Seventy years of Hall-Petch, ninety years of superplasticity and a generalized approach to the effect of grain size on flow stress

The grain size, and therefore the grain boundary density, is known to play a major role in the flow stress of metallic materials. A linear relationship to the inverse of the square root of the grain size was identified about 70 years ago giving rise to the well-established Hall-Petch grain refinement strengthening effect. Nevertheless, grain refinement softening is known to take place at high homologous temperatures and both effects have been given separate treatments. A recent model showed that a general relationship can explain both the Hall-Petch strengthening effect at low temperatures and superplasticity at high temperatures. The present review discusses recent advances in structural and mechanical characterization to provide an updated analysis of trends observed in the relationship between the grain size and the flow stress. The model of grain boundary sliding is evaluated using multiple sets of data in the literature and a general description is provided for the transition between grain refinement hardening and grain refinement softening. The analysis incorporate data from over 30 different metals and alloys with different grain sizes and after testing at different strain rates and temperatures. Data from molecular dynamic simulations are also included and show supporting evidence to the model of grain boundary sliding. The thermal contribution of the grain size strengthening and threshold stress is discussed including the trends observed in the strain rate sensitivity of fine-grained materials.