Theories and applicability of grain size piezometers: The role of dynamic recrystallization mechanisms

The average grain size (d) arising from dynamic recrystallization (DRX) is often used as an indicator of flow stress (σ); however, a theoretical basis for the scaling relation between d and σ has yet to be well established. In this paper, theories for the development of recrystallized grain size are reviewed and their applicability is examined. Special attention is paid to the dependence of the d–σ relation on DRX mechanisms. Steady-state DRX is classified into discontinuous DRX with bulging (BLG) nucleation + grain boundary migration (GBM) and continuous DRX with subgrain rotation (SGR) nucleation + GBM. The nucleation-and-growth model derived from Derby–Ashby theory describes the former case, whereas that derived from Shimizu theory applies to the latter. A static energy-balance model derived from Twiss theory is applicable to subgrain size, but not to recrystallized grain size. The lower limit of grain size is possibly constrained by a change in deformation mechanism from dislocation creep to diffusion creep, because deformation-induced grain size reduction ceases in the diffusion creep field. Scaling relations determined in the laboratory support the Shimizu model in the case of SGR + GBM. The theoretical piezometer calibrated for quartz suggests significant temperature effects under low-temperature metamorphic conditions.