Estimation of forming limit diagrams by the use of the finite element method and Monte Carlo simulation

A stochastic finite element-based approach for forming limit calculations of sheets is proposed and evaluated. Material inhomogeneities are represented by spatial thickness variations of the sheet which are modelled by the use of random fields. The effects of changing the smoothness, wavelengths, amplitude and anisotropy of the field realisations on the forming limit diagram are investigated. Further, the effects of the patch size and plastic anisotropy on the forming limit diagram are studied. The assumed thickness variations result in a quite wide scatter band, and changes of the characteristics of the thickness field result in changes of the shape and variance of the forming limit diagram.