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

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

Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham
United Kingdom

Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham
United Kingdom

Department of Manufacturing and Mechanical Engineering School of Engineering University of Birmingham
United Kingdom

Corus R, D and T, Swinden Technology Centre

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
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part 1 – Yield Criteria and Flow Rules for Porous Ductile Media, J. Engng. Matr. Tech., 99, 1977.

L.M. Kachanov, Time to the rupture process under creep conditions, Izv. Akad. SSR. Oid. Tekh. Nauk., 8, 26–31, 1958.

J. Lin, D.R. Hayhurst, and B.F. Dyson, The standard ridges uniaxial creep testpiece: computed accuracy of creep strain, J. of Strain Analysis, 28, 2, 101–115, 1993.

B.F. Dyson, Creep and fracture of metals: mechanisms and mechanics, Revue Phys. Appl., 23, 605–613, 1988.

A.C.F. Cocks and M.F. Ashby, On creep fracture by void growth, Progress in Material Science, 27, 189–244, 1982.

J.R. Rice and D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields, J. of the Mechanics and Physics of Solids, 17, 201–217, 1969.

N. Bonora, Identification and measurement of ductile damage parameters, J. of Strain Analysis, 34, 463–478 1999.

S. Dhar, et al., A continuum damage mechanics model for ductile fracture, International Journal of Pressure Vessels and Piping, 77, 335–344, 2000.

J.S. Vetrano, et al., Evidence for excess vacancies at sliding grain boundaries during superplastic deformation, Acta Materialia, 47, 4125–4129, 1999.

M.A. Khaleel, et al., Constitutive modeling of deformation and damage in superplastic materials, International J. of Plasticity, 17, 277–296, 2001.

D.R. Hayhurst, Creep rupture under multi-axial states of stress, J. Mech. Phys. Solids, 20, 381–390, 1972.

J. Lin and Y. Liu, A set of unified constitutive equations for modelling microstructure evolution in hot deformation, J. of Materials Processing Technology, 143–144, 281–285, 2003.

L.G. Lim and F.P.E. Dunne, Modelling central bursting in the extrusion of particulate reinforced metal matrix composite materials, Int. J. of Machine Tools and Manufacture, 37, 901–915, 1997.

A.A. Howe, D.C.J. Farrugia, Alloy design: from composition to through process models, Materials Science and Technology, 15, 15–21, 1999.

J. Lin, F.P.E. Dunne and D.R. Hayhurst, Physically-based temperature dependence of elastic viscoplastic constitutive equations for copper between 20 and 500 ◦C, Philosophical Magazine, A, 74, 2, 655–676, 1996.

B. Li, J. Lin, and X. Yao, A novel evolutionary algorithm for determining unified creep damage constitutive equations, Int. J. of Mech. Sci., 44, 5, 987–1002, 2002.

J. Lin, B.H. Cheong, and X. Yao, Universal multi-objective function for optimising superplastic-damage constitutive equations, J. of Mat. Proc. Tech., 125–126, 199–205, 2002.

DOI: 10.24423/engtrans.230.2007