Computational modeling of polycrystals using gradient crystal plasticity

Licentiate thesis, 2007

This thesis treats the modeling of grain size dependence in microstructure models of metals. It is shown how gradient hardening, in a thermodynamically consistent fashion, can be included into a crystal plasticity model, which is used as the constitutive model in each grain of the polycrystal. In effect, the flow stress on each slip system is expanded to depend on the second spatial derivative, along the slip direction, of the hardening variable. A numerical strategy is proposed, formulating a two--field coupled finite element problem in order solve the arising equations, by constructing an auxiliary finite element problem to identify nodal values for the gradient variables involved in the gradient hardening formulation. Furthermore, the model is implemented in a two--dimensional finite element model of a grain structure. A solution algorithm based on subdividing the grain structure into separate finite element problems for each grain is presented, and the efficiency of the algorithm is studied. Finally, different formulations of boundary conditions on the auxiliary gradient problem are discussed and some numerical results are given.