Anisotropic yield function based on stress invariants for BCC and FCC metals and its extension to ductile fracture criterion

It is essential to accurately model the anisotropic plastic deformation and ductile fracture of metals in order to guarantee the reliable numerical analysis and optimization of metal forming. For this purpose, the Drucker function is revisited. Effect of the third stress invariant in the Drucker function is analyzed and calibrated for metals with body-centered cubic (BCC) and face-centered cubic (FCC) crystal systems based on the yielding and plastic flow of both crystal plasticity and biaxial tensile experiments. The calibrated Drucker function is extended into an anisotropic form using a fourth order linear transformation tensor. The anisotropic flexibility is enhanced by two approaches: non-associate flow rule (non-AFR) and the sum of n-components of the anisotropic Drucker function. The proposed anisotropic Drucker function is applied to model the anisotropic behavior of both BCC and FCC metals. The predicted anisotropic behavior is compared with experimental results. The comparison demonstrates that the anisotropy is accurately modeled for both BCC and FCC metals by the anisotropic Drucker function. The anisotropic Drucker function is also implemented into numerical analysis of tension of specimens with a central hole to investigate its computation efficiency under spatial loading compared with the Yld2000-18p function. It is found that the proposed anisotropic Drucker function can reduce about 60% of computation time in case that the Yld2000-18p function is substituted by the anisotropic Drucker function in numerical computation due to its simplicity compared to the Yld2000-18p function. A ductile fracture criterion is also developed by coupling the Drucker function with the first stress invariant. The modified Drucker function is reformulated to investigate the effect of the stress triaxiality and the normalized third invariant on ductile fracture. Comparison of the modified Drucker fracture locus with the experimental results of AA2024-T351 demonstrates that the modified Drucker criterion accurately illustrates the fracture stress of the alloy in wide stress states with the stress triaxiality ranging from −0.5 in plane strain compression to 0.6 in tension of notched specimens. The modified Drucker fracture criterion is expected to be less sensitive to the change of strain path considering that the criterion describes fracture in the stress space. Accordingly, the anisotropic Drucker yield function and the pressure-coupled Drucker fracture criterion are suggested to model anisotropic plastic deformation and to predict the onset of failure for both BCC and FCC metals due to simple implementation in numerical analysis under spatial loading and computation efficiency with brick elements.