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

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.

  Extension of plastic zone in a fracture mechanics specimen (left), distribution of configurational forces (right). Bulk configurational forces are induced in a homogeneous elastic-plastic material; their magnitude is proportional to the stress and the gradient of the plastic strain. Due to the bulk configurational forces, the J-integral Jep becomes path dependent.


Important publications

N.K. Simha, F.D. Fischer, G.X. Shan, C.R. Chen, O. Kolednik, J-integral and crack driving force in elastic-plastic materials. Journal of the Mechanics and Physics of Solids 56 (2008) 2876-2895.

F.D. Fischer, N.K. Simha, J. Predan, R. Schöngrundner, O. Kolednik, On configurational forces at boundaries in fracture mechanics. International Journal of Fracture 174 (2012) 61-74.

O. Kolednik, R. Schöngrundner, F.D. Fischer, A new view on J-integrals in elastic‒plastic materials, International Journal of Fracture 187 (2014) 77–107.

W. Ochensberger, O. Kolednik, A new basis for the application of the J-integral for cyclically loaded cracks in elastic‒plastic materials. International Journal of Fracture 189 (2014) 77–101.

W. Ochensberger, O. Kolednik, Physically appropriate characterization of fatigue crack propagation rate in elastic–plastic materials using the J-integral concept. International Journal of Fracture 192 (2015) 25–45.


Part of this research has been funded by the Austrian COMET Competence Center Programme via the COMET K2 Center for Materials, Processing and Product Engineering in Leoben.