Modelling of porphyroclasts in simple shear and the role of stress variations at grain boundaries

Grain-scale numerical experiments involving simple shear of a two-phase non-linear viscous material are described and compared with mineral fish or lozenge-shaped porphyroclasts, such as muscovite. Two types of 2D models are considered; either a single elongate grain or two parallel elongate grains, in both cases supported by a weaker polygonal grain matrix. The relative viscosities of the contrasting grain structures were systematically varied, allowing us to observe the effects of non-linear viscous rheology on the resulting microstructure and flow patterns. The results show that the finite rotation of the hard elongate grain was similar within any one experiment, but was largely influenced by viscosity contrast, the geometry of the model and the imposed shear strain. Models involving single elongate hard grains show increasing instability at their ends and less strain compatibility with the deforming matrix grains, as the viscosity contrast is increased. In the paired grain models the greatest variation in the matrix grain microstructure is seen in the region where the two hard grains are oriented at a high-angle to the direction of shear. Finally, we consider the changes in intragranular stress by comparing microstructural observations using different viscosities with the distribution of stress in space and during progressive shear. In the plane approximately parallel to the maximum principal stress direction (σ1), a localised change of stress occurs across and along the interface between the hard and soft grains. Variations in the mean stress at these boundaries are directly attributable to changes in the minimum principal stress. We propose that with shear strains greater than γ = 2 it is the minimum principal stress that can control diffusion processes at the grain boundary rather than mean stress. In conclusion we suggest that our models have the potential for providing useful insights into why metamorphic reactions can occur at the interface between a porphyroclast and matrix at high shear strains and how stress distribution can control the initiations of such reactions.