On the reliability of yield functions in deep drawing simulations

Abstract

Abstract In sheet metal forming simulations, the yield functions are usually calibrated based on experimental data, and validated by comparing the modelled and measured r-values and (in more advanced models) yield stresses along various in-plane directions. The fitted yield function should ideally reproduce (or interpolate) all the experimental values used for the fitting. However, this requirement does not guarantee accurate results in a forming process simulation, and it can even lead to unexpected results. The performance of a yield function, in addition to the fitting procedure, depends on the active loading modes which the material experiences during the simulation. The active loading modes are in turn determined by the die geometry as well as the process parameters like blank holder force and lubrication. As a consequence, the performance of a yield function, which is fitted to simple experimental data, is not identical for different forming conditions. Therefore, the application of each model is usually limited to a range of materials and processes, and this applicability is often evaluated based on experience. In the present study, we examine three phenomenological yield functions and a new crystal plasticity based material model for cup drawing process simulation with an AA6016-T4 aluminium alloy. These functions are different in their input data types used for the calibration. The results surprisingly shows that the models with more experimental data (in particular, yield stresses in different directions) in their formulation not only predict unexpectedly wrong results, but also show strong sensitivity to some of those additional input data and even to modelling parameters like the friction coefficient.