On a Gradient Theory of Crystalline Plasticity

Morton E. Gurtin
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract:

This work develops a general theory of crystalline plasticity based on:

1. a collection of slip systems for dislocation glide;
2. microforces for each slip system consistent with a microforce balance;
3. a mechanical version of the second law that includes, via the microforces, work performed in the rearrangement of atoms as described by the microshear-rates on the individual slip systems;
4. a rate-independent constitutive theory that includes dependences on plastic-strain gradients. A central result is the equivalence of the microforce balances and yield conditions for the individual slip systems. In contrast to standard theories, the yield conditions account for variations in the free enrgy due to slip. When the free energy is the sum of an elastic strain energy and a defect energy quadratic in the plastic-strain gradient, the resulting theory has a form identical to the standard theory of crystalline plasticity, except that the yield conditions contain an additional term involving the Laplacian of the plastic strain.