Computation of the Crack-Driving Force in Elastic-Plastic Materials - A Comparative Study

Abstract

In fracture mechanics a material force, or the crack-driving force, is defined as the energy release rate due to a small variation of the position of the crack tip. For material, that does not dissipate energy due to irreversible (dissipative) mechanisms, the material force and the classical J-integral are equivalent. The main advantage of using the material force is that it is defined even in the case of elastic-plastic response. In this thesis, two numerical examples are studied. The first example is a central crack in a plate with prescribed stress on the boundary, where linear elastic fracture mechanics (LEFM) is used to obtain the crack-driving force. The results show that the computed stress-intensity factor coincides with the analytic result. The second example describes an edge crack in a plate with prescribed displacement on its upper and lower boundary. In this example, non-linear fracture mechanics (NLFM) is used, in terms of the computation of the material force, to obtain the crack-driving force. The results show that the elastic-plastic material response has significant influence on the investigated measure of the material force.