On Micro-Damage in Hot Metal Working Part 2: Constitutive Modelling

Damage constitutive equations are formulated to model the evolution of grain boundary and plasticityinduced damage for freecutting steels under hot forming conditions. During high temperature, high strain rate deformation, material degradation has characteristics of both creep damage at grain boundaries, and ductile damage surrounding hard inclusions. This has been experimentally observed and is reported in the companion paper. This paper describes the development of unified viscoplasticdamage constitutive equations, in which the nucleation and growth of both damage types are considered independently. The effects of deformation rate, temperature, and material microstructure on damage evolution are modelled. The proposed damage evolution equations are combined with a viscoplastic constitutive equation set, enabling the evolution of dislocation hardening, recovery, recrystallisation, grain size, and damage to be modelled. This set of unified, mechanismbased, viscoplastic damage constitutive equations is determined from experimental data of a freemachining steel for the temperature range 11731373 K. The fitted model is then used to predict damage and failure features of the same material tested using a set of interrupted constant strain rate tests. Close agreement between the predicted and experimental results is obtained for all the cases studied.