Void-sheet analysis on macroscopic strain localization and void coalescence

An operational definition for the onset of macroscopic strain localization is established through the localization analysis on the overall response of a unit cell in a void-sheet. The constitutive relations are obtained from the homogenization of a representative volume element, which is taken to be a void-containing unit cell characterizing a void-sheet in a ductile solid. The unit cell is subjected to three macroscopic normal stresses and one macroscopic shear stress and is proportionally stressed under a maximum reduced shear stress condition. Together with the definition for the onset of void coalescence established previously, it is shown that the two onsets are distinct and separate, with the strain localization being a precursor to void coalescence. It is also shown that for Lode parameter −1≤L≤1, the difference between the effective strains for the onsets of strain localization and void coalescence decreases as stress triaxiality T increases, suggesting that both onsets may occur simultaneously for sufficiently large T. This difference in the effective strains are found to be large for moderate to lower T and in the range between generalized compression (L=−1) and generalized shear (L=0). For the range of T and L considered, there exists three scenarios involving strain localization and void coalescence: (1) both strain localization and void coalescence are possible, (2) strain localization is possible but void coalescence is not possible, and (3) both strain localization and void coalescence are not possible. The effects of orientation of the void-sheet on the onset of macroscopic strain localization are also investigated.