Abstract :
An original phenomenological thermo-visco-plastic model is reported that encompasses strain hardening, strain rate
and temperature sensitivity. The model is based to some extent on the concept of physical modeling proposed earlier
by Klepaczko [Klepaczko, J.R. 1975. Thermally activated flow and strain rate history effects for some polycrystalline
FCC metals. Mater. Sci. Engng. 18, 121–135] , and also by different authors, for example: [Becker, R. 1925. Uber die plastizitat
amorpher und kristalliner fester korper. Z. Physik 26, 919–925; Seeger, A., 1957. Dislocations and Mechanical Properties
of Crystals, Wiley, New York; Conrad, H., 1964. Thermally activated deformation of metals J. Metals 16, 582;
Gilman, J.J. 1968. Dislocation dynamics and response of materials to impact Appl. Mech. Rev. 21, 767–783; Gibbs,
G.B., 1969. Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles. Mater. Sci. Engng. 4,
313–328; Kocks, U.F., Argon, A.S., Ashby, M.F., 1975. Thermodynamics and kinetics of slip. In: Progress in Materials
Science, vol. 19. Pergamon Press, New York, p. 19; Kocks, U.F. 1976. Laws for work-hardening and low-temperature
creep. J. Eng. Mater. Technol. 98, 76–85, and later by many others.
The thermo-visco-plastic formulation, called RK and applied in this paper, has been verified experimentally for strain
rates of 10 4 s 1 6 _ ep 6 5 103 s 1 and temperatures 213 K 6 T 6 393 K, it covers the range of dynamic loadings
observed during crash tests and other impact problems. In order to implement the RK constitutive relation, a thermovisco-
plastic algorithm based on the J2 theory of plasticity is constructed. The type of algorithm is a return mapping
one that introduces the consistency condition ðf ¼ r ry ; f ¼ 0Þ, without the overstress state proposed by Perzyna [Perzyna,
P. 1966. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, vol. 9. Academic Press, New
York, pp. 243–377]. The coupling of the RK constitutive relation with the integration scheme of the thermo-visco-plastic
algorithm has demonstrated its efficiency for numerical analyses of different dynamic processes such as Taylor test [Zaera,
R., Ferna´ndez-Sa´ez, J. 2006. An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations
in adiabatic conditions and finite deformations. Int. J. Solids Struct., 43, 1594–1612.], ring expansion [Rusinek, A.,
Zaera, R., 2007. Finite element simulation of steel ring fragmentation under radial expansion. Int. J. Impact Eng. 34, 799–
822], dynamic tension test [Rusinek, A., Zaera, R., Klepaczko, J.R., Cherigueme, R., 2005. Analysis of inertia and scale
effects on dynamic neck formation during tension of sheet steel. Acta Mater. 53, 5387–5400], perforation of metallic sheets
[Rusinek, A., 2000, Mode´lisation thermoviscoplastique d’une nuance de toˆ le d’acier aux grandes vitesses de de´formation.
Etude expe´rimentale et nume´rique du cisaillement, de la traction et de la perforation, Ph.D. thesis, University of Metz,
