Dimensional Analysis of Superplastic Processes with the Buckingham Π Theorem

Abstract

This work applies the Buckingham Π theorem from dimensional analysis on superplastic processes in order to obtain laws of behaviour in a simple way. For this reason, a mathematical background is developed. The particular behaviour of superplastic materials makes it necessary to adapt the way in which these are treated, modelling them by a viscosity function of the strain-rate. Then, dimensional analysis is applied on a set of free-inflation tests in order to obtain a formula that defines the forming time as single function of geometric and material variables. Dimensional analysis allows us to reduce the number of variables to analyse from six to only three. Finally, two different forming time estimators are compared to measure the accuracy of our method, showing a significant improvement over previous methods.