Fatigue crack initiation and damage characterization in Brazilian test specimens for adhesive joints

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Adhesion Science and Technology, Volume 28, Issue14-15, on 2014, available at: https://doi.org/10.1080/01694243.2012.698099 En idUS Licencia Creative Commons CC BY-NC-ND * Corresponding author. Tel.: +34 954 487 300; Fax.: +34 954 461 637. Email address: [email protected] FATIGUE CRACK INITIATION AND DAMAGE CHARACTERIZATION IN BRAZILIAN TEST SPECIMENS FOR ADHESIVE JOINTS D. Vicentini1,*, A. Crocombe2, A. Barroso1, F. París1 and V. Mantič1 1School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain 2Mechanical, Medical and Aerospace Engineering, University of Surrey, Guildford GU2 7XH, UK ABSTRACT The present study is focused on the fatigue failure initiation at bimaterial corners by means of a configuration based on the Brazilian disk specimens. These specimens were previously used for the generalized fracture toughness determination and prediction of failure in adhesive joints, carried out under static compressive loading. Under static loading, local yielding effects might affect the asymptotic two-dimensional linear elastic stress representation under consideration. Fatigue loading avoids this fact due to the lower load levels used. The tests were performed using load control; video microscopy and still cameras were used for monitoring initiation and crack growth. The fatigue tests were halted periodically and images of the corner were taken where fatigue damage was anticipated. Damage initiation and subsequent crack growth were observed in some specimens, especially in those which presented brittle failure under static and fatigue tests. These analyses allowed the characterization of damage initiation for a typical bimaterial corner that can be found in composite to aluminium adhesive lap joints. Keywords: adhesive joints, failure, crack initiation, composites, fatigue. 1. Introduction Many proposals to determine the stress state in adhesive joints, for failure prediction, have been presented over the years. Several analytical works studying adhesive lap joints can be found in the literature. The classical works of Volkersen [1], de Bruyne [2] and Goland and Reissner [3] that used elasticity and a strength of materials approach (based on thin plates or beam theory, for 2 example) are generally recognized as constituting the pioneering work in this field. Later on, Wah [4] introduced composites in the analysis of lap joints and Hart-Smith [5, 6], in addition, included other improvements for designing adhesive joints, such as the study of thermal stresses, joint efficiency, the effect of the stacking sequence, unbalanced joints, etc. More recently, the work of Tsai and co-workers [7, 8] in which the shear stresses are assumed to vary linearly through the thickness direction are highlighted. Also Bigwood and Crocombe [9, 10] proposed a generic analysis from plate bending theory for different types of configurations of joints under complex loading. A good review of the literature concerning the stress analysis of adhesive joints can be found in da Silva et al. [11]. Another interesting work by da Silva et al. [12] compares some of the analytical models against experiments, finding that models were too conservative. All these works, however, aimed, in part, to predict the joint strength based on nominal stresses under static loading. Other proposals using a fracture mechanics approach and motivated by the existence of stress singularities at the corners in the joints have been presented in [13, 14, 15, 16], among others. More recently, a criterion based on the local singular stress state of the bimaterial corner encompassed by the joint, where the failure is expected to initiate, was proposed [17] and verified experimentally [18]. A new test for the determination of the critical values of the Generalized Stress Intensity Factors (GSIFs) appearing in this corner configuration was proposed, based on the original Brazilian Test (BT) specimen [19]. This geometry was chosen because it allows the entire range of mode mixities to be covered [17, 18]. The experiments carried out [18] strongly suggest that the proposed criterion could be applied in real adhesive joints [20] with the same local corner configuration at the end of the overlap zone. Following this line, the present work studied the failure generated in the corner but under fatigue loads. The lower level of load that is applied in fatigue tests generally produces a stress state free of plasticity effects. Also, this work aimed to characterize the development of fatigue cracks (initiation and propagation) for the present type of geometry. 3 Although thermal stresses have been reported to have a significant influence on the behaviour of adhesive joints between dissimilar materials [21], the stresses being actually more severe in the Double Lap Joint (DLJ) than in the BT specimen, thermal analysis has not been included in the present work, following previous experience in similar corner geometries [22]. 2. Failure criterion based on fracture toughness for adhesive joints By analogy to the Linear Elastic Fracture Mechanics (LEFM) for homogeneous and brittle (or quasi-brittle) materials, the present work seeks to predict the failure onset by using critical values of the GSIFs (or generalized fracture toughnesses), under which the failure of the corner is expected to initiate [17, 18]. According to this hypothesis and assuming generalized plane strain, the singular stress state around the tip of a multimaterial corner can be approximated by a truncated sum of n terms (see [17] for pertinent references): k nk k ij ij 1 k1 K (r, ) f ( ) r       , for i, j = r, (1) where the characteristic exponents k have a positive real part, Re k>0, fijk are the characteristic angular shape functions, and (r,) are the polar coordinates centred at the corner tip (Fig. 1 a). When Re (1-k) is between 0 and 1, (1-k) is called the stress singularity order. When r tends to zero, the corresponding terms of Eq. (1) go to infinity. The GSIF (Kk) can be determined numerically, e.g. by using a least squares technique, while the angular shape functions and characteristic exponents can be determined semi-analytically (see [17, 23 or 24] for more details). In some corner configurations, stresses ij(r,) for r0 are well approximated by the most singular term in the asymptotic expansion (1), defining the singular stress state by only one Kk. Under increasing static load in a configuration controlled by only one Kk, once the corner reached the maximum admissible level of stress, the generalized fracture toughness KkC can be determined. Following this reasoning, when singular stresses are approximated by two or three terms of the series expansion (Eq.1), the critical combinations of GSIFs would define a failure envelope curve or surface, enclosing the safety region. This failure envelope should be determined by testing 4 several load configurations. These tests can define some intermediate points to obtain the hypothetical failure curve or surface, as schematically shown in Fig. 1b (see Hattori [13] for single lap joints and Wang and Suo [25] and Banks-Sills et al. [14] for interfacial cracks). 3. Configuration of the specimens The problem under consideration is defined by a particular corner of a DLJ, in which the stress state is the most severe and thus the failure is expected to initiate. This corner is formed by a Carbon Fibre Reinforced Polymer (CFRP) laminated adherend and adhesive layer and spew fillet, as can be seen in Fig. 1 c. In the original problem, the DLJ (whose adherends were aluminium and CFRP) was bonded using a structural adhesive (Fig. 1 c). The same adhesive and CFRP were used in both geometries, DLJ and BT (Fig. 1 c and d). For the bimaterial corner in the BT, R was the radius and t the thickness of the specimen (Fig. 1 d).The following material properties (given by the manufacturer’s data sheet) were considered: E = 68670 MPa (Young’s Modulus), = 0.33 (Poisson’s ratio) for aluminium 2024-T3; Ex = 141300 MPa, Ey = Ez = 9580 MPa, xy = xz = 0.3, yz = 0.32, Gyz = 3500 MPa, Gxy = Gxz = 5000 MPa for CFRP AS4/8552 unidirectional fibre laminate [0]12 (x being the fibre direction, Fig. 1 d) and E = 3000 MPa, = 0.35 for the adhesive FM®73 OST (toughened epoxy film, from Cytec). For this particular corner, the three first terms in Eq. (1) were considered (n = 3), so the asymptotic stress state in the neighbourhood of the corner tip can be expressed by the following series expansion [24, 26]: 1 2 3 123 3 12 ij ij ij ij 1 1 1 K KK (r, ) f ( ) f ( ) f ( ) rrr            (for r0+ and Re k>0) (2) where 1 = 0.763, 2 = 0.889 and 3 = 1.107 (from [20]) are the stress singularity exponents (for example in LEFM for a crack problem in mixed mode I and II these exponents would be 1 = 2 = 0.5); K1, K2 and K3 are the GSIFs which represent the weight of each term of the series expansion. The characteristic exponents (k) and angular shape functions (fijk) depend on the local geometry, 5 material properties and boundary conditions at the corner tip and they were obtained using the semi-analytical procedure developed in [24], normalized according to Pageau et al. [27] and studied in [17]. When r tends to zero, the two first terms (which are singular) are the most significant ones in this equation; thus in this work, for very small distances (r) from the corner tip, the third term in Eq. (2) can be neglected, without loss of generality. So the stress field can be expressed as: 12 12 ij ij ij 0.236764 0.110611 KK (r, ) f ( ) f ( ) rr       (for r0+) (3) The stresses can be obtained numerically when, considering for example the bimaterial rounded corner, a uniform load P (see Fig. 1 d) is diametrally applied along the thickness. Then K1 and K2 can be evaluated in order to isolate each term. 3.1. The proposed failure envelope based on critical GSIF The BT (indirect tensile or splitting tensile test) represented in Fig. 1 d, also known as diametral compression test, is used for the assessment of the tensile strength of brittle or quasi-brittle materials, especially concrete and rocks. The test consists of a cylindrical specimen (with radius R and thickness t) diametrally loaded (P) under compression. It was first published by Carneiro in 1943, according to the reference [19]. As a curiosity, this test was proposed to check the strength of concrete cylinders which would have been required for moving the ancient São Pedro Church in Rio de Janeiro to another location within the city. The test was independently proposed by Akazawa (according to the reference [28]) some months later and has become a very popular test due to its versatility, usage and consistency (scatter less than 10%) compared with other methods [29]. Varying the direction of the symmetrical load P according to different angles () for the particular bimaterial corner under study (Fig. 1 d), the distributions of the GSIFs (K1 and K2) are presented in Fig. 2 [17]. 6 From this graph, it can be deduced that the isolation of the mode related to K1 (where K2 vanishes) is achieved for  ≈ 13º or  ≈ 115º, and the mode related to K2 for  ≈ 60º or  ≈ 143º (where K1 vanishes). It is important to note that the GSIFs depend on the specimen geometry, material properties and boundary conditions. From the observation that the GSIFs are proportional to the load and inversely proportional to the specimen radius and thickness [18], the critical GSIF value KkCspec (the value of GSIF at failure) can be correlated to the numerical GSIF value Kknum by means of the following expression: spec num num spec num kC k num spec spec P R t KK P R t  (4) where KkCspec, Pspec, Rspec, tspec are the parameters from the tested specimens: GSIF (critical, calculated from Eq. (4)), ultimate (compressive) load (given by the test, thus Pspec = Pu), radius and thickness of the specimen (both measured before testing). Kknum, Pnum, Rnum, tnum are the analogous parameters from the numerical analysis, the values used in this work being Rnum = tnum = 1 mm and Pnum = 100 N. The parameters measured in experimental test, the estimated Pu from previous static tests [18] and the critical GSIFs calculated from this estimation are presented in Table 1. Defining a failure criterion in terms of strength, some size-scale effects will appear. Applying a dimensional analysis, the generalized stress intensity factor can be expressed as (see [17, 18, 30] and references therein): k 1 Re( ) k nom k K R A   (k=1,2) (5) where nom is a nominal stress in the problem, R is a characteristic distance (the radius in the present case) and Ak is a shape factor taking into account the geometry and material properties of the problem. A generalized fracture-toughness based failure criterion could be expressed, in the generic form, as: )(  C K (6) 7 where     22 2 2 1 1 CC K K K K K is a normalized GSIF modulus (a dimensionless magnitude) and  is a normalized fracture mode-mixity angle, )//()/(tan 1122 CC KKKK  . Unlike the traditional mode mixity definition in the case of a crack, )/(tan 12 KK  , the inclusion of the fracture toughnesses is due to the different units of K1 and K2 in the present case. The parameterization ))(,(  C defines a hypothetical failure envelope based on generalized fracture-toughness concepts [18]. It should be emphasized that using (5) and (6), an explicit expression for the sizescale effect on the specimen strength can be deduced. 4. Fabrication of the BT specimens For the fatigue tests, BT disk specimens were manufactured by curing in an autoclave. Eight different angles  (for application of P, according to Fig. 2) were tested, using 3 specimens for each angle. From previous experience [18, 31], the following detailed process was adopted because it seemed to be the most suitable, in order to obtain the best quality samples (absence of porosity). First, a CFRP laminate of 120 plies previously manufactured was cut to adopt the shape of a square prism, which was partitioned into little square slices of dimensions 20 x 20 x 10 mm, the thickness being 10 mm and the direction of fibres being parallel to one of the 20 mm length edges. The slices were then cleaned with acetone. The adhesive was supplied as a tacky film which was left out of the freezer some hours before bonding. The adhesive film was cut and layered with intermediate vacuum compaction between every five laminas for 10-15 min until completely covering the CFRP square width (Fig. 3.a). The procedure was carried out inside a clean room. The entire set was placed on an aluminium plate covered with Teflon®. Cork was used to separate and contain all specimens, accommodating and fixing them to the plate. Next, the cork was covered with a high temperature tape to avoid spilling of the adhesive during the curing process (Fig. 3.b). The entire set was covered with Teflon®, followed by an Airweave® breather fabric (from Airtech 8 Europe Sarl, Luxembourg). Then a vacuum bag was prepared, and the specimens were cured inside the autoclave under 0.28 MPa (2.8 bar), 120ºC (393 K) and 105 min in total. After the curing process, every specimen was a square plate (see Fig. 3.c). In [18] a schematic figure of the whole manufacturing process is available. Once the curing cycle was finished, every sample was carefully cut, using a water-cooled diamond for cutting the circular disk, around the marked circumference of the final geometry (Fig. 3 c). Then the specimens were abraded in order to smooth the cut surfaces, leaving them as round as possible. The final dimensions (in terms of R and t) of the specimens are presented in Table 1. Finally, the angle of the load application was marked and both "flats" on which the load was applied (Fig. 3.d) were cut. This allowed a uniform application of the compressive load during the test (by Saint-Venant principle the stress state at the corner tip is not affected by the local detail of the load application, as can be verified in [32], for example, among other studies). 5. Experimental test In a previous work [18], BT disk specimens were tested under static load in a displacement controlled machine for different angles , in order to achieve the failure envelope according to the theory presented in [17] and summarized in previous sections. A failure envelope based on the critical combinations of a pair of GSIFs at the corner tip was presented and proposed as a criterion for joints having the corner shown in Fig. 1 d. The results were compared (in [18]) with real adhesively bonded DLJs loaded in tension (that were previously tested in [20]), presenting good agreement. In addition, if plasticity occurred it could affect the stress state of the corner. In this sense, fatigue tests could be useful to avoid possible yielding effects. Such tests have been carried out in the present work in order to further characterize the crack initiation and damage progression. Failure initiation in the current work was defined as the first of the following phenomena: initial observation of whitening or a crack. The fatigue tests were halted every 5000 cycles to check the integrity of the specimen on both planar surfaces. The test was considered to be finished either when the failure length was 15 The group of specimens with  = 60º did not show any visible failure. This fact, together with the retarded failure observed in the specimen with  = 143º (angles 60º and 143º, where K1  0), suggests that K1 drives the fatigue failure. Thus, fatigue life diminishes drastically when approaching angles with significant K1 values associated, Figs. 2 and 7. The study carried out corresponds to a critical point for the prediction of failure in the most commonly bimaterial corner found in structural adhesive joints. This study can be easily extended to other corner configurations also present in adhesive joints. Acknowledgments This work was supported by CAPES Brazilian Ministry of Education, EADS chair in Seville, also by the Junta de Andalucía and European Social Fund through the Projects of Excellence P08-TEP- 4071 and P08-TEP-4051. The authors would like to give thanks to Peter Haynes for the help in setting up the testing. References [1] O. Volkersen. Luftfahrtforschung 15, 41 (1938). [2] N. A. de Bruyne. Aircraft Eng. Aerospace Technol. 16, 115 (1944). [3] M. Goland and E. Reissner. ASME Trans., J. Appl. Mech. 11, A17 (1944). [4] T. Wah. ASME Trans., J. Eng. Mater. Technol. 95, 174 (1973). [5] L. J. Hart-Smith. NASA CR-112235 (1973). [6] L. J. Hart-Smith. NASA CR-2218 (1974). [7] M.Y. Tsai, J. Morton and D. W. Oplinger. Expl. Mech. 36, 297 (1996). [8] M.Y. Tsai, D. W. Oplinger and J. Morton. lnt. J. Solids Struct. 35, 1163 (1998). [9] D.A. Bigwood and A.D. Crocombe. Int. J. Adhesion Adhesives 9, 229 (1989). [10] D.A. Bigwood and A.D. Crocombe. Int. J. Adhesion Adhesives 10, 31 (1990). [11] L. F. M. da Silva, P. J. C. Neves, R. D. Adams and J. K. Spelt. Int. J. Adhesion Adhesives 29, 319 (2009). [12] L. F. M. da Silva, P. J. C. Neves, R. D. Adams, A. Wang and J. K. Spelt. Int. J. Adhesion Adhesives 29, 331 (2009). [13] T. Hattori. J. Jpn. Soc. Mech. Eng. 34, 326 (1991). 16 [14] L. Banks-Sills and D. Ashkenazi. Int. J. Fract. 103, 177 (2000). [15] M. L. Dunn, C. Y. Hui, P. E. W. Labossiere and Y. Y. Lin. Int. J. Fract. 110, 101 (2001). [16] D. Leguillon and E. Sanchez-Palencia, Computation of Singular Solutions in Elliptic Problems and Elasticity. Masson Ed., Paris (1987). [17] A. Barroso, D. Vicentini, V. Mantič and F. París. Determination of generalized fracture toughness in composite multimaterial closed corners with two singular terms. Part I: test proposal and numerical analysis (submitted for publication in Eng. Fract. Mech., 2011). [18] D. Vicentini, A. Barroso, J. Justo, V. Mantič and F. París. Determination of generalized fracture toughness in composite multimaterial closed corners with two singular terms. Part II: experimental results (submitted for publication in Eng. Fract. Mech., 2011). [19] F. Carneiro and A. Barcellos. RILEM Bull. 13, 97 (1953). [20] A. Barroso, F. París and V. Mantič. Composites Sci. Technol. 69, 1746 (2009). [21] I.A. Ashcroft, D.J. Hughes, S.J. Shaw, M. Abdel Wahab and A. Crocombe. J. Adhesion 75, 61 (2001). [22] A. Barroso, D. Vicentini, F. París and V. Mantič. Composites Part A 42, 1084 (2011). [23] A. Barroso, E. Graciani, V. Mantič and F. París. Eng. Anal. Boundary Elem. 36, 458 (2012). [24] A. Barroso, V. Mantič and F. París. Int. J. Fract. 119, 1 (2003). [25] J.S. Wang and Z. Suo. Acta Metall. Mater. 38, 1279 (1990). [26] M. L. Williams. ASME Trans., J. Appl. Mech. 19, 526 (1952). [27] S. P. Pageau, K. S. Gadi, Jr. S. B. Biggers and P. F. Joseph. Int. J. Fract. 77, 51 (1996). [28] M. T. Akazawa. RILEM Bull. 16, 12 (1953). [29] G. Tesoriere and S. Marino, in: Proceedings of the 4th Int. Symp. held by RILEM, Budapest, 320-328 (1990). [30] A. Carpinteri and M. Paggi. Mater. Sci. 42, 95 (2006). [31] D. Vicentini, A. Barroso, V. Mantič, F. París and D. Canales, in: Proceedings of IX MATCOMP, Girona, Spain, 861 (2011). [32] M. K. Fahad. J. Mater. Sci. 31, 3723 (1996). [33] M. A. Miner. ASME Trans., J. Appl. Mech. 67, A 159 (1945). [34] I. A. Ashcroft, V. Shenoy, G. W. Critchlow and A. D. Crocombe. J. Adhesion 86, 1203 (2010). 17 Table 1. Summary list of data from numerical and experimental analyses. K1* and K2* were obtained from the estimation of Pu ([18] results), being presented as averaged and normalized values. Where:  is the tested angle; Ris the specimen radius (or Rspec); tis the specimen thickness (or tspec); Puis the ultimate static load (estimated from static results in [18]); K1*, K2*(or K1Cspec, K2Cspec normalized in order to obtain dimensionless values) are K1and K2 at the instant of failure divided by the critical GSIF (estimated from static results in [18]); N0is the corresponding number of cycles at which the first change was observed in the corner; and N1mm , N3mm are the corresponding numbers of cycles necessary for the observed damage to reach at least 1 mm and 3 mm in length, respectively. Specimen a (º) R (mm) t (mm) Pu (N) K1* K2* N0 N1mm N3mm PC1 20,24 8,24 14207 1141 1141 1141 PC2 20,4 8,28 14389 1600 1600 1600 PC3 13 20,38 8,16 14167 1 -0,063 1521 1521 1521 PC4 20,23 8,3 12232 7500 12500 27500 PC5 20,12 8,14 11931 2500 2500 - PC6 30 20,12 8,23 12063 0,585 0,360 2500 7500 82500 PC7 20,16 8,19 14151 - - - PC8 20,5 8,21 14425 - - - PC9 60 20,6 8,27 14602 -0,032 1 - - - PC10 20,67 8,26 12130 2500 2500 7500 PC11 20,18 8,32 11928 2500 2500 4250 PC12 90 20,28 8,08 11642 -0,548 0,743 2500 2500 5000 PC13 20,36 8,28 14026 2500 2500 7500 PC14 20,6 7,97 13660 2500 2500 22500 PC15 115 20,55 8,22 14054 -0,639 -0,009 2500 7500 32500 PC16 20,5 8,17 15373 2500 27500 37500 PC17 20,63 8,3 15716 2500 22500 67500 PC18 120 20,65 8,34 15807 -0,592 -0,165 2500 17500 52500 PC19 20,87 8,24 13006 72500 87787 87787 PC20 20,44 8,46 13078 92500 - - PC21 143 20,84 8,25 13003 -0,011 -0,634 27500 47500 82500 PC22 20,72 8,1 10851 7500 22500 57500 PC23 20,64 8,26 11022 2500 17500 27500 PC24 150 20,72 8,04 10770 0,154 -0,595 2500 32500 67500 Where:  is the tested angle; Ris the specimen radius (or Rspec); tis the specimen thickness (or tspec); Puis the ultimate static load (estimated from static results in [18]); K1*, K2*(or K1Cspec, K2Cspec normalized in order to obtain dimensionless values) are K1and K2 at the instant of failure divided by the critical GSIF (estimated from static results in [18]); N0is the corresponding number of cycles at which the first change was observed in the corner; and N1mm , N3mm are the corresponding numbers of cycles necessary for the observed damage to reach at least 1 mm and 3 mm in length, respectively. Specimen a (º) R (mm) t (mm) Pu (N) K1* K2* N0 N1mm N3mm PC1 20,24 8,24 14207 1141 1141 1141 PC2 20,4 8,28 14389 1600 1600 1600 PC3 13 20,38 8,16 14167 1 -0,063 1521 1521 1521 PC4 20,23 8,3 12232 7500 12500 27500 PC5 20,12 8,14 11931 2500 2500 - PC6 30 20,12 8,23 12063 0,585 0,360 2500 7500 82500 PC7 20,16 8,19 14151 - - - PC8 20,5 8,21 14425 - - - PC9 60 20,6 8,27 14602 -0,032 1 - - - PC10 20,67 8,26 12130 2500 2500 7500 PC11 20,18 8,32 11928 2500 2500 4250 PC12 90 20,28 8,08 11642 -0,548 0,743 2500 2500 5000 PC13 20,36 8,28 14026 2500 2500 7500 PC14 20,6 7,97 13660 2500 2500 22500 PC15 115 20,55 8,22 14054 -0,639 -0,009 2500 7500 32500 PC16 20,5 8,17 15373 2500 27500 37500 PC17 20,63 8,3 15716 2500 22500 67500 PC18 120 20,65 8,34 15807 -0,592 -0,165 2500 17500 52500 PC19 20,87 8,24 13006 72500 87787 87787 PC20 20,44 8,46 13078 92500 - - PC21 143 20,84 8,25 13003 -0,011 -0,634 27500 47500 82500 PC22 20,72 8,1 10851 7500 22500 57500 PC23 20,64 8,26 11022 2500 17500 27500 PC24 150 20,72 8,04 10770 0,154 -0,595 2500 32500 67500 18 Fig. 1. (a) Bimaterial corner, (b) scheme of a failure envelope based on critical values of GSIF considering 3 terms, (c) DLJ indicating a detail of the amplified corner with diametral forces being applied (d), as in Brazilian Test specimens. Con resultados normalizados (resultados MEF 1mm esp 100N compresión) -0.015 -0.01 -0.005 0 0.005 0.01 0.015 030 60 90 120 150 180 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 K1 K2   P P   1 (1 ) 1 K MPa mm    2 (1 ) 2 K MPa mm  Fig. 2. Distribution of K1 and K2 for different angles (in degrees). 19 Fig. 3. Fabrication of specimens. a) Adhesive film being layered; b) Cork covered with high temperature tape demarcating the region; c) After curing, specimens are like “cookies” and d) Final geometry of samples. Fig. 4. Examples of sequential frames of pictures of PC21, case = 143º. The strain gauge is seen in these pictures. Fig. 5. Measurement of the size for irregular failure paths a) type I and b) type II, where Dz is the damage zone (or crack) length. 20 Damage zone x Number of cycles 0 2 4 6 8 10 12 14 0250 500 750 1000 1250 1500 1750 2000 N (cycles) Dz (mm) PC1 under -8409N PC2 under -8409N PC3 under -8409N a)=13º Damage zone x Number of cycles 0 2 4 6 8 10 12 14 16 18 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC4 under -8409N PC5 under -8409N PC6 under -8409N b)=30º Damage zone x Number of cycles 0 2 4 6 8 10 12 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC10 under -6540N PC10 under -8409N PC11 under -6540N PC11 under -8409N PC12 under -8409N c)=90º Damage zone x Number of cycles 0 2 4 6 8 10 12 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC13 under -6540N PC13 under -8409N PC14 under -8409N PC15 under -8409N d)=115º 0º Failure path scheme 0º Failure path scheme 90 º Failure path scheme 90 º Failure path scheme Damage zone x Number of cycles 0 2 4 6 8 10 12 14 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC16 under -8409N PC17 under -8409N PC18 under -8409N e)=120º Damage zone x Number of cycles 0 1 2 3 4 5 6 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC19 under -8409N PC20 under -8409N PC21 under -8409N f)=143º Damage zone x Number of cycles 0 2 4 6 8 10 12 14 020000 40000 60000 80000 100000 N (cycles) Dz (mm) PC22 under -8409N PC23 under -8409N PC24 under -8409N g)=150º 90 º Failure path scheme 0º Failure path scheme 0º Failure path scheme Fig. 6. Damaged zone (Dz) vs. number of cycles (N) for every tested angle (). A scheme of the failure path observed during the test is also indicated in each case. 21 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 010 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160  (º) N (cycles) 0 10 20 30 40 50 60 70 80 90 % Pu N0 vs. Angle N1mm vs. Angle N3mm vs. Angle (%Pu) vs. Angle 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 010 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160  (º) N (cycles) 0 10 20 30 40 50 60 70 80 90 % Pu N0 vs. Angle N1mm vs. Angle N3mm vs. Angle (%Pu) vs. Angle Fig. 7. Averaged number of cycles (N0, N1mm and N3mm, left axis) and % of ultimate load (right axis) versus load orientation (). 0 0.2 0.4 0.6 0.8 1 1.2 020 40 60 80 100 120 140 160  (º) N0/N1mm N0/N3mm N0/N1mm N0/N3mm N0/N3mm N0/N1mm (1, -0.06)  =13º (0.59, 0.36)  = 30º (-0.55, 0.74)  = 90º (-0.64, -0.01)  = 115º (-0.59, -0.17)  = 120º (-0.01, -0.63)  = 143º (0.15, -0.59)  = 150º Fig. 8.N0/N1mm and N0/N3mm versus angle ,with (K1*, K2*) indicated. -2.8 -2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 05000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 Cycles Displacement (mm) Max min (Max-min) N0 N1mm N3mm min Max Max-min -2.8 -2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 05000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000 Cycles Displacement (mm) Max min (Max-min) N0 N1mm N3mm min Max Max-min min Max Max-min Fig. 9. Crosshead displacement during the test for PC16 (=120º).