An analytical evaluation of $T$-stress influence in the process zone modelling for the interface crack kinking

This study presents an analysis of the influence of T-stresses on the stress field near the tip of an interfacial crack under plane strain conditions, specifically examining the initial stage of crack kinking from the interface. The analysis focuses on the formation of a small-scale process zone within the less crack-resistant elastic material of a bimaterial joint. The process zone is modeled as a discontinuity line of normal displacement, where the normal stress is assumed to be equal to the failure stress of the respective material. T-stresses are incorporated into the model by including their contribution to the asymptotic stress field near the crack tip. This asymptotic field is subsequently used to formulate the condition at infinity for the corresponding boundary value problem within the theory of elasticity. The parameters of the process zone (its length and angle of inclination) are calculated by solving the boundary value problem using the Wiener-Hopf method. From the derived solution, an equation is obtained for calculating the length and angle of inclination of the process zone. This calculation is based on the criterion of maximum potential energy accumulated within the zone. Furthermore, the energy release rate and crack opening displacement are also determined, providing essential metrics for formulating crack initiation conditions based on energy or deformation criteria. A numerical analysis was conducted to investigate the dependence of the zone's parameters on the applied load and to specifically study the effect of T-stresses on its orientation. Finally, a comparative analysis of the model's predictions for the kinking angles was performed against values reported in extant theoretical and experimental literature.