Unified characterisation of in-plane and out-of-plane constraint based on crack-tip equivalent plastic strain

摘要

Constraint can be divided into two conditions of in-plane and out-of-plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in-plane and out-of-plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ε_p) distribution ahead of crack tips for specimens with different in-plane and out-of-plane constraints, and the FEM simulations based on Gurson-Tvergaard-Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in-plane and out-of-plane constraints based on crack-tip equivalent plastic strain has been investigated. The results show that the area A_(PEEQ) surrounded by the ε_p isoline ahead of crack tips can characterize both in-plane and out-of-plane constraints. Based on the area A_(PEEQ), a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_(IC)/J_(ref ) and √A_p regardless of the in-plane constraint, out-of-plane constraint and the selection of the ε_p isolines. The unified J_(IC)/J_(ref ) - √A_p reference line can be used to determine constraint-dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_(IG)/J_(ref ) - √A_p reference line for materials with ductile fracture.