Analytical model for characterizing the pear-shaped tribotest for tube hydroforming. Part 1

Abstract

An analytical model to characterize the pear-shaped tribotest is presented. In this test, a tubular specimen is pressurized, forcing the material to flow towards the apex of a pear-shaped die. The height of the pear-shaped tube is a function of the magnitude of friction stress at the tube—die interface. Through a mechanistic approach, a closed-form solution for field variables die—tube contact pressure, effective stress/strain, longitudinal stress/strain, and hoop stress/strain can be computed as a function of input pressure loading. The model has been validated by finite element analysis. The closed-form solution can be used rapidly to establish the calibration curves for determination of friction coefficient in the pear-shaped tribotest. Of equal importance, the analytical model can be used to optimize both process and die geometric variables to suit specific needs such as die wear studies through monitoring local interface pressure loading, types of material to be tested, tube sizes, and so on. Details on the applications of the developed analytical model can be found in Part 2 of this paper.