J-integral as driving force parameter for elastic-plastic materials

Project Leader: Otmar Kolednik

The configurational forces concept has allowed us also to shed new light on fundamental problems in fracture mechanics that have been unsolved for decades. One of these problems was the application of the J-integral concept for elastic-plastic materials. The conventional J-integral relies on the so-called “deformation theory of plasticity”, i.e. elastic-plastic materials are treated as if they were nonlinear elastic. This theory is not applicable in cases of non-proportional loading, i.e. if unloading processes appear in elastic-plastic materials. However, such unloading processes are inevitable during crack extension or during cyclic loading of a structure and, therefore, the conventional J-integral cannot be used in these cases. Moreover, the conventional J-integral does not characterize the crack driving force in elastic-plastic materials.  

Simha et al. (2008) derived a new type of J-integral, called Jep, which overcomes all these limitations. This has led to a new basis for the application of the J-integral in elastic-plastic materials. In recent papers, we have demonstrated that the J-integral for elastic-plastic materials Jep is very useful for characterizing the crack growth rate in fatigue for cases where linear elastic fracture mechanics and the stress intensity range ΔK are not applicable, e.g. in low-cycle fatigue or for the propagation of short fatigue cracks.