Evaluation and calibration of anisotropic yield criteria in shear Loading: Constraints to eliminate numerical artefacts

Abstract

Many anisotropic phenomenological yield functions have been proposed in the literature in which their predictive capabilities strongly depend on the experimental calibration data as well as the calibration procedure to identify the anisotropy parameters. In this paper, emphasis is placed upon the experimental and numerical calibration procedure of anisotropic yield functions in the region of shear loading (zero hydrostatic stress with equal and opposite in-plane principal strains and stresses). Conventional anisotropic calibration procedures are shown to introduce non-physical artefacts into constitutive models which manifest as a non-zero hydrostatic stress or through-thickness strains generated under in-plane shear stress that violate the definition of the shear loading condition. To overcome this issue, a new physically necessary constraint is applied on the plastic potential to enforce equal and opposite principal strains in the shear state and correct the shear region of anisotropic yield functions. Using this necessary constraint, the widely used Yld2000-2d anisotropic yield function was calibrated using an associated flow rule for aluminum alloy sheet using published data for AA2090-T3 to demonstrate how enforcing this constraint can be readily implemented to correct the shear region of the anisotropic yield surface. Furthermore, to investigate the influence of the shear constraint, an AA7075-T6 alloy was experimentally characterized in uniaxial tension, equal-biaxial tension and shear. It was revealed that with the additional shear constraints, non-physical artefacts of plane-stress anisotropic yield functions such as Yld2000-2d can be removed during the calibration procedure. However, due to the additional shear constraints, available anisotropic models may become over-constrained and alternate yield functions with more flexibility or non-associated flow rules may be required.