The M-Integral based failure description on elasto-plastic materials with defects under biaxial loading

This paper presents a M-Integral based failure description of the elasto-plastic materials containing multiple defects, such as voids, subjected to biaxial loading conditions. A non-dimensional Π-parameter is defined, and a novel failure criterion based on the Π-parameter is proposed to assess the multi-defected media. Analytical, numerical and experimental investigations are conducted to evaluate the Π-parameter for different types of problems in order to elucidate the Π-parameter based failure criterion. The explicit definition of the Π-parameter is first derived from the case of elastic inclusion problems in plane elasticity being subject to biaxial loading conditions. And then the Π-parameter is regarded as a damage driving force, and its critical value indicates the occurrence of failure of elasto-plastic materials with defects under biaxial loading. This Π-parameter based failure criterion is further validated through a series of numerically elasto-plastic analyses of cruciform biaxial specimens containing multiple and randomly distributed local defects. In addition, an experimental procedure on evaluating the Π-parameter for elasto-plastic materials is proposed by using the digital image correlation.