Simple constitutive relationship for C–Mn steels deformed at elevated temperatures

Abstract

The strain, strain rate and temperature dependence of a C-Mn steel (BS grade 430) deformed under plane strain compression conditions have been investigated in the temperature range 1173-1373 K, at strain rates of 0.25-25 s-1. It has been determined that the stress-strain behaviour of this material can be modelled satisfactorily in a rational manner by combining the exponential saturation law advanced by Sah et al., for description of the evolution of the flow stress, and modified appropriately to account for dynamic recrystallisation effects, with the kinetic models advanced by Kocks and Sellars-Tegart-Garofalo. The Kocks model has been introduced for description of the temperature and strain rate dependence of both the initial flow stress, at the beginning of plastic flow, and the apparent saturation stress, achieved at elevated strains. The Sellars-Tegart-Garofalo model has been employed for the description of the actual saturation stress, achieved after the work softening transient brought about by the operation of dynamic recrystallisation, also in terms of temperature and strain rate. The relaxation strain, in the Sah et al. law has been found to be dependent on the effective strain rate and it has been determined that such a dependency can be described by means of a simple parametric power law relationship. Also, it has been found that the optimised value for activation energy for deformation at elevated temperatures is very close to the activation energy of self-diffusion of iron in austenite, which emphasises the need to introduce into this kind of analysis scaling parameters as the temperature dependent shear modulus of the material. The stress-strain/strain rate/temperature relationship that has been developed in the present work is able to characterise satisfactorily both the flow stress and work hardening rate of the material under the deformation conditions explored, allowing a valid interpolation of the flow stress at any strain, temperature, and strain rate.