Re Dick

Plane stress yield function for aluminum alloy sheets—part 1: theory

Abstract A new plane stress yield function that well describes the anisotropic behavior of sheet metals, in particular, aluminum alloy sheets, was proposed. The anisotropy of the function was introduced in the formulation using two linear transformations on the Cauchy stress tensor. It was shown that the accuracy of this new function was similar to that of other recently proposed non-quadratic yield functions. Moreover, it was proved that the function is convex in stress space. A new experiment was proposed to obtain one of the anisotropy coefficients. This new formulation is expected to be particularly suitable for finite element (FE) modeling simulations of sheet forming processes for aluminum alloy sheets.

Earing prediction in cup drawing based on non-associated flow rule

An anisotropic constitutive model based on Non‐Associated Flow Rule (Non‐AFR), which incorporates plane stress yield functions (Hill’s quadratic function and Yld2000‐2d by Barlat et al.), was implemented to finite element codes (ABAQUS, LS‐DYNA 3D) by using User Material options. By using Non‐AFR, Yld2000‐2d is capable of predicting more than four ears which is possible only with Yld2004 by Barlat et al. when used with an Associated Flow Rule. A short review of the Non‐Associated Flow Rule was provided. Simulation of the cup drawing process for a rigid container sheet alloy using mini‐die geometry was performed to show the cup height profile (earing profile) obtained from Non‐AFR. The simulation results were compared with experimental earing profile data and it was shown that the simulations using Yld2000‐2d and the Non‐AFR led to the excellent prediction of the earing profile.

Convolute Cut‐Edge Design for an Earless Cup in Cup Drawing

A convolute cut‐edge design is performed using FEM (Finite Element Method) for a single step cup drawing operation in order to produce an earless cup profile. Mini‐die drawing based on a circular blank shape is initially carried out in order to verify the earing prediction of the Yld2004 model for a body stock material. A realistic cup geometry is then employed to design a non‐circular convolute edge shape. An iterative procedure based on finite element method is initially used to design a convolute shape for an earless target cup height. A constant strain method is suggested to obtain a new convolute prediction for the next iteration from the current solution. The Yld2004 model is also introduced to predict the anisotropy of the materials precisely.

Convolute Cut‐Edge Design for a Circular Cup Based on FEM and an Analytical Approach

A convolute cut‐edge design was developed for a single step cup drawing operation in order to produce an earless cup profile. An iterative procedure, based on the finite element method and a constant strain method using a new anisotropic yield function (Barlat et al., called Yld2004‐18p), was used to design a convolute shape for an earless target cup height. A simplified analytical approach that relates the earing profile to r‐value directionality was presented in this work. R‐value directionality was included with the incompressible condition from the compressive mode at the rim. The result obtained from the iterative procedure was compared with the one from the analytical approach suggested. It is proven that both Yld2004 model and the simplified analytical method provide an accurate prediction of the convolute cut‐edge shape.

New distortional hardening model capable of predicting eight ears for textured aluminum sheet

The effects of the anisotropy evolution and of the directionality in hardening on the predictions of the earing profile of a strongly textured aluminum alloy are investigated using a new distortional hardening model that incorporates multiple hardening curves corresponding to uniaxial tension along several orientations with respect to the rolling direction, and to biaxial tension. Yielding is described using a form of CPB06ex2 yield function (Plunkett et al. (2008)) which is tailored for metals with no tension‐compression asymmetry. It is shown that even if directional hardening and its evolution are neglected, this yield function predicts a cup with eight ears as was observed experimentally. However, directional hardening can be of considerable importance for improved accuracy in prediction of the non‐uniformity of the cup height profile.