Comparison of efficiency and stability maps obtained by various methods

Abstract

One of the most widely accepted tools for the identification of the optimum processing conditions for hot-working is the Dynamic Material Model, whose final aim is the representation of efficiency and stability maps. In the present work, a revision of various stability criteria and calculation of efficiency is conducted and the equations of Ziegler, as revised by Kumar and Prasad, and Lyapunov as revised by Malas and Gegel and Prasad are established. Determination of the strain rate sensitivity exponent, m is essential to establish the stability regions. This parameter is usually determined by fitting the curves strain rate, , 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. Furthermore, we introduce our method where all experimental points are fitted to a single hyperbolic sine equation of Garofalo type and then m is calculated for each and T using this equation. An analysis of the maps that are obtained based on various methods and models to compare the predictions with experimental results on different materials is performed.

Keywords:

• Dynamic material model
• Garofalo equation
• constitutive equations
• hot forming
• stability maps