A reformulation of mechanism-based strain gradient plasticity

Abstract

We reformulate the theory of mechanism-based strain gradient plasticity (MSG) [J. Mech. Phys. Solids 47 1239 (1999); ibid 48 99 (2000); J. Mater. Res. 15 1786 (2000)] that involves the third-order tensor of higher-order stress to a much simpler version within Fleck and Hutchinson's theoretical framework of strain gradient plasticity theory [J. Mech. Phys. Solids 49 2245 (2001)]. Similar to MSG, the new theory is also based on the Taylor dislocation model, but the higher-order stress is a vector (rather than a third-order tensor) and is the work conjugate of the gradient of plastic strain. The intrinsic material length in the new theory is still related to the shear modulus, yield stress and Burgers vector in the same way as in MSG, but the simplicity of the new theory makes it much easier to be implemented in the finite element analysis. We present a few examples that display strong size effects at the micron and submicron scales, including the shear of an infinite layer, torsion of thin wires, bending of thin beams and growth of microvoids. These examples show that this new strain gradient plasticity theory based on the Taylor dislocation model captures the strong size effect.