Intrinsic instability and nonuniformity of plastic deformation (Q1267578)

In agreement with works of D. C. Drucker and Ming Li in the early 1990s, where it was concluded that plastic deformation is an intrinsically unstable process in initially homogeneous materials that obey a nonassociated flow rule, it is shown here that using the observed small non-normality, the predicted critical hardening modulus for the onset of shear instability, is in remarkable agreement with the observed occurrence of microshear bands. Far smaller strength differential effects than previously calculated (by, in particular, R. J. Asaro and J. R. Rice) are required to account for the localization in single crystals. It is also shown on account of initial inhomogeneities, that the emerging shear bands should be confined, both spatially and temporally, as is indeed observed experimentally. Finally, it is noted that the \(J\)-integral of fracture mechanics is also path-independent for shear bands but, according to the authors, for different reasons.