Size effects in metallic polycrystals in the context of strain-integral crystal plasticity

The development of constitutive models usually relies on the framework of strain-gradient plasticity to consider the size and gradient effects that affect the thermomechanical behavior of crystalline materials. In this work, an alternative strategy, which fits into the category of strain-integral plasticity models, is explored. The underlying idea consists of evaluating the spatial average and the spatial covariance of the plastic deformation gradient tensor. These non-local variables are treated as additional internal state variables that provide some information regarding the spatial distribution of the plastic deformation gradient tensor.

In the present paper, the method used for the evaluation of the average and the covariance of the plastic deformation gradient tensor is first detailed. Particular attention is paid to the treatment of near-boundary regions, for which different options are proposed. Then, a general strategy to include the average and the covariance of the plastic deformation gradient tensor in constitutive relations in a thermodynamically consistent manner is exposed. Finally, a crystal plasticity-based model developed within the framework of strain-integral plasticity is presented for the purpose of illustration. The numerical results obtained for different polycrystalline microstructures indicate that the hardening behavior is impacted by the mean grain size. However, such a size-dependent behavior largely depends on the method used for the treatment of near-boundary regions.