Transverse biaxial tests on long fibre reinforced composites

Composite Structures 297 (2022) 115868 Available online 16 June 2022 0263-8223/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Transverse biaxial tests on long fibre reinforced composites Patricia Lucía Zumaquero , Elena Correa * , Jesús Justo , Federico París Group of Elasticity and Strength of Materials, School of Engineering, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain ARTICLE INFO Keywords: Matrix failure Biaxial tests Experimental Manufacturing ABSTRACT The study and prediction of the failure mechanisms affecting long fibre reinforced composites is a fundamental field that provides an essential knowledge for the structural design with composites. Transverse failure, generated at ply level by the mechanism of damage known as inter-fibre/matrix failure, usually determines the damage initiation in any laminate which justifies its relevant role and the need to understand its micromechanical stages. Previous numerical results established that in the case of transverse biaxial loads (T-nT and T- nC cases) the stages of the damage mechanism detected in the uniaxial case could be affected. The most outstanding conclusion anyhow was that the effect of a secondary tension did not significantly alter the ultimate value of the tension nominally responsible for the failure, whereas a secondary compression could advance the failure appearance. In order to experimentally check the validity of these conclusions the performance of transverse biaxial tests is undertaken in this paper. The present investigation begins with the presentation of the cruciform geometry selected for the specimen and is followed by the description of the specific manufacturing procedure employed. The results of the testing campaign carried out agree with the previous numerical prediction and provide relevant information for the prediction of failure initiation. 1. Introduction The study and prediction of the failure mechanisms affecting long fibre reinforced composites is a fundamental field that provides an essential knowledge for the industrial use of these materials. The transverse failure, generated at ply level by the mechanism of damage known as inter-fibre/matrix failure, may occur in unidirectional laminates when transverse loads are applied, or in multidirectional laminates subjected, for instance, to impact loads. This damage mechanism has been numerically studied at the micromechanical level for the case of uniaxial loads by París et al. [1] (tension) and Correa et al. [2,3] (compression), being able to identify the different stages that lead to the macro-failure. This mechanism, of enormous importance given that it usually determines the damage initiation in any laminate, has focused the attention of many researchers. Specifically, in the field of numerical studies, various numerical tools (BEM and FEM) and approaches have been used, involving models with a greater or lesser number of fibres, see, for example, the case of Sandino et al. [4], using two-fibres BEM models, Kushch et al. [5] employing multifibre FEM models with cohesive elements and T´ avara et al. [6], applying LEBIM (Linear Elastic Interface Models) in multifibre FEM models. This problem has also been analyzed based on Finite Fracture Mechanics, for example in the tensile uniaxial case, Mantiˇ c [7], or other loading situations such as the one studied by Carraro and Quaresimin [8], who proposed a Finite Fracture Mechanics based model to analyse the initiation of fibre–matrix debonding under a combination of plane tension and out of plane shear. Some authors have focused on the most initial phase of the damage, such is the case of Hojo et al. [9] and, more recently, Sharifpour et al. [10]. Instead, other authors have concentrated on the step prior to the formation of the macro-crack, as is the case of Zhuang et al. [11,12]. This type of numerical analysis is also being used to study ultra-thin plies and related phenomena of great relevance for the design with composite materials, such as the scale effect (see for instance Saito et al. [13] Arteiro et al. [14] and París et al. [15]). Although to a lesser extent than in the case of numerical studies, especially with regard to the micromechanical level, there are some authors who have approached this problem from an experimental point of view. To the already classic and outstanding works of Zhang et al. [16] and Gamstedt and Sjr¨ ogren [17] in the observation of interface cracks in static load tests [16] and dynamic load tests [17], it can be added the works of Genz et al. [18], who evaluated the presence of thermal residual stresses; Baral et al. [19], who studied the effect of the fibre type; Hobbiebrunken et al. [20], who analysed the behaviour at * Corresponding author. E-mail address: [email protected] (E. Correa). Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct https://doi.org/10.1016/j.compstruct.2022.115868 Received 7 February 2022; Received in revised form 17 May 2022; Accepted 1 June 2022 Composite Structures 297 (2022) 115868 2 both high and low curing temperatures, Saito et al. [21], who analysed the effect of a 90◦ply thickness on the appearance of damage in cross-ply laminates; and Martyniuk et al. [22], who employed X-ray microtomography in single fibre specimens to evaluate debonding initiation and propagation. More recently, Correa et al. [23] carried out measurements of the different phases of the tensile damage mechanism in cross-ply laminate specimens by means of optical microscopy, and Zumaquero et al. [24] employed similar tools in the microscopical observation of the compression damage mechanism. The matrix failure under tension, characterized by a plane of failure perpendicular to the applied tension, is assumed to be formed by the generation of cracks in the fibre–matrix interfaces that, after reaching a certain length in the interface, kink towards the matrix giving rise to the macro-crack, París et al. [1]. This failure mechanism is represented in Fig. 1a where, together with a scheme of a 90◦unidirectional laminate subjected to tension, a microscopic image of the failure is shown. The inter-fibre failure under compression, Fig. 1b, is characterized by an orientation of the fracture plane around 53◦(Puck and Schürman [25] and Christensen and De Teresa [26]), whose explanation also lies in the micromechanical formation stages of the identified damage [2,3] and it is based again on the length of the interface cracks and their posterior kinking angle. With reference to the biaxial transverse loading cases, it has been historically assumed that the matrix failure takes place in the plane governed by the components of the stress vector associated with the referred plane, Hashin and Rotem [27], and, therefore, the presence of a secondary transverse traction (compression or tension, as shown in Fig. 1c) was not considered relevant in the generation, for instance, of matrix failure under tension. In order to check this hypothesis Correa et al. [28,29], numerically analysed the effect that the presence of a secondary load (perpendicular to the main load causing the failure) might have in the failure initiation and progress. The conclusions obtained showed that the stages of the damage mechanism detected in the uniaxial case could be affected. Specifically, the presence of a secondary tension, perpendicular to the tension nominally responsible for the failure, could alter some features of the initial phases of the damage mechanism established for the uniaxial case such as the length of the interface crack and its morphology. It was concluded, anyhow, that the effect of this secondary tension did not significantly alter the failure value of the tension nominally responsible for the failure. In contrast, when the sign of the secondary traction turns into compression, in addition to some differences established in the micromechanical stages of the damage mechanism, it was shown that the appearance of failure could be advanced. Aiming to experimentally check the validity of these conclusions and also the adequacy of some of the hypotheses in which the numerical studies were based, the performance of transverse biaxial tests is undertaken in this paper. A cruciform base shape is selected to define the specimen geometry. Over the years there have been many works where possible geometries of cruciform specimens have been developed, both for metallic materials and for composite materials, although none specifically deals with the problem raised here: application of biaxial loads in the plane transverse to the fibre direction. Specifically, Smits et al. [30] developed a biaxial test equipment and, after a comparative test of various configurations, made a proposal for a metallic specimen on which some later studies have been based. Makris et al. [31] and Liu et al. [32] proposed, the first for composite materials and the second for metallic materials, a parameterization tool to achieve the specimen geometry that best fulfils the requirements; Rashedi et al. [33] proposed a mixedmode fracture criterion based on biaxially testing cruciform fibre glass specimens from cross-ply laminate. Xu et al. [34] studied a specimen with a shape similar to a cube, manufactured from a process in which pyrocarbon matrix is infiltrated in the set of carbon fibres arranged at 0◦and 90◦. Skinner et al. [35] studied the fatigue behavior of carbon fibre composite material subjected to biaxial loads, and French et al. [36] proposed a new coupon design made up of two aluminum sheets, the material to be tested being placed between them, in this case, carbon fibre and epoxy resin. Lastly, and more recently, Kang et al. [37] studied PEEK composites presenting a specimen with a circular thickness reduction in the center and applying four longitudinal notches in each arm. A series of requirements must be taken into account for the design of the specimens subjected to transverse biaxial loads, they are: (i) Generation of a uniform biaxial stress state in the specimen during the test and in the area susceptible to fail. (ii) Maximization of the area nominally subjected to biaxial stresses. (iii) Minimization of the possibility of stress concentration zones. (iv) Failure occurrence must take place within the area subjected to the uniform biaxial stress state. This problem was initially addressed in Correa et al. [38] where 4 designs of cruciform specimens with 90◦unidirectional laminates were studied at different load levels by means of Finite Element models. These designs revealed that there was a remarkable concentration of stresses arising for all cases in the free edge region of the specimen. From the performance of experimental tests using a biaxial device adapted to a universal uniaxial testing machine, Barroso et al. [39], these numerical predictions were validated. Subsequent geometrical modifications of the specimens gave rise to a significant reduction in the stress concentrations and made it possible to obtain an area with uniform stresses. However, the best proposed design presented a geometry that was difficult to reproduce in a manufacturing process and its real behaviour could not be experimentally tested. The objective of the present work is the definitive design and the manufacture of a cruciform specimen based on what is stated in [38] and the development of an experimental testing campaign in a biaxial testing machine that allows the effect of secondary transverse traction (tension Fig. 1. Inter-fibre/matrix failure under (a) tension, (b) compression. (c) Biaxial transverse loads. P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 3 or compression) in the failure of specimens subjected to a primary transverse tensile load, Fig. 1c, to be determined. The paper is structured as follows: in Section 2.1 the geometry of the specimen to be manufactured is presented, in Section 2.2 the manufacturing process followed is described. Section 3 is devoted to the experimental campaign of biaxial tests and the discussion of the results obtained. The analysis of results will be completed with the search in the tested specimens of the initial point of failure, Section 4, and the measurement of strains in the center of the specimen, Section 5. 2. Manufacturing of the specimens 2.1. Geometry of the specimen The starting point for this work has been the D-M2 proposal of a cruciform coupon presented in [38]. However, a series of modifications were performed after some preliminary manufacturing trials in order to, first, overcome the limitations of the manufacturing process and the complexity of the machining phase and, second, improve the specimens’ behaviour. First, the new cruciform specimen to be manufactured presents a reduction in size with respect to the D-M2 specimen, both in length and width of the arms which also lead to a consequent reduction of the central zone thickness (although its shape is maintained). The specimen will have a total thickness of 7.5 mm and a central zone thickness of 2 mm, the minimum recommended avoiding undesirable splitting during the machining process (see Section 2.2). Second, and as indicated in [38], the stress concentration that could exist in the boundary between the central zone and the transition zone could be smoothed thanks to a new fillet radius of 1.5 mm that could be achieved through the machining process. Finally, the distance between the outer edge of the transition zone and the join between arms is also 1.5 mm, the minimum value allowed which avoids breakage in that zone during the machining process (see Section 2.2). Fig. 2 shows a design of the final configuration specimen to be manufactured. 2.2. Manufacturing process The manufacturing process of the cruciform specimens whose geometry is shown in Fig. 2 begins with the elaboration of a cross-section prism from a carbon/epoxy prepreg (HexPly® 8552/34%/UD194/AS4/ 150 ATL) from which the coupons are cut, and finishes with the numerically controlled machining process that allows the final desired shape and size of the specimens to be obtained. The different phases of this process are listed next, briefly explained and schematically summarized in Fig. 3: Step 1: Material cutting, fresh panels lay-up and preparation for the prism set-up. Two sets of 108 plies are laminated forming two 300 ×150 mm 2 unidirectional laminates. This process involves intermediate precompactions of 10′after 5 plies are staked (Fig. 3a). Next, one of the panels is divided in two halves. Step 2: Assembly of the cross-sectional prism. The three laminates are cut to achieve their final dimensions (Fig. 3b) and the cross-sectional prism is built using the three prepared arms and 4 300x60 mm 2 aluminium blocks, Fig. 3c, helping to maintain the cruciform shape during the curing stage. Step 3: Curing process. The prism is placed in a vacuum bag (Fig. 3d), vacuum is performed and then the whole set is introduced in an autoclave. The curing cycle reaches a maximum temperature of 180 ◦C and lasts 8′5h. The cured prism can be observed in Fig. 3e. Step 4: Cutting process. The specimens are cut from the prism using a water refrigerated diamond disk. It is a very challenging stage given the size of the prism, the amount of material in the central area of the piece and the fact that the arms are cantilevered when meeting the cutting disc. These difficulties were overcome; an image of the successful cutting process is shown in Fig. 3f. Step 5: Inspection of the specimens. Optical inspection with both a magnifying glass and an optical microscope is performed on all specimens to check if they present any defect as result of the cutting or manufacturing process, Fig. 3g. Step 6: Numerically controlled machining of the cruciform specimens. Fig. 2. Geometric proposal (dimensions in mm). P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 4 The type of material, the position of the fibre in the specimen and the fact that two thickness reductions in the central area of both faces of the specimen have to be machined, make the machining process very complicated, and premature breakage of the coupon may occur. To overcome these difficulties a special fixing device is manufactured, Fig. 3h, and a specific process consisting in the progressive reduction of the thickness of the specimen in the central zone alternating both transverse faces followed by the machining of the boundary is applied. Step 7: Adhesion of the tabs to the specimens. Tabs are manufactured from glass fibre 45/-45 fabric. They are stuck to the specimens by means of an epoxy nylon base adhesive and, finally, they are introduced in the autoclave. The adhesive curing cycle reaches 125 ◦C. Fig. 3i shows the final coupon. This manufacture was based on the process summarized in [38] although some improvements have been made. First, in Steps 1 and 2, the final dimensions of each fresh laminate (set of plies stacked before curing) have been reduced once cut in order to avoid undesirable bending during the curing stage. The lay-up process has also been modified using a steel frame that avoids the bending of the edges of the fresh laminate during the successive compactions that are made along this step. In Step 3, no clamping system was used during the autoclave curing cycle in order to avoid undesirable boundary conditions that could limit the natural expansion of the piece. Referring to Steps 4 and 5, the specimens were not sanded after cutting to prevent differences in the thickness direction; as an alternative, a specific cutting process has been established for these specimens mainly based in a constant, controlled and very slow advance of the prism towards the cutting disc that assures an excellent result both in the flat and smooth aspect of the cutting surfaces and the parallelism between them. This precise process lasts around 30′for each specimen. With reference to Step 6, it was decided, after some preliminary tests, to include the edging of the join between the arms of the specimens as part of the numerically control machining. Finally, a totally new numerical control process has been designed (which includes the design and manufacture of auxiliary tools) to obtain the shape and various thicknesses specified in Fig. 2. The final manufacturing process shown here is the result of numerous trials, ensuring the success of all manufactured specimens. 3. Testing campaign The tests were performed on a biaxial electromechanical machine EM4/50/FR from Microtest, expressly designed for them, which comprises four electromechanical load actuators, in orthogonal arrangement and facing two by two. They present a maximum force of 50 kN and a Fig. 3. (a) Step 1: Compaction process. (b) Step 2: Fresh laminate cutting. (c) Step 2: Prism assembly. (d) Step 3: Vacuum bag prepared for curing. (e) Step 3: Cured prism. (f) Step 4: Cutting by diamond disk saw. (g) Step 5: Optical inspection. (h) Step 6: Fixing device for numerically controlled machining. (i) Step 7: Final specimen with tabs. P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 5 speed of 0 to 50 mm/min variable from the control system that includes 4 manual clamping jaws. The machine is capable of applying both tensile and compressive biaxial loads. On the other hand, the actuators, together with the transducers and the clamps, are numbered and arranged as shown in Fig. 4a. Furthermore, the machine considers one actuator as a master and another as a slave on each axis. In the case of the vertical axis (2-axis in the material reference system), the master actuator is number 2 and the slave is number 4. For the horizontal axis (3-axis in the material reference system), the master actuator is number 1 and the slave is number 3. 3.1. Tension-tension transverse tests Tension-tension transverse tests (T-nT tests) have been carried out by placing the specimen in the machine in such a way that the continuous material arm is held by clamps 2 and 4 of the vertical axis of the machine, and the discontinuous material arm is held by clamps 1 and 3 of the horizontal axis of the machine, Fig. 4. In addition, the actuators on the vertical axis of the machine will apply the main tension while the actuators on the horizontal axis will apply the secondary tension. Preliminary tests were performed to assure that no undesirable bending was introduced in the specimens during the tests. The control mode used has been displacement although a few specimens were force controlled in order to check the influence of this choice. A biaxiality coefficient n is defined: it represents the ratio between the horizontal displacement of the horizontal clamp and the vertical displacement of the vertical clamp. Therefore, the limit case n = 0 would correspond to the uniaxial case (in which only an external vertical load is applied at the vertical arm and the specimen is free in the horizontal direction), whereas n =1 represents the symmetrical biaxial case in which the same amount of load is applied along both arms. In order to be able to monitor the beginning of the formation of cracks up to the breaking of the specimen, a high-speed camera model Min AX200 and Photron PFV software have been used to record the tests. Prior to initiating the experimental testing campaign the material characterization both under tension and compression was carried out. The transverse tensile strength measured was Y T =61.5 MPa (CV = 11%) and the transverse compressive strength was Y C =238 MPa (CV = 4.5%). The testing campaign started with the tensile uniaxial tests (T-0 tests) performed on cruciform specimens. 6 coupons were tested, half of them in a universal tensile testing machine and the other half in the biaxial testing machine only employing the actuators in the vertical direction. No relevant differences were found between the results provided by both machines. The results of the ultimate force applied at the vertical axis, F v , are collected in Table 1. Notice that F v is the media between the values provided by actuators 2 and 4 (Fig. 4a). If the ‘apparent’ stress at the vertical arm, σ V , associated with the F v value of each specimen and calculated dividing F v by the sectional area of the arm of each specimen, a mean value of 19.5 MPa (CV =10.4%) is obtained, which supposes a slight scatter for transverse tests. Note in any case that the scatter of all tests performed on the cruciform geometry proposed in this work is conditioned by two factors: first, the thickness differences that might exist between the arms of each specimen and, second, the thickness differences that could exist between the central zones of the different specimens. This second factor should be more critical since the failure actually takes place in the central zone. Additionally, it can be noticed that the mean σ V value calculated is far from the tensile transverse strength of this material; this result is completely coherent since, as mentioned, the rupture of the specimens takes place in their central zone and the arm thickness is 3.75 times the central zone thickness, see Fig. 2. This idea will be better explained in Section 3.3. Once the tensile uniaxial tests were performed, the tension–tension (T-nT) biaxial testing campaign was undertaken intending to cover different biaxiality ratios (specifically, n =0.25, 0.5, 0.75 and 1). In Table 2 the values of the ultimate forces applied both in the vertical axis, F v , and horizontal axis, F h , are included as well as the specific values of n coefficient measured at the instant of failure. The control mode was displacement in all cases except for TT1, TT2, TT3 and TT4 specimens where it was force controlled. No mean forces or stress values are detailed now and the discussion of these results in comparison with those presented for the T-0 and T-nC cases will be discussed in Section 3.3. 3.2. Tension-compression transverse tests The tension–compression transverse tests (T-nC tests) were performed using the same procedure than in the T-nT campaign. The Fig. 4. (a) Biaxial electromechanical machine EM4/50/FR. (b) Scheme of the location of the continuous and discontinuos arm of the specimens. Table 1 T-0 experimental results. Specimen F v (kN) T-0 T0-1 2,58 T0-2 3,07 T0-3 2,34 T0-4 2,89 T0-5 2,73 T0-6 2,58 P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 6 continuous material arm is held by clamps 2 and 4 of the vertical axis of the machine, and the discontinuous material arm is held by clamps 1 and 3 of the horizontal axis of the machine, Fig. 4. The actuators located along the vertical axis of the machine applied the main tension while the actuators along the horizontal axis applied the secondary compression. Preliminary tests were performed to assure that no undesirable bending was introduced in the specimens during the tests. This testing campaign was performed intending to explore different values of the biaxiality ratio (specifically, n =-0.25, −0.5, −0.7, −0.8 and −1). In Table 3 the values of the ultimate forces applied both in the vertical axis, F v , and the horizontal axis, F h , are included as well as the values of n coefficient measured at the instant of failure. All tests were displacements controlled. As explained in Section 3.1 the discussion of these results together with those corresponding to the T-0 and T-nT coupons will be performed in Section 3.3. 3.3. Discussion of results In order to analyse the effect of the secondary tension/compression in the final failure occurrence, the nominal rupture values of all loading cases are represented together in Fig. 5. These results are presented in terms of ‘apparent’ stresses associated both with the vertical and horizontal actuators, σ v and σ h respectively, in the instant of failure (i.e.: σ v =F v /A, σ h =F h /A, A being the specific area of the transverse rectangular section of the arms of each specimen). Although this stresses do not correspond to the stresses located in the zone were the failure takes place they can be used as an indicative of the state of each specimen in the instant of failure. Analysing the tendencies shown by the different loading cases in Fig. 5 it can be observed that whereas the presence of the secondary horizontal tension does not significantly alter the value of the vertical tension needed to promote the failure of the specimens, the presence of a secondary compression seems to reduce the value of the vertical tension required for it, at least from a certain amount of applied compression. These experimental results are in agreement with the conclusions exposed in Correa et al. [28] derived from the micromechanical numerical analysis there performed. This idea is perhaps better represented by Fig. 6 where the vertical stress is represented versus n; in this Figure the σ v mean value obtained for the T-0 tests is taken as a reference including it as a horizontal line. This new representation also helps to check the scatter of the results for each loading case (i.e. those corresponding to the same n value). Another important feature is the location and orientation of the plane of failure, see Fig. 7 where pictures of broken specimens appear for different loading conditions. This plane was in all cases (T-nT and T-nC) perpendicular to the main tension. When more than one crack is produced (see for instance Fig. 7c and 7e) the inspection of the videos allowed identifying the crack responsible for the failure. This question will be specifically addressed in Section 4. The main tension is associated with the vertical axis in all tests except in some T-T (n =1) specimens where the tension in the horizontal axis was slightly higher than the vertical one. Coherently, the plane of failure was always horizontal for all specimens except in those mentioned n =1 coupons where it was vertical. These results also prove the success of steps 1 and 2 of the manufacturing process, in particular, of the designed sequence for the assembly of the cross-sectional prism. Remember that whereas the prism was formed by a single laminate in the vertical direction, two independent laminates were necessary for the horizontal arm. It could be then have been thought that this discontinuity would perhaps lead to some weakness in the horizontal direction of the coupons and thus induce to a premature failure in the vertical direction, but the experimental results have demonstrated that the orientation of the plane of failure is exclusively governed by the dominant tension. The results on the orientation of the plane of failure obtained in this work are also in agreement with the conclusions exposed in Correa et al. [28] (exclusively derived from micromechanical numerical models). In [28] failure initiation was always associated with the tension nominally responsible for the failure and therefore the tensile matrix failure was considered to prevail over the compressive matrix failure in all T-nC cases. The experimental evidence presented in Fig. 7 also reveals an important result that could not be proven with the numerical analysis presented in Correa et al. [28]: for the n =1 limit case (T-T) the failure plane is always vertical or horizontal (i.e. perpendicular to the main tension). The numerical results [28] showed that all points of the interface had the same probability of housing an initial debond, but the evolution of this debond, as well the latter stages of the mechanism of damage that lead to the final macro-crack, where only analysed for the case in which this initial debond arose at one of the poles. It was proven in those cases that the failure plane had to be horizontal or vertical but it could not be checked what the orientation of the failure plane would be if the location of the initial debond were a different one. Table 2 T-nT experimental results. Specimen F v (kN) F h (kN) n T-0.25T 25T-1 2,93 0,71 0,25 25T-2 3,05 0,88 0,25 25T-3 3,11 0,80 0,25 T-0.5T 5T-1 2,53 1,56 0,50 5T-2 2,41 1,63 0,50 5T-3 3,33 1,78 0,50 5T-4 2,84 1,43 0,50 5T-5 2,47 1,24 0,50 T-0.75T 75T-1 2,53 1,82 0,75 75T-2 2,94 2,25 0,75 75T-3 2,66 1,76 0,75 75T-4 3,19 2,37 0,75 75T-5 3,04 2,30 0,75 T-T TT-1 2,78 2,81 1,02 TT-2 2,77 2,80 1,02 TT-3 2,38 2,42 1,02 TT-4 2,52 2,50 1,12 TT-5 2,84 2,54 1,00 Table 3 T-nC experimental results. Specimen F v (kN) F h (kN) n T-0.25C 25C-1 2,12 −0,23 −0,25 25C-2 2,26 −0,29 −0,25 25C-3 2,57 −0,25 −0,25 25C-4 2,69 −0,20 −0,25 25C-5 2,89 −0,20 −0,25 T-0.5C 5C-1 2,76 −1,28 −0,50 5C-2 2,85 −1,16 −0,50 5C-3 2,82 −1,32 −0,50 5C-4 3,40 −0,97 −0,50 T-0.7C 7C-1 2,26 −2,03 −0,70 7C-2 2,04 −1,66 −0,70 7C-3 2,14 −1,61 −0,70 7C-4 2,11 −1,39 −0,70 7C-5 1,80 −1,09 −0,70 7C-6 1,94 −1,30 −0,70 T-0.8C 8C-1 2,20 −1,66 −0,80 T-C TC-1 2,42 −3,22 −1,00 TC-2 2,04 −2,73 −1,00 TC-3 2,27 −2,37 −1,00 TC-4 1,70 −1,72 −1,00 P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 7 With reference to the location of the plane failure, see Fig. 7, for the uniaxial case and all T-nT cases the failure always started at the central zone of the specimens, as desired. It seems then that the thickness reduction machined in this central zone was enough to convert it in the failure zone, the result pursued since this is the biaxial stresses zone where the effect of the secondary traction wanted to be analysed. Therefore, this experimental evidence proves that the cruciform geometry presented in this paper fulfils its objective and does not produce any undesirable stress concentration under T-nT loading that could force the specimen to break in a non-biaxial stress zone (for instance in the joint between the arms). Focusing now on the T-nC cases, the location of the plane of failure occurred in the central zone of the specimens subjected to low-medium compression (i.e. n >−0.7). For n = − 0.7 (Fig. 7h) some of the specimens broke in the slope zone that enables the transition between the central zone and the rest of the specimen; this is still a biaxial stress zone although not as controlled and uniform as the central one. It was checked in the video recording of the tests that the origin of failure occurred in this transition zone and not in the outer boundary of the specimen. This situation also occurred for the specimens corresponding to the n = − 1 case, although some of them broke in the outer boundary. In this sense it should be remarked that this cruciform specimen was initially designed and adjusted to perform T-nT and not T-nC tests [38], therefore this evidence has shown that this geometrical proposal also works well for moderate compression. Geometrical modifications should be performed for a better adequacy to high compressive cases or, Fig. 5. Ultimate vertical stress, σ v, versus ultimate horizontal stress, σ h . Fig. 6. Ultimate vertical stress, σ v, versus n coefficient. P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 8 alternatively, a simpler rectangular specimen and a different compressive loading system could be employed, París et al [40]. In addition, a proposal has recently been made dealing with compression in biaxial tests, Serna and Horta [41], whose adequacy for these particular tests could be explored. 4. Identification of the initial point of failure The video recording of the tests by means of a high-speed camera has been essential for the analysis of the specimens failure. The photograms were analysed in order to detect the initiation of the first crack. As mentioned in the former Section, this was very useful in the cases where the specimen presents more than one crack once broken. The photograms were also used to try to locate the exact point where the first crack appears. This identification requires a complementary post-mortem optical inspection of the broken specimen, since the point/area of failure location currently shows a subtle change in colour and texture in the carbon-epoxy specimen. The xy coordinates of the initial failure points where measured for all specimens and they are all represented together in Fig. 8 superimposed on a real image of the central zone of the specimens. It must be noted that failure points out of the area represented in the Figure are not included as well as failure points whose location was Fig. 7. Location and orientation of the failure plane in broken specimens. P. Lucía Zumaquero et al. Composite Structures 297 (2022) 115868 9 not clear enough. The first noticeable feature in Fig. 8 is that there is a significant number of failure points that are placed right on the vertical axis. Specifically, the uniaxial case and all the T-nT cases for n ≤0.5 and some n =0.75 specimens. However, the initial points of failure of some n =0.75 specimens and all n =1 specimens move away from that axis. These cases, specifically those with n =1, are anyhow located symmetrically with respect to both axes (remember the double symmetry of the coupons) so that, in fact, they correspond to points with the same stress state. Regarding the T-nC cases, they are also quite close to the vertical axis, and those corresponding to the same n value are located in a similar position, only in the n =-0.25 group some discrepancies are detected. To sum up, most initial points of failure are located in the vertical axis, except for biaxial cases close to the T-T situation. This ordered distribution of points on the one hand reinforces the idea of a successful result of the manufacturing process in terms of the symmetry of the geometry achieved, also of an adequate alignment of the load during the tests, and, on the other hand, shows a dependence of the failure initiation on the biaxial stress state that would be worth studying by means of a numerical model. 5. Analysis of the strain state at the centre of the biaxial zone The experimental data directly collected during the tests refer fundamentally to the value of the external loads at the instant of failure that, in some way, can be related to the longitudinal stress in the arms of the coupon, as it has been done in Section 3.3. In order to obtain information about the value reached by the elastic variables in the zone of greatest interest, that is, the biaxial (central) zone of the specimen (the one in which the failure also occurs), a selection of specimens was instrumented with strain gauges. The aim was to accurately measure during the tests the normal strains in the centre of the biaxial zone. The size of the area in which the strain gauges were to be adhered is really small and also presents some complexity, given that its width is barely one centimetre and the zone is surrounded by inclined walls. With this premise, a small rosette was selected, specifically CEA-06-062WT-350 from Micro- Measurements® (Vishay Precision Group). It is a tee rosette formed by two perpendicular gauges from which to measure the normal strains associated with the vertical axis, ε 22 , and the horizontal axis, ε 33 . The results of the measurements of these gauges provided the value of the strains at the moment of rupture in the centre of the area where the specimen breaks. In this sense, and although as shown in Fig. 8 the initial point of failure is not exactly the centre in all cases, the strain state in this failure point must be quite similar to the central one since the design of the specimen in which this one is based, ensured a fairly uniform strain state in the biaxial zone [38]. In addition, as it is well known, the strain measurements, although associated with the central point, in fact represent the strain state in the zone occupied by the bands. Fig. 9 shows an image of a coupon with an already glued rosette. As mentioned in Section 3, in a preliminary testing campaign strain gauges were employed on both transverse sides of the specimens to verify that no bending was introduced. Subsequently, for the specimens whose results are being presented in this work, and given that the beginning and generation of the failure process wanted to be observed, only the rear face of the specimens was instrumented in order not to occupy the front face with the bands, since that is the area to be recorded by the video camera. Regarding the results obtained by these strain gauges, Fig. 10 shows the force applied in the vertical axis, F v , compared to the measure of the vertical band, ε 22 , in a specimen corresponding to the uniaxial loading case (T0-6 specimen) from the beginning of the test until failure. An expected almost linear elastic behaviour is observed during the whole test. A similar behaviour is observed in most loading cases dominated by tension (T-nT cases). However, in the loading cases in which the secondary external load is a compression, a certain non-linear behaviour is observed during the whole test, as shown in Fig. 11 where F v is plotted against the measure of the vertical band, ε 22 , for the 8C-1 specimen. This behaviour, typical of transverse compressive tests (Soden et al. [42]), indicates in this case an effect of the secondary compression even though the damage mechanism that prevails is dominated by the main tension, as shown in Section 3. Fig. 12 shows, for the set of representative specimens of the cases tested, the measurement at failure of the vertical gauge, ε 22 , compared to the measurement at failure of the horizontal gauge, ε 33 . Observing the points obtained, it is noticeable in the first place that the distribution of the state of biaxial strains in the centre of the specimen at the moment of rupture, at least apparently, shows a linear trend. It is observed that as the secondary compression increases, the value of ε 22 also does, to which the Poisson effect will undoubtedly contribute, while, as the secondary traction increases, ε 22 decreases. During the material characterization tests prior to the biaxial testing campaign, it was found that the transverse tensile failure strain, ε 2T , was 6540 με . Observing the results presented in Fig. 12, it is now verified that this value would be located in the neighbourhood of the points associated with the T-0.25T case and not T-0, as would be expected. This result suggests that in the centre of the specimen the biaxiality relationship is not the same as that calculated from the applied external load. This circumstance can be better understood if the normal stresses σ 22 and σ 33 associated with the strains measured by the strain gauges are calculated. An estimation of these values can be obtained through the stress–strain law assuming generalized plane stress and transverse isotropic behaviour of the material. If these stresses are calculated using the proposed estimation, the approximate value of the normal stress Fig. 8. Points of location of initial failure. Fig. 9. View of a specimen prepared with strain gauges. P. Lucía Zumaquero et al.