Improved concept for iterative crack propagation using configurational forces for targeted angle correction

Abstract

In many applications, fracture mechanics is indispensable in predicting structural failure. In this paper, a concept for predicting discrete crack paths according to the criterion of maximum energy release rate, which uses the finite element method, is presented. Within existing approaches to determine the incremental crack propagation direction, on the one hand, the information of the current crack is used in explicit approaches, leading to inaccuracies. On the other hand, the information of introduced virtual cracks can be used in implicit approaches, with the required number of virtual cracks determining the computational effort. This work introduces a 2D concept for quasi-static crack propagation in elastic materials and that uses configurational forces to estimate an angle error of a virtual crack increment; the concept uses this angle error in an iterative crack correction. The concept is evaluated using a simplified model for one crack propagation increment and a three-point bending model that contains holes for predicting crack paths in combination with the incremental crack propagation method. The results are compared with those of existing explicit and implicit crack propagation direction concepts, as well as experimental results. It is shown that the presented concept fulfils the concept for maximum energy release rate as accurately as a computationally expensive implicit concept, while the computational effort of the proposed concept is close to fast explicit concepts.