A normalized stress invariant-based yield criterion: Modeling and validation

Abstract Transforming five different stress invariants-based yield criteria in I-J2-J3 framework into η-ξ- σ ¯ framework demonstrates that all of these yield criteria are the product formulation of the equivalent stress and the function of the normalized third invariant ξ and stress triaxiality η. The function of ξ is replaced by a polynomial function to construct a generalized yield function for describing both asymmetry and Lankford coefficients under associated flow rule(AFR) framework, in which the linear combination of a series of ξ with odd powers is utilized to model the effect of materials' strength differential (SD). Since there are more parameters in the polynomial function of ξ than the function of ξ in those existing yield functions, and the independent basis functions ξ, ξ2, ξ3 … are informative enough to describe the SD effect and Lankford coefficients, the proposed yield function shows potential flexibility. The conditions for the convexity of the proposed yield criterion are obtained by using the method of order principal minor determinant. To describe sheet metals' anisotropic characteristics in tension and compression, the proposed isotropic criterion is further generalized to orthotropy through introducing the fourth-order linear transformation to the deviatoric stress tensor. To improve the flexibility of the yield criterion through introducing more fourth-order linear transformations, several extended proposed isotropic criteria are added together. The effectiveness and flexibility of the constructed yield criterion have been verified by applying to AA2008-T4(a BCC material) and AA2090-T3(a FCC material). Comparisons with Yld2000-2d and Yoon 2014 criteria show that the proposed yield criterion has the same ability as Yld2000-2d to describe metals’ tensile properties and the proposed yield criterion can capture the SD effect like Yoon 2014, which validates that this generalized yield criterion can accurately describe not only the SD effect of metals but also the Lankford coefficients under uniaxial tensile loading and balanced biaxial tension based upon the AFR assumption. The flexibility of the proposed yield criterion is further validated by applying to zirconium through describing the evolution of yield surface for a clock-rolled plate with various levels of pre-strains during through-thickness compression. It is found that the proposed yield criterion can capture the asymmetry and the local deformation characteristic of the yield surfaces if the pre-strain is very large.