Assessment of constitutive equations in modelling the hot deformability of some overaged Al–Mg–Si alloys with varying solute contents

In this study five constitutive models with varying numbers of fitting parameters are assessed for modelling the stress–strain curves of four high-purity Al–Mg–Si alloys. Four of the five models are composed of the general exponential saturation equation as proposed by Sah et al. (J.P. Sah, G.J. Richardson, C.M. Sellars, J. Austr, Inst. Met. 14 (1969) 292), with a strain rate dependence which is either power law-like, exponential, power law-like with a temperature dependent strain rate sensitivity, or hyperbolic sine-like. The fifth model consists of a single modified hyperbolic sine equation. The compositions of the experimental alloys facilitated the examination of the effect of solute Mg and Si content on the parameters of the constitutive equations. The alloys were plane strain compression tested in an over-aged condition at temperatures and at strain rates relevant to hot rolling and hot extrusion. A good fit of the experimental curves with just one parameter set per alloy is obtained for the four models based on the exponential saturation equation, whereas the modified hyperbolic sine law yields a less satisfactory fit. On the basis of the quality of the fit, the complexity of the model, and the fit parameter values obtained, it is concluded that the Sah-saturation equation combined with the hyperbolic sine law is the most favourable of the five models. It is shown that the deviations between the apparent activation energy values obtained and the literature value of the activation energy for lattice diffusion in pure aluminium can be attributed to the temperature dependence of the solubility of Mg and Si.