Predicting crack patterns at bi-material junctions: A coupled stress and energy approach

Abstract

Failure of bi-material joints is affected significantly by the elastic material properties of both adherends as well as by geometrical parameters such as material interface orientation. Addressing these effects, scarf joint specimens made of a polymer foam and either PMMA or aluminum are examined employing a four-point bending test setup with varying scarf angle. The joints’ effective strengths are predicted using a coupled stress and energy criterion within the concept of finite fracture mechanics defining failure as spontaneous formation of finite sized cracks. Since numerous competing crack configurations are admissible, efficient modelling is crucial. Crack initiation triggered by the singular stress field at the bi-material junction is modelled using a semi-analytical approach based on the method of matched asymptotic expansions. In order to accurately capture stresses in the vicinity of the notch and energy dissipation due to crack onset, higher order terms associated to complex deformation modes are considered in the asymptotic expansion. Results based on the asymptotic approach are compared to numerical reference data. Theoretical predictions of the effective joint strength as well as the orientation of the associated initiating cracks are validated against experimental findings from literature.