A THEORETICAL SENSITIVITY ANALYSIS FOR FULL-DOME FORMABILITY TESTS - PARAMETER STUDY FOR N, M, R, AND MU

Sheet material formability has been assessed by many kinds of tests and analyses presented in the literature; the most popular ones are based on hemispherical punch stretching geometry. An axisymmetric version of such a test was analyzed using SHEET-3 [a three-dimensional (3-D) finite element method (FEM) program] to determine the sensitivity of the test to parameters n, m, r, and mu. A realistic and self-consistent failure criterion was established to predict the limiting cup height at failure (LDH(f)) in sheet specimens from calculated strain distribution data. A 2(k) factorial experiment was conducted for variations in the four variables (k = 4). The sensitivity of LDH(f) to variations in n and m is constant, while its sensitivity to variations in mu is decreased as mu is increased. The significance of the influence of normal anisotropy on LDH(f) is unclear, being dependent upon the choice of yield theory. Direct interactions between material properties and friction were, for the most part, not found to strongly influence test results at the parameter levels examined. Materials with different properties will typically not fail under the same strain conditions in full-dome cup tests. Cup test results are influenced by a number of parameters, including some not considered here, e.g., sheet thickness and test temperature. The FEM model for the full-dome cup test, including a prediction of forming limits, provides a useful technique for sorting out important effects that individual parameters have on the strain state in the sheet at failure and the predicted final punch height at failure.