A New Stability Criterion for the Hot Deformation Behavior of Materials: Application to the AZ31 Magnesium Alloy

In the present work, a new stability criterion is presented that uses the single sine hyperbolic equation of Garofalo for all values of the thermomechanical variables of the hot-working process. In this procedure, the efficiency and stability are calculated for each \( \dot{\varepsilon } \) and T by means of this equation. This is carried out directly applying the Garofalo equation on Lyapunov conditions in the framework of the dynamic material model (DMM), which simplifies operations and minimizes errors. This procedure, therefore, is straightforward, starting with experimental data and reaching the new established Lyapunov stability criterion. It is an alternative to the stability conditions using Lyapunov criteria, as established by Malas and Gegel and Prasad, where the strain-rate-sensitivity exponent, m, was determined by fitting the curve strain rate, \( \dot{\varepsilon } \), vs stress, σ, by means of a potential equation named power law, or by a polynomial of second or third degree, and calculating the slope of the logarithmic curve at each point using successive derivatives. In addition, a revision of various stability criteria and calculations of efficiency is conducted to delineate the framework of our new criterion. The developed method allows obtaining inequations that determine the more or less stable regions in the form of maps. These maps predict optimal temperatures and strain rates that are different from those given in the maps of Malas and Gegel and Prasad, although significant matches with various authors may also be observed. An analysis of maps for the magnesium alloy AZ31 based on various methods and models was performed to compare the predictions with the experimental results of other authors.