A new in situ peeling test for the characterisation of composite bonded joints

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 A new in-situ peeling test for the characterisation of composite bonded joints J. Ca˜nasa, L. T´avaraa,⇤, A. Bl´azqueza, A. Estefania, G. Santacruzb aGrupo de Elasticidad y Resistencia de Materiales, Escuela T´ecnica Superior de Ingenier´ıa, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain bAirbus Operations SL Getafe, Madrid, Spain Abstract At the moment, bonded joints quality on composites used in aeronautical industry is verified based on the determination of the interlaminar fracture toughness (Gc) obtained by means of the Double Cantilever Beam (DCB) or the Climbing Drum Peel (CDP) tests. Although they are well-established tests, they have known limitations. This investigation presents the design and validation of a new device that carries out a peeling test, its main advantage being the capability to perform the test in-situ, i.e. directly on the actual aircraft production line without the necessity to extract coupons for a laboratory test. An experimental campaign has been carried out, the obtained results being comparable to those obtained with the traditional DCB and CDP procedures. Numerical studies have allowed to understand the delamination mechanisms presented at the di↵erent tests, confirming that experimental Gcevaluation obtained is adequate. Keywords: Interlaminar fracture toughness, DCB, Climbing drum peel, in-situ test ⇤Corresponding author. Tel.: +34 954487299; fax: +34 954461637. Email address: [email protected] (L. T´avara) Preprint submitted to Composites Part A June 1, 2018 *Manuscript reviewed Click here to view linked References This is an Accepted Manuscript of an article published by Elsevier on Composites Part A: Applied Science and Manufacturing, Vol. 113, on October 2018, available at: https://doi.org/10.1016/j.compositesa.2018.07.014 Copyright Elsevier 2018. En idUS: Licencia Creative Commons CC BY-NC-ND 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1. Introduction The evaluation of composite-composite bonded joints quality is a major problem for the industry, in particular for the aerospace sector where the use of composite materials in primary structures has considerably increased. Given by the fact that a defective joint not only could paralyze the productive process, but it could also involve very high repairing costs. Experimental tests and numerical tools have been implemented in order to understand the failure modes and critical loads in this kind of component/structures [1, 2, 3]. A very common aeronautical structural components are the sti↵ened panels which include a skin reinforced by the addition of a set of stringers which are usually bonded. The main advantages of bonded joints against bolted joints are the relevant reduction of production time and that holes and other disruptions are avoided. On the contrary, the quality of the bonded joint can not be guaranteed by usual non-destructive tests (NDTs). This kind of tests are only able to determine if a large discontinuity (interface crack) between the adherent parts exists, but they are not capable to guarantee the conditions of these bonded joints. Thus, a quality control of the bonding process are demanded for Certification Authorities. Then, a test that should be able to evaluate the quality of the resulting joint of the whole process is necessary. The results of the test will capture any deficiency derived from: store conditions of the materials before the process itself, the use of an inadequate combination adherent-adhesive, the presence of pollutant agents within the bonded joint, among others. Currently, the quality of a bonded joint in aeronautical industry is quantified by interlaminar fracture toughness (Gc) tests. The most commonly used are the Double Cantilever Beam (DCB) [4, 5, 6, 7, 8, 9] and the Climbing Drum Peel (CDP) [10, 11] tests. These tests measure Gc in a specimen that is bonded suppositionally under the same conditions as actual parts 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (usually taken from these components). One disadvantage on both tests is that they cannot be carried out “in-situ”, i.e. on specimens over actual parts. Moreover, there are still some open questions e.g. regarding the way Gcis calculated and the actual fracture mode occurring on the tests, among others. Although DCB and CDP are the most common tests, there are some alternatives as the peel test [12] or the mandrel peel test [13] but they also have similar disadvantages. The aim of the present investigation is to design and validate a new device able to determine Gc“in-situ”, preserving the advantages of the DCB and CDP tests and also overcome some of their drawbacks. The paper is organized as follows. The main characteristics of the currently used tests (DCB and CDP) are described in Section 2. Then, the principles for the new test are discussed in Section 3. The results for the test campaign are presented in Section 4 and the numerical results (virtual testing) are included in Section 5. Finally, Section 6 contains the conclusions of the present investigation. Some Appendices are also presented with the aim to answer some of the questions raised on the new test concept. 2. Gctests overview In general terms, DCB and CDP tests relies on the fracture toughness calculus defined as the released energy by area unit within an interface crack Gc, defined as: Gc=4E 4S=4E b4a(1) where Eis the energy necessary for crack propagation as function of the load and associated displacement, Sis the surface formed due to crack propagation, ais the crack length and bis the specimen width. Previous expression assumes that the crack extends across the whole width of the 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 specimen. Usually on every test configuration this asumption is correct as the crack front is regular. In the following the main aspects of both tests are described. It is important to recall that Gconly equals GIc (fracture toughness in pure fracture mode I) under very specific loading and geometrical conditions of the specimens, as it will be discussed later on. 2.1. DCB test The widest used test to obtain the fracture toughness is the DCB test. This test is used to determine the interlaminar fracture toughness in a composite material (i.e. between two laminaes within a laminate) [4, 6, 7] or to determine the interface fracture toughness of adhesively bonded joints (i.e. an interface crack grows along an adhesive layer) [5]. In the aeronautical industry, usually companies use their own standards [4, 5]. These standards use the load - displacement plot, obtained during the test, to calculate the fracture toughness using: Gc=A ba (2) where Ais the area of the pseudo-triangle defined by the origin and the loaddisplacement plot between two points, bis the specimen width and a is the increment of the crack length between the chosen points (usually 60 mm). Nowadays, DCB is the reference test to evaluate Gc. Its main advantages includes: (i) it is able to determine the fracture toughness in pure mode I (Gc=GIc) when symmetrical configurations are used, (ii) it is easy to perform, moreover expensive tooling is not necessary. Nevertheless, it also has some disadvantages: (i) standards require to measure the crack length which is not always an easy task, (ii) for thin laminates (when finite displacements appear) Gcformulae in the standards are not adequate even 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 using the correction factors included there [14], (iii) when non-symmetrical laminates are used the way fracture toughness is calculated is not adequate due to Gc6=GIc [15, 16] , (iv) it is not possible to perform the test “in-situ”. 2.2. CDP test An alternative to the DCB test is the so-called Climbing Drum Peel (CDP) test [11]. This test was originally conceived to evaluate the bonded joints between a flexible adherent and a rigid adherent or between the skin (laminate) and the core in a sandwich panel [10]. The test consists in winding a flexible laminate (which peels at the same time it winds) using a drum with two di↵erent radii (r2>r 1). The laminate is fixed to the drum in its central part which has radius r1. The outer parts (borders) of the drum (with larger radius, r2) includes two loading straps which will apply the torque required for the drum progression along the specimen. The ends of the loading straps are fixed at the bottom of a universal testing machine, while the un-cracked end of the specimen is attached to the upper jaws of the machine. Once the specimen is collocated, the upper cross-head of the machine moves up provoking that the flexible laminate gets into contact (winds) with the inner part of the drum. Then, the drum “climbs” along the specimen propagating the initial pre-cracked zone while the flexible laminates winds. Ascheme of the test can be found in [11]. In the load-displacements plots obtained during the tests, two constant load levels can be clearly observed. One associated to the winding load (Fw) and the other one associated to the winding+delamination process (Fd). Usually, Fwis calculated on a second stage of the test once a very large precracked zone is presented. Then, the fracture toughness is evaluated using (3). Gc=(FdFw)(r2r1) br1 ,(3) 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 where b is the width of the specimen. It is remarkable that the configuration of the test and the imposed kinematics leads to a stable crack propagation, under a constant applied force. Then, Gccalculation is straightforward as it is proportional to the constant applied force. Moreover, the crack growth is directly related to the applied displacement during the test. This fact implies that it is not necessary to measure the crack length. On the other hand, it is clear that the obtained fracture toughness with this test is not associated to pure fracture mode I(Gc6=GIc), thick laminates (>1mm) could not be tested (undesirable break of the laminate may occur) and finally, the test can not be performed “in-situ”. 3. Horizontal Drum Peel (HDP) test As described in the previous section, both DCB and CDP tests use a universal testing machine to apply the load. This fact makes impractical to perform these tests “in-situ”. The aim of the present investigation is to design a new test configuration with the following characteristics: (i) no need to measure the crack length, (ii) easy to perform, (iii) straightforward Gc evaluation, and (iv) able to perform “in-situ” [17]. The initial idea was to perform a Drum Peel in ahorizontal position and without the use of a universal testing machine. Thus, the rotation could be applied directly to the drum using an engine which moves a kinematic chain in order to get an adequate speed rotation. A torque cell will measure the torsional moment needed along the test. Obtained numerical results for the simplified problem presented in the Appendices, showed that critical radius values, Rc(producing the critical moment, Mc, that causes delamination), are di↵erent for each bonding configuration. A design able to reproduce these Rcvalues at the crack tip would be the ideal one. 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 If the drum radius, RD, plus half of the thin laminate thickness, t/2, equals Rcthe laminate will touch the drum during the whole delamination process, on the contrary it will separate. When RD+t/2<R cresults will depend on the gripping system, then a self-similar crack propagation is not assured. Finally, when RD+t/2>R cthe thin laminate separates from the drum. This separation is produced as the curvature (on the thin laminate) progressively changes in order to reach its corresponding Rcvalue at the crack tip. Moreover, during the whole delamination process Rcremains the same, i.e. a self-similar crack propagation occurs. Due to this fact, it is unnecessary to measure the crack length during the test and, additionally, results will not be a↵ected by this separation. That is why, this is the chosen condition. The complete test in the chosen HDP configuration includes two parts: (i) the laminate “winds” over the drum and (ii) after increasing the applied torque in the drum, “‘winding+debonding” occurs. It is important to notice that the bending moment occurring in the section of the thin laminate which is over the crack tip (M) is the only responsible of the crack growth. Thus, when this moment is lower than the critical one debonding will not occur. Two stages occurring after “winding only” part of the test can be identified: 1. Initially, the separation of the laminate from the drum increases while Mincreases too. Once Mreaches a certain value, Mc, the crack starts to propagate while the laminate also increases the separation from the drum. 2. After a while, the separation of the drum remains constant, leading to a self-similar crack growth i.e. the crack advance is equal to the winding in the upper part of the drum. On Figure 1, the present Horizontal Drum Peel (HDP) concept is shown. Notice that, the thick laminate is fixed at the bottom and the thin laminate is clamped to the drum in one of its extremes. A torque is imposed at the 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 θ 1 θ 2 ∆ θ= θ 2 −θ 1 ∆a T RD Figure 1: Scheme of the HDP concept. centre of the drum while it is free to move both horizontally and vertically. During the delamination process the crack length increment, 4a, and the applied increment of rotation of the drum, 4✓, are related by: 4a=RL4✓,with RL=RD+t 2(4) It is important to note that, during this stage, Mcremains constant and it is directly related to Rc, in the section over the crak tip. Moreover, although the curvature changes on the part where the laminate separates, the moments produced in any other section of the laminate do not a↵ect the crack advance. Although, Rccan not be controlled, it can be calculated as it is function of the laminate properties and the adhesive used, see Appendix A. This fact is confirmed by the numerical analysis done in Section 5. An energetic balance and expression (4) allows to compute 4E: 4E=(TdTw)4✓,(5) where Tdand Tware the moments (torque) associated to the wind8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 ing+delamination process and only winding process, respectively. Finally, Gccan be obtained using: Gc=(TdTw) bRL ,(6) where bis the width specimen. In order to prove HDP results validity, a test campaign and a virtual testing was done in the present investigation. Moreover, CDP tests are also performed for comparison purposes. 4. Experimental tests campaign Two bonding configurations were used for the campaign with two options for the thin laminate: Unidirectional 2 with t=0.5 mm (tape) and Woven fabric [+45/-45] with t=0.75 mm (fabric), see Tables 3 and 4 for the laminate and bonding configuration properties. Manufacturing of every coupon follows a co-bonding procedure. First, the thick laminate is cured using common procedures but leaving the peelply on one side. After this curing cycle, the peel-ply is removed and the thin laminate is joined to the thick laminate using an adhesive layer over the surface where the peel ply has been removed. The pre-crack is obtained by including a teflon film in the desired zone. Then, the whole system is subjected to a curing cycle, where both the thin laminate and the adhesive are cured at the same time. The materials used are: Adhesive: FM 300.k05, Tape: M21E35%/UD194/T800S-24k and Fabric: GM926+RTM6. The CDP tests were performed following [10]. A drum made of steel with inner radius r1= 75 mm and outer radius r2= 95 mm is used. Two steel loading straps with 0.2 mm in thickness and 25 mm in width, complete the tooling of the test. The total weight of the tooling was 25.5N. In figure 2, the set-up of the test is shown. Five coupons were tested for each configuration (tape or fabric). 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Table 2: CDP and HDP tests characteristics and Gcresults for the fabric. Climbing Drum Peel Horizontal Drum Peel Coupon b[mm] t[mm] Fd[N] Fw[N] Gc[J/m2] b[mm] t[mm] Md[Nm] Mw[Nm] Gc[J/m2] 125.14 0.58 198.2 145.0 557.6 25.18 0.52 1.94 0.51 598.5 225.27 0.60 201.3 143.8 598.3 25.18 0.53 2.09 0.48 671.6 325.19 0.60 206.5 143.8 654.5 25.28 0.56 1.84 0.52 549.5 425.18 0.58 198.5 143.1 579.2 25.18 0.56 1.97 0.54 598.5 525.15 0.55 203.1 141.7 642.8 25.34 0.55 1.86 0.49 568.5 fabric show a debonding + stitching failure mechanism where the failure of part of the laminate occurs, i.e. some fibres are detached. Figure 7: Fracture surfaces obtained for the fabric (left) and tape (right) case in the HDP test. 5. Virtual testing The aim of the FEAs is to reproduce numerically the curves obtained in the experimental test campaign. These numerical results helped to understand the behaviour of the delamination during the test. Moreover, the Virtual Testing also includes numerical results for CDP tests. 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5.1. FE model The FEA includes a 2D model in the commercial code Abaqus [18]. CDP and HDP models has the following similar characteristics: (i) both laminates include orthotropic properties as described in Table 3, (ii) the drum is modelled through an analytical rigid surface with a central node that controls the displacements and rotations, (iii) non-linear geometries (finite displacements and rotations) are used in the model, (iv) contact interactions between the drum and the thin laminate and between both laminates are also included, (v) the interface between the thin and the thick laminate includes a pre-cracked zone, (vi) and finally, the adhesive behaviour is included by using Abaqus built-in cohesive elements (COH2D4) which includes a bilinear traction-separation law and the Benzeggagh-Kenane damage criterion [19], see Table 4. GIc values used are obtained from a DCB test campaign for a tape/adhesive/tape configuration and a fabric/adhesive/fabric configuration when a FM300.k05 adhesive is included. GIIc values are assumed using the proportions found in [20] for the same kind of adhesive. Table 3: Properties in material coordinate system of the laminates used for the simplified model. Laminate E11(GPa)E33 (GPa) G12(GPa) ⌫12 Unidirectional 1 182 10 5 0.3 Unidirectional 2 135 10 5 0.3 Woven fabric 66 10 4.5 0.05 Additionally to the previous common characteristics, specific boundary conditions for the HDP consider, see Figure 8(a): •The bottom line of the thick laminate is fixed. •The free lateral edge of the thin laminate is attached to the drum by means of a Multi-point constraint (MPC) restriction. 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Table 4: Properties of the interface model used for both bonding configurations, ⌘=2 always. Bonding configuration c(MPa) ⌧c(MPa) GIc (Jm2)GIIc (Jm2) BC1 6 40 600 1200 BC2 6 40 870 2000 Thin laminate Adhesive layer Thick laminate Pre-crack Drum radius Imposed rotation (a) Imposed displacement Drum inner radius Drum external radius Loading strap Thin laminate Adhesive layer Thick laminate Pre-crack (b) Figure 8: Boundary conditions over the (a) HDP model and (b) CDP model. •A rotation is imposed on the central node controlling the drum, provoking the winding of the thin laminate and its subsequent delamination. On the other hand, the FEA for the CDP test includes, see Figure 8(b): •The extreme where the thick and the thin laminates are bonded is where the applied displacement is imposed. 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 •The drum weight is included by imposing an equivalent force in the centre of the analytical circumference, modelling the drum. •The loading straps are also included, with 0.2 mm in thickness and 50 mm in width (modelling two straps with 25 mm in width). They are modelled using steel properties, i.e. E= 210 GPa and ⌫= 0.33. The length of the straps is that corresponding to an inner radius equal to 97 mm (slightly larger than the outer CDP drum radius). •Contact conditions are also included between the loading straps and the drum. 5.2. Experimental and numerical correlation In this section, numerical results for the cases studied experimentally are presented and compared to them. In Figure 9, experimental and numerical force-displacement curves for the CDP tests are presented. As can be seen, there is a very nice correlation between both results. 623.5 and 948 J/m2were the Gcvalues obtained numerically for the tape and fabric case, respectively. The experimental values being 606.5 and 932.6 J/m2 respectively, leading to a di↵erence lower than 3% in both cases. In Figure 10, experimental and numerical torque-displacement curves are presented. Once again, there is a very good correlation between both results. 615 and 923 J/m2were the Gcvalues obtained numerically for the tape and fabric case, respectively. The experimental values being 597.3 and 952.6 J/m2respectively, leading to a di↵erence lower than 4% in both cases. It is also interesting to observe that the deformed shape obtained for HDP numerical model is almost identical to the one obtained during the experimental tests, as can be seen in Figure 11. In that figure the green lines correspond to the numerical obtained solution which are superposed to an experimental picture. 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (a) (b) Figure 9: Numerical and experimental results obtained using the Climbing Drum Peel test for (a) tape and (b) for a fabric. Finally, the numerical results allowed us to measure the fracture mode mixity occurring during the delamination in both CDP and HDP simulations. It is done by a post-process of the data obtained following [21], see details in Appendix B. values were 9.1and 14.6for the CDP models (tape and fabric, respectively), while were 8.2and 13.2for HDP models 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (a) (b) Figure 10: Numerical and experimental results obtained using the new Horizontal Drum Peel test for (a) tape and (b) for a fabric. (tape and fabric, respectively). This means that although a mixed mode appear during both tests Gcvalues will be very close to GIc values. Moreover, numerically obtained values (mode mixity measure) on HDP tests are lower than those for CDP tests. 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Figure 11: Numerical and experimental deformed shape of the HDP test for a specific moment. 6. Conclusions The basis for a new in-situ peeling test (HDP) able to determine the interlaminar fracture toughness are set. A test campaign including CDP and the new HDP configuration was developed. Obtained experimental results showed that Gcvalues obtained using both tests are in very good agreement with each other. Similar results were obtained in the virtual testing (by means of a FEA). Some characteristics of the HDP test includes: (i) A one step test, leading to obtain Twand Td(needed to calculate Gc) easily. (ii) A self-similar crack growth avoiding the necessity to measure the crack length. (iii) A separation of the thin laminate from the drum, tending to its critical radius. Nevertheless, the main advantage of the HDP configuration is the possibility to perform the test “in-situ”, without the necessity to extract coupons for their posterior testing in a laboratory. Some other relevant questions regarding the delamination behaviour on the CDP and HDP tests are analysed. Specifically, this study allowed to 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 confirm that: (i) Crack growth during delamination on CDP and HDP tests are self-similar, i.e. the same pattern is obtained during crack evolution. (ii) A mixed-mode fracture occurs for any coupon (iii) Gcvalues are very similar to GIc when the fracture mode mixity angle is lower than 20, condition that is fulfilled in both cases in the analysed configurations. Acknowledgements The authors acknowledge Prof. Vladislav Mantiˇc for the fruitful discussions about interfacial fracture mechanics and Mar´ıa del Mar Castro and Antonio Ca˜nas for their help on the test campaign. This research was conducted with the support of the Spanish Ministry of Economy and Competitiveness (Projects MAT201571036-P and MAT2015-71309-P) and the Junta de Andaluc´ıa and European Social Fund (Project of Excellence No. P12-TEP-1050). Appendix A. Delamination mechanisms. Critical moment and critical radius In this appendix a Finite Element Analysis (FEA) of a simplified problem is presented. The problem includes a specimen with two laminates bonded by an adhesive, see Figure A.11(a). The boundary conditions are a fixed line on the bottom edge of the thick laminate and an applied rotation, ✓, at the pre-cracked end of the thin laminate. It is interesting to recall that the imposed rotation causes a constant bending moment (M) and a corresponding constant curvature with radius R, along the thin laminate in the pre-cracked zone. The FEA was done using the software Abaqus [18]. A 2D FE model including orthotropic properties for the laminates, see Table 3, and geometrically non-linear analysis is considered. 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (a) (b) Figure A.12: (a) Simplified model of HDP device and (b) bending moment, M, vs applied rotation, ✓, produced in the simplified model. The bonding configuration is modelled by means of the Abaqus built-in Cohesive Zone Model (CZM) [3], its properties being critical normal traction (c), critical shear traction (⌧c), fracture toughness in mode I (GIc), fracture toughness in mode II (GIIc) and the biaxility parameter of the BenzeggaghKennane criterion (⌘) [19] shown in Table 4. It is interesting to recall that although both configurations include the same adhesive (FM 300.K05), they have di↵erent fracture toughness values. This is due to the fact that the bonding characteristics depend on the adhesive but also on the adherents. The characteristics of bonding configuration 1 represents the FM 300.K05 adhesive joined to a unidirectional laminate while bonding configuration 2 represents the same adhesive joined to a woven fabric. Sti↵ness parameters needed for the CZM formulation (Knn = 41861.54 MPa/mm and Kss = 6976.92 MPa/mm) are obtained considering the equations presented in [22] and the following adhesive properties: shear modulus, µ= 2.54 GPa [23] and Poisson ratio, ⌫= 0.4 [24]. Thicknesses of the thick laminate, adhesive layer and thin laminate are 15 mm, 0.1mm and t(three values are used 0.5, 0.75 and 1mm), respectively. The numerical model includes conforming meshes between the di↵erent parts, element length being 0.5mm. Thick laminate elements are 1 mm 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 in thickness (15 elements through the thickness), cohesive elements along the interface are 0.1 mm in thickness (1 element over the thickness), and the thin laminate has 3 elements through its thickness. Table A.5: Mcvalues obtained for the di↵erent studied configurations in Nm. Laminate Interface t=0.5 mm t=0.75 mm t=1 mm Unidirectional 1, Exx =182GP a BC1 1.23 2.27 3.52 Unidirectional 2, Exx =135GP a BC1 1.06 1.96 3.03 Woven fabric [0/90], Exx =66GP a BC2 0.89 1.65 2.56 Woven fabric [+45/-45], Exx =182GP a BC2 0.44 0.82 1.26 Numerical results showed that the bending moment, M, initially increased linearly with the applied rotation, ✓, and it reaches a critical value, Mc, when the delamination starts, see Figure 10(b). It is interesting to notice that Mvalue keeps constant (M=Mc) during the crack propagation. Mcvalues obtained by the FEAs for the di↵erent studied configurations are shown in Table A.5. It can be clearly seen from these results that the Mc value is function of the bonding configuration properties as well as the thin laminate sti↵ness, i.e. function of the longitudinal sti↵ness, Exx, and the section moment of inertia, I, which is directly related to the thickness, t; leading to an Mcincrease for larger values of Exx and t. Each Mcvalue is associated to a critical curvature, 1/Rc. The critical radius, Rc, can be measured from the numerical results, nevertheless a preliminary Rcvalue can also be estimated using basic bending beam theory relations: Rc=(ExxI) Mc ,(A.1) Rcvalues obtained numerically and using (A.1) are presented in Table A.6. Similarly to Mc,Rcvalues increase for larger values of Exx and t.Itis also interesting to notice that results obtained using (A.1) represent a good 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 [22] V. Mantiˇc, L. T´avara, A. Bl´azquez, E. Graciani, F. Par´ıs. A linear elastic - brittle interface model: Application to the onset and propagation of a fibrematrix interface crack under biaxial transverse loads, International Journal of Fracture 195 (2015) 15-38. [23] Cytec. FM R 300 Epoxy Film Adhesive. Technical Data Sheet. Tempe, Arizona, USA: Cytec Industries Inc. (2013). [24] W.S. Johnson, S. Mall. A fracture mechanics approach for designing adhesively bonded joints. In: Delamination and Debonding of Materials (Eds. W.S. Johnson). (1985) 189–199. [25] J.W. Hutchinson, Z. Suo. Mixed mode cracking in layered materials. Advances in Applied Mechanics 29 (1992) 63–191. 32