# Effect of yield locus exponent on draw-in prediction during deep drawing of commercially pure titanium

## TL;DR

This paper studies how changing a parameter in a metal forming model affects predictions for titanium sheets, finding higher values give better results.

## Contribution

The study demonstrates the need for material-specific calibration of the yield locus exponent in HCP metals like titanium.

## Key findings

- Higher exponent values (a > 9) improve the accuracy of titanium sheet forming simulations.
- Fixed exponent values based on crystal structure are insufficient for hexagonal close-packed metals.
- Material-specific calibration is necessary for accurate modeling of titanium forming behavior.

## Abstract

The Yld2000-2D yield locus is widely employed to model anisotropic plasticity in sheet metal forming. Its exponent, a, critically influences the shape of the yield surface and is typically assigned fixed values based on crystal structure–commonly \documentclass[12pt]{minimal}
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\begin{document}$$a=6$$\end{document} for body-centered cubic (BCC) and \documentclass[12pt]{minimal}
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\begin{document}$$a=8$$\end{document} for face-centered cubic (FCC) materials. However, no universally accepted value exists for hexagonal close-packed (HCP) metals such as commercially pure titanium, which exhibit pronounced anisotropy and complex hardening behavior. This study explores the influence of the value of a on accurately modeling the forming response of commercially pure titanium sheets. To examine the impact of the exponent value a comparison between finite element (FE) simulations and experimental draw-in profiles obtained from cup-drawing tests is performed. To account for evolving anisotropy during plastic deformation, the Yld2000-2D yield locus is further augmented with strain-dependent coefficients, while the loading asymmetry commonly present in HCP metals is neglected. The results show a clear preference for larger exponent values with \documentclass[12pt]{minimal}
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\begin{document}$$a>9$$\end{document} giving the best results. This highlights the necessity of material-specific calibration for HCP alloys and provide actionable insights for improving the predictive fidelity of titanium sheet forming simulations.