Grain size-dependent crystal plasticity constitutive model for polycrystal materials.

Consideration of a core and mantle configuration for individual grains is a prominent method to capture the grain size-dependence in the constitutive models for polycrystal material. The mantle represents a region of the grain volume near the grain boundary where mechanical deformation is influenced by the grain boundaries, while the core represents the inner region of the grain volume. The grain size-dependence is then realized by assigning a set of values for the mechanical properties in the mantle that are different from those of the core region. However, these values for the mechanical properties of the mantle region are typically chosen arbitrarily, guided solely by the quality of the agreement between a model's predicted stress-strain behavior with that obtained experimentally. In the present study, a physics-based method to develop the grain size-dependent crystal plasticity constitutive model on the core and mantle configuration for polycrystal materials is presented. The method is based on the assumption that any resistance to dislocation nucleation and motion in a material manifests as an increase in yield strength and a decrease in strain-hardening modulus, and the mutual relationship between yield strength and strain-hardening is an inherent material property that determines the plasticity of that specific material. Accordingly, the same single crystal plasticity constitutive model that describes the behavior of the material under loading can be used to capture the increased resistance to dislocation nucleation and motion in the grain boundary influence region. The physics-based modeling is facilitated by introducing a shear flow strain distribution in the phenomenological formulation and a pile-up of dislocation density distribution in the dislocation based formulation, such that, the resulting variations in the yield strength and the strain-hardening modulus are identical to that produced by the increased resistance in the grain boundary influence region. Thus, the increase in strength and the decrease in the strain-hardening modulus, determined as spatially varying local material properties in the mantle, are mutually related through the grain size-independent inherent plastic properties specific to the material. A simplified model that considers the grain boundary effect averaged over the grain volume is also developed under this general framework. Implementation of this simplified model is demonstrated by considering the case of a power law flow rule and a hyperbolic-secant hardening rule for the phenomenological formulation, and Taylor strength relation for the dislocation based formulation. Finally, the grain size-dependent constitutive model is validated by comparing the predicted stress-strain behavior of polycrystal copper samples under uniaxial loading with experimental results.