Modeling of forming limit for multilayer sheets based on strain-rate potentials

In order to evaluate the forming limits of planar anisotropic multilayer sheet materials, the Marciniak–Kuczynski (M−K) model was formulated based on the strain-rate potential. A common practice to predict the forming limits of sheet materials has been based on yield stress potentials defined in the stress field. As an alternative, a method based on plastic stain-rate potentials, which are especially convenient to apply for rigid-viscoplasticity, was considered in this work. The formulation based on the strain-rate potential facilitates the modeling of forming limits for multilayer sheet materials because the number of unknown variables is significantly reduced by assuming the iso-strain condition for each layer without delamination. As for the strain-rate potential, Srp2003-2d, which is the pseudo-conjugate of the yield stress potential Yld2000-2d, was applied along with Hill's 1948 strain-rate potential for comparison. In the approach proposed, rigid-viscoplasticity was formulated according to the incremental deformation theory based on the minimum plastic work path. The rotation of anisotropic symmetry axes in the groove region was also properly accounted for in the formulation. For verification purposes, the predicted forming limit criteria such as the strain-based forming limit diagram (FLD), the stress-based forming limit diagram (FLSD) and the effective strain-based forming limit diagram (x-EPS) were experimentally validated for a monolithic aluminum alloy (AA5182-O) sheet and a three-layer AA5182-O/polypropylene/AA5182-O (AA/PP/AA) sandwich sheet, which confirmed good agreement. In addition, the path-sensitivity of the strain-based FLD and the path-insensitivity of the FLSD and x-EPS were numerically proven based on the M−K model for the three-layer sandwich sheet. Finally, the M−K model was compared with a maximum force model most recently developed.