Engineering Transactions, 55, 1, pp. 43–60, 2007

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

J. LIN
Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham

A. D. FOSTER
Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham

Y. LIU

D. C. J. FARRUGIA
Corus R, D and T, Swinden Technology Centre

T. A. DEAN
Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham

Damage constitutive equations are formulated to model the evolution of grain boundary
and plasticity-induced damage for free-cutting 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 viscoplastic-damage 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, mechanism-based, viscoplastic damage constitutive equations is
determined from experimental data of a free-machining steel for the temperature range 1173–
1373 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.
Keywords: creep damage, ductile damage, constitutive equations, hot metal forming, viscoplasticity
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