Yield function calibration for orthotropic sheet metals based on uniaxial and plane strain tensile tests

Abstract

Plastic anisotropy in numerical analysis of sheet metal forming operations can be described very efficiently by means of analytical yield functions. However, for an anisotropic sheet material acceptable calibration of an appropriate yield function requires numerous mechanical testing procedures involving different loading modes such as directional uniaxial tensile tests and an equibiaxial tensile or bulge test. Realization of the mentioned loading modes requires the usage of different testing devices that are not always available. Therefore, a calibration procedure for advanced yield functions involving only a single tensile test machine seems appealing. In the present article a calibration method involving three directional uniaxial tensile tests and two plane strain tensile tests is proposed. This calibration method is applied to the recently introduced yield function Yld2003 [H. Aretz, Applications of a new plane stress yield function to orthotropic steel and aluminium sheet alloys, Model. Simul. Mater. Sci. Eng. 12 (2004) 491–509; H. Aretz, A non-quadratic plane stress yield function for orthotropic sheet metals, J. Mater. Process. Technol. 168 (2005) 1–9] using different materials. The obtained results are compared to those obtained by using the conventional calibration based on uniaxial and equibiaxial test data. It is shown that for all considered materials the proposed calibration procedure gives satisfying results. Finally, for selected materials and with respect to the different calibration procedures sensitivity analyses concerning the predicted forming limit diagram (FLD) are carried out using the finite element based FLD simulation approach proposed by Lademo et al. [O.-G. Lademo, T. Berstad, O.S. Hopperstad, K.O. Pedersen, A numerical tool for forma-bility analysis of aluminium alloys. Part I. Theory, Steel Grips 2 (2004) 427-431; O.-G. Lademo, T. Berstad, O.S. Hopperstad, K.O. Pedersen, A numerical tool for formability analysis of aluminium alloys. Part II. Experimental validation, Steel Grips 2 (2004) 433–438].