PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction The application of adhesively bonded joints is gaining importance in lightweight over the traditional joints over the past 70 years design due to its advantages of weight reduction, ease of assembly, and mitigate the drawbacks of fastened joints such as – stress concentrations, reduction in joint strength and ease of assembly (He, 2011). Hence, it is important to determine the failure strength of such bonded joints. In the design of such joints, adhesive selection has a crucial role in the mitigation of the peel stress concentration by load distribution, that arises due to a complex state of loading (Campilho et al., 2011a; Silva et al., 2011). In the case of a ductile adhesive, such as, Araldite 2015, there exists the presence of fracture process zone (FPZ) which experiences significant yielding and thereby higher fracture toughness (G c ) in contrast to brittle adhesives. In the case of brittle adhesives, G C is independent of adhesive thickness (da Silva et al., 2010; Loureiro et al., 2020). In the case of single lap joint (SLJ), numerous studies exist to describe the influence of joint parameters, ranging from bond line thickness (t a ) to overlap length (L o ) (Campilho et al., 2012; Campilho et al., 2011a; da Silva et al., 2009). From these studies, it is evident that joint strength is primarily influenced by its L o . However, in reality, the improvement of SLJ design based on the dependence on L o alone leads to slender joints, which is unsuitable for geometrically constrained joints. Meanwhile adhesive bondline thickness (t a ) and its corresponding G c account for 25% improvement in SLJ joint strength (da Silva et al., 2009). For aeronautical industries, (t a ) is between 0.05 -0.20 mm and other civil industries up to 1.0 mm. In the case of SLJ, it has been emphasized that an increase of t a leads to a decrease in P m which has been attributed to cracks introduced due to more microvoids and the eccentric bending moment (Adams and Peppiatt, 1974; da Silva et al., 2009; Fernandes et al., 2015). In the case of ductile epoxy adhesives, it is elucidated that G c is maximum when plastic zone size is nearly equal to the bond-line thickness (Bascom et al., 1975). In the current study, G c is determined using mixed-mode bending (MMB) tests. G c along with other cohesive traction parameters influence the fracture load (P m ) . The influence of G c on the traction separation law (TSL) is foreseen in the stiffness degradation during the damage propagation phase (Abaqus Analysis User's Manual (6.9), 2009; Balzani et al., 2011). While over prediction of G c does not influence the P m values, an under prediction of G c (by 80%) is detrimental to the accuracy, for L o greater than 80 mm in contrast to L o equal to 20 mm in our SLJ model (Campilho et al., 2012). Currently, numerous methods and data reduction methods exist to determine the cohesive parameters (t n 0 , t s 0 , G n , G s ). However, every technique has its limitation. In the case of the direct method, precise cohesive law shape is determined which is too complex for numerical simulation. On the other hand, property identification and inverse method involve the assumption of a simplified TSL (Campilho et al., 2012). Based on a study on epoxy adhesive, these CZM shapes and their parameters vary with the bondline thickness t a from a triangular shape for smaller t a to a trapezoidal for thicker t a due to the presence of a plastic zone. Furthermore, with an increase of t a , parameters t n 0 , t s 0 reduced while G n and G s increased (Carlberger and Stigh, 2010). Another study indicates that traction parameters (t n and t s ) are thickness independent, however, they are influenced by the loading rate. And their thickness independent hypothesis holds good as long the mode of failure remains the same – that is a cohesive failure in this case (Desai et al., 2016). SLJs are subjected to a combination of tensile and shear loads and hence the study of fracture under a mixed-mode loading is necessary for determining the P m and develop a fracture envelope. In case of such a loading scenario, adhesive behaviour (fracture toughness G c ) in-situ tests such as mixed-mode test are different from those of bulk tests. In case of bulk tests, crack propagation is perpendicular to the direction of maximum principal stress, however in a joint such as SLJ, the crack tends grow along the bondline leading to a cohesive failure in both cases but with different fracture toughness. Such a difference in behaviour could be attributed to the constraining effect of substrates induced on the adhesive bondline (Campilho et al., 2012; Zou et al., 2004). In these in-situ tests, P m increased in with an increase in MMR (mixed mode ratio) due to the presence of a Mode-II component. However, as a function of t a , the value of P m remained moreover constant (Sadeghi et al., 2019). Assessment of fracture surfaces for an epoxy adhesive revealed a smoother fracture indicating that the Mode-I component dominates fracture until 75% MMR. An introduction of the Mode-II component leads to more energy dissipation by shear deformation leading to a rougher surface and a higher G c . In this study, MMB 75% is independent of bond-line thickness (Khoo and Kim, 2011). In comparison to pure modes testing, the determination of fracture energy for mixed modes is challenging to predict owing to the path-dependent feature. The crack path has to be contained within the adhesives to depict a cohesive failure. It must be noted that fracture energies of adhesive joints cohesive failure are higher than interfacial failure