Statistical Safety Margins for Forming Limit Curves

The Forming Limit Curve (FLC) is widely used in the sheet metal forming industry as a failure criterion. Necking limit, i.e., the initiation of local necking, is used as a failure condition in FLC. In the FLC determination process, uncertainties arise due to variations in material properties, lubrication, tool alignment, friction, and strain measurement. Due to these uncertainties, engineers apply a safety margin during actual production time. A safety margin in an FLC is created by shifting the original FLC 10–20% downward. The concept of introducing a safety margin is straightforward: the deformed sheet will remain safely below the true failure limit, even if the actual material is somewhat weaker or the process conditions vary. FLCs are commonly generated using Marciniak (flat-bottom punch) and Nakazima (hemispherical punch) tests performed on multiple specimens with different widths to achieve a range of strain paths, from uniaxial tension to plane-strain tension to equi-biaxial tension. For each specimen width, several tests are conducted to capture the inherent scatter in forming limits. This study presents a statistical framework for quantifying the probability of failure across various strain states and evaluating the dispersion in measured forming limit data. Instead of relying on an arbitrary safety margin, the proposed approach enables the selection of an appropriate, statistically justified safety margin derived from the distribution of experimental FLC data.