Micromorphic modelling of grain size effects in metal polycrystals

A long‐standing problem in the modelling of polycrystal behavior from the knowledge of the constitutive equations of single crystals is the incorporation of grain size effects. Standard ho‐mogenization procedures efficiently take into account grain to grain interaction primarily induced by strain incompatibilities at grain boundary and grain morphology effects. Continuum crystal plasticity models are available that satisfactorily describe dislocation forest hardening associated with multiplication and dynamic recovery of dislocation populations. One strong limitation of these techniques is that the local crystal plasticity constitutive parameters at the grain scale are assumed to be known. Conversely, these material parameters can be identified from the macroscopic polycrystal response by an inverse approach involving the homogenization model. But then the found crystal plasticity model will be valid only for the considered grain size and the model can hardly be used for prediction of polycrystal behavior for another grain state of the material. Generalized continuum approaches arise as the suitable mechanical framework for formulating enhanced crystal plasticity models that intrinsically include grain size dependent local material responses. They incorporate the dislocation density tensor as a consitutive variable. Recent developments have shown the limitations of existing strain gradient models in the case of a two–phase laminate microstructure under single or double slip [1]. They plead for a theory even more general than the strain gradient or Cosserat approach, namely the micromorphic model presented here. The effect of the dislocation density tensor is introduced into the classical crystal plasticity framework by means of a micromor‐phic theory of single crystals. A computational homogenization strategy is presented in order to simulate the global and local responses of two–dimensional polycrystalline aggregates for grain sizes ranging from 1 to 200 microns. The model is shown to induce a size–dependent kinematic hardening component which is responsible for the observed strong size effects. The yield stress at a given averaged plastic deformation is shown to follow a power law scaling relation for grain sizes larger than a critical grain size. The field of plastic deformation is also strongly affected by grain size, micron–size grains leading to the formation of intense slip bands crossing several grains. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)