Intrinsic instability and nonuniformity of plastic deformation

It has recently been concluded (Drucker and Li, 1992, 1993, 1994, 1995) that in initially homogenous materials obeying a nonassociated flow rule, plastic deformation is intrinsically unstable and should proceed in a temporally discontinuous manner in the hardening regime. Examination of the physical bases of plastic (or inelastic) deformation of materials indicates that metals and alloys, as well as geomaterials, exhibit non-normality to some extent from appreciable to negligible. In metals and alloys, the effect is small and negligible for many purposes. However, it is shown here that using the observed small non-normality (Spitzig et al., 1975, 1976), the predicted critical hardening modulus for the onset of shear instability is in remarkable agreement with the observed occurrence of microshear bands (Anand and Spitzig, 1980). Furthermore, far smaller strength differential (SD) effects than previously calculated (Asaro and Rice, 1977) are required to account for the localization in single crystals. When initial inhomogeneities are taken into account, the emerging shear bands should be confined spatially as well as temporally, as observed in experiments. For exploring theoretically the propagation of such bands, it is noted that the J-integral commonly used for treating crack mechanics is also path-independent for shear bands, but for different reasons. (C) 1997 Elsevier Science Ltd. All rights reserved.