J−Δσ Quantification of Out-of-Plane Constraint Loss in Mode-I Fracture

Abstract

The effect of out-of-plane constraint associated with a thickness on the toughness of three-dimensional bodies is a primary concern in fracture mechanics. The $J - \Delta \sigma$ approach has been shown to be capable of quantifying crack tip constraint loss in high and low constraint geometries using a deformation parameter, $J/z\sigma_{o}$. The present study is motivated to use the parameter to assess the nature of out-of-plane constraint loss under Mode-I loading in a deeply cracked compact tension (CT) specimen. The assessment focuses on the variation in crack tip stress fields across the specimen thickness, which was examined through finite element analysis of full-field CT models in comparison with two-dimensional plane strain and plane stress solutions to identify the constraint loss pattern. The models with a sharp crack tip were constructed using quadratic brick elements and subjected to a displacement-controlled loading that corresponded to a limit load analysis. The results show that the state of three-dimensional stress fields in CT specimens departs from a plane strain condition at the midplane to a plane stress field near the free surface. Using the parameter $J/z{\sigma }_{o}$, the loci of out-of-plane constraint loss in different specimen thicknesses subjected to varying deformation levels were unified into a single curve, and thus verifying the capability of the $J - \Delta \sigma$ approach to characterize the out-of-plane constraint loss in high constraint geometries of deeply cracked CT specimens.