On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model

This paper scrutinizes in detail the synergy between physical and virtual testing of the mechanical response of sheet metal. In this context, physical testing refers to the usage of physical samples onto which mechanical tests are conducted, while virtual testing refers to multi-scale plasticity simulations onto a model representation of the metallic microstructure derived from microstructural measurement. An extensive experimental campaign was conducted to capture the plastic material response of mild steel sheet in the first quadrant of the biaxial stress space, i.e. for tensile stresses along the Rolling Direction (RD) and Transverse Direction (TD). The experimental data was acquired using state-of-the-art stress-controlled material tests enabling to probe the material up to large plastic strains in the first quadrant of stress space. Identical stress paths were simulated using the Virtual Experimentation Framework (VEF) software suite adopting the ALAMEL multi-scale plasticity model. The ALAMEL model was calibrated solely on the basis of the initial crystallographic texture of the material and a reference hardening curve obtained through a uniaxial tensile test in the rolling direction. The predictive accuracy of the ALAMEL model to reproduce the experimentally acquired material response has been thoroughly assessed. To avoid any bias in the assessment due to extrapolation of the material behavior, predictions were limited to the pre-necking regime of the material. The predictions of the VEF show good agreement with the physical test results. Subsequently, the experimental and virtual test data were used to calibrate Hill’s quadratic yield criterion and the Yld2000-2d yield function. The calibration accuracy of these yield criteria is thoroughly assessed by comparing theoretical predictions and experimental data. In addition, the calibrated yield functions are used to simulate a hydraulic bulge test and the results are compared with experimental observations. It is shown that the adopted virtual material testing procedure has reached a sufficient level of maturity to potentially serve as a viable alternative for physical material testing of steel sheet.