Reliability analysis of forming limits of anisotropic metal sheets with uncertain material properties

This paper presents a probabilistic method for estimating the reliability of the forming limits of anisotropic metal sheets with uncertain material properties. This method is based on Marciniak–Kuczynski (M–K) analysis and a first-order reliability method. The M–K approach is applied to the computation of both the strain-based and stress-based forming limits, and the anisotropic behaviour of the metal sheets is described by the Yld2000-2d yield criterion. Based on the measured statistics of material properties, forming limit curves with various reliability levels are calculated. The effects of uncertain material properties on the calculated forming limit curves are discussed. In addition, the effects of correlation strength among the uncertain properties are also investigated. Numerical results show that (i) the variation of the calculated forming limit strain curves with an increase in the reliability level is different both qualitatively and quantitatively from that of the forming limit stress curves and (ii) correlations among uncertain material properties may greatly affect the failure probability of metal sheets.