There are various methods to evaluate the forming limit of a sheet, and these criteria can be classified as position-dependent, time-dependent, and position-time dependent according to the basis of judgment. However, these criteria have a single function and can only find the forming limit of the sheet and cannot determine the strain distribution, strain change, or fracture location during the sheet forming process. This paper introduces a time–location-dependent method, i.e., the spatial strain rate method, which is used to detect the onset of necking of a sheet. The spatial strain rate is directly based on the strain and can not only find the forming limit of the sheet but also depict the strain distribution and strain variation during the two phases of the experimental process—distributed instability and concentrated instability—as well as predict the location of sheet fracture. The spatial strain rate of AA5083 aluminum alloy of different widths was analyzed and verified in detail via Nakazima experiments using digital image correlation techniques and compared with the guidelines published in the literature in recent years.

Blaise MH, et al. Korean J Neurotrauma. 2025 Oct;21:e31. https://doi.org/10.13004/kjnt.2025.21.e31

The temperature and strain rate have significant effect on the formability of Al-Mg alloy sheet during warm forming process. Forming limit curve (FLC) is widely used for predicting sheet failure in warm forming simulation. However, the current simulation and optimization may lead to non-robust results, due to not considering the variation of FLC caused by the randomness of sheet temperature and deformation velocity, etc. In this study, a theoretical approach is developed to predict the temperature and strain rate dependent FLC. Backofen constitutive equation is extended, in which the material parameters are fitted as a function of temperature and strain rate by response surface method (RSM). Based on the M-K theory and Logan-Hosford yield criterion, the FLCs of 5083 Al-Mg sheet under different temperature and strain rate conditions are predicted and compared with the experimental results. By integrating the theoretical approach and Monte-Carlo simulation, the temperature and strain rate uncertainties are involved in FLC prediction to reflect manufacturing reality. The upper and lower margins of the FLC variation band are established, which covers the dispersion of the limit strains propagate from temperature and strain rate fluctuation. It is shown that under the combination of a higher temperature and a lower strain rate, the FLC of 5083 Al-Mg sheet is quite sensitive to small fluctuation of temperature or strain rate. In a particular temperature range (413 K–453 K), the FLC of 5083 Al-Mg alloy sheet becomes less sensitive to the fluctuation of temperature or strain rate. All these findings will advance the understanding of the design quality and robustness of the warm forming process.