Inverse Analysis Used to Determine Plastic Flow and Tribological Characteristics for Deep-drawing Sheet

Abstract

The present paper aims to develop a simple method based on inverse analysis that allows us to determine the laws of plastic flow coefficients and the friction coefficient between the material and punch. Selecting from different types of tests, we have chosen the Hecker test, because this test requires a single form of punch, the hemispherical one. In this test, the friction between the punch and the blank-sheet is caused by the blank-sheet strains and not by the movement it makes (as in deep drawing case). Besides the friction coefficient, other parameters like hardening and strength coefficients (n and k), influence the distribution of stresses and strains in the material. Using the Hecker test, we determined the curves force vs. displacement and major strain vs. displacement for three points located at different heights on the dome. Obtained from the test, these curves will stay on the basis of multi-criteria optimization analysis performed with LS-Dyna and Ls-Opt. The force vs. displacement curve was obtained using a hydraulic transducer and the major strains vs. displacement curves were obtained using the optical system Aramis which provides full information on the three-dimensional coordinates, displacements, strain variations, etc. On the other hand, using the Ls-Dyna software we will simulate the Hecker test and we will get the same types of curves (force vs. displacement and principal strains vs. displacement). Inverse analysis will consist in minimizing the “distance” between the curves obtained by simulation and experimentally obtained curves. We must to mention that this paper contains a big hypothesis: the identification is valid only for the chosen mesh and modelling of friction.