Sheng, Z., "A Temperature and Time Dependent Forming Limit Surface for Sheet Metal Forming at Elevated Temperatures," SAE Int. J. Mater. Manf. 5(2):277-284, 2012, doi:10.4271/2012-01-0016.
Sheet metal forming at elevated temperatures, or so-called sheet metal warm/hot forming, is a relatively new forming process to make sheet metal parts with low mass. An accurate and convenient description of forming limit is critical for the success of forming process design and improvement. Strain-based Forming Limit Diagram has long been used to describe forming limit in cold sheet metal forming. However, at elevated temperatures, the formability of those sheet metals is strongly governed by both temperatures and strain rates. In order to extend the Forming Limit Diagram method into elevated temperature domain, a large number of forming limit curves are intuitively required to cover different temperatures and strain rates. It is not only costly to obtain but also inconvenient to apply those forming limit curves in industrial practice. In this study, Zener-Hollomon parameter, which was used to describe both temperature and strain rate effect on flow stress, is proposed to represent time and temperature effect on forming limit curves. Under a hypnosis, a polynomial relationship between natural logarithm of Zener-Hollomon parameter and major strain exists at each corresponding minor strains, a forming limit surface, which is constructed in a three-dimensional Cartesian coordinate system with three axes of major strain ε1, minor strain ε2 and natural logarithm of Z (ln(Z)), is then proposed. The hypothesized correlation between ln(Z) and forming limit curves is validated by published test data on Aluminum alloy 5083 at temperatures ranging from 293K to 573K and strain rates ranging from 0.0001 to 0.1 s-1. A forming limit surface is then constructed. Since only one surface is needed, the method could reduce the efforts of laboratory testing and provide a convenient tool in the development of thermal forming processes.