Gradient crystal plasticity as part of the computational modelling of polycrystals

This paper describes how gradient hardening can, in a thermodynamically consistent fashion, be included into a crystal plasticity model. By assuming that the inelastic part of the free energy includes contributions from the gradient of hardening along each slip direction, a hardening stress due to the second derivative of the hardening along each slip direction can be derived. For a finite element model of the grain structure a coupled problem with displacements and gradient hardening variables as degrees of freedom is thereby obtained. This problem is solved using a dual mixed approach. In particular, an algorithm suitable for parallelization is presented, where each grain is treated as a subproblem. The numerical results show that the macroscopic strength increases with decreasing grain size as a result of gradient hardening. Finally, the results of different prolongation assumptions, i.e. how to impose the macroscopic deformation gradient on a representative volume element, are compared. Copyright q 2007 John Wiley & Sons, Ltd