Constitutive Equations for Commercial-Purity Aluminum Deformed Under Hot-Working Conditions

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Abstract
A rational analysis of a number of stress-strain curves for a commercial-purity aluminum has been carried out in order to derive a set of constitutive equations capable of describing the flow stress of the material in terms of the applied strain, rate of straining, and deformation temperature. Such an analysis combines the exponential saturation strain-hardening function earlier proposed by Voce (1948; 1955) with the exponential relationship developed from steady-state creep data at high stresses, and considers the existence of two different regimes of work-hardening. The proposed formalism requires only the use of seven material constants which include the temperature-dependent shear modulus, the activation energy for self-diffusion, one pre-exponential factor, and four stress sensitivity parameters of the strain rate. A satisfactory correlation has been obtained between the experimental values of the flow stress and those predicted for the model, which enables it to be used in conjunction with any algorithm based on finite differences methods or finite elements codes to simulate hot-working operations carried out in this material.