Microscopical observations of inter-fibre failure under tension

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Composites Science and Technology, Vol. 158, on February 2018, available at: https://doi.org/10.1016/j.compscitech.2017.12.009 © 2017 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND Microscopical observations of inter-fibre failure under tension Elena Correa, María Inmaculada Valverde, María Luisa Velasco, Federico París Departamento de Mecánica de Medios Continuos y Teoría de Estructuras, Grupo de Elasticidad y Resistencia de Materiales, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, España Abstract The numerical study of the inter-fibre failure at micromechanical level predicts the appearance of different stages in the development of this damage mechanism; these studies have also allowed the main features of each stage (such as the interfacial debond length and the kinking angle) to be identified. The development of experimental studies aiming to check the relevance of the aforementioned numerical results is crucial. Based on this, this research focused on the tensile test under different loading levels of specimens manufactured from carbon-epoxy cross-ply symmetrical laminates. The microscopic observation of the 90º layers leads to the analysis of the appearance of the transverse cracks as a function of the load, the identification of the previously numerically predicted stages of the mechanism of damage, the measurement of key parameters and the evaluation of the influence of nearby fibres. A clear connection between the numerical and experimental results has been found. Keywords: debonding; transverse cracking; optical microscopy; cross-ply. A.1. Introduction Matrix/Inter-fibre failure arises in plies subjected to transverse loads, being characteristic, among others, of 90° plies belonging to cross-ply laminates subjected to loads parallel to their 0° plies. Previous numerical studies allowed the identification of three main stages in the mechanism of damage at micromechanical level, Figure A.1. In particular, in the case of tensile loads (París et al [1]), damage initiates with the appearance of small debonds at the fibre-matrix interfaces aligned with the applied load (Stage I); these debonds grow unstably in Mixed Mode along the interfaces until reaching an extension (semi-debonding angle,  d) of 60°-70° (Stage II); at this position, a change to stable growth in pure Mode II takes place (caused by the appearance of a physically relevant contact zone at the crack tip), favouring the kinking of the crack towards the matrix (Stage III). The crack finally propagates along the matrix (unstably and in Mode I) following the direction perpendicular to the load applied. The coalescence of this type of cracks coming from different fibres gives rise to transverse macro-cracks in the ply, eventually leading to its catastrophic failure. Figure A.1. Stages of the mechanism of damage. París et al [1]. The effect that the presence of a secondary load (París et al [2], Correa et al [3]) has on the evolution of these stages, the consideration of thermal residual curing stresses (Correa et al [4]), and the case of cyclic loading (Correa et al [5]), have also been studied numerically. The important role that micromechanical studies can play in helping first in the understanding of the mechanism of failure and second in verifying and proposing failure criteria was point out in these works. In particular, this outstanding question was deeply analysed in París [6]. A common pattern of these studies is the usage of a single fibre (assumed isolated) Boundary Element model. More recent works, focusing on Stage II of the mechanism of damage, also include a large number of fibres, see for instance Sandino et al [7] (two-fibres models), Távara et al [8] (ten-fibres models) and Távara et al [9] (one hundred-fibres models). FEA has also been used to study this problem; see for instance Hojo et al [10], Kushch et al [11] y Saito et al [12]. At this point, it turns out crucial to check, by means of experimental studies, the validity of the results derived from the numerical models, specifically, by means of microscopic observation of tested samples. Previous works from different authors focusing on the experimental micromechanical observation of the matrix failure can be found in the literature; among them it can be stood out the already classical works by Zhang et al [13] (single fibre tests under tension) and Gamstedt and Sjögren [14] (based on Zhang but studying the effect of cyclic load), and also those from Saito et al [15] (analysing the effect of the 90º ply thickness in cross ply laminates), Baral et al [16] (studying the effect of the fibre type), Hobbiebrunken et al [17] (comparing the behaviour between high and low curing temperature resins in three points bending tests) or STAGE I a ≈10º  d=60-70º STAGE II STAGE III Genz et al [18] (evaluating the presence of thermal residual stresses). In the present work, an optical microscope is used to observe the 90 plies of cross-ply specimens tested under longitudinal tensile load (which will be thus transverse to the 90 plies), in order to check if the numerically predicted micromechanical stages of the matrix/inter-fibre failure are in fact present and can be distinguished. The identification of the differences that these stages show in real laminates with a high fibre volume content versus the numerical single (and isolated) fibre models, is also pursued. In addition, the measurement of the final extension of the crack at the interface that gives rise to the kinking towards the matrix (  d= 60-70, from the numerical models), as well as the study of the different damage typologies, the analysis of the influence of the applied loading level and the effect of the presence of neighbouring fibres, are also objectives of the study. A.2. Coupons manufacturing and testing [03,903]s tensile coupons were manufactured from carbon-epoxy (AS4-8552) pre-preg, reinforcing their ends with glass-epoxy tabs. Their dimensions are detailed in Figure B.2. Figure A.2. Coupons dimensions. A first set of 5 coupons was selected for testing under tension. The results provided by the tensile strength (X) show a mean value of 942.47 MPa, a standard deviation of 41.25 MPa and a variation coefficient of 4.38%, therefore implying an excellent result in terms of dispersion. Subsequent testing campaigns were performed under maximum loads lower than the previously measured X, in order to generate damage in the 90 plies without reaching the catastrophic failure of the whole laminate. In particular, the loads applied can be grouped in 5 levels: 80%X, 60%X, 40%X, 30%X and 20%X. The number and denomination of the coupons tested as well as the exact loading level applied are included in Table A.1. Table A.1. Denomination of the coupons and corresponding testing load. Coupons denomination Testing load (%X) 80-1 84.2 80-2 82 60-1 62.4 60-2 59.5 60-3 60.5 40-1 42.6 40-2 40.3 40-3 39.2 30-1 31.5 30-2 29 30-3 27.6 20-1 21 A.3. Preparation of samples The central part of the specimens was cut in two halves of approximately 28 mm length; each pair was encapsulated in resin (using the VersoCit-2 kit). After that, the samples were polished using Saphir 20 polisher (automatic head and programmable) from NEURTEK Instruments, LaboDoser liquide dispenser and LaboPol-5 as peripheral polisher from Struers. The result of the polishing process must allow the fibres corresponding to the 90 plies to be clearly observed in an optical microscope at 1000x magnification. A suitable polishing process should also avoid the appearance of marks that could interfere in the later microscopical inspection. To this particular end, a specific polishing process was designed and tested, consisting of four steps. 40N pressure and 50rpm speed are selected for all steps, the disc type, refrigerator liquid and time used are detailed next: Step 1: Disc: SiC #320. Liquide: Water. Time: 5’. Step 2: Disc: MD-Largo. Liquide: DiaPro Allegro/Largo 9 μm (2). Time: 6’. Step 3: Disc: MD-Dac. Liquide: DiaPro Dac 3 μm (1). Time: 5’. Step 4: Disc: MD-Dac. Liquide: DiaPro Nap B1 1 μm (3). Time: 4’. A.4. Microscopic observation Once the samples have been polished the microscopic inspection is undertaken. There is a double objective here: first, using low magnification (25x), the analysis of the appearance of transverse cracks in the 90 plies as a function of the load applied. Second, the stages of the mechanism of damage previously identified by the numerical models want to be detected, along with the experimental values of their main parameters; to this end, observation at high magnification (500x and 1000x) is required. A.4.1. Inspection at low magnification A first inspection is made at 25x in order to count the number of transverse macro-cracks that appears in each specimen, and thus its loading level dependence. In Table A.2 the number of cracks observed per cm in each coupon is detailed. The most relevant conclusion is that for loads lower than 30%X no transverse macro-cracks are observed in the samples. A later inspection at greater magnification will also show, Section A.4.2, that no damage of any type is detected below this loading level. It is also observed that the number of cracks encountered increases as the loading level does. Notice in any case the reduced number of samples chosen for the lowest loading levels. Table A.2. Number of macro-cracks as a function of the loading level. %X Number of macro-cracks/cm 84.2 9 82 9.2 62.4 6.4 59.5 4 60.5 3.6 42.6 3.5 40.3 1.2 39.2 0.8 31.5 2.3 29 0 27.6 0 21 0 Although not being directly the objective of this paper, making use of the Classical Laminate Theory (CLT) and selecting a suitable failure criterion it is possible to predict the stress associated with first-ply failure (XFPF). Then, it is interesting at this point to check if the lowest stress value for which damage has been detected in the material (31.5%X in this case, see Table A.2) is accurately predicted by the Laminate Theory in combination with failure criteria. To this end, a selection of failure criteria (Maximum Stress, Tsai-Hill (Azzi and Tsai [19]), Tsai- Wu [20], Maximum Strain, Hashin [21], Hashin and Rotem [22] and Puck [23]) has been performed, and their XFPF predictions calculated, see Table A.3. Table 3. First-ply and ultimate failure predictions for a selection of failure criteria. Failure Criterion XFPF (MPa) XUF (MPa) XFPF/XUF (%) Maximum Stress 374.4 1112.9 33.6 Tsai-Hill 374.1 1109.5 33.7 Tsai-Wu 368.1 1149.1 32.0 Maximum Strain 367.2 1124.6 32.7 Hashin 374.4 1112.9 33.6 Hashin-Rotem 374.4 1112.9 33.6 Puck 374.4 1113.8 33.6 First of all, it can be observed that all failure criteria show similar predictions with a mean value of 372 MPa. This value can be compared with the lowest experimental load for which transverse cracks are observed, 31.5%X in this case, which corresponds to a stress value of 297 MPa. Taking into account that the number of coupons included in the 30%-40%X group is small (see Table A.2) and also that all of them show a very reduced number of transverse cracks, a good agreement between the analytical prediction and the experimental result is found. The appearance of the first crack at a value lower than that predicted by the criteria for the failure of the ply is, on the other hand, a very coherent fact, as the appearance of one transverse crack does not mean the total failure of the ply. The appearance of transverse cracks in a 90 ply is a continuous (not sudden) phenomenon, and it can be checked that (as mentioned above), for the first ply failure predicted by the criteria, only a very reduced number of cracks appear in the specimen, this fact not implying a significant reduction in the contribution of the 90 ply to the properties and performance of the laminate. Another interesting feature arises when using the CLT to also predict the stress associated with the ultimate failure (XUF) and then to calculate the ratio between XFPF and XUF (Table A.3), i.e. using only the analytical tool to evaluate at which percentage of the analytical ultimate stress the theory predicts the initiation of damage. This calculation of XUF has been performed by means of a progressive damage model, using a degradation coefficient D equal to 0.1 that acts on all material properties but just slightly in this particular case due to its small value. The results show again similar predictions for all criteria and an approximate value of 33%XUF is obtained for XFPF. An excellent agreement is found now between this prediction and the experimental result, as the first transverse cracks were detected at 31.5%X. The observation of the 25x micrographs shows some relevant differences between the different loading levels, in particular: 1) Specimens tested at 20%X (see Figure A.3a as an example): No damage is detected. 2) Specimens tested at 30%X (see FigureA.3b as an example): Just a few and very thin transverse cracks are found in one specimen. A reduced number of delaminations between 90º and 0º plies are present. 3) Specimens tested at 40%X (see Figure A.3c as an example): Some transverse cracks are found although they appear like thin lines in the microscope. Delaminations between 90º and 0º plies are present. 4) Specimens tested at 60%X (see Figure A.3d as an example): Many and well defined transverse cracks are found. Some cracks show a path deviated from the transverse direction. Delaminations between 90 and 0 plies are detected. 5) Specimens tested at 80%X (see Figure A.3e as an example): Many and well defined transverse cracks are found (more than in the previous case). Most of them appear like thick lines at the microscope, which is associated with a clearly developed damage and probably with a significant opening of the crack lips. More deviated cracks are observed. Delaminations between 90 and 0 plies are also detected. It should be remarked that the through thickness crack location does not show a preferential pattern, which seems to be in accordance with CLT predictions (assuming the 90 ply as homogeneous) and also with the outcomes of a recent numerical study by the authors (modeling the 90º ply as heterogeneous and distinguishing between fibres and matrix), París et al [24]. (a) (b) (c) (d) (e) Figure A.3. 25x micrography from (a) 20-1 specimen, (b) 30-1 specimen, (c) 40-1 specimen, (d) 60-1 specimen, (e) 80-2 specimen. A.4.2. Inspection at high magnification The inspection of the samples using a greater magnification is next performed in order to try to experimentally identify the different phases of the mechanism of damage numerically predicted in [1] (Figure A.1); in particular, the occurrence of Stages I, II and III, their connection with the loading level as well as the measurement of specific parameters relevant for the development of the mechanism of damage, are pursued. Indeed, the observation of samples at high magnification exposes the appearance of all stages of the failure mechanism (I, II and III, Figure A.1) for loading levels higher than 30%X. Specifically, damage appears in clearly less quantity in the 30%X group, maximizing its appearance in the 60%X group (probably associated with the fact that in the 80%X group isolated stages disappear forming a greater number of macro-cracks). Figure A.4 shows 1000x images of Stages I and II (a), and Stage III (b). Notice that the nominal fibre radius is 3.56 m, useful as scale reference for Figure A.4 and the forthcoming Figures A.5, A.7, A.8 and A.9. (a) (b) (c) Figure A.4. 1000x micrographies of: (a) Stages I and II (30%X), (b) Stage III (40%X), (c) Aligned debonds (40%X). It is necessary to remark that it is not possible to distinguish between Stages I and II with the available tools because, among other things, it is not numerically clear if a real separation between both stages exists. The unstable character of the mechanism of failure and the dependence of the initiation of failure on the properties of the interface (in particular on the fracture toughness) are some of the features that point it as an open question. The more recent publications on Finite Fracture Mechanics (Mantič [25], Mantič and García [26]) study in depth this problem. With reference to Stage II, it is common to find the debonds at this stage very close to areas where macro-cracks already exist, although at low loading levels they are also detected as isolated, far from these areas. The Stage II debonds often appear aligned in high fibre density zones, so that the path followed by the future macro-crack can be envisaged, Figure A.4c. Not very frequently, fibres with bi-lateral debonds are observed (Figure A.5a) although currently both debonds do not present the same extension and thus, no simultaneous growth is deduced. The existence of these bi-lateral debonds can be also observed in macro-cracks, Figure A.5b; in these cases the bi-lateral debond seems to appear when the fibre is placed in the middle of the path of the macro-crack. (a) (b) Figure A.5. 1000x micrographies of bi-lateral debonds (a) at Stage II (60%X), (b) in macro-cracks (60%X). Referring to Stage III, several kinking paths additional to the numerical theoretical one have been identified using the microscope. Figure A.6 shows all typologies found, having been named as detailed: A. Theoretical, B.1. Deviated +, B.2. Deviated –, C. Bilaterally tangential, D. Gradual transition and E. Splitting. STAGE I STAGE II STAGE III [20] S.W. Tsai, E.M. Wu, J. Comp. Mat. 5 (1971) 58-80. [21] Z. Hashin, Failure criteria for unidirectional fiber composites, J Appl. Mech. 47 (1980) 329- 334. [22] Z. Hashin, A. Rotem, A fatigue failure criterion for fiber reinforced materials, J. Comp. Mat. 7 (1973) 448-464. [23] A. Puck, Festigkeitanalyse von Faser-Matrix-Laminaten, Modelle für die Praxis (Strength analysis of fibre-matrix/laminates, models for design practice), Carl Hanser Verlag, Munich, 1996. [24] F. París, M.L. Velasco, E. Correa, Micromechanical study of the influence of scale effect in the first stage of damage in composites, Compos. Sci. Technol. submitted for publication. [25] V. Mantič, Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion, Int. J. Solids Struct. 46(6) (2009) 1287–1304. [26] V. Mantič, I.G. García, Crack onset and growth at the fibre–matrix interface under a remote biaxial transverse load. Application of a coupled stress and energy criterion, Int. J. Solids Struct. 49(17) (2012) 2273–2290. [27] E. Correa, F. París F, V. Mantič, Effect of friction on inter-fibre failure under tension at micromechanical level, 2nd ECCOMAS Thematic Conference on the Mechanical Response of Composites, Imperial College, London, 2009.