Plastic deformation analysis of cracked adhesive bonds loaded in shear

The plane strain elastoplastic stress field around an interface crack in adhesively bonded joints deforming in shear was determined from a large strain, incremental plasticity finite element analysis. Two particular specimens were analysed, i.e. the end-notched flexure and the end-loaded split, with the bond thickness varying from 18 μm to 0.4 mm. The yield behavior of the adhesive was modeled by the von Mises (J₂) and the extended Drucker-Prager (EDP) material models, the latter being more appropriate to polymeric adhesives. Associated and non-associated flow rules were considered for the J₂ and EDP models, respectively. The adhesive stress-strain response was assumed to be elastoplastic, and it incorporated various levels of strain hardening. The analysis shows that the stresses at the crack tip are triaxial, with the deformations dominated by the shearing component, the latter being localized at the very edge of the crack tip, an effect which tended to increase with increasing bond thickness or decreasing degree of strain hardening. The numerical predictions of the length of the plastic zone that developed ahead of the crack tip and of the distribution of average shear strain across the bond within that zone agreed well with experimental results. In contrast with the behavior for the analogous mode I loading case, the mean stress declined monotonically with increasing distance from the crack tip.