Inverse analysis of the stress–strain curve to determine the materials models of work hardening and dynamic recovery

A constitutive equation has been established based on the dislocation theory, the work hardening and dynamic recovery theory. The stress–strain curves of bainite steel have been measured by a hot compression experiment at temperatures of 1173, 1273, 1373, and 1473 K with strain rates of 0.01, 0.1, 1, and 10 s−1 on a thermo-mechanical simulator Gleeble-1500. The material constants involved in the constitutive equation have been optimized by an inverse analysis of the stress–strain curves. This information is used to determine the materials models of work hardening and dynamic recovery, and the strain–stress relationship of the investigated steel in high temperature deformation. The results are in agreement with those obtained from experimental measurements. They demonstrate that the material constants determined by the stress–strain curves can capture the underlying materials science of high temperature deformation. On this basis, the evolution law of dislocation density has been obtained in work hardening and dynamic recovery. A relationship function between the critical dislocation density for dynamic recrystallization and deformation parameters has been established. And an equation for recovery kinetics has been proposed with reference referring to the Avrami equation.