Onset of dynamic void coalescence in porous ductile solids

Abstract

This paper investigates void growth and coalescence in porous ductile solids under dynamic loading condition. A physical definition for the onset of void coalescence in porous ductile solids under dynamic loading is proposed. The onset is deemed to occur when the third invariant of the tensorial form of the Hill–Mandel condition attains a zero value. The definition allows for systematic investigations on the effects of dimensionless stress rate $\kappa$ and stress state, defined by the stress triaxiality $T$ and Lode parameter $L$, on the onset of void coalescence via micromechanical analyses. The analyses reveal that the critical macroscopic effective strain for the onset of void coalescence displays an increasing–decreasing transition trend as the dimensionless stress rate increases, for all levels of $T$ and $L$ considered. The macroscopic effective strain at the transition is identified as the “ductile–brittle” transition strain. The dimensionless stress rate at which the transition strain occurs is found to be relatively constant. A mapping in the $\kappa -T$ space for $L=-1$, representative of a generalized uniaxial tension typical in spall fracture experiments, is established which depicts regions where coalescence and non-coalescence can take place, as well as the ductile–brittle regions demarcated by a ductile–brittle transition curve. The results also show that the critical void volume fraction and macroscopic effective strain at the onset of void coalescence are insensitive to inertia at high stress triaxialities at $L=-1$.