Comparative studies of hyperbolic sine constitutive models for constant pressure superplastic tests

Abstract

The constant pressure free-inflation test is a very versatile and simple tool for analyzing different features of superplastic forming. In recent years, different methods have been proposed to measure constitutive parameters of the stress–strain relationship for the superplastic material, specifically the K and m parameters of the power law model. However, this law is restricted to be used in narrow strain-rate ranges, and poor results are obtained when applied in a broader spectrum. To overcome this problem, numerous constitutive models covering the full strain-rate range applicable in superplastic forming have been proposed historically, including the hyperbolic sine equation. However, there is no clear consensus on the type of hyperbolic sine function to use. Some authors include a sensitivity parameter while others do not. This article aims to study the characteristics of the hyperbolic sine constitutive model, checking which of the historically proposed models achieves better results in the test at free deformation and constant pressure.