A model for strain hardening, recovery, recrystallization and grain growth with applications to forming processes of nickel base alloys

An ensemble of n spherical grains is considered, each of which is characterized by its radius ri and by a hardening variable ai. The hardening variable obeys a Chaboche-type evolution equation with dynamic and static recovery. The grain growth law includes the usual contribution of the grain boundary energy, a term for the stored energy associated with the hardening variable, and the Zener pinning force exerted by particles on the migrating grain boundaries. New grains develop by recrystallization in grains whose stored energy density exceeds a critical value. The growth or shrinkage of the particles, which restrain grain boundary migration, obeys a thermodynamic/kinetic evolution equation. This set of first order differential equations for ri, ai and the particle radius is integrated numerically. Fictitious model parameters for a virtual nickel base alloy are used to demonstrate the properties and capabilities of the model. For a real nickel alloy, model parameters are adjusted using measured stress-strain curves, as well as recrystallized volume fractions and grain size distributions. Finally the model with adjusted parameters is applied to a forming process with complex temperature-strain rate histories.