Stress-Invariants-Based Anisotropic Yield Functions and Its Application to Sheet Metal Plasticity

Abstract

The yield criterion, or so-called yield function, plays an important role in the study of the plastic working of a sheet because it governs the plastic deformation properties of the sheet during the plastic-forming process. In this paper, we propose a novel anisotropic yield function useful for describing the plastic behavior of various anisotropic sheets. The proposed yield function includes the anisotropic version of the second stress invariant J2 and the third stress invariant J3. The proposed yield function can explain the anisotropic plastic behavior of various sheets by introducing the parameters α and β and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model were determined with an optimization algorithm from uniaxial and biaxial experimental data under a proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford anisotropic coefficient R-value derived from the experimental results. Applications of the proposed anisotropic yield functions to an aluminum sheet showed symmetrical yielding behavior and, to pure titanium sheets, showed asymmetric yielding behavior; thus, it was shown that the yield curve and yield behavior of various types of sheet materials can be predicted reasonably by using the proposed new yield anisotropic function.

Keywords

• invariant <i>J₂</i>
• invariant <i>J₃</i>
• stress deviator
• anisotropic yield function
• symmetric yield function
• asymmetric yield function