On the effects of higher order stress terms in pure mode III loading of bi-material notches

Abstract

The effects of higher order terms (HOTs) on the stress distribution at the vicinity of the sharp corner of two bonded dissimilar materials were investigated under pure out-of-plane (mode III) loading. To achieve this aim, finite element (FE) analysis in conjunction with the over-deterministic technique were performed for two specimens, each containing four different notch opening angles. The coefficients of singular and non-singular stress terms were then computed from the displacement field determined from the FE analysis. The elastic stresses obtained directly from the FE analysis were compared with those reconstructed from the truncated series expansions, in order to validate the accuracy of the calculated coefficients. The numerical results show that although the contribution of HOTs in the out-of-plane stress field is less than that of the in-plane notch problems, ignoring their effects can lead to considerable errors in the stress field estimation. The magnitude of numerical error depends on the geometry and loading conditions of the bi-material notch.