Modeling the plastic deformation of crystals with thin precipitates

Precipitates, present in most commercial alloys, can have a strong influence on strength and hardening behavior of a single crystal. The effect of thin precipitates on the anisotropy of initial slip resistance and hardening behavior of crystals is modeled in this article. For the convenience of the computational derivation and implementation, the material formulation is given in the unrotated intermediate configuration mapped by the plastic part of the deformation gradient. Material descriptions for the considered two phased aggregates consisting in lattice hardening as well as isotropic hardening and kinematic hardening are suggested. The corresponding elastic–plastic rate-independent algorithmic treatment is derived and numerical simulations of various loading cases are presented to discuss and assess the performance of the suggested model and its rate-independent algorithmic treatment.