Prediction of plane-strain specimen geometry to efficiently obtain a forming limit diagram by Marciniak test

Plane-strain forming limit strain (also known as FLD0) is an important data point on a forming limit diagram (FLD). The effects of friction coefficients and material parameters on the specimen width associated with the FLD0 (WFLD0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_{{{\text{FLD}}_0}}$$\end{document}) in Marciniak test were studied by finite element simulation. WFLD0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_{{{\text{FLD}}_0}}$$\end{document} was expressed as a function of the Lankford coefficients, n-value, k-value and sheet thickness and validated with various sheet materials. The determination of WFLD0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_{{{\text{FLD}}_0}}$$\end{document} is of significance not only to reduce iterative attempts to accurately obtain FLD0, but also to obtain a full valid FLD with the least number of test specimens, which largely increases the efficiency and reduces cost to experimentally measure valid FLDs.