Constitutive relations in 3-D for a wide range of strain rates and temperatures - Application to mild steels

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, JR. 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) <= epsilon(p) <= 5 x 103 s(-1) and temperatures 213 K <=, T <= 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 thermo-visco-plastic algorithm based on the J(2) theory of plasticity is constructed. The type of algorithm is a return mapping one that introduces the consistency condition (f = a sigma- sigma(y) = 0), 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., Fernandez-Saez, 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, 799822], dynamic tension test [Rusinek, A., Zaera, R., Klepaczko, JR., 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, Modelisation thermoviscoplastique d'une nuance de tole d'acier aux grandes vitesses de deformation. Etude experimentale et numerique du cisaillement, de la traction et de la perforation, Ph.D. thesis, University of Metz,France], and other cases. All the equations are implemented via the user subroutine VUMAT in the ABAQUS/Explicit code for adiabatic conditions of plastic deformation. (c) 2007 Elsevier Ltd. All rights reserved.