A refined theoretical model for mode I crack near the interface of strength and plasticity mismatched materials in K dominant regime

Abstract

The paper investigates a cracked bi-material, comprising elastic-plastic materials that are elastically identical but strength and plasticity mismatched, under the action of monotonic and uniform far field tension in small scale yielding (SSY) or K dominant regime. A through, mode I, edge crack in weaker material is assumed to advance perpendicularly toward the interface of stronger material. The interface between the materials is considered to be thin, strong and perfect. A theoretical model is developed with the help of basic mathematical principles to account for the influence of non-linearity in plastic behavior of constituent materials during estimation of plastic energy transfer toward stronger interface material when the crack tip is near the interface. The criterion of the onset of yielding of interface material is included in the model. Energy transfer is represented by the component of energy release rate of the crack due to inhomogeneity caused by property mismatched interface. Shielding effect over the crack is quantified by energy release rate and stress intensity parameter at the crack tip. Two elastically similar steels with different yield strengths and plasticity properties are chosen for computational purpose under plane stress condition. Differences between fracture results of the proposed model and those of an available model based on Dugdale’s criterion that ignores material non-linearity and is valid for elastic-perfectly plastic materials are presented. The proposed model is validated.