3D modelling of the effect of thermal-elastic stress on grain-boundary opening in quartz grain aggregates

During the exhumation of rocks and the associated temperature and pressure decrease, the anisotropic thermoelastic properties of minerals lead to internal stresses on the grain scale, which in turn cause fracturing and opening of grain and phase boundaries. To gain deeper insight into the onset of grain-boundary cracking and the subsequent evolution of grain-boundary fracture networks after crack initiation, 3D grain-scale numerical modelling has been performed. In detail, the fracturing and opening of quartz grain boundaries during exhumation of quartzite with millimeter-scale grains and randomly oriented crystallographic axes, accompanied by cooling from 300 to 25 degrees C and decompression from 300 to 22 MPa, have been modelled with contact mechanics and the finite-element method. Model grains have an anisotropic linear-elastic rheology and an anisotropic thermal-expansion tensor. Grain boundaries are modelled as contact surfaces with a non-linear strain-softening rheology in tension and a Mohr-Coulomb rheology in shear. Grain-boundary fractures nucleate at grain vertices and triple lines, in agreement with observations in nature and experiment. Comparison with grain-boundary opening data from natural quartzite indicates that the tensile yield strength (sigma(gamma)) of quartz grain boundaries has an upper bound of 75 MPa, with best-fit results for sigma(gamma) = 25 MPa. Moreover, the best-fit model implies that quartz grain-boundary opening initiates after a temperature and pressure decrease of around 80 degrees C and 80 MPa.