To ensure a more representative simulation of meso-scale and macro-scale deformation, it is important that the underlying constitutive relations are advanced to more effectively incorporate the micro-mechanisms, such as those operative near the grain boundaries. Critical features necessary for accurate predictions include the influence of grain size, morphology and misorientation on the local deformation.
In this study, published in Volume 152 of International Journal of Plasticity, Dr Anna Kareer and her collaborators incorporated a length scale dependence into classical crystal plasticity simulations. The implementation was based on the influence of dislocation slip pile-up at grain boundaries based on the Hall-Petch theory in materials, and was achieved by applying a purpose-built algorithm to extract the slip distance in adjacent grains along each slip direction.
The extracted data was used to adjust the critical resolved shear stress within the grain. The adjusted slip law was then implemented in constitutive models to predict the yield stress and hardening evolution of material for different grain sizes.
The interaction of the slip systems between grains was also considered, which resulted in adjusting the extent of slip transfer permitted between grains based on misorientation. This approach can be applied in both finite element and spectral methods for solving the continuum differential equations.
The accuracy of the model was investigated by considering the meso-scale predictions using three-dimensional models. In addition, the validity of the method was experimentally supported by tracking the development of intragranular residual elastic stresses, measured via high-resolution electron backscatter diffraction.
This method provides potential to enhance the way in which complex grain boundary interactions contribute to local deformation in crystal plasticity simulations.