Anisotropic yield function calibration strategies for thickness prediction by FE hole expansion test

Abstract

The constitutive model is a crucial tool for the prediction of the behaviors of materials in numerical simulations of sheet metal forming. However, it is a challenge to get accurate results for all the processes because of the limitations of the constitutive model and the specific stress states involved in the process. Therefore, the adaptation of a constitutive model according to the types of process considered is a way to get more reliable results. During sheet metal forming, typical multiaxial stress states are dominant in certain processes such plane strain tension during stretch flanging. The stretch-flange ability of a sheet material is actually well characterized using the hole expansion test (HET) by providing not only the hole expansion ratio but, in addition, the material thickness anisotropy near the periphery of the hole and the localization strain at the end of the process. For the description of plastic anisotropy, a suitable yield condition and different strategies may be developed to determine the corresponding coefficients. In this work, the plane stress anisotropic yield condition Yld2000-2d is employed. The coefficients are usually calculated using a method, called original, that was explained in the original article. In this work, two additional calibration methods are proposed, which consider the dominant stress state during HET, namely, plane strain tension. In the first method, so-called semi-analytical, the coefficients are the solution of a set of equation while in the second, called optimized, the coefficients result from an optimization procedure. To produce input data for this model, uniaxial tension and bulge tests are conducted to produce the standard Yld2000-2d coefficients. For the two new methods, which will be explained in detail in this thesis, additional data are generated from biaxial tension tests with various stress ratios, including for plane strain tension. Hole expansion test simulations are conducted with the different strategies to determine the Yld2000-2d coefficients, i.e. standard, semi-analytical and optimized methods. Thickness true strain profiles along the circumference hole edge and 3 mm away from it are predicted. The simulated and experimental profiles are compared and the best agreement is obtained using the coefficients of the analytical method. However, it is shown that the thickness reduction is not a proper indicator of the fracture location.