Processing Maps for the Hot Forming of Polycrystalline Metallic Materials Using the Garofalo Equation

Abstract

Processing maps have been built for > 30 years to predict the stable conditions for metal forming at high temperatures and strain rates. These maps, which also include efficiency conditions, are based on the stability criterion of Ziegler–Prasad (Z–P) within the framework of the dynamical materials model (DMM). In the present work, this criterion is drastically modified by introducing a Garofalo equation in the expression of the dissipative co-content, J, maintaining its definition in the framework of the DMM. This modification applies to its derivative with respect to the strain rate and also to the definition of efficiency, η. This new parameter developed in this work, named rho, ρ, is different from the stability parameter, xi, ξ, of the Z–P criterion since it is based on different constitutive equations. Rho is based on a Garofalo equation and xi on a power law equation. Both are obtained from experimental data and give rise to different stability maps that can be applied to any polycrystalline metallic material. In this work, a well-documented Ti-10V-4.5Fe alloy has been chosen to contrast the differences and similarities between the two methods of characterizing the stability conditions. Special emphasis is given to the predictions for the optimum forming temperatures.