Numerical Verification of Simplified Identification Method of Yield Function Using Circumscribing Polygon of Yield Locus

Abstract

A method for identifying the yield function using simple material tests is proposed. The identification accuracy of this method is verified by finite element analysis. In the proposed method, a polygon circumscribing the equal plastic work contour is defined through uniaxial tensile tests, hydraulic bulge test, and plane strain tensile tests. The parameters of the anisotropic yield function are identified as a smooth curve inscribed in the polygon. The virtual material tests of three material models, namely, mild steel, aluminium alloy, and pure titanium, are conducted by the finite element method. On the basis of the results, stress measurement error and yield surface identification error are discussed. When the material exhibits strong in-plane anisotropy, the measurement error of equi-biaxial stress in the hydraulic bulge test becomes large. When the initial gradient of work hardening is large, the stress value of the circumscribed line of the small plastic strain stage in the plane strain tensile test is estimated to be lower than that on the true yield surface. These errors affect the identification accuracy of the material parameters of the yield function quantitatively, but the difference between the identified locus and true yield locus is small. The proposed method is feasible as a simple identification method of the yield function.