Some Considerations on the J-Integral under Elastic-Plastic Conditions for Materials Obeying a Ramberg-Osgood Law

Among the approaches available for structural analysis, the J-integral has received an excellent feedback as a fracture parameter under elastic-plastic conditions. In the literature and dealing with the crack case, it is proposed to evaluate the J-integral as a sum of elastic and plastic contributions. However, some uncertainties arise when applying this method to a Ramberg-Osgood law, especially under large scale yielding conditions. The aim of the present paper is to discuss how the J-integral evaluation can be performed for elastic-plastic cracked components. Two different non-linear behaviours have been considered for the material: the Ramberg-Osgood law and power law. Numerical and finite element results from different approaches have been accurately compared, proving that the most appropriate way to evaluate the J-integral for a material obeying Ramberg-Osgood law is to perform two finite element analyses evaluating separately the elastic contribution (through a linear elastic analysis) and the plastic contribution (through a nonlinear analysis considering power law behaviour).