Composite flow laws for crystalline materials with log-normally distributed grain size: theory and application to olivine

Conventional steady-state flow laws describing combined grain size insensitive dislocation creep and grain size sensitive diffusion creep incorporate grain size as a single (mean) value. However, rocks exhibit distributed grain size and variations in the shape of the distribution, such as its width, will accordingly affect rheological behavior. To evaluate this effect, we have derived composite dislocation–diffusion flow laws describing upper and lower bounds on the rate of deformation of materials showing a grain size distribution of the commonly observed log-normal type. The upper and lower bound flow laws obtained allow systematic investigation of the influence of the grain size distribution parameters, i.e. the median and standard deviation, on composite rheology. The results demonstrate major effects of distribution width as well as median value. Application to polycrystalline olivine, deforming by Coble creep and power law dislocation creep, reveals significant implications for interpreting deformation experiments and modeling flow in the Earthʹs mantle. The flow laws also provide an improved basis for modeling the deformation of rocks during geological processes in the crust and mantle.