Numerical models of stiffness and yield stress growth in crystal-melt suspensions

Magmas and other suspensions that develop sample-spanning crystal networks undergo a change in rheology from Newtonian to Bingham flow due to the onset of a finite yield stress in the crystal network. Although percolation theory provides a prediction of the crystal volume fraction at which this transition occurs, the manner in which yield stress grows with increasing crystal number densities is less-well understood. This paper discusses a simple numerical approach that models yield stress in magmatic crystalline assemblies. In this approach, the crystal network is represented by an assembly of soft-core interpenetrating cuboid (rectangular prism) particles, whose mechanical properties are simulated in a network model. The model is used to investigate the influence of particle shape and alignment anisotropy on the yield stress of crystal networks with particle volume fractions above the percolation threshold. In keeping with previous studies, the simulation predicts a local minimum in the onset of yield stress for assemblies of cubic particles, compared to those with more anisotropic shapes. The new model also predicts the growth of yield stress above (and close to) the percolation threshold. The predictions of the model are compared with results obtained from a critical path analysis. Good agreement is found between a characteristic stiffness obtained from critical path analysis, the growth in assembly stiffness predicted by the model (both of which have approximately cubic power-law exponents) and, to a lesser extent, the growth in yield stress (with a power-law exponent of 3.5). The effect of preferred particle alignment on yield stress is also investigated and found to obey similar power-law behavior.