New biaxial yield function for aluminum alloys based on plastic work and work-hardening analyses

Yield locus measurements and their analytical descriptions has been the bases for modeling metal processing. These analytical descriptions play a role in models to predict limit strains observed during determination of forming limit diagrams of flat metal stock as means to evaluate their fabrication performance. Some of these analytical descriptions use the isotropic or anisotropic plastic potentials that take into account the crystallographic texture of the material. The applicability of such potentials is validated by comparing their predictions to that of unidirectional tensile data. In the current work, this approach is reversed to examine whether the constitutive relations, which replicate the measured stress-strain diagrams, can generate a two-dimensional section of the yield locus. The strategy is to sum the computed plastic work (PW) from unidirectional mechanical tests in two principal directions which also accommodates the biaxial interaction strains. The resulting yield function includes fθ and fφ, the prescribed stress ratios and the texture parameters Rφ and Rθ in their respective principal directions. The prescribed PW at an arbitrary strain during unidirectional tensile test is equated to the work sum from the biaxial stresses on the premise that the plastic flow-stress registers only the increasing density of obstacles it generates. The computed biaxial yield stresses showed good fits for AA5154 and AA5754 with only small modification due to latent work hardening.