A practical stress-strain-strain rate-temperature constitutive relation of the power form

Abstract

Many technical processes have been analysed using a double-power constitutive relation of the form: σ = B σ ϵ n ϵ ̇ m Such an equation can be used, for example, in the simulation of many bulk metal-forming processes, in forming-limit diagrams, and in many other situations. The problem, however, arises when this constitutive relation has to be used at different temperatures. Earlier analysis has indicated that in such relations, material constants such as the plasticity modulus B(T), the strain-hardening exponent n(T) and the logarithmic rate-sensitivity m(T) are temperature-dependent. A new approximation for these parameters as a function of temperature is proposed. Within the framework of temperature generalization all material constants are identified for three materials: commercially pure polycrystalline aluminium, OFHC copper and steel. Special attention is paid to 1018 cold-rolled steel (1018 CRS) where the response of the material to plastic deformation is more complicated. These three materials are analysed over a wide range of temperatures: θ < T < T m/2 and a wide range of shear strain rates: 5×10 −4 s −1 < Γ ̇ < ∼5×10 2 s −1 , where T m is the melting temperature. In addition, the generalized form of the constitutive relation is discussed for the whole temperature range, i.e. θ < T < T m . For the purpose of demonstration, several characteristic material responses during plastic deformation at different temperatures and different strain rates have been simulated using a computer program and computer graphics: the program is available from the author. Results are shown in the form of plots, along with experimental points. The predictions of the calculations are confirmed by experimental data.