Issue 49

F.J.P. Moreira et alii, Frattura ed Integrità Strutturale, 49 (2019) 435-449; DOI: 10.3221/IGF-ESIS.49.42 441 discontinuous shape function, H ( x ), across the crack surfaces. The method is based on the establishment of phantom nodes that subdivide elements cut by a crack and simulate separation between the newly created sub-elements. Propagation of a crack along an arbitrary path is made possible by the use of these phantom nodes that initially have exactly the same coordinates than the real nodes and that are completely constrained to the real nodes up to damage initiation. After being crossed by a crack, the element is partitioned in two sub-domains. The discontinuity in the displacements is made possible by adding phantom nodes superimposed to the original nodes. When an element cracks, each one of the two sub-elements will be formed by real nodes (the ones corresponding to the cracked part) and phantom nodes (the ones that no longer belong to the respective part of the original element). These two elements that have fully independent displacement fields replace the original one. Thus, the crack size increment for a given crack orientation is equal to the distance between the cracked element’s edges. From this point, each pair of real/phantom node of the cracked element is allowed to separate according to a suitable damage law up to failure. At this stage, the real and phantom nodes are free to move unconstrained, simulating crack growth. Tab. 2 summarizes the parameters introduced in Abaqus ® . A linear softening XFEM law was initially considered with an energetic failure power law criterion of the type I II IC IIC 1, G G G G                 (5) in which  is the damage law exponent (  =1 for linear softening). Property AV138 2015 7752 E [GPa] 4.89 1.85 0.49 G [GPa] 1.81 0.70 0.19  0 max [MPa] 39.45 21.63 11.48  0 max [%] 1.21 4.77 19.18 t n 0 [MPa] 39.45 21.63 11.48 t s 0 [MPa] 30.2 17.9 10.17  n 0 [%] 1.21 4.77 19.18  s 0 [%] 7.8 43.9 54.82 G IC [N/mm] 0.20 0.43 2.36 G IIC [N/mm] 0.38 4.70 5.41 Table 2: Parameters of the Araldite ® AV138, Araldite ® 2015 and Sikaforce ® 7752 for XFEM modelling. R ESULTS Experimental failure modes ll failures took place beginning with crack propagation at x / L O =0 and growing towards the other edge. After failure, the fracture surfaces were inspected and cohesive failures were found for all adhesives and t P2 . However, in some cases, especially for the joints bonded with the Araldite ® AV138, failure sometimes took place near to one of the adherend/adhesive interfaces (Fig. 4 shows an example for the joints with t P2 =2 mm), such that visually it resembled an adhesive failure. However, careful surface inspection including optical microscope observations revealed that the adherends that at first hand suffered form an adhesive failure actually were covered by a thin layer of adhesive. These findings are consistent with previous observations on this particular adhesive [27]. The fracture surfaces for the joints bonded with the Araldite ® 2015 and Sikaforce ® 7752 were smoother, indicative of ductile fractures, with a clearer evidence of cohesive failures. L-part adherend plasticization was detected in all joints bonded with the Araldite ® 2015 and t P2 =1 mm, and also with the Sikaforce ® 7752 and t P2 =1 and 2 mm, although for this last case it was under 0.1%. A