Multi-parameter fracture mechanics: crack path in a mixed-mode specimen

Abstract

A mixed-mode geometry has been chosen to investigate a crack propagation using the multi-parameter fracture mechanics concept. The so-called Williams� series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behaviour, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams� expansion in fracture criteria (describing the crack stability and/or crack propagation direction) can bring more precise results. The coefficients of the Williams� expansion must be calculated numerically (for instance by means of the over-deterministic method in this work) for each cracked configuration, which is very time-consuming, and the analysis is very extensive even for a few basic cracked specimen configurations. On the other hand, a suitable choice of the geometrical configuration of the cracked disc enables performing experiments only on the specimens that could prove the theory about the importance of using the higher-order terms.

Keywords

• Crack-tip field; Multi-parameter fracture mechanics
• Finite element analysis
• Mixed-mode
• Williams� expansion