Study of localization in a void-sheet under stress states near pure shear

Abstract

A recent study of a porous ductile material under pure shear has indicated that no failure is predicted, whereas a number of micro-mechanical analyses for simple shear have shown that a maximum shear stress is reached and failure occurs. Both simple shear and pure shear are characterized by zero stress triaxiality and in both types of stress states the analyses show that the voids collapse to micro-cracks. The possibility of failure in pure shear is further investigated here by studying the effect of an initial imperfection in the form of a row of circular cylindrical voids inclined to the principal tensile stress. A number of previous investigations have shown that such imperfections can lead to plastic flow localization in a shear band and subsequently lead to void-sheet fracture inside the band. The present analyses confirm that the imperfection results in localization failure, even at moderate or rather low stress triaxiality. But in pure shear, with zero stress triaxiality, no failure is predicted. Initially the imperfection results in increasing shearing along the row of voids, but this tendency towards increasing shearing is interrupted if the voids collapse to micro-cracks. For the largest imperfection considered, i.e. a relatively large ratio of the void radius to void spacing, there is still a range of stress states in the vicinity of pure shear, where no localization is predicted, and for smaller imperfections this range is larger.