The Prediction of the Crack Propagation Direction According to the Criterion of Maximum Energy Dissipation

An efficient tool is presented to predict the behavior of cracks in all kinds of multi-phase or composite materials where the material properties exhibit a spatial variation. Based on the material (or configurational) force approach, this tool accurately computes the crack driving force and the crack growth direction in inhomogeneous elastic or elastic-plastic materials. The local crack driving force vector Jtip is evaluated as a vector sum of the far-field J-integral vector Jfar and the so-called material inhomogeneity term vector, Cinh. The latter term quantifies the crack tip shielding or anti-shielding effect of the material inhomogeneities. For example, an increase of the elastic modulus or the yield stress in the direction of crack extension induces a negative material inhomogeneity term which provides a shielding effect [1,2]. The components of the vector Jfar are evaluated using a conventional J-integral evaluation procedure by assuming virtual crack extensions in two different directions, e.g., along and perpendicular to the direction of a pre-existing crack. The components of Cinh are evaluated by a post-processing procedure after the conventional finite element stress analysis [1,2]. In accordance with the criterion of maximum energy dissipation [3,4], the crack extension follows the direction of the local crack driving force vector Jtip