Treatment of Concurrent Microstructure Evolution and Deviation from Steady-State Flow in Constitutive Relationship for Superplastic Deformation

Superplasticity is the ability of certain polycrystalline materials to exhibit exceptionally large elongations by grain boundary sliding and its accommodation by diffusion, dislocation slip, or both. One of the critical requirements for this phenomenon to occur is the fine equiaxed grains, which should be stable during deformation at elevated temperature. Under this condition, there exists a unique relationship between stress and strain rate as a function of temperature and grain size, with the high values of strain rate sensitivity index m of greater than 0.3. However, there is ample evidence of the variation in flow stress with strain along with concurrent microstructural evolution. Often the microstructures are known not to be equiaxed yet exhibit superplasticity by rapid change in morphology and size during early stage of deformation. This leads to flow softening and hardening with strain as a result of the dominance of one type of change over the other. Mechanistically, accommodation of grain boundary sliding by grain boundary migration leads to grain growth, resulting in flow hardening, whereas the absence of the same may cause the formation of cavities because of stress concentration at triple points and at two-phase or particle-matrix interphase boundaries. In view of this, the constitutive relationship needs to be modified by incorporating the dependence of stress on strain and concurrent microstructure changes. The present work critically examines the nature of stress-strain curves and microstructure evolution in an attempt to account for the non-steady-state flow and attain a generalized form of constitutive relationship for superplastic deformation. An attempt is made to quantify the variations in flow stress and microstructures interdependently as well as with strain by exploring the suitable trend lines. These equations can numerically and physically help in correlating the microscopic and macroscopic properties to the mechanisms for superplastic deformation.