Mechanisms of membrane rupture: From cracks to pores

Abstract

The rupture kinetics under isotropic tension of solid membranes with central-force interactions are studied as a function of temperature and the range of the interparticle interactions. At zero temperature, rupture occurs homogeneously at the mechanical instability point. At low temperature, rupture is heterogeneous, mainly by the nucleation of a single crack, branching out into several cracks. This is accompanied by a homogeneous expansion, and the critical rupture tension drops very rapidly with increasing temperature. At high temperature, rupture involves the nucleation of dislocation dipoles, merging to form pores, and the critical rupture tension varies almost linearly with temperature. The temperature $T_1$, separating these two regimes, is higher the shorter the range of interaction, for potentials of equal depth. We find that under isotropic tension, the crack favors the path along the direction with lowest surface energy, in contrast to that observed under uniaxial tension. The identification of the rupture point is facilitated by the fact that the elastic constants, in particular the bulk modulus, usually show precursor effects. Transverse fluctuations can play an important role as evidenced by a one-dimensional model of self-assembled particles in a ring, pressurized by an ideal gas. These fluctuations are dominant at high temperature, where the rupture pressure is only weakly dependent on temperature.