ply laminates under tension–tension cyclic loading is performed. First, a [04/903/04] laminate made of plies with conventional thickness (150 g/m2) is analysed. After looking for the expected fatigue damage mechanisms in this case, a [04/90/04] laminate with a single ultra-thin 90⁰ ply (30 g/m2) is studied. All specimens have been carefully examined by means of an optical microscope, detecting the expected damage mechanisms for [04/903/04] and non-conventional types of damages for [04/90/04]. The change of fatigue damage mechanisms for cross-ply laminates involving an ultra-thin 90⁰ ply is microscopically detailed, meaning the evidence of the delay of transverse damage onset in the 90° layer under cyclic loading. This evidence shows the existence of a scale effect concerning the appearance of the fatigue damage mechanisms. 22 PAPER D [63] • Name of the publication: Non-conventional failures caused by the edge effect in cross-ply laminates made of ultra-thin plies. • Authors: Serafín Sánchez-Carmona, Alberto Barroso, Vladislav Mantič, Elena Correa, Federico París. • Data of the journal: Composites Part B – Engineering, volume 254, number 110576, April 2023. • Abstract: In a fatigue testing programme of carbon/epoxy cross-ply laminates made of ultra-thin plies, non-conventional failures are observed. These nonconventional failures consist in longitudinal cracks in the 90° layer parallel to the loading direction instead of the conventional transverse cracks in the 90° layer perpendicular to the load direction. A potential reason for this failure is the presence of a normal stress in the thickness direction. Classical Lamination Theory predicts zero values for this stress component under longitudinal loading, but the presence of a free-edge alters the stress state. The so-called “edge-effect” has been widely studied in the past, but the presence of ultra-thin plies introduces new lower limits of the thickness of the 90° layer. Additionally, the presence of a stress singularity, in the bimaterial corner generated by the 0° and 90° plies, is also investigated to check its influence on the stress state due to the low thickness values of the 90° layer. A slight geometrical modification is conceived to remove the stress singularity, isolating its effect from the pure edge effect. Numerical simulations of the stress alteration in the free edge of the samples, due to mechanical and thermal loading, are carried out, and stress distributions are numerically computed, depending on the 90° layer thickness. Detailed failure inspection by 3D tomography is also done to assess the throughthe-width propagation of the non-conventional failures from the free edge. Numerical predictions and experimental 3D X-ray inspections seem to corroborate that the edge effect is responsible for these non-conventional failures. 23 Additionally, some contributions have been performed on different conferences, both national and international, which are not invoked in the compendium. They are derived from the work developed in this Thesis, and they are also listed next: 1) XXXVII Congreso del Grupo Español de Fractura (GEF21). Estudio experimental a fatiga de laminados unidireccionales a 90⁰. Serafín Sánchez- Carmona, Elena Correa, Alberto Barroso, Federico París. June, 2021. (Presentation) 2) The Eighth International Conference on Fatigue of Composites (ICFC8). Experimental assessment of fatigue damage mechanisms in [04/90n]s laminates using carbon-epoxy ultrathin plies. Serafín Sánchez-Carmona, Elena Correa, Alberto Barroso, Federico París. June, 2021. (Presentation) 3) XIV Congreso Nacional de Materiales Compuestos (MATCOMP21). Tipología de daños observados ante carga cíclica en laminado cross-ply con lámina de 90º ultradelgada de 30 g/m2. Roberto Prieto-García, Serafín Sánchez-Carmona, Elena Correa, Federico París. June, 2022. (Poster) 4) XIV Congreso Nacional de Materiales Compuestos (MATCOMP21). Mecanismos de daño ante carga cíclica en laminados cross-ply fabricados con láminas ultradelgadas. Serafín Sánchez-Carmona, Elena Correa, Alberto Barroso, Federico París. June, 2022. (Presentation) 5) XIV Congreso Nacional de Materiales Compuestos (MATCOMP21). Efecto borde en laminados cross-ply con láminas ultradelgadas. Serafín Sánchez- Carmona, Alberto Barroso, Elena Correa, Federico París, Vladislav Mantič. June, 2022. (Presentation) 6) 20th International Conference on Fracture and Damage Mechanics (FDM2022). Flexural Behaviour after Tension-Tension Fatigue Testing of Cross-ply Laminates Made of Carbon/Epoxy Ultra-thin Plies. Serafín Sánchez-Carmona, Alberto Barroso, Elena Correa, Federico París. Indexed in Web of Science: Sánchez-Carmona, S., Barroso, A., Correa, E., París, F. (2023). Flexural Behaviour after Tension-Tension Fatigue Testing of Cross-ply Laminates Made of Carbon/Epoxy Ultra-thin Plies. AIP Conference Proceedings, In press. 25 2. Characterisation of ultra-thin composites In the framework of this Thesis two different raw materials are used. Both of the tape prepregs are made of carbon fibres and epoxy resins: CYCOM 970/T300 from Solvay, and TP 402/T700SC from North Thin Ply Technology. The former has 190g/m2 and the latter has 150, 100, 50 and 30g/m2. Both prepreg materials have similar fibre weight percentages, 62% and 65%, respectively. The first material is used for a particular study which is going to be covered in this Chapter, whereas the second prepreg is the main material used to achieve the objectives of this Thesis. Two different sections are presented. First, the novelty of the low grammage prepregs entails the necessity of a deep characterisation of their properties both mechanically and thermally as the supplier does not provide them. And second, the fatigue life of the unidirectional 90º laminates made of UTPs is obtained to define the starting point, as a first rough estimation, of the experimental programs carried out in Chapter 3. 2.1. Determination of low-grammage material properties With the idea in mind of assuring that the characterisation of the different prepreg grammages from the tape prepreg TP 402/T700SC can be performed independently of the grammage used, a mechanical (under tension), as well as thermal, characterisation is carried out for the different prepreg grammages. Five different laminates were manufactured by hand-lay-up in the clean room of the facilities of Laboratory of Elasticity and Strength of Materials. 0º unidirectional, 90º unidirectional, ±45º equiangular-ply, 10º off-axis and unidirectional samples for thermal testing. The next manufacturing matrix (Table 1) summarizes the laminates performed from each prepreg grammage. 32 a1) a2) b1) b2) Figure 9. [Fig. 2 from PAPER C] Measurement of the thermal stress relaxation using the curvature radius (R) for [04/904] laminate manufactured with (a) 100g/m2 and (b) 30 g/m2. Figures a1) and b1) just after curing process and a2) and b2) after 1030h. Figure 10. [Fig. 3 from PAPER C] Curvature radius versus time after the curing process for [04/904] fully manufactured with 100g/m2 and 30 g/m2. 33 2.2. Fatigue life of 90º unidirectional laminates As was previously mentioned, the starting point for the experimental programs performed in PAPER C [62], which are going to be discussed in Chapter 3, was an estimation of the transverse damage onset in the 90º ply block of cross-ply laminates. This rough estimation was done following the ideas taken from Hashin and Rotem [69] and Hosoi et al. [70]. Both of them developed fatigue failure criteria using S-N curves of 90º unidirectional laminates. For that reason, the fatigue life of ultra-thin 90º unidirectional laminae has been obtained. The S-N curves of both conventional and ultra-thin 90º unidirectional laminates were actually measured in PAPER B [61], the second publication invoked in the compendium, in order to compare the difference between the two material systems with different thicknesses under cyclic loading. In this study, different material features and testing conditions were used to comprehend the fatigue performance of this unidirectional composite laminate. The four features studied as possible critical points were: the external surface finishing, overheating due to high load frequency, the presence of voids and the different plies thicknesses. The three first features were analysed for the first raw material mentioned in the first part of this Chapter, CYCOM 970/T300. Although Sisodia et al. [71], among others, showed that the presence of voids has a relevant detrimental effect on fatigue behaviour of composites, the percentage of porosity was so low in this study that it does not imply any alteration on the S-N curve. The main conclusion from these three features was a negligible effect on the fatigue performance as can be seen in PAPER B [61]. All the experimental results for this material, named as conventional one, were charted together as shown in Figure 11 (from PAPER B [61]), obtaining a unique S-N curve well correlated with the experimental results as a R2 = 0.935 was achieved. Regarding the use of low grammages to manufacture 90º unidirectional laminates, it is worth highlighting that the comparison between conventional and ultra-thin 90º laminates was performed with different materials (CYCOM 970/T300 from Solvay, and TP 402/T700SC). Nevertheless, the fibre and matrix volume fraction are very similar (both before and after curing) and they have similar stiffness properties in perpendicular-to-fibre direction. Bearing these ideas in mind, the study revealed that there is an improvement in the fatigue life of the 90º unidirectional laminate made of 34 UTPs. In Figure 12 (from PAPER B [61]), it is shown that the S-N curve slope for ultrathin 90º laminate is lower than for the conventional one, reaching one order of magnitude higher at high cycle fatigue (using both the absolute and the dimensionless stress level). This conclusion seems to be in accordance with the physically based explanation of the scale effect in composite laminates involving UTPs, París et al. [50], which was detailed in section 1.1. Figure 11. [Fig. 9 from PAPER B] S-N curve and the 95% confidence and prediction levels for conventional material specimens at any frequency tested. 35 (A) (B) Figure 12. [Fig. 11 from PAPER B] Comparison of S-N curves obtained: (A) S being the dimensionless maximum stress, and (B) S being the maximum stress, for which the 95% confidence and prediction levels for conventional (Conv.) and ultra-thin (UTP) UD-90 laminate are shown. 37 3. Fatigue damage mechanisms in composite laminates with UTPs As was mentioned in Chapter 1, the fatigue damage mechanisms are deeply known in cross-ply laminates. Nevertheless, the development of low-grammage prepregs and the recent findings related to the so-called scale effect phenomenon motivated the main objective of this Thesis. In this Chapter, a profound microscopic identification of the fatigue damage mechanisms is performed for cross-ply laminates when an ultra-thin 90º ply block is used. Special attention has been focused on the analysis of the differences in the generation of the damage mechanisms to obtain an explanation of the potential presence of a scale effect under T-T cyclic loading. In order to achieve this goal, 4 different cross-ply laminates were manufactured using the tape prepreg TP 402/T700SC. The selected stacking sequence was [04/(90)/04] varying the 90º ply block thickness. The thickest 90º ply block was manufactured with 3 plies of 150 g/m2 prepreg, whereas the thinnest one was made of only 1 ply of 30 g/m2. Two other intermediate thicknesses were manufactured, one using 1 ply of 100 g/m2 and other with 1 ply of 50 g/m2. In what follows, each previous laminate is referred to as CP-450, CP-30, CP-100, and CP-50, the thickness of each 90º ply block being 485, 60, 100 and 65 µm, respectively. For simplicity, regarding to the explanation of the obtained results, only data from the cross-ply laminates with the thickest and the thinnest 90º ply block, CP-450 and CP-30, were published in PAPER C [62] invoked in the compendium. Nevertheless, all the experimental results obtained are going to be detailed next. 38 The 4 cross-ply laminates were made following the same procedure as previously detailed in section 2.1 (hand-lay-up manufacturing and curing in autoclave). The specimens were prepared following recommendations of ASTM D3479 [72]. All the samples performed were thoroughly sanded and polished to avoid dirtiness that could lead to misunderstand the damages observed in the sample free edges both after surface preparation and during fatigue. This process is almost the most important step during testing programs in order to detect precisely the first damages in the 90º ply block. Before reaching good quality surface, several months of previous trials were needed to define a good sanding and polishing procedure. The machine used for this purpose only had a rotating head to sand and polish encapsulated samples. For that reason, a tailor-made device needed to be developed to be able to sand and polish the whole sample free edge. With this issue in mind, several attempts were made, designing different tailor-made devices to keep the sample in vertical position whereas the free edge is being sanded and polished. The first attempt was the simplest one (Figure 13), using two light rectangular metallic profiles to keep the sample in vertical position whereas the user could move the specimen while the sanding and polishing disc was rotating. At the same time, the user needed to pressure with a metallic wire above the paper to keep contact between sample and disc during the whole process. Figure 13. Attempt 1 to develop a tailor-made device to sand and polish. After this first attempt, the author got different polishing planes, the device being needed to be improved, keeping two of the requirements mentioned: sample in vertical position and application of pressure to ensure friction between sample and the sanding and polishing disc, as the author did not know if the relative movement between the 39 sample and the sanding and polishing disc was creating even more marks on the free edge. This decision was taken in an attempt to reach an automatic process in which the user could not introduce these undesirable results. The next attempt was done after machining the tailor-made device shown in Figure 14. In this case, a solid metallic profile was placed crossing the sanding and polishing machine and 3 metallic U profiles were attached to it. In this way, the requirements were achieved, avoiding the relative movement. Nevertheless, the results were not completely satisfactory after trying different pressures by means of the upper springs. Figure 14. Attempt 2 to develop a tailor-made device to sand and polish. To understand if the springs were exerting too much pressure on the sample, another attempt was made, collocating only some weights over the upper part of the metallic U profiles as can be seen in Figure 15. However, the results were neither satisfactory. Figure 15. Attempt 3 to develop a tailor-made device to sand and polish. Finally, the accurate tailor-made device to sand and polish all the samples in the experimental programs is shown in Figure 16 (from the PAPER C [62]). The addition of 40 the relative movement between samples and the sanding and polishing disc provided a satisfactory surface quality. a) b) Figure 16. [Fig. 5 from the PAPER C] Tailor-made device to sand and polish carbon/epoxy samples: a) scheme and b) actual device. Once the samples were sanded and polished, fatigue testing was performed in an Instron 8801 hydraulic machine by means of a load control, using a sinusoidal function with a stress ratio R=0,1 (i.e., T-T loading) and combining two different frequencies (1 and 3 Hz). Before defining the force levels to perform cyclic testing, the ultimate tensile force (Fu) of each laminate was also statically obtained. The different force levels selected for each cross-ply laminate can be seen in Table 4, where the maximum in-plane transverse stress of the 90º ply block (𝜎22,𝑚𝑎𝑥) is shown for each cross-ply laminate. The 41 calculation of these stresses was performed through CLT, using the thermo-mechanical properties obtained in section 2.1 and considering a percentage of the residual thermal stresses to take into account the potential stress relaxation previously observed. After the relaxation study of the non-symmetric laminates shown in section 2.1, a 40% of the thermal stresses were taken into consideration. Table 4. Maximum in-plane transverse stress of the 90º ply block for each cross-ply laminate at each force level tested. F/Fu 𝜎22,𝑚𝑎𝑥 𝐶𝑃−450 (𝑀𝑃𝑎) 𝜎22,𝑚𝑎𝑥 𝐶𝑃−100 (𝑀𝑃𝑎) 𝜎22,𝑚𝑎𝑥 𝐶𝑃−50 (𝑀𝑃𝑎) 𝜎22,𝑚𝑎𝑥 𝐶𝑃−30 (𝑀𝑃𝑎) 0,60 96,51 - - 88,86 0,40 67,67 - - - 0,30 53,25 - - - 0,26 - - - 44,27 0,20 38,92 - 39,67 35,94 0,18 - 35,03 36,81 - 0,16 33,06 - - - 0,12 - - 27,66 - During testing, the machine was stopped at a certain number of cycles and the damages were quantified. These observations have been performed as ex-situ inspections, removing the sample from the machine and looking at the microscope, and as in-situ inspections, using the replica system which offers the advantages indicated in section 1.1. Even both methods have been used simultaneously for the thinnest 90º ply block in order to assure the observation of all the damages encountered in this ultra-thin case. The variety of damages encountered in cross-ply laminates made of ultra-thin 90º ply block gave rise to define different typologies of both transverse and longitudinal damages, which are going to be presented next, pointing out the main results in each case. All these damages are listed in tables and shown by means of micrographs in PAPER C [62] for CP-30 particularly. The experimental results obtained for each cross-ply laminate and for each type of damage is analysed through the damage density (ρD) defined as the number of identified damages divided by a gauge length of 50mm. This damage density is charted versus the number of cycles in all the charts pointed out. 48 (a) (b) (c) (d) Figure 25. The main transverse damages for each cross-ply laminate, with all the replicas scaled by the 90º ply block thickness. Simultaneously to the appearance of transverse damages in cross-ply laminates involving an ultra-thin 90º ply block, LDs occur in a remarkable quantity. However, as was previously mentioned in section 3.2, LDs are not induced by transverse damages as the other horizontal damages, they are due to the so-called edge effect. The next damage mechanism which appears can be better understood observing the fatigue damage scenarios for two cross-ply laminates, CP-450 and CP-30, which are shown in Figure 26. CP-450 shows a 90º ply block full of transverse cracks and the induced delaminations in the 0º/90º interface, Figure 26.(a), whereas CP-30 presents a different damage scenario, as can be seen in Figure 26.(b). From left to right in Figure 26.(b), three GTDs are shown, two DTs are induced by the two first GTDs, and LDs can be observed in more than the half of the micrograph. It is remarkable that delamination 49 damages are clearly delayed, or even suppressed (depending on the force level tested) when an ultra-thin 90º ply block are involved. (b) Figure 26. Fatigue damage scenarios under the same testing conditions for: (a) CP-450 and (b) CP-30. As the 90º ply block thicknesses are different, the damage densities (ρD) of each crossply laminate need to be scaled in order to be compared. Then, each damage density can be multiplied by the 90º ply block thickness (t90), reaching the scaled magnitude ρ* (= ρD * t90). Different comparisons can be found in PAPER C [62] between damage densities for CP-30 and CP-450; however, a comparison of the four studied cross-ply laminates is shown in Figure 27. It can be deduced that the saturation level of transverse damages reduces substantially while the 90º ply block thickness decreases, which implies that there is an important change of the main damage mechanism in the weakest lamina. In other words, a relevant delay of transverse damages is observed, which is greater while the 90º ply block thickness decreases. 50 Figure 27. Comparison between transverse damage densities at the same nominal 𝜎22,𝑚𝑎𝑥 (≈35MPa), considering transverse cracks for CP-450 and GTDs for the other three laminates (some GTDs evolve to transverse cracks in CP-100). 51 4. Analysis of the edge effect in cross-ply laminates The non-conventional damages, previously named as LD in Chapter 3, appeared along the sample’s free edges as paths of debonds longitudinal to the loading direction in the 90º ply block. These non-expected horizontal damages can not be analysed using CLT exclusively as no normal stress in the thickness direction (σ33) are involved in CLT model. Nevertheless, the presence of free edges implies local alterations on the stress state. 4.1. Alteration of the stress state along free edge In the framework of this Thesis, the scheme of the edge-effect problem under study is shown in Figure 28 (from PAPER D [63]). Due to the symmetry, only a quarter part of the 2D sample cross-section problem Figure 28.(c) was modelled in the software ANSYS® using symmetry boundary conditions. Following the axes plotted in this Figure 28, the in-plane transverse stress (σ22) is named as σzz and the out-of-plane transverse stress (σ33) is named as σyy. After simulating the problem, the out-of-plane transverse stress are shown in Fig. 3 from PAPER D [63]. From this simulation, it can be confirmed that an alteration of the stress state exists in the neighbourhood of the free edge, which only affects a characteristic distance (in the width direction) of the order of the laminate thickness. This result corroborates the edge effect phenomenon. Nevertheless, a more local alteration of the stress state is shown in Fig. 3.(c) from PAPER D [63], where unbounded stresses appear (stress singularity) in the neighbourhood of the bimaterial corner formed by the 0º/90º interface. With the aim to discriminate between the effect of 52 each phenomenon (edge effect and stress singularity), that necessarily appear together, on the alteration of the stress state all along the thickness length at the sample’s free edge, the stress singularity was studied separately due to its intrinsic difficulty. Figure 28. [Fig. 2 from PAPER D] Scheme of the problem under analysis. Figure 29. [Fig. 3 from PAPER D] σyy contour plots, in MPa, for (a) the whole problem domain, (b) the whole problem domain with selected σyy contour values, (c) details, at different scales, at the bimaterial corner between 0° and 90° plies. s yy s yy x y x y (a) (b) 0o 90o 0o 90o 10-4 mm 10-3 mm 5·10-2 mm x y (c) 53 Under the assumption of linear elastic behaviour, the stress singularity arises at the 0º/90 interface. Then, the unbounded stresses are calculated at this bimaterial corner considering a polar coordinate system as explained in PAPER D [63]. Although a weak singularity was reached, it is needed to elucidate if these unbounded stresses affect the whole 90º ply block as the studied thicknesses are very low. Using the strategy previously followed by Barroso et al. ([73], [74]), the singularity was removed modifying the solid wedge angle at the corner tip. In any case, it is important to remark that the problem under analysis can not be directly modelled as a generalised plane strain problem (with εzz=0) using the semi-analytical procedure proposed in Barroso et al. [75] and Mantič et al. [76] because εzz is different from zero in the actual problem. To address this issue, the powerful Stroh formalism of anisotropic elasticity was applied to the actual problem after separating it into two problems which can be overlapped, detailed in Figure 30 (from PAPER D [63]). In this figure, the actual problem is divided in one alternative problem without stress singularity and another with the same solution in terms of stress singularity which is solved in plane strain (εzz=0). The achievement of the alternative problem without stress singularity was obtained using the Eshelby’s imaginary cut, deform and bond again procedure [77]. The alternative problem to calculate stress singularity has no stress-free faces, Figure 30.(b)- (c), although the displacements compatibility of 0º and 90º plies along the common interface can be guaranteed using another alternative solution as indicated in PAPER D [63]. Figure 30. [Fig. 5 from PAPER D] Superposition of the (a) alternative problem with a uniform stress solution, (b) additional problem (with εzz=0) to get the original configuration, and (c) detail of the loaded bimaterial corner. (a) (b) (c) 54 A notch at the bimaterial corner was added in the FEM model which was explained at the beginning of this section, looking for the angle at which the stress singularity vanishes. At the end, the edge effect problem was isolated using a solid wedge angle of 55º. Nevertheless, the extent of the singular stress field is below 10-2 mm as can be observed in Figure 38 (from PAPER D [63]). This means that the characteristic distance affected by the stress singularity is only one sixth of the lowest thickness of the studied 90º ply block. Hence, the numerical predictions performed in the next section are going to be carried out without the presence of the notch but not considering the results in the close neighbourhood of the 0º/90º interface. Figure 31. [Fig. 6 from PAPER D] Stress singularity removal at the bimaterial corner. 4.2. Numerical predictions associated with the edge effect The edge effect phenomenon was numerically analysed differentiating two different aspects, the contribution associated with the mechanical loading due to the differences in the Poisson ratio of 0º and 90º plies when they are subjected to the same longitudinal strain (εzz>0), and the contribution associated with the thermal decrement suffered during the cooling stage of the curing cycle due to the different CTEs. Average values of the properties shown in the section 2.1 of Chapter 2 were used in the numerical models. The mechanical problem was modelled in ANSYS® as Generalised Plane Strain, allowing a longitudinal displacement (uz) perpendicular to the 2D geometry which was carefully introduced in the elastic centre of the problem. Regarding to the thermal analysis, it was completely considered, without stress relaxation, to know the upper limit of the residual thermal stresses in the actual problem. It is worth -10 0 10 20 30 40 50 60 1.E-06 1.E-04 1.E-02 1.E+00 syy (MPa) x (mm) 90º 75º 70º 65º 60º 55º 50º a x s yy a (o) 0o 90o 55 highlighting that only a percentage of the thermal stresses would be taken into account in discussion as stress relaxation was previously corroborated (section 2.1 of Chapter 2). From Figure 32, Figure 33 and Figure 34 of PAPER D [63], the different edge-effect stresses contributions can be obtained. Table 5 summarises the mechanical (MECH) and thermal (TEMP) contributions for each studied cross-ply laminate to provide a clarification of the different edge-effect stresses both longitudinal (σzz) and transverse (σyy) to the loading direction. Mechanical contributions are referred to the nominal applied σzz, whereas the thermal contributions are referred to the transverse strength of the material, YT, which is the most relevant property in the non-conventional failure under analysis. Figure 32. [Fig. 7 from PAPER D] syy stress component along the free-edge, due to a mechanical loading (szz). Figure 33. [Fig. 8 from PAPER D] syy stress component along the free-edge, due to the thermal effect (T=-110°C). 0 0.5 1 1.5 2 2.5 0 0.4 0.8 1.2 1.6 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 syy / szz syy / Yt y/thickness of the 90oply MECH_30 MECH_50 MECH_100 MECH_450 s yy y x 0o 90o 0o 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 syy / Yt y/thickness of the 90oply TEMP_30 TEMP_50 TEMP_100 TEMP_450 y s yy x 0o 90o 0o 56 Figure 34. [Fig. 10 from PAPER D] szz stress component along the free-edge, due to a) mechanical loading, b) thermal effect (T=-110°C). Table 5. Mechanical (MECH) and thermal (TEMP) stresses along the sample free edges for each cross-ply laminate. CP-450 CP-100 CP-50 CP-30 MECH 𝜎𝑦𝑦 𝑀𝐸𝐶𝐻 𝜎𝑧𝑧 𝑛𝑜𝑚 ⁄ 0,4 – 0,7 0,75 – 0,85 0,8 – 1,0 0,8 – 1,0 𝜎𝑧𝑧 𝑀𝐸𝐶𝐻 𝜎𝑧𝑧 𝑛𝑜𝑚 ⁄ 1,2 – 1,3 1,4 – 1,5 1,4 – 1,5 1,4 – 1,5 TEMP 𝜎𝑦𝑦 𝑇𝐸𝑀𝑃 𝑌𝑇 ⁄ 1,0 – 1,4 1,6 – 2,0 1,8 – 2,2 1,8 – 2,2 𝜎𝑧𝑧 𝑇𝐸𝑀𝑃 𝑌𝑇 ⁄ 0,9 – 1,2 1,3 – 1,4 1,4 -1,6 1,4 -1,6 These stresses due to the so-called edge effect need to be added to those originated by the applied mechanical loading. Although some stress relaxation which may appear is considered, only residual thermal stresses due to edge effect are high enough (close to or higher than YT) to provoke the non-conventional damages (longitudinal to the loading direction) which had appeared even before fatigue testing (Figure 35). Figure 35. Longitudinal damage (LD) only after sanding and polishing process in CP-100. 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 szz / Yt y/thickness of the 90oply TEMP_30 TEMP_50 TEMP_100 TEMP_450 0 0.5 1 1.5 2 0 0.5 1 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 szz / szz_nom szz / Yt y/thickness of the 90oply MECH_30 MECH_50 MECH_100 MECH_450 y x s zz y x s zz (a) (b) 0o 90o 0o 0o 90o 0o 57 4.3. Experimental evidence Meanwhile the edge-effect stresses were identified and quantified, non-destructive inspections were carried out using a 3D Computed Tomography from CITIUS (Centro de Investigación, Tecnología e Innovación de la Universidad de Sevilla) in order to check if the longitudinal damages (before fatigue testing) had through-the-width propagated, or it was only located at the sample’s free edge vicinity. As was previously mentioned in section 4.1 of this Chapter, these non-conventional damages should be limited to a characteristic distance (of the order of the laminate thickness) in the width direction. This fact was due to compression out-of-plane transverse stresses which appear in the rest of the width direction to fulfil global equilibrium in the y-direction. It is worth pointing out that the tomographic inspections were extremely difficult due to the slight opening of the lips of the longitudinal fibre-matrix interface debonds, which were below 1-2µm, as can be seen in Figure 36. Figure 36. Maximum openings of the lips of the LDs only after sanding and polishing process in CP-100. A 3D computed tomography reconstruction is shown in Figure 37 (from PAPER D [63]). However, Figure 38 has been added to clarify the next explanation. As the samples were sanded and polished, a removal of approximately 1mm of material in the width direction had been performed, only 85µm remaining from the edge after tomographic inspection. 64 ratios are predominant in the thickness direction after sanding and polishing process. Hence, LDs can be expected in all cross-ply laminates. However, the unique cross-ply laminate that analytically present enough level of out-of-plane transverse stress to provoke LDs are CP-30 and CP-50. Nevertheless, it is true that CP-100 has a close stress in the thickness direction to YT to provoke LDs under the presence of a minimum flaw in the laminate. The biaxial stress state that exists in each 90º ply block during the minimum and the maximum sinusoidal load can also be consulted from Table 6. It can be noticed how CP-450 always shows more stress in the loading direction (σ22) than transversally (σ33), although it is worth mentioning that the out-of-plane transverse stress at the minimum peak of cycling loading is almost the same as in-plane transverse stress. Nevertheless, they are so low that LDs are not expected to occur, even when the maximum peak loading is reached. In the rest of CP laminates, the predominant stress from the biaxial stress state changes from the minimum to the maximum peak load. Whereas the out-of- plane transverse stress (σ33) is predominant in the minimum peak load, the in-plane transverse stress (σ22) is predominant in the maximum peak load. Then, there is even a point during each load cycle where the biaxial ratio is T-T (n=1), which may condition the opening orientation of a potential debond. For that reason, it can be seen from Table 3 to Table 6 in PAPER C [62] how the evolution of LDs and GTDs are pretty similar to the CP-30 case, in which both stresses are high enough to produce damage (they are above YT) when the biaxial stress state T-T occurs. 65 6. Conclusions, on-going developments and future work In this final Chapter, the conclusions derived from the work developed in the publications invoked in this compendium are going to be detailed in first place. Second, on-going developments that have arisen from this work are going to be presented. Finally, additional experimental and numerical tasks for cross-ply laminates with UTPs are proposed as future work. 6.1. Conclusions In the framework of this Thesis, different experimental programs have been designed and developed to understand how UTPs impair in the behaviour of composite materials under cyclic loading. A profound tensile mechanical characterisation has been carried out for TP 402/T700SC material (30-150 g/m2) as well as a thermal characterisation. Stiffness and strength properties under tensile loading have been obtained for the four different prepreg grammages, reaching very similar experimental results (taking the singular 150 g/m2 case into account). For that reason, the in-plane shear stiffness and strength have been only obtained for one of the different prepreg grammages. Similarly, CTEs in the 3 elastic symmetry planes have been obtained for different grammages, the results being quite similar. Taking both mechanical and thermal characterisation into account, it can be concluded that a material characterisation can be performed for a long fibre composite material independently on the prepreg grammage used. 66 As the material transverse strength, YT, plays an important role in the 90º ply block failure, the strength life of the ultra-thin material has been characterised under fatigue. Furthermore, the obtained S-N curve has been useful to predict a very first rough estimation of the onset of transverse damage in order to economise experimental testing programs. Considering the use of two different materials (one for conventional and another for ultra-thin thickness), an improvement of one order of magnitude at high cycle fatigue loading has been obtained when 90º unidirectional laminates with the same total thickness are manufactured with UTPs (50 g/m2) instead of conventional prepreg (190 g/m2). All the mechanical and thermal properties were used to calculate the maximum in-plane transverse stress of the 90º ply block using CLT. In this way, the load levels required to test the different cross-ply laminates could be selected choosing similar stress state in the 90º ply block. The cross-ply laminates made of an ultra-thin 90º ply block have shown different fatigue behaviour than ones with a conventional 90º ply block. The differences on the fatigue damage mechanisms are summarised next: • Regarding the first damage mechanism, transverse damages appear as IDs and/or I-CDs mainly and their development to become GTDs is much more progressive for cross-ply laminates made of an ultra-thin 90º ply block (CP-30, CP-50, and CP-100) than the formation of transverse cracks in CP-450. In addition to that, the characteristic damage state of transverse damage when UTPs are used seems to be lower, obtaining a relevant delay on their formation. • With respect to the second damage mechanism, the main delamination damages when UTPs are involved are DTs and very few DLs occur. Hence, the delaminations seem to be importantly delayed or even supressed. • Finally, a new damage mechanism has appeared, named as LDs. These nonconventional damages have been deeply analysed numerically in order to understand what is the physical explanation for their appearance. The so-called edge effect phenomenon has been considered, analysing how it influences the stress state of the 90º ply block along the samples’ free edge. It is worth pointing out that the so-called edge effect phenomenon has provided new contributions to the stress state of the 90º ply block along the samples’ free edge. The in-plane transverse stress (σ22) in the 90º ply block has changed after the calculations of 67 the edge-effect contributions. In addition, an out-of-plane transverse stress (σ33) has appeared in the 90º ply block, implying a biaxial stress state in the 90º ply block along the samples’ free edge. Thus, the edge-effect contributions have increased both stresses in the 90º ply block when its thickness decreases. The aforementioned conclusions for the fatigue damage mechanisms are even more marked as the compared nominal inplane transverse stress (σ22) is lower than the real one in addition to the appearance of an out-of-plane transverse stress (σ33) in the 90º ply block. This biaxial stress state occurs on the samples’ free edge after considering the edge-effect contribution (the lower the 90º ply block thickness, the higher the in-plane transverse stress (σ22) and the out-of-plane transverse stress (σ33)). 6.2. On-going developments 6.2.1. Numerical predictions of the onset of transverse damages As part of the research tasks performed during the stays of this author at the University of Padova (Italy), analytical and numerical studies have been developed with the research group of Professor Quaresimin, who has a well-known scientific trajectory on the study of the fatigue assessment of the different damage mechanisms that take place on composite laminates. The main objective of this collaboration has been to predict the onset of transverse damages using its analytical multiscale strategy, well detailed in Carraro et al. [78]. The prediction of the damage’s initiation has been performed considering that transverse damages are too far away to interact between them and hence, the stress state is constant in the 90º ply block thickness (non-interactive regime). With this aim, different analytical and numerical tasks have been performed: • Numerical assessment of the fibre volume fraction in the different 90º ply block of each studied cross-ply laminate. • Estimation of the elastic properties using the rule of mixtures and the Halpin- Tsai estimation in order to compare the experimental and the numerical elastic properties obtained according to the different fibre volume fractions. • FE analyses for the calculation of the Local Hydrostatic Stress (LHS) in the Elementary Representative Volume (ERVs). These ERVs are being modelled as plane stress and the biaxial stress state along the sample free edge due to the edge effect phenomenon is considered. 68 • Analytical prediction of the transverse damage density has been calculated in the non-interactive crack multiplication regime. This step has been the most important part of the collaboration work. All the previous tasks performed have been taken into the model account to achieve satisfactory predictions. The transverse damage density, ρ, has been obtained following eq. (1): ρ(Ni)={1−exp[−(LHS K0∙N𝑖a)m]}∙ w l0∙c0 (1) where Ni is the number of load cycles and w is the sample width. L0 and c0 are the representative dimensions of the crack initiation zone. a is the slope of the crack initiation S-N curve. m and K0 are parameters calibrated with a Weibull distribution due to the statistical nature of the fatigue strength to crack onset. The model has been calibrated with the experimental results from CP-450 and the results from the rest of CP laminates have been predicted with this model to check if the different transverse damages can be captured with it. Quite satisfactory predictions have been obtained for CP-100 and CP-50 (Figure 42.(a)); nevertheless, the experimental results for CP-30 are being analysed to understand why the predictions do not totally correlate with the experimental results (Figure 42.(b)). In this way, micromechanical considerations are being taken into account to evaluate the magnitude of the residual thermal stresses that appear in the local problem as Correa et al [79] showed. 69 (a) (b) Figure 42. Predictions for CP laminates after calibrating the model with CP-450: (a) CP-100 and CP-50, and (b) CP-30. 6.2.2. Flexural behaviour of cycled cross-ply samples The sixth conference contribution indicated in Chapter 1 (AIP Conference Proceedings) dealt with the preliminary experimental results about this topic. Bending or torsion are loads that can be borne by in-service structural components made of composite materials. Hence, after the different fatigue damages encountered in cross-ply laminates when UTPs are used for the 90º ply block, stiffness performance under bending testing is being studied. Two cross-ply laminates, CP-450 and CP-30, have been selected to analyse the flexural behaviour after they have been tested under fatigue loading. The samples are experimentally tested at the same time that the problem is numerically modelled in ANSYS®, Figure 43, to correlate the results in order to assess the effect of UTPs instead of using conventional ones. 70 (a) (b) Figure 43. Cross-ply laminates with fatigue damages under bending: (a) experimental test and (b) numerical model. The experimental results seem to show that similar stiffness degradation occurs for CP- 30 and CP-450 under similar fatigue testing conditions, although the stiffness performance of CP-30 is higher. Furthermore, the numerical results have captured the stiffness degradation of both laminates, showing a correlation with the experimental results. 6.2.3. Inter-fibre failure analysis under biaxial loads using BEM The non-conventional damages observed in an ultra-thin 90º ply block have been related to the biaxial stress state (T-nT) which appears in the samples’ free edges due to the edge effect phenomenon. A previous study from Correa et al. [80] has been got back to analyse how the studied load cases affect to the appearance of these LDs (Figure 44). It is worth pointing out in that fibre/matrix debonds lengths are approximately around 180º which can be correlated with the Energy Release Rate obtained after revisiting the BEM model in [80]. 71 Figure 44. Longitudinal debonds (LDs) after the first load cycle (at 0.6Fu) in CP-30, showing fibre/matrix debonds lengths around 180º. 6.3. Future work 6.3.1. Through-the-width propagation of the different fatigue damages There are two different ideas which would motivate some new experimental programs to explain how the different damage mechanisms observed in CP laminates with UTPs in the 90º ply block propagate through the width (tunnelling) during fatigue testing: first, the encouraging results for the through-the-width propagation of LDs due to the thermal edge effect by means of 3D computed tomography, and second, the knowledge about the stiffness degradation of cycled cross-ply laminates under bending. 6.3.2. Damage mechanisms under Tension-Compression and Compression- Compression cyclic loading It would be also important to comprehend how damages mechanisms occur under different compression fatigue scenarios when UTPs are used. It would be interesting to use T-C and C-C cyclic loading to completely analyse the behaviour of UTPs under tension and compression fatigue scenarios. An anti-buckling device for the compression cyclic loading may be designed and manufactured, following different suggestions taken from literature (Jeon et al. [24], Liu et al. [81] and Huang et al. [82]). 6.3.3. Comparison between development of damages on ultra-thin and ultrathick 90º ply blocks Although the scale effect shows that damage mechanisms change when UTPs are used in composite laminates (delaying their appearance and decreasing their saturation level under fatigue loading), the industrial sector is considering to expand the use of ultrathick prepreg grammages which would reduce the manufacturing time. In this way, new 72 experimental programmes would be designed to analyse the influence of the ultra-thick plies in contrast to the experimental results of UTPs. 73 Bibliography [1] J. Bachmann, C. Hidalgo, and . Bricout, “Environmental analysis of innovative sustainable composites with potential use in aviation sector—A life cycle assessment review,” Sci China Technol Sci, vol. 60, no. 9, pp. 1301–1317, Sep. 2017, doi: 10.1007/s11431-016-9094-y. [2] H. T. Hahn and L. Lorenzo, Fatigue Failure Mechanisms in Composite Laminates. International Congress on Fracture (ICF), 1984. doi: 10.1016/b978-1- 4832-8440-8.50041-7. [3] B. Harris, Fatigue in composites. Woodhead Publishing, 2003. doi: 10.1533/9781855738577. [4] C. Bathias, “An engineering point of view about fatigue of polymer matrix composite materials,” Int J Fatigue, vol. 28, no. 10 SPEC. ISS., pp. 1094–1099, 2006, doi: 10.1016/j.ijfatigue.2006.02.008. [5] K. Tohgo, . akagawa, and H. Araki, “Damage behavior and life prediction in CFRP cross-ply laminates under fatigue loading,” Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A, vol. 72, no. 7, pp. 1041–1048, 2006, doi: 10.1299/kikaia.72.1041. [6] R. Talreja, “Fatigue of composite materials: Damage mechanisms and fatigue life diagrams,” Proc R Soc Lond A Math Phys Sci, vol. 378, no. 1775, pp. 461–475, 1981, doi: 10.1098/rspa.1981.0163. 80 [59] C. Mittelstedt, W. Becker, A. Kappel, and . Kharghani, “Free-Edge Effects in Composite Laminates-A Review of Recent Developments 2005-2020,” Appl Mech Rev, vol. 74, no. 1, Jan. 2022, doi: 10.1115/1.4054145. [60] S. Sánchez-Carmona, M. L. Velasco, A. Barroso, and E. Correa, “Thermomechanical characterisation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy tape prepreg TP 02/T 00 ,” Data Brief, vol. 47, pp. 0–7, 2023, doi: 10.1016/j.dib.2023.108966. [61] S. Sánchez-Carmona, E. Correa, A. Barroso, and F. París, “Fatigue life of unidirectional 90o carbon/epoxy laminates made of conventional and ultra-thin plies varying manufacturing and testing conditions,” Fatigue Fract Eng Mater Struct, no. 13966, pp. 1–11, 2023, doi: 10.1111/ffe.13966. [62] S. Sánchez-Carmona, E. Correa, A. Barroso, and F. París, “Experimental observations of fatigue damage in cross-ply laminates using carbon/epoxy ultrathin plies,” Compos Struct, vol. 306, no. 116564, 2023, doi: 10.1016/j.compstruct.2022.116564. [63] S. Sánchez-Carmona, A. Barroso, V. Mantic, E. Correa, and F. París, “ onconventional failures caused by the edge effect in cross-ply laminates made of ultra-thin plies,” Composites Part B, vol. 254, no. 110576, pp. 1–10, 2023, doi: 10.1016/j.compositesb.2023.110576. [64] orth Thin Ply Technology, “ TPT ThinPreg 02 data sheet,” NTPT Product Data Sheet, 2017, [Online]. Available: https://www.thinplytechnology.com/assets/mesimages/NTPT-DS-ThinPreg-402- May2017-v3.pdf [65] “A TM E 31: tandard Test Method for Linear Thermal Expansion of olid Materials by Thermomechanical Analysis,” Annual Book of ASTM Standards, vol. April, pp. 1–5, 2019, doi: 10.1520/E0831-19. [66] “A TM D3039/D3039M: tandard Test Method for Tensile Properties of Polymer Matrix Composite Materials,” Annual Book of ASTM Standards, pp. 1– 13, 2017, doi: 10.1520/D3039. [67] J. C. Marín, J. Justo, A. Barroso, J. Cañas, and F. París, “On the optimal choice of fibre orientation angle in off-axis tensile test using oblique end-tabs: 81 Theoretical and experimental studies,” Compos Sci Technol, vol. 178, no. April, pp. 11–25, 2019, doi: 10.1016/j.compscitech.2019.04.022. [68] A. Barroso, D. Vicentini, F. París, and V. Mantič, “Thermal tresses in Composite Joints,” in Encyclopedia of Thermal Stresses, R. B. Hetnarski, Ed., Dordrecht: Springer Netherlands, 2014, pp. 5333–5344. doi: 10.1007/978-94- 007-2739-7_419. [69] Z. Hashin and A. Rotem, “A fatigue failure criterion for fiber reinforced composite laminae,” J Compos Mater, vol. 7, pp. 448–464, 1973, doi: 10.1016/0263-8223(90)90081-O. [70] A. Hosoi, . akuma, Y. Fujita, and H. Kawada, “Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction,” Compos Part A Appl Sci Manuf, vol. 68, pp. 398–405, 2015, doi: 10.1016/j.compositesa.2014.10.022. [71] . isodia, E. K. Gamstedt, F. Edgren, and J. Varna, “Effects of voids on quasistatic and tension fatigue behaviour of carbon-fibre composite laminates,” J Compos Mater, vol. 49, no. 17, pp. 2137–2148, 2015, doi: 10.1177/0021998314541993. [72] “A TM D3 9/D3 9M: tandard Test Method for Tension-Tension Fatigue of Polymer Matrix Composite Materials,” Annual Book of ASTM Standards, vol. 96, no. August, p. 6, 2012, doi: 10.1520/D3479. [73] A. Barroso, J. C. Marín, V. Mantič, and F. París, “Premature failures in standard test specimens with composite materials induced by stress singularities in adhesive joints,” Int J Adhes Adhes, vol. 97, 2020, doi: 10.1016/j.ijadhadh.2019.102478. [74] A. Barroso, B. Lauke, V. Mantič, and F. París, “Tensile and shear strength of bimaterial interfaces within composite materials,” Compos Sci Technol, vol. 124, pp. 81–88, 2016, doi: 10.1016/j.compscitech.2016.01.003. [75] A. Barroso, V. Mantič, and F. París, “ ingularity analysis of anisotropic multimaterial corners,” Int J Fract, vol. 119, no. 1, pp. 1–23, 2003, doi: 10.1023/A:1023937819943. 82 [76] V. Mantiĉ, A. Barroso, and F. París, “ ingular elastic solutions at anisotropic multimaterial corners. Applications in composites,” Mathematical Methods and Models in Composites, pp. 425–496, 2014. [77] J. D. Eshelby, “The Determination of the Elastic Field of an Ellipsoidal nclusion, and Related Problems,” Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 241, no. 1226, pp. 376–396, 1957. [78] P. A. Carraro, L. Maragoni, and M. Quaresimin, “Prediction of the crack density evolution in multidirectional laminates under fatigue loadings,” Compos Sci Technol, vol. 145, no. October, pp. 24–39, 2017, doi: 10.1016/j.compscitech.2017.03.013. [79] E. Correa, V. Mantič, and F. París, “Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis,” Compos Sci Technol, vol. 71, no. 5, pp. 622–629, Mar. 2011, doi: 10.1016/j.compscitech.2010.12.027. [80] E. Correa, F. París, and V. Mantic, “ umerical study of the inter-fibre failure under Biaxial loads,” Procedia Eng, vol. 10, pp. 2560–2565, 2011, doi: 10.1016/j.proeng.2011.04.422. [81] H. Liu et al., “Fatigue modeling for carbon/epoxy unidirectional composites under various stress ratios considering size effects,” Int J Fatigue, vol. 120, no. October 2018, pp. 184–200, 2019, doi: 10.1016/j.ijfatigue.2018.11.009. [82] J. Huang, L. Guo, L. Chen, Z. X. Wang, and J. Li, “Damage evolution of 3D woven carbon/epoxy composites under the tension–compression fatigue loading based on multi damage information,” Int J Fatigue, vol. 154, no. June 2021, p. 106566, 2022, doi: 10.1016/j.ijfatigue.2021.106566. APPENDED PUBLICATIONS PAPER A: Thermomechanical characterisation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy tape prepreg TP 402/T700S The original version of this paper can be found in: https://doi.org/10.1016/j.dib.2023.108966 ▪ Journal name: Data in brief ▪ ISSN: 2352-3409 ▪ Journal Citation Reports (2021): o Citation Indicator: 0.28 o Multidisciplinary Sciences: Q3 Data in Brief 47 (2023) 108966 Contents lists available at ScienceDirect Data in Brief journal homepage: www.elsevier.com/locate/dib Data Article Thermomechanical characterisation data of 30 g/m 2 and 150 g/m 2 cured unidirectional carbon/epoxy tape prepreg TP 402/T700S Serafín Sánchez-Carmona ∗, María Luisa Velasco , Alberto Barroso , Elena Correa Group of Elasticity and Strength of Materials, Department of Continuum Mechanics and Theory of Structures, School of Engineering, Universidad de Sevilla, 41092 Seville (Spain) a r t i c l e i n f o Article history: Received 9 January 2023 Revised 12 January 2023 Accepted 3 February 2023 Available online 9 February 2023 Dataset link: Tensile static tests and thermal expansion coefficients evaluation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy prepreg TP402/T700S (Original data) Keywords: Mechanical properties Elastic Modulus Ultimate Tensile Strengths Shear Modulus Coefficient of Thermal Expansion (CTE) Ultra-thin ply Composite a b s t r a c t With the aim to calculate through the Classical Laminate Theory the most reliable stress value generated in the 90 ° layer of cross-ply laminates tested under fatigue loading [1] , the mechanical and thermal properties were measured for a novel composite material TP402/T700S 12K/35% using two different unidirectional tape prepregs, 30 and 150 g/m 2 . 0 °unidirectional (UD-0), 90 °unidirectional (UD-90), ±45 °, 10 °off-axis and samples for thermal properties measurements were manufactured in an autoclave. Tensile and thermal tests were performed in an Instron 4482 and in an oven, respectively, using strain gauges for all of them. Data collected was analysed following technical standards. The values of the mechanical properties, i.e., elastic and shear stiffness and strength, and the coefficients of thermal expansion (CTEs), α1 and α2 , were calculated also obtaining the corresponding statistics. © 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ) DOI of original article: 10.1016/j.compstruct.2022.116564 ∗Corresponding author’s email address and Twitter handle E-mail address: [email protected] (S. Sánchez-Carmona). Social media: @sersancarmona (S. Sánchez-Carmona) https://doi.org/10.1016/j.dib.2023.108966 2352-3409/© 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ) 2 S. Sánchez-Carmona, M.L. Velasco and A. Barroso et al. / Data in Brief 47 (2023) 108966 Specifications Table Subject Engineering Materials Science Specific subject area Mechanical and thermal characterisation of a composite material using two different grammages supplied by North Thin Ply Technology (NTPT) for aerospace applications Type of data Table Graph How the data were acquired Composite laminates were manufactured by hand-lay-up and cured in an autoclave. Tensile tests were performed using an Instron 4482 and thermal test was carried out in an oven also employing a Wheatstone bridge. The strains were measured placing strain gauges 1-XY31-3/120 and/or 1-LY41-6/120. Data collected was analysed following technical standards. Data format Raw Analysed Description of data collection The composite samples made of TP402/T700S 12K/35% using two different grammages, 30 and 150 g/m 2 , were cured in an autoclave. The samples were cut following the technical standards ASTM D3039 [2] and ASTM E831 [3] , and Marín et al. [4] . Tensile tests were controlled under displacement at a speed between 1 and 1.5mm/min for UD-0, ±45 °and 10 °off-axis specimens and 0.3mm/min for UD-90 samples. Thermal test was performed in an oven and the strains were captured with a Wheatstone bridge, reaching 3 different control temperatures. Data source location Data was collected by these authors, members of the Group of Elasticity and Strength of Materials of the Department of Continuum Mechanics and Theory of Structures from the School of Engineering of the University of Seville (Seville, Spain). Data accessibility The raw dataset can be found in Mendeley Data (DOI: 10.17632/s2pp9hbbzf.1) Direct URL to data: https://data.mendeley.com/datasets/s2pp9hbbzf Related research article [1] S. Sánchez-Carmona, E. Correa, A. Barroso, and F. París, “Experimental observations of fatigue damage in cross-ply laminates using carbon/epoxy ultra-thin plies,” Compos. Struct. , vol. 306, no. 116564, 2023. Value of the Data • This dataset provides a complete thermomechanical characterisation of a material which is not detailed neither in the supplier datasheet nor in any previous publication. • Researchers will benefit from this composite characterisation when they are working with this material or a similar one. • These experimental properties can be used for analytical and numerical models, achieving more realistic results. • Elastic stiffnesses and tensile strength together with CTEs are reported. 1. Objective Composite laminates made of low grammage prepregs involve ultra-thin layer thicknesses. The related research article provides experimental aspects about the appearance of damage in composite laminates involving ultra-thin plies under fatigue loading. Hence, the objective of this article is to provide experimental values for the thermomechanical properties of the different prepreg materials used in the related article to take them into account for the calculation of the required stresses in the studied composite laminates. Furthermore, this experimental characterisation can help the scientific community to assess if these properties are dependent on the prepreg grammages used for the manufacture of composite laminates. S. Sánchez-Carmona, M.L. Velasco and A. Barroso et al. / Data in Brief 47 (2023) 108966 3 2. Data Description The data reported herein contain the values of the elastic modulus in the fibre direction, E 11 , the elastic modulus perpendicular to fibre direction, E 22 , and the in-plane Poisson ´ s coefficient, ν12 , for the 30g/m 2 prepreg ( Table 1 ) and for the 150g/m 2 prepreg ( Table 2 ). The in-plane shear modulus is also reported in Table 2 , showing the value obtained after a ±45 °test, G 45 12 . Table 3 shows, for the 30g/m 2 prepreg, the ultimate tensile strength in the fibre direction, X T , and the ultimate tensile strength perpendicular to fibre direction, Y T , and Table 4 shows the same strength values for the 150g/m 2 case. Moreover, the in-plane shear strength, S, is also reported in Table 4 , which was obtained from 10 °off-axis tests. Table 5 details the CTEs for the 30g/m 2 material after a thermal test reaching 3 different control temperatures to compare the values after two different thermal increments. All the tables report the statistics values of the standard deviation in the same unit than the property and the coefficient of variation (CV), i.e. percentage (%). On the one hand, the stress-strain curves obtained from tensile testing of 150g/m 2 specimens are illustrated for UD-0 samples in Fig. 1 and for UD-90 in Fig. 2 . For the same prepreg, the results from ±45 °specimens tensile test are shown in Fig. 3 . On the other hand, Figs. 4 and 5 chart the stress-strain curves of 30g/m 2 specimens for UD-0 tensile test and for UD-90 tensile test, respectively. Table 1 Stiffness properties for TP402/T700S 12K/35% using 30g/m 2 prepreg. Average Standard deviation CV (%) E 11 (GPa) 112.257 ±5.637 5.021 E 22 (GPa) 7.921 ±0.111 1.398 ν12 0.334 ±0.024 7.300 Table 2 Stiffness properties for TP402/T700S 12K/35% using 150g/m 2 prepreg. Average Standard deviation CV (%) E 11 (GPa) 104.630 ±7.212 6.893 E 22 (GPa) 8.159 ±0.293 3.593 ν12 0.308 ±0.050 16.221 G 45 12 (GPa) 3.254 ±0.120 3.703 Table 3 Ultimate tensile strength properties for TP402/T700S 12K/35% using 30g/m 2 prepreg. Average Standard deviation CV (%) X T (MPa) 1955.952 ±107.044 5.473 Y T (MPa) 36.880 ±3.473 9.417 Table 4 Ultimate tensile strength properties for TP402/T700S 12K/35% using 150g/m 2 prepreg. Average Standard deviation CV (%) X T (MPa) 1875.999 ±148.861 7.935 Y T (MPa) 31.923 ±5.427 17.001 S (MPa) 67.917 ±7.885 11.611 Table 5 CTEs for TP402/T700S 12K/35% using 30g/m 2 prepreg. Average Standard deviation CV (%) α1 ( ◦C −1 ) -1.30e-5 ±1.34e-6 10.33 α2 ( ◦C −1 ) 1.78e-5 ±4.03e-6 22.63 ORIGINAL ARTICLE Fatigue life of unidirectional 90carbon/epoxy laminates made of conventional and ultra-thin plies varying manufacturing and testing conditions Serafín S anchez-Carmona | Elena Correa | Alberto Barroso | Federico París Group of Elasticity and Strength of Materials, Department of Continuum Mechanics and Theory of Structures, School of Engineering, Universidad de Sevilla, Seville, Spain Correspondence Serafín S anchez-Carmona, Group of Elasticity and Strength of Materials, Department of Continuum Mechanics and Theory of Structures, School of Engineering, Universidad de Sevilla, 41092, Seville, Spain. Email: [email protected] Funding information Universidad de Sevilla, Grant/Award Number: VIPPIT-2018-II.2; Consejería de Economía y Conocimiento, Junta de Andalucía, Grant/Award Number: P18-FR-3360; Spanish Ministry of Science, Innovation and Universities, Grant/Award Number: PID2021-126279OB-I00 Abstract Unidirectional 90laminates (UD-90) have been tested under tension–tension loading (R=0.1) to comprehend the effect of different conditions on their fatigue life. Four different case studies have been evaluated: the existence of porosity using two different UD-90 laminates cured at different pressures in an autoclave, the importance of the surface finishing when a pressure plate is used, the effect of load frequency, and the relevance of the prepreg thickness comparing 190 and 50 g/m 2 prepregs while keeping the total thickness of the laminates constant. All these case studies have been analyzed employing S–N curves as the starting point of the authors' current research for the prediction of the onset of transverse damages in ultra-thin plies in the assessment of different cross-ply laminates under cyclic loading. KEYWORDS composites, fatigue analysis, fiber/matrix failure, mechanical testing, tensile mechanical properties, ultra-thin prepreg Highlights •Ultra-thin plies motivate this work to look into scale effect under fatigue. •90unidirectional laminates are tested under tension–tension fatigue loading. •Conventional (190 g/m 2 ) and ultra-thin (50 g/m 2 ) carbon/epoxy prepregs are used. •S–Ncurves are obtained at different cyclic loading conditions without losing accuracy. Received: 31 October 2022 Revised: 13 January 2023 Accepted: 22 January 2023 DOI: 10.1111/ffe.13966 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2023 The Authors. Fatigue & Fracture of Engineering Materials & Structures published by John Wiley & Sons Ltd. Fatigue Fract Eng Mater Struct. 2023;1–11. wileyonlinelibrary.com/journal/ffe 1 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 1|INTRODUCTION The fatigue behavior of any material is a relevant issue due to its cyclic load environment when they are under service. For instance, aircraft suffer fatigue loads when flying, and the wind turbine blades are constantly subjected to rotative cyclic loads. For that reason, composite materials' fatigue life is a continuously updating research area. Due to the enormous number of possibilities when composite material is used, many issues have to be considered if an accurate assessment wants to be achieved. As many authors expounded in Harris, 1 fatigue failure on composite materials depends on material features and testing conditions due to the accumulation of different damages, such as fiber/matrix debonding, matrix cracking, delaminations, splitting, and fiber breakage. On the one hand, composite type, stacking sequence, lay-up manufacture, ply thicknesses, and position, among other material features, need to be considered to precisely assess fatigue life. And, on the other hand, loading type, stress ratio, stress levels, and frequency, among others testing conditions, must be taken into account to efficiently analyze the fatigue behavior of composite materials. Over the last four decades, several research groups have looked into different combinations of material features and testing conditions. There are some studies, see for instance, previous studies, 2-7 that have employed unidirectional composite materials to assess different fatigue case studies. These works have aimed to understand how simple material configurations behave as a first step to comprehend the performance of more difficult stacking sequences. Many other researchers have used complex composite material configurations to directly analyze how fatigue behavior develops according to these particular material features. In order to show the multiple combinations in different research works over the last decades, some studies have been selected. Previous studies 8-18 have a common feature in their work, all of them mainly study cross-ply laminates. However, each piece of work analyzes different material features and testing conditions. Whereas Gamstedt and Sjögren, 12 Berthelot and Le Corre, 13 and Carraro et al. 17 deal with glass fiber reinforcements, the rest of them deal with carbon ones. All of them work with thermoset resins, epoxy mainly, except Henaff-Gardin and Lafarie-Frenot 10 who also treat thermoplastic matrices. A similar case occurs when loading type is considered, as all of them analyze the fatigue behavior under uniaxial loads, except Tohgo et al. 15 who studies it under multiaxial loading. Other studies deal with different stacking sequences covering very diverse materials and testing features as expounded before for cross-ply laminates. For instance, previous studies, 19–26 among others, have analyzed the fatigue behavior of quasi-isotropic and/or angle-ply laminates. According to lay-up manufacture, any configuration may imply voids and its quantity mainly depends on the curing method. As Sisodia et al. 25 and El-Dessouky and Lawrence 27 have expounded, porosity is a detrimental and hard-damaging effect on the fatigue performance of composite materials. Hence, it is worth analyzing the minimum quantity of porosity that can be produced after curing in an autoclave to consider it, avoiding any detrimental effect on fatigue performance. Another important feature to take into consideration is the ply thickness. During the last decades, a phenomenon related to this parameter, the scale effect, has been studied by the scientific community. Many researchers have experimentally assessed the influence of the thickness of the weakest lamina under quasi-static load although few of them have used ultra-thin plies. Recently, París et al. 28,29 have physically explained the scale effect based on the damage mechanisms involved in quasi-static failure after a wide variety of experimental programs and numerical correlations, demonstrating that the first damage in the weakest lamina is delayed as long as its thickness decreases and expounding the change in the quasi-static damage mechanisms. However, few researchers have micromechanically looked into this phenomenon under cyclic loading. Some studies, such as Sihn et al. 22 and Kötter et al., 30 among others, have provided some encouraging improvements related to better fatigue performance macroscopically when ultra-thin plies are involved in the manufacturing process of composite laminates. These studies, among others, have been well reviewed by Galos 31 both under static and fatigue testing. Among the different testing conditions affecting failure, load frequency is one of the most detrimental features for composite specimens tested under fatigue loading due to the associated overheating that can produce undesirable degradation of the material properties. This issue has been and continues being, an ongoing fatigue topic. In this way, Chen and Hwang 32 and Marín et al. 33 have expounded the detrimental frequency effect on the fatigue performance of unidirectional composite laminates associated with the viscoelastic behavior of polymer matrix composites. Due to the fact that damage in carbon/epoxy composite materials is more difficult to observe than in glass/ epoxy composites, it is very useful to predict the onset and the progression of the transverse cracking on the 90 ply of a cross-ply laminate. As a good starting point, this initiation prediction can be reached using the S–Ncurve for UD-90 laminate as Hosoi et al. 16 expounded. Furthermore, Hashin and Rotem 34 established a fatigue failure 2S ´ ANCHEZ-CARMONA ET AL. 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License criterion from the S–Ncurves of 90plies in material characterization, which may be useful as a first estimation of the fatigue damage density in a cross-ply laminate. Considering these two predictions, both the onset and the progression, as a first rough estimation, the definition of more complex experimental testing programs in which the authors are involved can be carried out. These more complex works are specifically focused on detecting the first transverse damage in the weakest ply of a laminate, that is, the 90ply. In this sense, the main objective of this work is to perform a profound fatigue life study of UD-90 laminates. To comprehend the fatigue performance of this type of composite material, several UD-90 configurations have been tested under different material features and testing conditions. In this way, four critical features for the UD 90 layer of multidirectional laminates to be subjected to fatigue testing have been identified and their effect is going to be analyzed; they are surface finishing, overheating due to high load frequency, porosity, and different plies thicknesses. 2|EXPERIMENTAL PROGRAMS Four test batches have been defined to analyze the effect of different conditions on the fatigue life of unidirectional 90laminates. First, the existence of different external surface finishing in the samples has been analyzed to comprehend its effect on the fatigue life of this laminate type. Second, the effect of fatigue load frequency has been measured for all UD-90 laminates manufactured, assuring that the maximum thermal increment is lower than the allowed by the technical standard 35 in order to avoid a relevant degradation of their mechanical properties. Third, the effect of porosity level on the fatigue performance has been evaluated; the laminates have been cured in an autoclave at two different pressures, 3 and 7 bars, both of them are recommended by the manufacturer but for different applications (multidirectional laminate and sandwich, respectively), aiming to reach two different voids scenarios. And the last batch studied has been the significance of the prepreg thickness on the fatigue performance of the UD-90 laminates, manufacturing these laminates with different lamina grammages (including ultra-thin values) while a constant total thickness has been kept for them. 2.1 |Specimens' preparation Aiming to assess the four case studies, two different raw materials have been used: the tape prepreg CYCOM 970/T300 of 190g/m 2 from Solvay and the tape prepreg TP 402/T700SC of 50g/m 2 from North Thin Ply Technology. Both materials have similar fiber percentages, 62% and 65%, respectively. Three types of panels have been manufactured: a 3-bar conventional (3bC) panel and a 7-bar conventional (7bC) panel, both from the former raw material, and a 7-bar ultra-thin (7bUT) panel from TP 402/T700SC. In each case, the bar value indicated shows the work pressure for the autoclave curing. The curing process of all the panels has been carried out in an autoclave using a suitable vacuum bag. Once cured, the fiber volume fraction of each laminate has been numerically measured using three different micrographs from each laminate, obtaining very similar values: 53.4% for 3bC samples, 55.2% for 7bC specimens, and 54.6% for the 7bUT panel. After curing, E-glass fiber-reinforced tabs have been bonded ahead and behind at each side of the panels to prevent a premature failure, assuring the convenient gripping of the clamps during testing. Once the panels have been prepared, the specimens have been machined with a diamond disc. The dimensions selected have been w=25 mm, L s =180 mm, t=2 mm, and L t =50 mm, Figure 1, following the recommendations from technical standards. 35,36 The slightly reduced gauge length has been chosen after preliminary tests performed by the authors to optimize the material used and to economize the manufacturing process. Although the 3-bar pressure is suggested by the manufacturer to cure sandwich laminates, it has been used here to cure a UD-90 laminate. Whereas 7bC samples have not shown any porosity, a small quantity of porosity has appeared on 3bC specimens' free edges as can be shown in Figure 2A; these specimens will be used to check if this scarce porosity value has a detrimental effect on the fatigue life. The quantity of porosity has been measured by means of an automatic image analysis, following TMS PT 2701 standard. 37 The results of this test show that a void percentage of 0.3% is found after the curing cycle at the lowest pressure indicated by the manufacturer. An inspected piece is presented in Figure 2B where the seven red marks correspond to voids. In this way, to ensure that the 3bC panel has been accurately cured, two dynamic mechanical analysis (DMA) tests have been performed following ASTM D7028-07 standard 38 : one for the 3bC panel and another FIGURE 1 Specimen scheme with selected dimensions in mm. S ´ ANCHEZ-CARMONA ET AL.3 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License for the 7bC. The results have shown that T g onset is 181C for 3bC and 185C for 7bC, a difference that can be considered negligible to affect any mechanical property. Due to the use of airweave in the vacuum bag, a rough surface is obtained in one of the sample's faces. To achieve a smooth finishing on both sample external surfaces, a pressure plate between the airweave and panels has been placed during the vacuum bag preparation. In order to avoid the inadequate extraction of air during curing, glass fiber yarns have been distributed along the laminate perimeter as paths to facilitate air extraction. This change of finishing has been carried out to assess if the microscopic irregularities on the external sample surface due to the airweave may imply any stress concentrations that might be the potential nucleation point of a transverse crack. 2.2 |Test preparation A significant number of tests have been carried out to analyze the four case studies proposed. On the one hand, static tension tests have been performed to evaluate both the elastic moduli and the tensile strength of each manufactured laminate. And, on the other hand, fatigue tension–tension (T–T) tests have been carried out to assess the fatigue life of each UD-90 laminate. The static tests have been performed in an Instron 4482 electromechanical machine under displacement control at a speed of 0.5 mm/min. During testing a 2630-112/84 extensometer and/or HBM 1-LY41-6/120, strain gauges have been used to measure the strain and hence, the elastic moduli. The cyclic tests have been carried out in an Instron 8801 hydraulic machine, controlling the load employing a sinusoidal function at a stress ratio R¼σmin =σmax ¼0:1. Different stress levels and load frequencies have been used to assess the fatigue life of the different laminates at room temperature. To ensure the viability of the use of the frequencies selected, a thermocouple has been fitted on the specimen surface to measure if relevant thermal increases exist on the specimens during fatigue testing. As ASTM D3479/D3479M standard 35 mentions, some material systems have demonstrated measurable degradation of material properties when suffering a 10C increase; therefore, frequencies leading to thermal increase greater than this value will be discarded. The frequencies selected have been chosen following previous experiences from the authors' research group (Marín et al. 33 ). 2.3 |Characterization From each manufactured laminate, five samples have been quasi-statically tested to obtain both its tensile transverse strength, Y T , and the corresponding elastic modulus, E 22 . The results are shown in Table 1, including the standard deviation (SD) and the coefficient of variation (CV) for each mechanical property measured. 2.4 |Fatigue testing In the first testing program 3bC samples have been tested at room temperature at two different frequencies, 10 and 15 Hz, under three different stress levels, 0.8, 0.7, and 0.65Y T ; 19 samples being the total number of specimens tested. All tests have shown a maximum thermal increment of 5C, lower than the 10C defined limit. The fatigue life of the 3bC laminate is illustrated in Figure 3 employing S–Ncurves of different colors for each frequency tested. In the second testing program, different 7bC laminates have been manufactured using a pressure plate as has been expounded in Section 2.1. Therefore, two different types of specimens have been obtained, rough and smooth samples, without using a pressure plate and using it, respectively. In what follows, the former is designated by R and the latter by S. The 7bC specimens have been tested at two different frequencies, 15 and 20 Hz, under three different stress levels, 0.8, 0.65, and 0.5Y T ; 36 samples being the total number of specimens tested. FIGURE 2 Porosity on 3bC sample free edge: (A) micrography in detail and (B) determination of the porosity content using automatic image analysis. [Colour figure can be viewed at wileyonlinelibrary.com] 4S ´ ANCHEZ-CARMONA ET AL. 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License In this case, all tests have shown a maximum temperature increase of 7C, also lower than the limit defined. In the same way as the previous program, the fatigue life of the 7bC laminate is illustrated in different colors employing S–Ncurves for each frequency and each surface finishing (Figure 4). In what follows, the run-out arrow indicates that there are specimens that have not failed after a certain number of cycles so the tests have been stopped at this point. And, finally, the third experimental program has been performed to test the 7bUT laminate. The specimens have been tested at 15 Hz, under two different stress levels, 0.8 and 0.65Y T ; 18 samples being the total number of specimens tested. All the tests performed have shown a maximum thermal increase of 4C, also below the limit defined. Figure 5illustrates the fatigue life of the 7bUT laminate employing a S–Ncurve at the frequency tested. To sum up, Table 2shows a test matrix to summarize the experimental data generated in these three experimental programs. It is worth highlighting that the authors have employed two identical stress levels for the three case studies and a third different level between the conventional laminates in order to observe if the S–N curves obtained would be independent of this fact. According to the fracture of UD-90 laminates, specimens are expected to fail after the appearance of the first transverse crack; a fact well corroborated after all the experimental programs. The sample has been divided into three different fracture zones in which the transverse crack may appear: A zone of 10 mm from one tab, C zone of 10 mm from the other tab, and B zone of 60 mm between the two other zones. Two of them, A and C, are the areas close to the tabs and the B zone is the regularized one. In order to analyze the differential behavior of each laminate, the experimental occurrence percentage of the transverse crack according to the different fracture zones has been measured. 3bC samples have shown a 73.7% of TABLE 1 Tensile transverse properties of each manufactured laminate. Y T (MPa) SD (MPa) CV (%) E 22 (GPa) SD (GPa) CV (%) 3bC 69.07 ±4.88 7.07 7.29 ±0.07 0.97 7bC 73.16 ±4.92 6.73 7.26 ±0.21 2.88 7bUT 38.07 ±6.32 16.59 7.58 ±0.08 0.99 FIGURE 3 S–Ncurves of 3bC UD-90 samples (markers for experimental values) at 10 (blue) and 15 Hz (red). [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 4 S–Ncurves of 7bC UD-90 samples (markers for experimental values) at 15 Hz for smooth (blue) and rough (red) samples and 20 Hz for smooth (green) and rough (yellow) samples. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 5 S–Ncurve of 7bUT UD-90 samples tested (markers for experimental values) at 15 Hz. [Colour figure can be viewed at wileyonlinelibrary.com] S ´ ANCHEZ-CARMONA ET AL.5 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License their fractures in the B zone, 7bC a 52.8%, and 7bUT has only shown a 22.2%. It is worth pointing out that for most laminates more than half of the specimens failures have occurred in the regularized zone whereas it might be expected the opposite situation, or even the occurrence in the tabs, due to the stress concentrations promoted by the geometry of the tabs. As it has been detailed, the highest number of occurrences has appeared in the regularized zone, B zone, except for 7bUT samples (although the manufacturing process has been identical in all cases). Therefore, the results of this laminate at 0.65Y T presented in Figure 5 should be analyzed from this perspective. 3|RESULTS AND DISCUSSIONS Each effect considered as one case study has been analyzed independently. However, to describe the fatigue data in view of the analysis of the results, the S–Ncurves have been shown at the same time that every experimental testing program has been presented. It is a wellknown fact that there are many different forms of S–N equations, which can be a linear curve on a log–log or semi-log plot. In this case, the next linear law is assumed for a semi-log chart: σmax YT ¼kmlogN,ð1Þ where σmax is the maximum stress level in the cyclic test, YTis the ultimate strength of the material (particularly, the tensile transverse strength), Nis the total cycle of fatigue life, and kand mare material parameters obtained by regression methods. These S–Ncurve parameters are shown in Table 3for each case study. Furthermore, a statistic fitting analysis has been performed. After obtaining the S–Ncurve parameters needed, R-squared (R 2 ) has been calculated to indicate if the regression model adequately fits the experimental data. Although R 2 is a slight estimation of the goodness- of-fit measure, this statistic variable has been obtained to give an indication of the variability of the results. The R 2 values have been also shown in Table 3. As can be observed, the R 2 values for the 3bC cases are very similar to the 7bC cases, all of them being close to 1. The remainder dispersion may be due to the variability of the transverse strength to the fiber direction. From the 7bC cases, 7bC 15 Hz Smooth has more dispersion than the rest of them and hence, its R 2 is smaller. The dispersion of the 7bUT case is remarkable due to the variability of fractures of ultra-thin 90laminates at 0.65Y T already mentioned and quantified at the end of Section 2.4. Nevertheless, its R 2 continues being quite satisfactory from a statistical viewpoint. In addition to this statistic parameter, the 95% confidence and prediction levels are going to be plotted for the different study cases in the following sections. These two probability intervals have been calculated using the Student's t-distribution with n2 degrees of freedom, taking a sample of nobservations. The interest of these statistical intervals has been related to the definition of more complex experimental programs on cross-ply laminates (see S anchez-Carmona et al. 39 ). In this recently published work, the authors have microscopically looked for the onset of transverse damages which appears in the weakest layer in cross-ply laminates, the 90one. After certain stops performed at TABLE 2 Test matrix summarizing the experimental programs performed, indicating the number of specimens tested under fatigue loading for each study case. Laminate Prepreg grammage Porosity Surface finishing Frequency (Hz) Stress levels (σ max /Y T )10 15 20 3bC CONV YES R 10 9 - 0.8, 0.7, 0.65 7bC CONV NO R - 9 9 0.8, 0.65, 0.5 CONV NO S - 9 9 0.8, 0.65, 0.5 7bUT UT NO R - 18 - 0.8, 0.65 TABLE 3 S–Ncurves parameters and the R 2 for fatigue life data of each experimental program. Case study kmR 2 3bC 10 Hz 0.9997 0.0710 0.9568 3bC 15 Hz 1.0011 0.0686 0.9386 7bC 15 Hz Smooth 1.0094 0.0685 0.9411 7bC 15 Hz Rough 1.0073 0.0759 0.9078 7bC 20 Hz Smooth 1.0063 0.0723 0.9399 7bC 20 Hz Rough 1.0045 0.0720 0.9393 7bUT 15 Hz 1.0016 0.0584 0.8180 6S ´ ANCHEZ-CARMONA ET AL. 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License different numbers of cycles, the main part of this work has been the microscopic inspections of the 90layer using an optical microscope. As has also been discussed in the last paragraph of the introduction section, the first transverse crack in a cross-ply laminate can be predicted using the unidirectional fatigue life. For that reason, knowing the confidence levels around the average of the S–Ncurve and the maximum and minimum values that can be obtained (prediction levels), the first transverse damage predictions can be calculated in a secure interval. Taking the lower and the upper unidirectional fatigue lives into consideration, an estimative cycle range at which the first transverse damage may appear can be predicted. In that way, the microscopic inspection stops are done in a secure interval to avoid missing the first transverse damages that could appear in the 90layer. 3.1 |Effect of surface finishing Although the scattering for unidirectional laminates under fatigue testing is expected to be high, the microscopic observations of the specimens fractured seem to show that the failures of UD-90 samples occur at some irregular areas which are created by the rough texture of one surface of the laminate due to airweave used in the manufacturing process (Figure 6). These irregularities seem to be potential stress concentrators for the fracture of the UD-90 samples. In order to analyze this issue, 7bC laminates have been manufactured using a pressure plate as has been previously explained. The results for the fatigue life of the second experimental program have been already shown in Figure 4. Considering each frequency case for the 7bC laminate separately, rough external surface finishing at 15 Hz seems to move the S–Ncurve slightly to the left, which means that fractures of the UD-90 laminate may occur prematurely due to the roughness of the surface finishing provoked by the airweave; otherwise, the S–Ncurves at 20 Hz are overlapped. Therefore, observing all the results together in Figure 4and taking into consideration the scattering of fatigue life for composite materials, the roughness of the external surface finishing can be neglected as the promoter for the premature fracture of UD-90 laminates. Taking into account this last assumption, the S–N curves from Figure 4are going to be reduced to only two trends, one at each frequency tested as is shown in Figure 7. In this way, the values for the S–Ncurves and their R 2 are shown in Table 4. FIGURE 6 Cracks in UD-90 samples occurring at irregular areas due to the rough surface of this laminate. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 7 S–Ncurve of 7bC UD-90 samples tested (markers for experimental values) and the 95% confidence and prediction levels at (A) 15 and (B) 20 Hz. [Colour figure can be viewed at wileyonlinelibrary.com] TABLE 4 S–Ncurves values and associated statistics for fatigue life data of the 7bC laminate. Case study kmR 2 7bC 15 Hz 1.0139 0.0729 0.9215 7bC 20 Hz 1.0097 0.0729 0.9494 S ´ ANCHEZ-CARMONA ET AL.7 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 3.2 |Effect of frequency Different frequencies have been used in the experimental programs for 3bC and 7bC laminates. The main objective has been to identify the highest frequency allowed to perform the tests in the quickest way, without producing an out-of-limit thermal increase. In this sense and as has been shown in the previous section, none of the frequencies used has implied an increment of 10C; particularly, the highest measurement has been 7C at 20 Hz. All S–Ncurves from 3bC and 7bC specimens have been charted together in Figure 8. On the one hand, 3bC samples have shown very similar S–Ncurves at both frequencies tested in the first fatigue program. Conversely, it is worth pointing out that the dispersion of experimental data at 15 Hz and 0.65Y T has produced a slight reduction of R 2 (Table 3). Although this statistic value is lower than that associated with 10 Hz, both frequencies, 10 and 15 Hz, have given rise to equivalent test results in UD-90 laminates. And, on the other hand, the experimental fatigue life of each frequency of the second program for 7bC samples can be also observed in Figure 8. In this case, the scatter of the results has been slightly lower than in the case of the 3bC samples as can be concluded from Tables 3and 4. Therefore, all frequencies tested can be employed to define the fatigue life of UD-90 laminates due to the similarity of all S–Ncurves obtained, reaching a common S– Ncurve and their statistic parameters as can be seen in Figure 9. Moreover, Table 5shows the values for this unique S–Ncurve. After all conventional results have been combined to obtain a unique S–Ncurve, the use of different stress levels in the conventional laminates has verified that a higher or lower stress level is independent of obtaining a good S–Ncurve. 3.3 |Effect of voids Taking into account that the existence of porosity is scarce after curing at any pressure in the interval given by the manufacturer, the fatigue life of both laminates, 3bC and 7bC, is similar if we compare the S–Ncurves calculated at any frequency tested, as Figure 8shows. Hence, the existence of a few voids, 0.3% or less, has a negligible effect on the fatigue performance of UD-90 samples. 3.4 |Effect of ply thickness Before starting to analyze the effect of ply thickness, it is important to remember that the damage in a 90layer of a composite laminate is dominated by fiber/matrix debonding. Hence, the development of the crack is produced through the fiber/matrix interfaces and not exclusively along the matrix. This idea is illustrated by the micrograph shown in Figure 10. FIGURE 8 Comparison of S–Ncurves obtained at all frequencies tested in each experimental testing program. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 9 S–Ncurve and the 95% confidence and prediction levels for conventional material specimens at any frequency tested. [Colour figure can be viewed at wileyonlinelibrary.com] TABLE 5 S–Ncurve values and associated statistics for fatigue life data of the conventional laminates at any frequency tested. Case study kmR 2 3bC and 7bC at any f1.0132 0.0731 0.9350 FIGURE 10 Fiber/matrix debonding in a 90layer. [Colour figure can be viewed at wileyonlinelibrary.com] 8S ´ ANCHEZ-CARMONA ET AL. 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License As Table 2summarizes, three different UD-90 laminates have been tested under cyclic loading, two of them are made of conventional prepreg (3bC and 7bC) and the other one of ultra-thin material. After checking that the previous effects (surface roughness, load frequency, and a scarce void content) are negligible for the fatigue life of UD-90 samples, the experimental data for conventional material (Figure 9) are going to be compared with the obtained for UT UD-90 samples (Figure 5). The conventional and ultra-thin materials employed are not composed of the same fibers and resin; hence, the S–Ncurves for both types of materials (conventional and ultra-thin) have also been plotted using the dimensionless stress level (divided by Y T ), Figure 11A. In this chart, it can be observed that the fatigue life of the UTP laminate has reached one order of magnitude higher at high cycle fatigue loading. It is worth mentioning that these results seem to be in accordance with the expected fact if both prepregs were made of the same fibers and resin. Specifically, according to the physically based explanation of the scale effect in composite laminates involving UTP prepregs, París et al., 28 the transverse damage is delayed when ultra-thin plies are involved. Furthermore, Figure 11B, represented as the maximum ultimate tensile stress versus the number of cycles, shows how the slope for conventional UD-90 samples is higher than for the ultra-thin ones, implying an improvement in the fatigue life of the ultra-thin UD-90 laminate. Additionally, the improvement of fatigue life may also be explained due to the different microstructure of the samples (Figure 12), discriminating between conventional and ultra-thin prepregs, and considering the different pattern for the appearance of transverse damage when ultra-thin plies are involved as París et al. 28 detailed. Whereas 3bC and 7bC have been manufactured using just 10 plies, 7bUT has been performed using 36 plies to achieve the same laminate thickness. This fact implies a different microstructure between laminates, showing more local resin-rich areas between plies in the 7bUT laminate. These resin-rich areas may act as barriers FIGURE 11 Comparison of S–Ncurves obtained: (A) S being the dimensionless maximum stress and (B) S being the maximum stress, for which the 95% confidence and prediction levels for conventional (Conv.) and ultra-thin (UTP) UD-90 laminate are shown. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 12 Microstructures at the same magnification for (A) 7bC and (B) 7bUT. [Colour figure can be viewed at wileyonlinelibrary.com] S ´ ANCHEZ-CARMONA ET AL.9 14602695, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ffe.13966 by University Of Padova Center Di, Wiley Online Library on [13/02/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Composite Structures 306 (2023) 116564 2 increases, also leading to the final fracture of the laminates. The first and the most relevant damage mechanism during the fatigue life of a cross-ply laminate is transverse cracking. This mechanism appears and evolves up to reaching a distinctive saturation level, which describes its characteristic damage state (CDS), a physical situation well defined in [30–31] and widely manifested in the previous studies from the different research groups. CDS is a unique and distinct situation for a given laminate in which each off-axis layer suffers damage up to reach a saturation level. CDS mainly depends on the laminate properties, including its stacking sequence, and it is the stable damage state which is formed prior to catastrophic failure. According to the observation of cross-ply laminates behaviour, no more additional transverse cracks (TCs) appear in the 90◦layers when CDS has been reached. In the first stages of the appearance of transverse damage when conventional thickness plies are involved (greater than 150 µm), only delamination traces are induced at the tip of transverse cracking close to the 0◦/90◦interfaces. Approximately at the same time as a laminate reaches its CDS, full delaminations between 0◦and 90◦layers start to appear, increasing considerably afterwards and thus implying a detrimental effect on the laminate mechanical performance. Finally, fibre breakage occurs in 0◦layers up to reaching the final failure of the specimens, i.e., reaching their fatigue life. During the last decades a special feature of the behaviour of composite materials, the scale effect, has attracted the attention of the scientific community. This phenomenon has always been related to the layer thicknesses reduction which has implied changes in the behaviour of the composite material. Many authors have attempted to provide an explanation for this phenomenon, from Parvizi et al. [32] and Flaggs and Kural [33] up to París et al. [34–35], among many others. In these recent publications [34–35], the scale effect has been physically explained based on the quasi-static damage mechanisms involved in failure, showing how the first damage occurring in the weakest lamina is less detrimental when decreasing its thickness and finding that the damage mechanism also changes as the thickness decreases. Furthermore, based on an energetic approach, the appearance of a progressive mechanism of damage in the case of ultra-thin plies versus an explosive mechanism of damage for thick plies is explained. According to this phenomenon but in connection with cyclic loads, some authors, such as Lafarie-Frenot and co-workers [5–9], have expounded that thinner 90◦plies in cross-ply composites improve their fatigue performance under certain conditions, naming this as size effect of the 90◦layer (using it as an alternative term for the scale effect). This improvement has mainly been analysed with conventional ply grammages, i.e., greater than 120 g/m 2 . Note that the term size effect can be also found in literature referring to a completely different phenomenon such as that accounting for the size of the coupons (see for instance, Zhu et al [36] for metals).To the best authors’ knowledge all the experimental studies related to the scale effect and composites laminates involving ultra-thin plies (UTPs), plies with grammages below 120 g/ m 2 , have been developed under quasi-static testing and only two studies, Sihn et al. [37] and K¨ otter et al.[38], have provided information about the scale effect under fatigue testing. In reference [37], undamaged and open-hole samples of CFRP unidirectional and quasi-isotropic laminates have been analysed, whereas in reference [38] undamaged and lowenergy impacted samples of CFRP quasi-isotropic laminates were tested. Both experimental works, the former by means of X-ray and the latter using computed tomography, have shown that fatigue performances improve as thinner layers are used. Particularly, important improvements are achieved in [38] under tension–compression fatigue loading (R=− 0.5, R being defined as the minimum applied stress divided by the maximum applied stress), matrix cracking and delaminations being significantly supressed. In addition to this, impactinduced delaminations do not spread in thin-ply layers under cyclic loading with R=− 0.5 ([38]); although reported for both studies, [37–38], the projected delaminations areas were larger after impact. Nevertheless, these two studies, [37–38], do not deal with the detail observation of damage mechanisms occurring at the micromechanical level and the damages densities evolution during fatigue load. The encouraging results about the scale effect and the appearance of UTPs have motivated the planning of the present experimental work, which consists in the observation of the fatigue damage mechanisms appearing in cross-ply laminates with the 90◦layer of both conventional and ultra-thin plies. It is worth highlighting that this investigation does not pursue a massive experimental testing program, instead the aim has been to microscopically evaluate the fatigue damage mechanisms in the most exhaustive way. The objective of the present work is to explore in detail which are the differences in the generation of the mechanisms of damage, if existent, that could lead to an explanation of the scale effect under tension–tension (T-T) fatigue loading in cross-ply laminates. 2. Experimental programmes In the search for an explanation of the scale effect under tensile quasistatic loading, París et al [34] performed an experimental programme to detect the appearance of the first damage in the 90◦layer for different cross-ply laminates, covering from conventional thicknesses of the 90◦ layer to ultra-thin ones. In the present work, in an attempt to follow a similar procedure, two different cross-ply laminates, [0 4 /90 3 /0 4 ] and [0 4 /90/0 4 ], have been selected to compare the onset and progress of damages under cyclic loading. In what follows, [0 4 /90 3 /0 4 ] (with 3 plies of 150 g/m 2 prepreg in the 90◦layer), is referred to as CP-450, and [0 4 / 90/0 4 ] (with a ply of 30 g/m 2 prepreg in the 90◦layer) as CP-30. 0◦plies are exactly the same in both laminates, using 150 g/m 2 prepreg. With the aim of investigating how scale effect alters the damage mechanisms under fatigue loading, it is important to know to which stress the 90◦layer is subjected in each laminate for the force levels selected for fatigue testing. The maximum stress of the 90◦layer for each laminate ( σ CP−450 22,max , σ CP−30 22,max) at each force level has been calculated using the Classical Lamination Theory (CLT). Analytical calculations both for CP-450 and CP-30 have been carried out using the thermo-elastic Fig. 1. Main damage mechanisms in cross-ply laminates under fatigue loading. S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 3 properties obtained experimentally from the quasi-static characterisation of the 150 g/m 2 and 30 g/m 2 prepregs, respectively [39]. Furthermore, it is interesting to point out that thermal stresses have also been taken into consideration during σ 22,max calculations. The thermal decrease after the curing process of composite laminates has an influence on their residual stress state, appearing at 3 different levels. First, the whole 90◦layer suffers a thermal residual stress due to the different thermal expansion coefficients of each layer at mesoscopic level as it is theoretically expounded, e.g., in Shokrieh M.M. [40]; these stresses can be calculated using the Classical Laminate Theory. Second, associated with the samples free-edge there exists a thermal stress along the thickness as Pagano et al. [41] showed. Third, the fibres and the matrix also have different thermal expansion coefficients so thermal residual stresses at micromechanical level arise as Correa et al. [42] detailed. Taking these influences into account the residual thermal contribution has been partially discarded for the σ 22,max selected for the discussion in the results section. The reasons for not considering the whole contribution of the thermal stresses have been the previous authors’ experiences, Barroso et al. [43], and a new study in which the thermal stresses relaxation has been experimentally analysed using the same materials than the present work in two different antisymmetric laminates [0 4 /90 4 ] (one fully manufactured with 100 g/m 2 prepreg and the other one with 30 g/m 2 prepreg). The noticeable difference between the two different prepregs is seen in Fig. 2, in which b1) shows the curvature radius of the laminate, R (cm), used to measure the thermal stress relaxation. In Fig. 3, this curvature radius versus the time after the curing process (h) is charted, showing the considerable relaxation, which is more marked for the ultra-thin prepreg CP-30. Based on these results, the thermal stresses considered have only been the 40% of those calculated by means of CLT. 2.1. Specimens’ preparation Both cross-ply laminates have been manufactured using carbon/ epoxy prepregs TP402/T700S from North Thin Ply Technology. Whereas all 0◦plies have been manufactured with the 150 g/m 2 prepreg for both cross-ply laminates and it has also been employed for the 90◦ plies in CP-450, the 30 g/m 2 prepreg has been used for the 90◦ply in CP- 30. These laminates have been manufactured by means of a hand lay-up in a clean room and cured in an autoclave using a vacuum bag. Once cured, glass–epoxy tabs have been bonded to both panel sides in the gripping zones and, afterwards, the panels have been cut by means of a water refrigerated diamond disc saw as recommended in ASTM D3039 [44]. The specimen dimensions are shown in Fig. 4, with L s =180 mm, w=25 mm and L t =55 mm. All coupons have been sanded and polished on their lateral free edge to be able to observe the damage by means of an optical microscope (exsitu inspections). Additionally, a replica system in the same lateral polished edge has been used in which the replica sample can be also observed in the optical microscope (in-situ inspections), combining them with ex-situ inspections. The sanding and polishing process is almost the most significant step during these experimental programmes because of the importance of Fig. 2. Measurement of the thermal stress relaxation using the curvature radius (R) for [0 4 /90 4 ] laminate manufactured with (a) 100 g/m 2 and (b) 30 g/m 2 . Figures a1) and b1) just after curing process, and a2) and b2) after 1030 h. Fig. 3. Curvature radius versus time after the curing process for [0 4 /90 4 ] fully manufactured with 100 g/m 2 and 30 g/m 2 . Fig. 4. Scheme of specimen and its dimensions. S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 4 detecting precisely the first damage that occurs in 90◦layer, in which inter-fibre/matrix cracks (debonds) can be involved, and thus dirtiness or certain marks could cast doubt on the experimental observations of the sample free edge after cyclic loading. With this issue in mind, a tailor-made device for the sanding and polishing process (Fig. 5) has been developed. This device assures that the specimen is kept in vertical position whereas the user can side-to- side move it manually (green arrow in Fig. 5.a), applying certain pressure in both sample ends (red circles in Fig. 5.a) while the sanding and polishing disc is rotating (blue arrow in Fig. 5.a). 2.2. Tests performance Before fatigue testing, five specimens from each laminate have been quasi-statically tested, obtaining their ultimate tensile force (F u ) and the apparent elastic modulus (E L ) (Table 1). These tests have been carried out in an Instron 4482 electromechanical testing machine, controlling the displacement at a speed of 1 mm/min. Dynamic tests have been carried out in an Instron 8802 hydraulic testing machine, controlling the load by means of a sinusoidal function with a force ratio R=0.1 (R being defined as the minimum applied force divided by the maximum applied force), using combined frequencies of Fig. 5. Tailor-made device to sand and polish carbon/epoxy samples: a) scheme and b) actual device. Table 1 Ultimate tensile force (F u ) and apparent elastic modulus (E L ) for CP-450 and CP- 30 laminates. CP-450 CP-30 Average SD CV Average SD CV F u (kN) 67.54 ±3.15 4.67 % 64.02 ±4.30 6.71% E L (GPa) 79.42 ±2.13 2.68% 95.21 ±5.55 5.83% S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 5 1 and 3 Hz. The different testing frequencies have been used to accelerate the number of cycles applied after 10 4 cycles, using a thermocouple to ensure that the specimen temperature increase during cyclic loading has been low and therefore, undesirable changes of the material behaviour have been avoided. Different force levels have been selected to perform fatigue testing, 0.6, 0.4, 0.3, 0.2 and 0.16 of their ultimate tensile force (F u ). Table 2 shows σ 22,max for each cross-ply laminate at each force level selected, first without considering thermal stresses and second taking the 40% of thermal stresses into account. Whereas the highest force level has been selected as a scenario in which transverse damage is going to be relevant from the first cycle, at least for CP-450 as it is known from literature, the lowest force level has been chosen as the situation in which the 90◦layer has a stress level below its transverse strength, which is around 30–35 MPa for the material used in the present work [39], in order to look at a more progressive appearance of transverse damage. 3. Results: Development of fatigue damage The experimental results of each cross-ply laminate have been analysed through the damage density ( ρ D ) versus the number of cycles, defining ρ D as the number of damages divided by a gauge length of 50 mm. 3.1. Typology of observed damages Prior to lay bare the observations carried out for the two cross-ply laminates under study, the nomenclature and description of the different damages encountered during the inspections (mainly for the novel CP-30) are going to be summarised in order to facilitate the understanding of their abbreviations: •Isolated Debond, named as ID, for a transverse debond that can take place either in an isolated fibre or in a non-isolated fibre but which neighbouring fibres have undamaged fibre/matrix interfaces, as is shown in Fig. 6.(a). •Isolated-Continued Debonds, named as I-CD, for certain transverse debonds that although forming a path, they have not kinked into the matrix. Thus, they are not connected, but some of them may correspond to touching fibres (Fig. 6.(b)). •Generalised Transverse Damage, named as GTD, for a path of transverse debonds that have not kinked but have progressed from one 0◦/90◦interface to the other, as can be seen in Fig. 6.(c), similarly to a TC for CP-450. •Longitudinal Debonds, named as LD, for a path of longitudinal/ horizontal debonds which appear indistinctly in any part of the 90◦ layer, both after the curing process and during fatigue testing (Fig. 7. (a)). •Delamination Trace, named as DT, which refers to longitudinal debonds induced at one extreme of a GTD or a TC close to the 0◦/90◦ interface. An example is illustrated in Fig. 7.(b). •Delamination, named as DL, for a separation of 0◦/90◦interface, as can be seen in Fig. 7.(c) for CP-30 or in Fig. 7.(d) for CP-450. It is worth highlighting that the large amount of damages inspections performed assures a uniform criterion. 3.2. Development of fatigue damage for CP-450 laminate Due to the fact that transverse cracking has been the main observed damage appearing for CP-450, Fig. 8 directly shows ρ TC (instead of ρ D in this case) versus the number of cycles for each force level tested. At two force levels two specimens (S1 and S2) have been tested in order to assure the repeatability of the experimental results. It is worth highlighting that the fatigue damage mechanisms for cross-ply laminates Table 2 Maximum transverse stress of the 90◦layer ( σ 22,max ) for CP-450 and CP-30 laminates at each force level tested. σ CP−450 22,max (MPa) σ CP−30 22,max (MPa) 0.6 F u [86.53, 96.51] [79.38, 87.80] 0.4 F u [57.68, 67.67] – 0.3 F u [43.26, 53.25] [39.69, 48.11] 0.2 F u – [26.46, 34.88] 0.16F u [23.07, 33.06] – Fig. 6. Types of damages involving transverse debonds in CP-30: (a) ID, (b) I-CD and (c) GTD. S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 6 with conventional layers are well-known and they are well-corroborated after checking the negligible scatter of the damage density trends in two tested samples. 3.2.1. Fatigue damage at the highest force level From the first cycle at 0.6F u , transverse cracking level seems to be close to its CDS, since ρ TC along the 90◦layer has only slightly increased up to 10 5 cycles, as observed in Fig. 9. Although incipient delaminations, DTs, have been detected since the first cycle, most TCs have shown delaminations, DLs, after 2⋅10 3 cycles approximately. 3.2.2. Fatigue damage at the intermediate force levels For these two force levels, 0.4 and 0.3F u , some TCs have appeared since the first cycle. However, the onset of the majority of the TCs up to reaching CDS have appeared between 10 2 and 10 5 cycles. At these force levels, DLs started to appear between 5⋅10 4 and 10 5 cycles, although DTs were almost detected from the appearance of TCs. 3.2.3. Fatigue damage at the lowest force level For 0.16F u no damage has appeared until 10 4 cycles. An I-CD, shown in Fig. 10, has been one of the three first damages observed at this number of cycles. Other I-CDs have appeared and grown in different parts of the 90◦ layer free edge. Three of them have evolved to a complete TC around 6⋅10 4 cycles. After this number of cycles, I-CDs and TCs have continued appearing and/or propagating up to 3⋅10 5 cycles when the number of I- CDs starts to decrease because many of them are evolving to TCs and the I-CDs appearance seems to be slowed down. This information is compiled in Fig. 11 where the density of I-CDs and TCs versus the number of cycles is shown for CP-450 at 0.16F u . At this force level, for CP-450 some DTs have been observed between 5⋅10 5 and 10 6 cycles, but DLs have never been observed at 10 6 cycles (the maximum number of cycles tested). 3.3. Development of fatigue damage for CP-30 laminate In this case, the appearance of damages has varied for the three force levels tested under cyclic loading. After each fatigue load increment, CP- 30 samples have been microscopically observed to capture the novel damages. From Table 3 to Table 6, the former types of damages defined are detailed carefully to understand how the existing damages either appear or evolve during the different fatigue load increments for each specimen tested. Note that each of these microscopic revisions takes between 1 and 6 h approximately; the minimum time is employed when the 90◦ply has no damage, for instance the six first stops for CP-30 sample at 0.2F u , and the maximum time is employed when the 90◦ply has a considerable quantity of several types of damages, for example the last stop for CP-30 sample at 0.6F u . Overall, after 47 inspections almost 8400 damages have been counted through these microscopic observations. It is important to highlight that these exhaustive microscopic revisions can not be performed automatically, as for instance proposed Glud et al. [45], due to the fact that there is a huge variety of fatigue damage appearance in the 90◦layer and moreover, debonds are not so marked as TCs in order to be directly identified by means of a damage detection software. For this laminate, two different types of charts have been represented to show the damage density while the specimens have been tested under fatigue loading. On the one hand, two charts for each force level tested are illustrated to show the onset evolution of each damage as described in the subsection 3.1 by means of ρ D versus the number of cycles: particularly, charts from Fig. 12 to Fig. 17. The purpose of these charts is to clarify the appearance for each detected damage and its evolution in order to understand how the fatigue damage mechanisms evolve when ultra-thin plies are involved. And, on the other hand, Fig. 18 directly shows ρ GTD versus the number of cycles for each force level tested with Fig. 7. Types of damages involving longitudinal debonds: (a) LD, (b) DT and (c) DL in CP-30, and (d) DL in CP-450 (replica image). Fig. 8. Transverse crack development ( ρ TC ) versus the number of cycles for CP- 450 (0.6F u, 0.4F u , 0.3F u and 0.16F u ). S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 7 the objective of comparing the main transverse damage, GTD, for each force level tested in this CP-30 laminate. It is worth highlighting that two specimens have been tested at one force level to evaluate the results representativeness which has been confirmed in view of the negligible scatter detected. Specifically, all damages trends have also been plotted in Figs. 14 and 15 for the specific force level observing that not only GTD Fig. 9. Microscopic observations in the specimen free edge tested at 0.6F u for CP-450: (a) at the first cycle (taken from replica), and (b) at 10 5 cycles (taken directly from sample). Fig. 10. I-CD observed in CP-450 at 0.16F u , going through a single ply of the 90◦layer. Fig. 11. I-CDs and TCs damage density ( ρ D ) versus the number of cycles at 0.16F u (CP-450). Table 3 Damages detected in the CP-30 sample at 0.6F u after each increment of cyclic load (N). N ID I-CD GTD LD DT DL Damages 1.0E+00 0 9 1 0 0 0 10 5.0E+00 0 12 8 0 0 0 20 2.0E+01 35 36 15 6 0 0 92 5.0E+01 48 52 38 13 9 0 160 3.0E+02 89 148 89 18 14 0 358 1.0E+03 161 187 147 26 57 0 578 3.0E+03 186 188 216 45 98 0 733 1.0E+04 137 146 286 51 220 5 845 1.5E+04 70 106 323 64 250 21 834 3.0E+04 33 59 362 98 302 34 888 6.0E+04 9 51 380 105 348 70 963 1.0E+05 5 48 385 107 360 89 994 Table 4 Damages detected in the S1 CP-30 sample at 0.3F u after each increment of cyclic load (N). N ID I-CD GTD LD DT DL Damages 1.0E+00 1 0 0 0 0 0 1 5.0E+00 1 1 0 0 0 0 2 2.0E+01 1 5 0 0 0 0 6 5.0E+01 1 6 0 0 0 0 7 1.0E+02 3 10 0 0 0 0 13 3.0E+02 6 12 0 0 0 0 18 1.0E+03 10 17 2 0 0 0 29 3.0E+03 24 36 5 0 0 0 65 2.0E+04 36 58 18 15 3 0 130 1.0E+05 13 81 41 39 6 2 182 S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 8 trends are similar, but also checking that all obtained trends correlate well. Since the representativeness of these novel results is an important issue, 6 additional samples (S2, S3 and S4 for 0.6F u , and S3, S4 and S5 for 0.3F u ) have been tested up to a very-high number of cycles to verify that the damages densities follow the provided trends and to check the low scatter of the results between specimens tested under the same loading conditions. The results are represented in Figs. 12, 13, 14 and 15 where the damage densities at 10 6 cycles have been plotted, leading to 3 additional points for each damage trend at each force level tested. The mean value of each set of 3 specimens has been linked to the single samples trends by means of dash lines. A soft continuity is observed between the results for 10 6 cycles and those associated with a lower number of cycles. 3.3.1. Fatigue damage at the highest force level At 0.6F u , as can be observed in Fig. 12, GTDs continue increasing after 10 3 cycles whereas IDs and I-CDs decrease substantially. These trends can be understood due to the fact that IDs and I-CDs evolve up to becoming GTDs. At the same time as GTDs increase significantly after 10 3 cycles, it can be seen in Fig. 13 how DTs start to evolve substantially Table 5 Damages detected in the S2 CP-30 sample at 0.3F u after each increment of cyclic load (N). N ID I-CD GTD LD DT DL Damages 1.0E+00 0 0 0 0 0 0 0 1.0E+02 0 6 0 0 0 0 6 1.0E+03 1 15 0 0 0 0 16 3.0E+03 1 20 2 0 0 0 23 1.0E+04 2 26 7 7 0 0 42 1.5E+04 7 37 11 18 2 0 75 3.0E+04 12 56 22 34 3 0 127 5.0E+04 9 64 24 37 3 0 137 7.0E+04 6 69 29 40 4 0 148 1.0E+05 4 78 38 43 5 1 169 Table 6 Damages detected in the CP-30 sample at 0.2F u after each increment of cyclic load (N). N ID I-CD GTD LD DT DL Damages 1.00E+00 0 0 0 0 0 0 0 5.00E+01 0 0 0 0 0 0 0 4.00E+02 0 0 0 0 0 0 0 3.00E+03 0 0 0 0 0 0 0 1.00E+04 0 0 0 0 0 0 0 3.00E+04 0 0 0 0 0 0 0 6.00E+04 0 4 0 0 0 0 0 1.00E+05 1 10 0 11 0 0 22 1.50E+05 8 24 2 22 0 0 56 3.00E+05 11 35 5 29 2 0 82 3.72E+05 12 43 6 36 2 0 99 4.50E+05 10 48 6 40 3 0 107 5.50E+05 8 50 7 44 3 0 112 7.00E+05 7 52 8 46 3 0 116 1.00E+06 3 54 10 46 4 0 117 Fig. 12. ID, I-CD and GTD damages density ( ρ D ) versus the number of cycles at 0.6F u (CP-30). Fig. 13. DT, DL and GTD damage density ( ρ D ) versus the number of cycles at 0.6F u (CP-30). Fig. 14. ID, I-CD and GTD damage densitiy ( ρ D ) versus the number of cycles at 0.3F u for the specimens tested (CP-30). Fig. 15. DT, DL and GTD damage density ( ρ D ) versus the number of cycles at 0.3F u for the specimens tested (CP-30). S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 9 too up to reaching almost the quantity of GTDs. During microscopic observations it has been observed that almost each GTD has one induced DT at least, which is in direct relation with the abrupt increase of DTs after 3⋅10 3 cycles. It is worth pointing out that some GTDs have kinked between 6⋅10 4 and 10 5 cycles at 0.6F u for CP-30 which seems to coincide with the GTD saturation level for this case. 3.3.2. Fatigue damage at the intermediate force level At 0.3F u , the main transverse damage appearing is I-CD without evolving enough to become GTD up to 10 5 cycles, Fig. 14. Hence, the number of GTDs is lower than the quantity of I-CDs up to the maximum number of cycles explored. As it can be seen in Fig. 15, the delamination damages (both DT and DL) are not relevant in the CP-30 samples up to 10 6 cycles. 3.3.3. Fatigue damage at the lowest force level At 0.2F u , the CP-30 sample was tested up to 10 5 cycles; however, the quantity of damage was so negligible that it was decided to test the CP- 30 specimen up to 10 6 cycles in order to observe at least a minimum damage evolution, Fig. 16. Nevertheless, not all types of damage introduced in Section 3.1 have been observed in the CP-30 sample. It is worth highlighting that only 10 GTDs have been found up to 10 6 cycles and very few DTs have been found whereas no DL has appeared, Fig. 17. 4. Discussion about the influence of ultra-thin 90◦layer thickness Taking into consideration experimental results obtained after fatigue testing of carbon/epoxy cross-ply laminates involving conventional and ultra-thin plies for the 90◦layer, both study cases can be compared to analyse how fatigue damage mechanisms change due to the decrease of the 90◦layer thickness. Due to the fact that the transverse damage density of the 90◦layer for each laminate does not reach the same CDS, their transverse damage densities are going to be scaled regarding their 90◦layer thicknesses with the aim of referring each density to their geometric transverse damage saturation. Hence, ρ * is defined as the transverse damage density of 90◦layer for each laminate multiplied by its thickness, i.e., ρ *= ρ D*t90◦, where ρ D is the transverse damage density of the 90◦layer for a specific cross-ply laminate at each stop carried out after fatigue testing and t90◦is the 90◦layer thickness of this laminate. This comparison can be performed in terms of the same either force level or stress level in the 90◦layer. In order to compare both cases, the main transverse damage for each laminate needs to be charted. In other words, TC has been selected for CP-450 whereas GTD has been chosen for CP-30. The authors have decided to maintain the differentiation to highlight the importance of finding different damages for each laminate. The most direct comparison comes from Fig. 19, where the scaled transverse damage density has been compared at two different force levels tested, 0.6F u and 0.3F u , for each laminate. And the other comparison can be performed discussing the results presented in Fig. 20, where two different force levels have been charted together as both cases lead to a similar stress level in the 90◦layer (~30 MPa). In this case, σ 22,max is either below (if the thermal stresses are Fig. 16. ID, I-CD and GTD damage densitiy ( ρ D ) versus the number of cycles at 0.2F u (CP-30). Fig. 17. DT, DL and GTD damage density ( ρ D ) versus the number of cycles at 0.2F u (CP-30). Fig. 18. GTD damage density ( ρ GTD ) versus the number of cycles for 0.6F u, 0.3F u and 0.2F u (CP30). Fig. 19. Comparison between the TC (CP-450) and GTD (CP-30) scaled damage densities ( ρ *) at two tested force levels. S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 10 neglected for CLT calculations) or approximately equal to the material transverse strength (if the residual thermal stresses are partially considered for CLT calculations). 4.1. Considerations on transverse damages It is worth pointing out that a damage mechanism change has been found for each force level tested when the 90◦layer thickness has decreased. First, the main transverse damage in the 90◦layer for CP-30 is GTD instead of TC as occurs for CP-450, as it is detailed using the energetic approach in París et al [34–35]: when the first ID can appear, CP-450 has the sufficient energy to directly produce a complete TC, whereas CP-30 has not enough energy to produce a complete transverse damage, mainly showing IDs or I-CDs up to become GTDs without reaching the whole 90◦layer. And, second, a relevant delay of transverse damage appearance has been found when the 90◦layer has an ultra-thin thickness. Whereas CP-450 shows the onset of conventional transverse cracks (TCs) and their subsequent density increases along its free edge (as it is well reported in literature and it has been obtained in this work), CP-30 shows an evolution of different forms of transverse damages up to evolving to generalised transverse damages (GTDs). In other words, the onset and progress of transverse damage in CP-30 seems to be more progressive, starting as isolated debonds (IDs) and/or isolatedcontinued debonds (I-CDs) up to becoming GTDs, without evolving to a full TC as it could be expected. This second relevant point is a direct consequence of the physical explanation of the scale effect previously provided by París et al [34–35]. It is important to highlight two relevant facts: only 10 GTDs have been detected for CP-30 at 0.2F u appearing between 10 5 and 10 6 cycles, and few GTDs have kinked from 6⋅10 4 to 10 5 cycles when the GTD level started to saturate, keeping almost constant up to 10 6 cycles. It is worth pointing out that I-CDs have been detected for CP-450 at 0.2F u , although their evolution to TCs has been less progressive and much faster than for CP-30. This conclusion is deduced from both comparisons, in terms of either force or stress level. Neither CP-450 nor CP-30 at the lowest force level tested have shown any type of damage up to either 10 4 or 6⋅10 4 cycles, respectively. This fact seems to corroborate the non-consideration of the whole residual thermal stresses during CLT calculations. Once the σ 22,max reaches the material transverse strength, Y T , the 90◦layer must show some transverse damage. In this specific case, the samples tested at σ 22,max ≈Y T have not presented any transverse damage after a high number of load cycles. Hence, this absence of transverse damage would be incoherent if this σ 22,max actually present were even higher considering the total thermal stresses. 4.2. Considerations on longitudinal damages Focusing on the longitudinal damage in 90◦layer (LD), it is important to highlight that the number of LDs is remarkable in relation to the number of GTDs; nevertheless, LDs seem not to be induced by transverse damage so its profound analysis will be performed separately in an ongoing publication. Finally, delaminations are clearly delayed, or seem to be even supressed, when the 90◦layer has an ultra-thin thickness. Whereas full delaminations appear in a considerable number for CP-450 after TCs reach CDS, just a few shorts DLs (that indicate the appearance of future full delaminations) have been detected for CP-30 (even at the highest force level tested when its GTD level starts to saturate). 5. Conclusions Specimens from two carbon/epoxy cross-ply laminates: [0 4 /90 3 /0 4 ] (named as CP-450 and manufactured from 150 g/m 2 prepreg) and [0 4 / 90/0 4 ] (named as CP-30 and manufactured from a 30 g/m 2 prepreg for the 90◦layer and a 150 g/m 2 for the 0◦layers) have been tested under T- T cyclic loading at different force levels (0.6, 0.4, 0.3, 0.2 and 0.16 of their ultimate tensile force, F u ). The study has focused on the exhaustive experimental microscopic observations of the fatigue damage appearing in each laminate, mainly centring on the differences encountered in the damages detected in the 90◦layer as the thickness decreases. The most highlighting fact is the noticeable difference of fatigue damage appearance detected between CP-450 and CP-30. First, the most relevant result is the inexistence of a full conventional TC for CP-30 at any of the force levels tested, GTD being the greatest transverse damage observed. And second, the appearance of transverse damage is more progressive when the 90◦layer thickness decreases (as has been detailed with the appearance of IDs and I-CDs evolving to GTDs for CP-30), a fact related to the delay encountered for the transverse damages, observing even the suppression of delaminations. The onset of the comparable transverse damage (TCs for CP-450 vs GTDs for CP-30) seems to slightly delay when the 90◦layers stress is the same. Nevertheless, the appearance of the first transverse damage in each laminate, I-CD, is produced approximately at the same number of cycles when the 90◦layer has the same stress level, as it could be deduced from París et al. [34–35]. The results obtained have led to conclude that transverse damage has substantially decreased for CP-30 in comparison with CP-450 and, consequently, the next expected damage (delaminations) changes its pattern too. Therefore, the present results show that a scale effect, concerning the appearance of the damage mechanisms in cross-ply laminate under fatigue loading, exists. The effect identified in the actual investigation, after observing mainly the first damage mechanism which appear, can be understood with the physically based explanation about the phenomenon called scale effect, profoundly studied under quasistaticloading as it is expounded in [34–35]. More experimental tests involving intermediate thicknesses and analysing the subsequent damage mechanisms, particularly focusing on delaminations, need to be performed to completely define the extension of the scale effect under fatigue loading. Fig. 20. Comparison between the TC (CP-450) and GTD (CP-30) scaled damage densities ( ρ *) at the same 90◦layer stress level. S. S´ anchez-Carmona et al. Composite Structures 306 (2023) 116564 11 6. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. CRediT authorship contribution statement Serafín S´ anchez-Carmona: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Data curation, Writing – original draft. Elena Correa: Conceptualization, Validation, Resources, Supervision, Writing – review & editing, Funding acquisition. Alberto Barroso: Conceptualization, Resources, Validation, Supervision, Writing – review & editing. Federico París: Supervision, Writing – review & editing, Funding acquisition. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability The authors are unable or have chosen not to specify which data has been used. Acknowledgements This work was supported by the Universidad de Sevilla [grant number VIPPIT-2018-II.2] and Consejería de Economía y Conocimiento Junta de Andalucía [project number P18-FR-3360] corresponding to the I+D+I Programa Operativo FEDER 2014-2020. The authors would rather appreciate to Dr. Jesús Justo Estebaranz and Dr. María Luisa Velasco L´ opez for their advice during the definition of fatigue tests and microscopic observations, respectively, and to Mr. Roberto Prieto García for his collaboration in some experimental tasks. References [1] Hahn HT, Lorenzo L. Fatigue failure mechanisms in composite laminates. International Congress on Fracture (ICF) 1984. https://doi.org/10.1016/b978-1- 4832-8440-8.50041-7. [2] Berthelot J-M. Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: Static and fatigue loading. Appl Mech Rev Jan. 2003;56(1):111–47. https://doi.org/10.1115/1.1519557. [3] Harris B. Fatigue in composites. Woodhead Publishing 2003. https://doi.org/ 10.1533/9781855738577. [4] Bathias C. An engineering point of view about fatigue of polymer matrix composite materials. Int J Fatigue 2006;vol. 28, no. 10 SPEC. ISS:1094–9. https://doi.org/ 10.1016/j.ijfatigue.2006.02.008. [5] Lafarie-Frenot MC, Henaff-Gardin C. Formation and growth of 90◦ply fatigue cracks in carbon/epoxy laminates. Compos Sci Technol 1991;40(3):307–24. https://doi.org/10.1016/0266-3538(91)90087-6. [6] Henaff-Gardin C, Lafarie-Frenot MC, Brillaud J, El Mahi A. Influence of the stacking sequence on fatigue transverse ply cracking in cross-ply laminates. Damage Detect Compos Mater 1992;1128:236–55. [7] Lafarie-Frenot MC, Henaff-Gardin C, Gamby D. Matrix cracking induced by cyclic ply stresses in composite laminates. Compos Sci Technol 2001;61(15):2327–36. https://doi.org/10.1016/S0266-3538(01)00125-7. [8] Gamby D, Henaff-Gardin C, Lafarie-Frenot MC. Propagation of edge cracking towards the centre of laminated composite plates subjected to fatigue loading. Compos Struct 2002;56(2):183–90. https://doi.org/10.1016/S0263-8223(02) 00004-1. [9] Foti F, Gigliotti M, Pannier Y, Mellier D, Lafarie-Frenot MC. The effect of the environment on high temperature fatigue of cross-ply C/epoxy laminated composites. Compos Struct 2018;202(April):924–34. https://doi.org/10.1016/j. compstruct.2018.04.065. [10] Takeda N, Ogihara S, Kobayashi A. Microscopic fatigue damage progress in CFRP cross-ply laminates. Composites 1995;26(12):859–67. https://doi.org/10.1016/ 0010-4361(95)90879-5. [11] Kobayashi S, Takeda N. Experimental and analytical characterization of transverse cracking behavior in carbon/bismaleimide cross-ply laminates under mechanical fatigue loading. Compos B Eng 2002;33(6):471–8. https://doi.org/10.1016/ S1359-8368(02)00028-8. [12] El Mahi A, Berthelot JM, Brillaud J. Stiffness reduction and energy release rate of cross-ply laminates during fatigue tests. Compos Struct 1995;30(2):123–30. https://doi.org/10.1016/0263-8223(94)00061-1. [13] Yokozeki T, Aoki T, Ishikawa T. Fatigue growth of matrix cracks in the transverse direction of CFRP laminates. Compos Sci Technol 2002;62(9):1223–9. https://doi. org/10.1016/S0266-3538(02)00068-4. [14] Tohgo K, Nakagawa S, Kageyama K. Fatigue behavior of CFRP cross-ply laminates under on-axis and off-axis cyclic loading. Int J Fatigue 2006;vol. 28, no. 10 SPEC. ISS:1254–62. https://doi.org/10.1016/j.ijfatigue.2006.02.011. [15] Taheri-Behrooz F, Shokrieh MM, Lessard LB. Residual stiffness in cross-ply laminates subjected to cyclic loading. Compos Struct 2008;85(3):205–12. https:// doi.org/10.1016/j.compstruct.2007.10.025. [16] Hosoi A, Kurihara K, Sato N, Kawada H. Prediction of first transverse crack formation in cross-ply CFRP laminates under fatigue loading. In: 8th Asian- Australasian Conference on Composite Materials 2012, ACCM 2012 - Composites, Kuala Lumpur, Malaysia; 2012. p. 173–8. [17] Amacher R, Cugnoni J, Botsis J, Sorensen L, Smith W, Dransfeld C. Thin ply composites: experimental characterization and modeling of size-effects. Compos Sci Technol 2014;101:121–32. https://doi.org/10.1016/j. compscitech.2014.06.027. [18] Shen H, Yao W, Qi W, Zong J. Experimental investigation on damage evolution in cross-ply laminates subjected to quasi-static and fatigue loading. Compos B Eng 2017;120:10–26. https://doi.org/10.1016/j.compositesb.2017.02.033. [19] Carraro PA, Maragoni L, Quaresimin M. Prediction of the crack density evolution in multidirectional laminates under fatigue loadings. Compos Sci Technol 2017;145 (October):24–39. https://doi.org/10.1016/j.compscitech.2017.03.013. [20] Carraro PA, Maragoni L, Quaresimin M. Characterisation and analysis of transverse crack-induced delamination in cross-ply composite laminates under fatigue loadings. Int J Fatigue 2019;vol. 129, no. August:105217. https://doi.org/ 10.1016/j.ijfatigue.2019.105217. [21] Corbetta M, Sbarufatti C, Giglio M, Saxena A, Goebel K. A Bayesian framework for fatigue life prediction of composite laminates under co-existing matrix cracks and delamination. Compos Struct 2018;187:58–70. [22] Tong J, Guild FJ, Ogin SL, Smith PA. On matrix crack growth in quasi-isotropic laminates - I. Experimental investigation. Compos Sci Technol 1997;57(11): 1527–35. https://doi.org/10.1016/S0266-3538(97)00080-8. [23] Takeda N, Kobayashi S, Ogihara S, Kobayashi A. Effects of toughened interlaminar layers on fatigue damage progress in quasi-isotropic CFRP laminates. Int J Fatigue 1999;21(3):235–42. https://doi.org/10.1016/S0142-1123(98)00072-3. [24] Hosoi A, Sato N, Kusumoto Y, Fujiwara K, Kawada H. High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 8 cycles (Initiation and propagation of delamination considering interaction with transverse cracks). Int J Fatigue 2010;32(1):29–36. https://doi.org/10.1016/j.ijfatigue.2009.02.028. [25] Just G, Koch I, Brod M, Jansen E, Gude M, Rolfes R. Influence of reversed fatigue loading on damage evolution of cross-ply carbon fibre composites. Materials 2019; 12(7):1–21. https://doi.org/10.3390/ma12071153. [26] Ben Kahla H, Varna J, Pupurs A. Microcracking in layers of composite laminates in cyclic loading with tensile transverse stress component in layers. In: 20th International Conferences on Composite Materials, ICCM - 20; 2015, no. July, pp. 19–24. [27] Carraro PA, Quaresimin M. Fatigue damage and stiffness evolution in composite laminates: A damage-based framework. Procedia Eng 2018;213(2017):17–24. https://doi.org/10.1016/j.proeng.2018.02.003. [28] Ben Kahla H, Ayadi Z, Edgren F, Pupurs A, Varna J. Statistical model for initiation governed intralaminar cracking in composite laminates during tensile quasi-static and cyclic tests. Int J Fatigue 2018;116(January):1–12. https://doi.org/10.1016/j. ijfatigue.2018.05.030. [29] Tohgo K, Nakagawa S, Araki H. Damage behavior and life prediction in CFRP crossply laminates under fatigue loading. Nihon Kikai Gakkai Ronbunshu, A Hen/ Transactions of the Japan Society of Mechanical Engineers, Part A 2006;72(7): 1041–8. https://doi.org/10.1299/kikaia.72.1041. [30] Reifsnider KL, Talug A. Analysis of fatigue damage in composite laminates. Int J Fatigue 1980;2(1):3–11. https://doi.org/10.1016/0142-1123(80)90022-5. [31] Li C, Ellyin F, Wharmby A. A damage meso-mechanical approach to fatigue failure prediction of cross-ply laminate composites. Int J Fatigue 2002;24(2–4):429–35. https://doi.org/10.1016/S0142-1123(01)00098-6. [32] Parvizi A, Garrett KW, Bailey JE. Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates. J Mater Sci 1978;13(1):195–201. https://doi.org/ 10.1007/BF00739291. [33] Flaggs DL, Kural MH. Experimental Determination of the In Situ Transverse Lamina Strength in Graphite/Epoxy Laminates. J Compos Mater Mar. 1982;16(2):103–16. https://doi.org/10.1177/002199838201600203. [34] París F, Velasco ML, Correa E. The scale effect in composites: An explanation physically based on the different mechanisms of damage involved in failure. Compos Struct Feb. 2021;257:113089. https://doi.org/10.1016/j. compstruct.2020.113089. [35] París F, Velasco ML, Correa E. Chapter 9: Modelling fibre–matrix interface debonding and matrix cracking in composite laminates. In: Multi-Scale Continuum Mechanics Modelling of Fibre-Reinforced Polymer Composites. Elsevier; 2021. p. 243–74. [36] Zhu S-P, Ai Y, Liao D, Correia JAFO, De Jesus AMP, Wang Q. Recent advances on size effect in metal fatigue under defects: a review. Int J Fract 2022;234(1):21–43. https://doi.org/10.1007/s10704-021-00526-x. [37] Sihn S, Kim RY, Kawabe K, Tsai SW. Experimental studies of thin-ply laminated composites. Compos Sci Technol 2007;67(6):996–1008. https://doi.org/10.1016/ j.compscitech.2006.06.008. S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 4 detailed in a previous work of the authors [26]. Fig. 3 shows, as an example, the σ yy component (in MPa) for the cross-ply laminate under axial extension u z >0 (values corresponding to a longitudinal ε zz =0.645%). As mentioned above, due to the existence of three symmetry planes, only a quarter part of the 2D transverse problem (the cross-section of the sample) is modelled, as depicted in Fig. 2c. Hence, only the top 0◦layer and half thickness of the 90◦layer are included in the analysis. The bottom and right sides of the model have symmetry boundary conditions. Fig. 3a shows the modelled geometry and illustrates that edge-effect only affects a characteristic distance (in the width direction) of the order of the laminate thickness. Fig. 3b shows the same stress component plot, but σ yy contour values range has been conveniently chosen to clearly see how the presence of tensions at the free-edge, generates slight compression values inside the sample, to fulfil global equilibrium in the vertical direction. The role of these σ yy tensile stresses at the edge will be analyzed later as the responsible for longitudinal cracking in the 90◦layer. Finally, Fig. 3c illustrates (by means of three different model magnifications) a more local stress alteration, in the neighbourhood of the bimaterial corner, where assuming linear elasticity, unbounded stresses appear (stress singularity). Results in Fig. 3c have been obtained with a mesh refinement towards the bimaterial corner tip, where the smallest element size is 10 −6 mm long. The edge effect and the stress singularity are phenomena which necessarily appear together, each one of them having a different influence (in terms of characteristic length) on the stress field. As can be clearly observed in Fig. 3c, the stress field (in the left-hand side of Fig. 3c) shows an alteration (edge-effect) all along the thickness length at the free edge, whereas the stress field associated with the bimaterial corner singularity (in the right-hand side of Fig. 3c) corresponds to a more local stress alteration, only in the neighbourhood of the bimaterial corner. Due to the intrinsic difficulty in analysing the stress singularity field, it will be studied in a separate section. 3. Stress singularity of the 0/90 bimaterial corner As mentioned previously in Section 2, stresses are unbounded at those points where material properties, geometry, and/or boundary conditions change abruptly. Obviously, unbounded stresses do not take place in a real specimen, and these stress singularities arise under the assumption of a linear elastic behaviour. Nevertheless, it is widely accepted that the singularity stress representation (in terms of Generalized Stress Intensity Factors and the order of stress singularities) are useful to predict failure initiation or propagation, based on generalized fracture toughness values instead of strength values. Considering a polar coordinate system (r,θ) at the bimaterial corner, and assuming variable separation, the singularity stress field in the neighbourhood of the corner takes the following form of asymptotic series (for r→0) (see [17,18] for further information): σ ij(r,θ) = ∑ k Kkr−δkf(k) ij (θ)(1) where K k is the Generalized Stress Intensity Factor of mode k, δ k is the corresponding order of stress singularity (0 <Re[δ k ] <1) and f(k) ij (θ)is the corresponding characteristic angular shape function. As will be seen later on, the stress singularity in the bimaterial corner, at the intersection of the interface between 0◦and 90◦layers and the free edge, has only one singular term in the stress representation (1), with δ k <0.5, representing a weak singularity. This term affects the characteristic distance where the singularity stress field acts. However due to the fact that the thickness of the ultra-thin plies is very low, it is necessary to try to elucidate whether the singularity affects the whole 90◦layer thickness. Slight geometrical changes at the corner tip, which consist in the modification of the solid wedge angle, allow the stress singularity to be removed, as already done in previous works by the authors (Barroso et al. [6,15]). The same strategy of singularity removal has been carried out in the present work, in order to separate both effects (edge effect and stress singularity) and to check the influence of each one in the zone of interest. The results of such stress singularity removal will be detailed at the end of this section. Moriya & Ichikawa [16] already proposed slight geometrical modifications of the ply solid angles at the free edge, to remove (or to reduce) the stress singularities appearing at the bimaterial corners between plies at the free-edge of the samples. With straight edges at the lateral faces, solid wedge angles for each material are equal to 90◦. The authors in Ref. [16] modified these wedge angles and evaluated the stress singularities for different material systems (high modulus graphite/epoxy, typical graphite/epoxy and typical glass/polyester). The orders of stress singularities (assuming singularities of the power type r δ , with −1<Re [δ]<0) were calculated in Ref. [16] assuming a 2D generalized plane strain state, with stress-free faces and perfect bonding between both materials. For checking purposes, the authors of the present work carried out the singularity analysis of the problem considered in Ref. [16], and have obtained the same results as those published in (Tables 2, 3 and 4 of Ref. [16]), by using their own semi-analytical procedure (Barroso et al. [17], and Mantiˇ c et al. [18]), which was developed for generalized plane strain problems (with ε zz =0). Nevertheless, the actual problem has ε zz ∕=0, and the equivalence, in terms of singularity results, with the ε zz = 0 problem is not straightforward. The tool developed by the authors [17,18] is based on the powerful Stroh formalism [25] of anisotropic elasticity assuming generalized plane strain problems with u i =u i (x 1 , x 2 ) (i =1, 2, 3). Stress singularities are obtained semianalytically as the roots of a characteristic equation which depends on the material properties, local geometry, and local boundary conditions of the corner configuration. The whole procedure is analytic except the search of roots of the characteristic equation, which is carried out numerically. Real and complex orders of stress singularities can be obtained. Only stress singularity orders (δ) in a power type structure r δ can be taken into account in the code developed. To understand this issue, the problem will be separated into two simpler problems, using Eshelby’s imaginary cut, deform and bond again procedure [19]. Let us move from the original problem of two bonded layers subjected to an axial extension ε zz >0 (Fig. 4a), to an alternative problem with each material isolated, no bonding between them (Fig. 4b). If we apply the prescribed ε zz >0 to both materials, both will elongate the same in the z-direction, but with different σ zz values (Fig. 4c), according to the differences in their Young moduli in this direction (E 11 for the 0◦layer, and E 22 for the 90◦layer). Due to the different values of the Poisson ratio for each ply, the transverse contraction ( ε xx <0) will also be different for each layer (Fig. 4c), higher for the 0◦layer and much lower for the 90◦layer, due to the fibre orientation in the 90◦layer (parallel to the x-direction). Let us now apply a uniform tensile loading, only to the 0◦layer, in the x-direction σ xx (Fig. 4d), but now, under plane strain conditions ( ε zz =0) which implies that the length in the z-direction does not change for this layer, and the corresponding ε zz component which should have appeared due to σ xx (and consequently, ε xx ) is zero. This generates an additional σ zz component (only in the loaded 0◦layer) associated with the plane strain solution of the problem. The value of the applied σ xx is the necessary one to make the final length of the 0◦ply, in the x-direc- tion, to be equal to the length of the already deformed 90◦layer in the same direction (Fig. 4e). In this situation, where both lengths (in the xdirection) are the same, we can bond again the materials, without any additional stress needed (Fig. 4f). At this point (Fig. 4f), stresses in both materials are uniform in the whole volume of each layer: S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 5 σ 0 ij = ⎛ ⎜ ⎜ ⎝ σ xx 0 0 0 0 0 0 0 σ 0 zz( ε zz) + σ 0 zz( σ xx) ⎞ ⎟ ⎟ ⎠ , σ 90 ij = ⎛ ⎜ ⎜ ⎝ 0 0 0 0 0 0 0 0 σ 90 zz ( ε zz) ⎞ ⎟ ⎟ ⎠ (2) where: σ 0 zz( ε zz) = ε zzE11 is the stress generated in the 0◦layer by the global ε zz and the longitudinal stiffness of the material E11, σ 0 zz( σ xx) = ε zz( σ xx)E11 = σ xx ν 31 E33 E11 is the stress generated, in the plane strain problem, associated with the σ xx >0⟹ ε xx = σ xx E33 ⇒ ε zz = ε xx ν 31 in the 0◦ply with the longitudinal stiffness of the 0◦ply E11 (the fibre orientation being parallel to the z-axis), and σ 90 zz ( ε zz) = ε zzE22 is the stress generated at the 90◦ply by the global ε zz with the transverse stiffness of the material E22. The problem depicted in Fig. 4f (repeated in Fig. 5a) is similar to the one under analysis, with a prescribed ε zz >0 in both materials, except that there is an additional uniform stress σ xx applied at the lateral faces of the 0◦layer. Let us remember that the stress solution to this problem is uniform in both materials. Now, if we just add to this problem (Fig. 5a), with a known uniform stress solution, another problem with the same geometry, with the materials being bonded together, and with a compression σ xx in the same lateral faces of the 0◦layer (Fig. 5b), assuming ε zz =0, the resulting problem would be the desired one under analysis. It is important to notice that, at the stage illustrated in Fig. 4c, there exists more than one alternative to fulfil the interface displacement compatibility of both solids. For example, instead of applying a σ xx >0 in the 0◦layer, it is also possible to apply a σ xx <0 in the 90◦layer, or a particular σ yy compression at the top surface of the 0◦ply and at the bottom surface of the 90◦ply. In this last alternative, the different Poisson ratio ν xy in both materials would generate different ε xx values, much lower in the 90◦layer, as the fibre is oriented in the x-direction. For these three particular solutions there is a value of the applied stress which makes compatible the displacements on both plies along the common interface of the plies. These alternative ways of facing the original problem also show two important ideas. •The first, and most important, is that the real problem (with ε zz >0) has the same solution, in term of stress singularities, as the additional problem (Fig. 5b), assuming ε zz =0, based on the evidence that the real problem is the superposition of a problem without stress singularities ( σ ij is uniform in each ply) (Fig. 5a) and another one which is solved in plane strain, ε zz =0 (Fig. 5b). •The second idea is that, although both problems (real and alternative) are equivalent in terms of stress singularities, but the alternative one giving rise to a problem with no stress-free lateral faces (Fig. 5b–c), this issue is associated with the selection of a particular solution of the problem. Let us remind that there is, one alternative particular solution to guarantee the displacements compatibility of both plies along the common interface, mentioned above (applying a σ yy <0) which does not introduce loaded lateral faces in the corner problem. Then, the assumption of stress-free lateral faces made in Ref. [16] does not violate the equivalence, and stress singularities calculated assuming ( ε zz =0) are the same than in the real (with ε zz >0) and alternative (with ε zz =0) problems. It is also important to notice that the situation is completely analogous if, instead of prescribing a ε zz >0 to both materials, we apply a Fig. 4. Decomposition of the original problem. Fig. 5. Superposition of the (a) alternative problem with a uniform stress solution, (b) additional problem (with ε zz =0) to get the original configuration, and (c) detail of the loaded bimaterial corner. S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 6 temperature decrement to both materials. The differences in the thermal expansion coefficients, parallel and perpendicular to the fibre direction respectively, will generate different elongations between both plies, in the x-direction, as previously shown in Fig. 4c under mechanical loadings. Notice also that results in Ref. [16] were obtained under the assumption of a power law r δ for the stress singularity field. This assumption does not agree with the necessary presence of a logarithmic term in the singular stress field predicted by Zwiers et al. [20] for some particular cases of the problem under analysis. Following the results in Ref. [20], the original corner configuration, with two solid wedges of 90◦(one for the 0◦layer and the other one for the 90◦layer) does not need the logarithmic term for the correct asymptotic stress representation, and the stress singularity order δ in a power type structure r δ has been proven to coincide between the numerical model and the semianalytical tool developed by the present authors [17]. Nevertheless, corners configurations with solid wedge angles different from 90◦(in any of the two layers) do not fulfil the condition to have just an r δ term, the presence of an additional ln(r) term being necessary. For the problem under analysis, a finite element model (similar to that used in Fig. 3 but including a notch at the bimaterial corner) has been prepared, with a mesh refinement towards the bimaterial corner tip, with the smallest element size of 10 −6 mm. The solid angle α of the 0◦layer has been progressively reduced (from the starting value of 90◦) using a circular notch in the 0◦layer, containing the corner tip. The σ yy stress component is plotted along the interface between both plies (Fig. 6), in which the x-axis is in the logarithmic scale. The results indicate that for a solid angle of α ≈55◦the stress singularity vanishes (the slope of the stress representation is horizontal). The notch slightly modifies the geometry of the problem (see detail in Fig. 6) but allows to isolate the edge effect and to quantify it separately from the singular stress source. In fact, the different results in Fig. 6 seems to indicate that the extent of the singular stress field (the length that is affected by the presence of the singularity) is below 10 −2 mm, one sixth of the lowest thickness of the thinnest layer under analysis, which is 0.06 mm (for the 30 g/m 2 ply). Once the influence (characteristic distance) of the stress singularity has been obtained, in the next section, numerical analyses will be carried out without the presence of the notch, to avoid in the stress field, the “pollution” of the geometrical modification. Obviously, results in the close neighbourhood of the corner vertex will be not taken into account for discussions. The relatively low value of the order of stress singularity (weak singularity) makes the influence of the singularity stress field to be low enough. 4. Numerical results Two aspects are investigated in this section: the edge-effect associated with the mechanical loading, and the edge-effect associated with the thermal expansion coefficient mismatch. As previously mentioned, the former one is due to the differences in the Poisson ratio of both plies when subjected to a same longitudinal strain ( ε zz >0), whereas the latter corresponds to different values of the thermal expansion coefficients (in the x-direction) when subjected to the same temperature decrement (cooling stage in the curing cycle). Both effects have been analyzed separately because, while the mechanical effect is a direct consequence of the Poisson’s ratio values, the thermal effect offers, at least, more uncertainties about the real values of the residual stresses developed in this cooling stage. There are several factors that may affect the full development of a thermal stress field associated with a nominal temperature decrement and a thermal expansion coefficient mismatch. Viscoelastic behaviour can take place in the first stage of the cooling period and stress relaxation can also take place (with time), as clearly shown by the authors, for the materials under study, as will be seen later on. See also [21,22] for other aspects influencing the potential residual stress field due to temperature. Mechanical properties and thermal expansion coefficients have been experimentally obtained for all materials by the authors (see, for example, Sanchez-Carmona et al. [23] with thermo-mechanical characterization of 30 g/m 2 and 150 g/m 2 plies). Due to the low differences of the mechanical properties obtained for the different materials, and with the aim of avoiding influences other than the role of the thickness itself, average values have been used for the present analyses. These properties, in orthotropic axes, are summarized in Table 1, where “1” is the fibre direction. Y t is the transverse strength of the material, which is of major importance in the longitudinal failure under analysis. It is important to notice that all numerical models consider all plies as equivalent orthotropic homogenous materials. The adequacy of considering the 90 ply as a heterogeneous or homogeneous material, depend on the object of the study, and in the present case, no particular interest is focused on any micromechanical aspect (at the level of fiber and matrix) of the failure. Nevertheless, only average values across the thickness having been used for reasoning and predictions, no stress-at-a-point has been used for these purposes. Also, for comparison purposes, all numerical models have been analyzed under this assumption. Notice that the obtained value for α 1 is unusually large, in comparison with other long unidirectional carbon fiber materials. The Coefficient of Thermal Expansion in the fiber direction ( α 1 ) is usually negative for long unidirectional carbon fiber materials, but the values are typically one order of magnitude lower than the values in the transversal directions ( α 2 , α 3 ). As ( α 1 , α 2 , α 3 ) have been obtained in a single test, and ( α 2 , α 3 ) are typical values, the authors have consistently decided to trust also on the obtained value for ( α 1 ). The numerical models are extremely simple in regard to geometry, equal to those in Fig. 3, and only changing the thickness of the 90◦layer (30 g/m 2 , 50 g/m 2 , 100 g/m 2 and 3 ×150 g/m 2 ). An adequate care has been taken into account to make a good progressive mesh refinement towards the bimaterial corner tip in order to avoid numerical errors which might affect the results far from the corner. For both numerical models, ANSYS® software has been used, with a 2D geometry (element type PLANE 182) using the Generalized Plane Strain option for this element type. For the mechanical problem, ANSYS® allows a longitudinal displacement (u z ) (perpendicular to the x-y 2D geometry) to be introduced in the analysis. Due to the double symmetry of the model, only a quarter of the real geometry has been modelled. In relation with this decision, it is important (not fully detailed in the software help manual) to introduce the longitudinal displacement in the elastic center of the problem (where tensile force and bending moments are uncoupled), in order to apply only tension and not bending moments. Due to the fact that the stiffness of the 0◦layer in the z-direction (fibre direction) is much higher than the stiffness of the 90◦layer in the z-direction, a constant ε zz applied to the sample makes the force resultant to be much closer to the center of the 0◦layer than to the center of the complete problem (0◦and 90◦). This elastic center has been calculated and results of the 2D model have been verified using a 3D model with the complete geometry of the sample (no symmetries applied). Fig. 6. Stress singularity removal at the bimaterial corner. S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 7 For the mechanical analysis, a displacement (u z ) giving rise to a longitudinal strain ε zz =0.003871 has been applied. This ε zz generates a nominal σ zz = ε zz ⋅E 22 =30 MPa in the 90◦layer, which is close to the experimentally obtained transverse strength of the material (Y t =38 MPa). All these values, predicted by the Classical Lamination Theory, have been verified in the numerical model, in areas far away from the free-edge. As the main numerical result for the present work, Fig. 7 shows the σ yy stress component, in the 90◦ply, along the free edge (x =0) of the sample. Horizontal axis represents the ratio between the y coordinate and half of the 90◦layer thickness of the model. Taking into account that only a quarter of the real problem is modelled, y/thickness =0 corresponds to the center of the 90◦ply, whereas y/thickness =1 corresponds to the upper part of the 90◦ply, in contact with the 0◦ply. This dimensionless parameter allows different models with different 90◦ thicknesses to be compared, which is the main objective of the present work. Two vertical axes have been used in Fig. 7, the left-hand side axis shows the ratio between the σ yy stress component and the transverse strength of the material (Y t ), while the right-hand side axis shows the ratio between σ yy and the applied longitudinal stress σ zz . Due to the fact that the transverse strength is Y t =38 MPa and the applied longitudinal stress is σ zz =30 MPa, both axes are slightly different. The text “MECH” in the legend, refers to “MECHanical loading”. In Fig. 7, four thicknesses (0.485 mm, 0.1 mm, 0.065 mm and 0.06 mm), associated with the four laminates under analysis (450, 100, 50 and 30) have been numerically studied. Let us remember that the results near the bimaterial corner vertex cannot be taken into account, due to the presence of the weak singularity. Far from the characteristic distance of the singularity field influence (for example, in the range 0 <y/ thickness<0.8) results are exclusively due to the edge-effect and are not affected by the stress singularity. Recall that Classical Lamination Theory predicts σ yy =0, and this result is valid as long as we go far away from the free-edge (see Fig. 3a–b). It is worth highlighting, from results in Fig. 7, that the thinner the 90◦ layer the higher the σ yy stresses along the free edge. For conventional 90◦layer thicknesses (for example 450 g/m 2 ) σ yy keeps below 50% of the longitudinal applied ( σ zz ) stress, but for ultra-thin plies in the 90◦ layer (for example 30 g/m 2 or 50 g/m 2 ) σ yy moves in the range between 0.6 σ zz < σ yy <0.8 σ zz . These values of σ yy are not high enough by themselves, to make longitudinal cracks to appear before the transverse cracks, associated with σ zz , but it should be also taken into account the contribution of the residual thermal stresses originated by the cooling stage of the curing cycle. Fig. 8 shows the same stress component along the same free edge, but now associated with the thermal effect. From the curing temperature (135 ◦C) to room temperature (25 ◦C) the bonded laminate suffers a ΔT = − 110 ◦C. Although, as mentioned previously, some stress relaxations might appear with time, let us take the results in Fig. 8 as an upper limit of the thermal residual stresses in the present problem. As in the mechanical case, σ yy (due to ΔT) gets negligible values far away from the free-edge, but at the free-edge, numerical results predict, with the exception of the 450 g/m 2 material, σ yy values higher than the transverse strength (Y t ) of the material, between 1.7 Y t < σ yy <2.0 Y t for the whole 90◦layer thickness. The text “TEMP” in the legend, refers to “TEMPerature” loading. These stresses should be added to those originated by the mechanical effect, and although some stress relaxation might appear, in the thinnest laminates (30 g/m 2 and 50 g/m 2 ) only the thermal stresses (or the sum of thermal and mechanical contributions in some cases) are high enough to make the longitudinal cracks to appear before transverse cracks, as experimentally observed, even before the mechanical loading is applied. The clear influence that the ply thickness has on the σ yy stress values along the free edge might be explained by using Eshelby’s imaginary cut, deform and bond again procedure, previously introduced in Fig. 4. Recall that, to fulfill compatibility with the 0◦layer, the 90◦layer is subjected to a prescribed displacement in the x-direction (applied along its top surface). This prescribed displacement is independent of the 90◦ layer thickness, thus, generating higher shear strains (and consequently the local strain and stress alteration) as the 90◦layer thickness Table 1 Thermo-mechanical properties of the materials. E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 (GPa) G 23 (GPa) ν 12 ν 13 ν 23 113.91 7.81 7.81 3.25 3.25 2.35 0.32 0.32 0.40 Yt (MPa) α 1 (◦C −1 ) α 2 (◦C −1 ) α 3 (◦C −1 ) 38 −1.37⋅10 −5 1.74⋅10 −5 1.70⋅10 −5 Fig. 7. σ yy stress component along the free-edge, due to a mechanical loading ( σ zz ). S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 8 decreases. In order to support more evidence of the stress relaxation associated with the thermal effect for these materials, non-symmetric [0 4 /90 4 ] laminates have been manufactured with 30 g/m 2 and 100 g/m 2 prepregs [1]. These laminates show a curvature after the curing cycle (curing temperature 135 ◦C), which changes with time. Fig. 9 shows the radius of curvature measured from instants after the curing cycle, to more than 1000 h later. The increment of the radius of curvature of the laminate with time R(t), in a laboratory temperature and relative humidity controlled ambient, and no external load applied, is a clear indication of the previously mentioned stress relaxation (at room temperature). Numerical (Finite Element) simulations, taking into account only the thermal effect derived from the cooling down stage after the curing process in the present laminates (no chemical shrinkage, or any other source of residual stresses), show that thermal stresses (after 1000 h) are between 50% and 60% of those generated by the nominal temperature decrement between curing and room temperatures, ΔT = − 110 ◦C. These values, by themselves, or added to those generated by the mechanical loadings, can still reach values close to the strength (Y t ) of the material. As a complementary result, Fig. 10 shows the alteration of the σ zz stress component at the free-edge, both due to the mechanical loading (Fig. 10a) as well as the thermal loading (Fig. 10b). Similarly, as done in Figs. 7 and 8 (with σ yy ), the stress values in the vertical axis are plotted with respect to the nominal applied σ zz , in the case of the mechanical load (Fig. 10a), and also with respect to Y t (Fig. 10a and b). This stress component does not have a direct responsibility in the longitudinal failures under analysis (if we assume that failure is governed by a maximum stress criterion), but it is clear, from Fig. 10a and b that, at the free-edge, the longitudinal σ zz values are higher than the nominal σ zz value generated as a result of the applied ε zz . 5. Failure inspection by 3D X-ray imaging Once the sources of the normal stresses in the thickness direction of the sample have been identified and quantified, it is of major importance to check if this failure had progressed along the width of the sample, or it was limited to the free-edge vicinity. Let us remember (Fig. 3b) that the tensile normal stresses σ yy appear along distance of one or two laminate thicknesses in the width direction, from the free edge, this stress component being slightly in compression ( σ yy <0), to guarantee global equilibrium in the y-direction. Therefore, if the onset of failure is due to the edge-effect, its influence should be limited to a characteristic distance in the width direction. Inspection of some longitudinal failures were carried out using a nondestructive 3D Computed Tomography (ZEISS® Xradia 620 Versa). The inspection was carried out near the low limit level of the equipment, with a pixel size of 0.3336 μ m, 4501 projections in a 180◦inspection range, source settings were 50 kV and 90 μ A. 3D reconstructions were done with Dragonfly Pro® software. It is worth remembering that, with a fibre diameter of 6–7 μ m, the maximum opening of the lips of the longitudinal fibre-matrix interface crack are below 1–2 μ m. As the crack grows in the width direction, Fig. 8. σ yy stress component along the free-edge, due to the thermal effect (ΔT = − 110 ◦C). Fig. 9. Stress relaxation in non-symmetric [0 4 /90 4 ] 30 g/m 2 and 100 g/m 2 laminates. S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 9 opening values are much lower and, in some cases, the crack length measurement might be a lower limit of the real crack length, due to the impossibility of the equipment to detect the crack opening. It is also noticeable that, while in glass fibre laminates, failures can be observed with the use of a back light source, this solution is not possible in the case of carbon fibre laminates, the adopted solution being one of the few possibilities to make this inspection. Some samples having longitudinal failures after the curing cycle were polished in the lateral face to identify (by optical microscopy) the location of the failure. It is important to notice that the lateral sanding and polishing of the sample removes approximately 1 mm of the sample material in the width direction, but it is mandatory for a good location of the damage before tomographic inspection. Some examples of 3D computed tomography reconstructions are shown in Fig. 11. •Fig. 11a is a lateral view of the sample, where 0◦plies can be seen at both sides of the 90◦ply (in the middle), with the longitudinal (vertical) failure (in yellow). •Fig. 11b shows an oblique perspective of the same failure, highlighting the longitudinal failure in a colors scale which identifies the opening distance of the two faces of the longitudinal crack. •Fig. 11c is exactly the same previous image but eliminating the laminate. •Fig. 11d is the zenithal view of the sample, which allows the crack length in the width direction (horizontal direction) to be measured. The left-hand side of the image is the sanded surface of the lateral side of the sample. The polishing of the lateral surface, removing almost 1 mm from the lateral side of the sample is necessary, as mentioned above, to precisely locate the longitudinal crack for the detailed inspection, but it avoids having a picture of the real edge failure extension. In Fig. 11d, after eliminating approximately 1 mm from the free edge, it was still possible to measure longitudinal failures penetrating only 85 μ m, in the width direction, from the free edge. What it is important is that these experimental observations indicate that the observed failure does not progress along the whole width of the sample, 25 mm, (no tunneling) and clearly support that the failures are a result of the edge effect. Due to its inherent complexity, a detailed analysis of the progression of these longitudinal failures along the width of the sample, under fatigue loading, falls out of the scope of this paper. The influence of the failure progression along the width on the stiffness degradation (mainly in bending) is currently being investigated. 6. Conclusions Non-conventional failures in cross-ply laminates with ultra-thin plies have been identified and a plausible explanation of their causes has been given by means of the edge effect. These non-conventional failures consist in longitudinal cracks/debonds (parallel to the loading direction) in the 90◦ply. The most important aspects of the present work are summarized below. •The observed non-conventional failures increase as the 90◦layer thickness decreases. The use of ultra-thin plies in the present work defines a clear difference with previous published works. Conventional transverse damage decreased with the same trend. •Stress singularity at the corner between the 0◦and 90◦interface with the free-edge has been characterized. Due to the extremely low values of the 90◦layer thickness, it is important to check the characteristic distance of the singularity stress influence. In the present work, slight geometric changes have been proposed in the corner to remove the singularity, isolating the influence of both effects (singularity and edge-effect). •Numerical analyses, under mechanical loading as well as under thermal loading, have been carried out to evaluate the alteration of the stress field at the free edge. Some experiments have been also Fig. 10. σ zz stress component along the free-edge, due to a) mechanical loading, b) thermal effect (ΔT = − 110 ◦C). Fig. 11. 3D reconstructions of the longitudinal failure inspection. S. S´ anchez-Carmona et al. Composites Part B 254 (2023) 110576 10 carried out to assess the relaxation with time of the residual thermal stresses for the materials under analysis. •Stresses originated by the edge effect due to the mechanical loading have shown to be close to the 70% of the longitudinal applied stress. For the thermal loading, stresses originated at the free edge are above the transverse strength of the material (Y t ) for the nominal temperature decrement between curing and room temperatures. •3D computed tomography was used at submicron level to evidence that failures under analysis have not crossed the whole width of the samples, but are limited to the close vicinity of the free edge of the samples. CRediT authorship contribution statement S´ anchez-Carmona S: Conceptualization, Experimental methodology, Writing – review & editing. Barroso A: Conceptualization, Investigation, Computational Methodology, Writing – original draft, Funding acquisition. Mantiˇ c V: Conceptualization. Investigation, Writing – review & editing, Funding acquisition. Correa E: Conceptualization. Investigation, Writing – review & editing, Funding acquisition. París F: Supervision, Writing - review & editing. Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Barroso A reports financial support was provided by Government of Andalusia Ministry of Economic Transformation Industry Knowledge and Universities. Mantic V reports financial support was provided by Spain Ministry of Science and Innovation. Correa E reports was provided by Spain Ministry of Science and Innovation. Data availability Data will be made available on request. Acknowledgements The research was conducted with the support of Spanish Ministry of Science, Innovation and Universities, Projects PID2021-126279OB-I00 and PID2021-123325OB-I00, Consejería de Transformaci´ on Econ´ omica, Industria, Conocimiento y Universidades, Junta de Andalucía and the European Regional Development Fund: P18-FR-1928 and P18-FR-3360; and the Universidad de Sevilla: grant VIPPIT-2018-II.2. The authors also acknowledge the valuable help of Agustín Cota and Simona Scrivano, Specialist Technicians from the X-Ray department at CITIUS, and the students Ester Culebras and Jorge Marín. References [1] S´ anchez-Carmona S, Correa E, Barroso A, París F. Experimental observations of fatigue damage mechanisms in cross-ply laminates using carbon-epoxy ultra-thin plies. Compos Struct 2023;306:116564. [2] Parvizi A, Garret KV, Bailey JE. Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates. J Math Sci 1978;13:195–201. [3] Flaggs DL, Kural MH. Experimental determination of the in situ transverse lamina strength in graphite/epoxy laminates. J Compos Mater 1982;16:103–16. [4] García IG, Justo J, Simon A, Mantiˇ c V. Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models. Mech Mater 2019;128:24–37. [5] París F, Velasco ML, Correa E. The scale effect in composites: an explanation physically based on the different mechanisms of damage involved in failure. Compos Struct 2021;257:113089. [6] Barroso A, Marín JC, Mantiˇ c V, París F. Premature failures in standard test specimens with composite materials induced by stress singularities in adhesive joints. Int J Adhesion Adhes 2020;97:102478. [7] Pipes RB, Pagano NJ. Interlaminar stresses in composite laminates under uniform axial extension. J Compos Mater 1970;4:538. [8] Pagano NJ, Soni SR. Chapter 1 - Models for studying free-edge effects. In: Pagano NJ, editor. Interlaminar response of composite materials, 5; 1989. p. 1–68. Composite Material Series. [9] Kassapoglou C, Lagace PA. Closed form solutions for the interlaminar stress field in angle-ply and cross-ply laminates. J Compos Mater 1987;21:292–308. [10] Becker W. Closed-form solution for the free-edge effect in cross-ply laminates. Compos Struct 1993;26:39–45. [11] Pagano NJ, Schoeppner GA, Kim R, Abrams FL. Steady-state cracking and edgeeffects in thermo-mechanical transverse cracking of cross-ply laminates. Compos Sci Technol 1998;58:1811–25. [12] Lorriot Th, Marion G, Harry A, Wargnier H. Onset of free-edge delamination in composite laminates under tensile loading. Composites Part B 2003;34:459–71. [13] Mittelstedt C, Becker W. Free-edge effects in composite laminates. ASME Appl. Mech. Rev. 2007;60:217–45. [14] Mittelstedt C, Becker W, Kappel A, Khargani N. Free-edge effects in composite laminates—a review of recent developments 2005–2020. ASME Appl. Mech. Rev. 2022;74:217–45. [15] Barroso A, Lauke B, Mantiˇ c V, París F. Tensile and shear strength of bimaterial interfaces within composite materials. Compos Sci Technol 2016;124:81–8. [16] Moriya K, Ichikawa T. A study on edge protection against delamination for composite laminates (The effects of edge shapes on stress singularities for cross-ply laminates). JSME Int J Ser III 1988;31:209–14. [17] Barroso A, Mantiˇ c V, París F. Singularity analysis of anisotropic multimaterial corners. Int J Fract 2003;119:1–23. [18] Mantiˇ c V, Barroso A, París F. Singular elastic solutions in anisotropic multimaterial corners. Applications to composites. In: Mantiˇ c V, editor. Mathematical methods and models in composites. Imperial College Press; 2014. p. 425–95. [19] Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc Roy Soc Lond Math Phys Sci 1957;241:376–96. [20] Zwiers RI, Ting TCT, Spilker RL. On the logarithmic singularity of free-edge stress in laminated composites under uniform extension. J Appl Mech 1982;49:561–9. [21] Barroso A, Vicentini D, París F, Mantiˇ c V. Representativity of thermal stresses in designing composite joints based on singular stress states at multimaterial corners. Compos Appl Sci Manuf 2011;42:1084–92. [22] Barroso A, Vicentini D, París F, Mantiˇ c V. Thermal stresses in composite joints. In: Hetnarski RB, editor. Encyclopedia of thermal stresses. Springer; 2014. p. 5323–33. [23] S´ anchez-Carmona S, Velasco ML, Barroso A, Correa E. Thermomechanical characterisation data of 30 g/m2 and 150 g/m2 cured unidirectional carbon/epoxy tape prepreg TP 402/T700S. Data in Brief 2023. Accepted for publication. [24] Neogia A, Mitrab N, Talreja R. Cavitation in epoxies under composite-like stress states. Compos Appl Sci Manuf 2018;106:52–8. [25] Ting TCT. Anisotropic elasticity: theory and applications. Oxford University Press; 1996. [26] París F, Velasco ML, Correa E. Micromechanical study on the influence of scale effect in the first stage of damage in composites. Compos Sci Technol 2018;160: 1–8. S. S´ anchez-Carmona et al.