Mode II fracture of an elastic-plastic sandwich layer

TL;DR

This paper predicts the shear strength of pre-cracked elastic and elastic-plastic sandwich layers with dissimilar substrates, analyzing crack tip stress fields and plasticity effects through analytical, numerical, and finite element methods.

Contribution

It introduces a comprehensive analysis of Mode II fracture in sandwich layers, incorporating elastic mismatch, plasticity models, and finite width effects, validated by finite element simulations.

Findings

Stress fields depend on elastic mismatch.

Plasticity influences crack tip stress intensity.

Failure maps relate geometry, crack length, and strength.

Abstract

The shear strength of a pre-cracked sandwich layer is predicted, assuming that the layer is linear elastic or elastic-plastic, with yielding characterized by either J2 plasticity theory or by a strip-yield model. The substrates are elastic and of dissimilar modulus to that of the layer. Two geometries are analysed: (i) a semi-infinite crack in a sandwich layer, subjected to a remote mode II K-field and (ii) a centre-cracked sandwich plate of finite width under remote shear stress. For the semi-infinite crack, the near tip stress field is determined as a function of elastic mismatch, and crack tip plasticity is either prevented (the elastic case) or is duly accounted for (the elastic-plastic case). Analytical and numerical solutions are then obtained for the centre-cracked sandwich plate of finite width. First, a mode II K-calibration is obtained for a finite crack in the elastic sandwich layer. Second, the analysis is extended to account for crack tip plasticity via a mode II strip-yield model of finite strength and of finite toughness. The analytical predictions are verified by finite element simulations and a failure map is constructed in terms of specimen geometry and crack length.