Mechanics of void growth and void collapse in crystals

Abstract

The mechanics of void deformation in single crystals is studied in a fully three-dimensional setting, taking into account all twelve slip systems for fcc and bcc crystals. The increments of the local field variables are calculated analytically using Eshelby's approach for the three-dimensional inclusion problem. The collapse or growth of voids in three dimensions is investigated when a rate-dependent elastoplastic material is subjected to compression and tension at a high rate. The deformation of an initially spherical cavity is calculated incrementally, and, it is shown that, even under all-around uniform loading, a void deforms into a complicated shape which is defined by the structure and symmetry of the slip systems. An equivalent ellipsoid is used to approximate the deformed void shape at each incremental step, and the procedure is continued until the equivalent ellipsoid collapses into a crack or a needle, or it expands or shrinks in a self-similar manner. Several numerical examples are presented, and the numerical results are compared with the experimental observations, obtaining good correlation. The significant effects of loading rate on the material response are illustrated. It is shown that the material becomes stronger at higher loading rates. The three-dimensional final void geometry under various loading conditions is studied. The difference between void deformation mechanism under tension and compression is illustrated. The possible overall failure mechanism caused by collapse and/or growth of pre-existing cavities is discussed. From the comparison of the corresponding results with those of the two-dimensional case it is shown that the double-slip system in two dimensions can be used effectively to simulate the three-dimensional problem.