Solution to problems caused by associated non-quadratic yield functions with respect to the ductile fracture

Abstract

Accurate material behaviour and its response to loading are needed for a reliable calibration of ductile failure criteria. Non-quadratic yield functions are often necessary for such a description. Nevertheless, it leads to the prediction of stress states that are inconsistent with the expected behaviour and deformations that are in contradiction with the experiments when the associated flow rule is adopted. These problems may be solved by applying a less restrictive non-associated flow rule. Therefore, an isotropic non-associated non-quadratic phenomenological plasticity model was developed as a function of the second and third invariants of deviatoric stress tensor. The yield function that is convex was proposed to allow for different yield stresses in tension, compression and shear. For simplicity, the same function was used for the plastic potential. Each of these functions is described by seven material parameters. The scheme of the so-called next increment corrects error method was adopted for the implementation of the proposed model within finite elements. Above that, three additional plasticity models were calibrated for 2024-T351 aluminium alloy. It is shown how the non-associated flow rule resolves the above-mentioned problems. Moreover, the possible extensions of the proposed yield function are described to include the hydrostatic stress dependence.Accurate material behaviour and its response to loading are needed for a reliable calibration of ductile failure criteria. Non-quadratic yield functions are often necessary for such a description. Nevertheless, it leads to the prediction of stress states that are inconsistent with the expected behaviour and deformations that are in contradiction with the experiments when the associated flow rule is adopted. These problems may be solved by applying a less restrictive non-associated flow rule. Therefore, an isotropic non-associated non-quadratic phenomenological plasticity model was developed as a function of the second and third invariants of deviatoric stress tensor. The yield function that is convex was proposed to allow for different yield stresses in tension, compression and shear. For simplicity, the same function was used for the plastic potential. Each of these functions is described by seven material parameters. The scheme of the so-called next increment corrects error method was adopted for the implementation of the proposed model within finite elements. Above that, three additional plasticity models were calibrated for 2024-T351 aluminium alloy. It is shown how the non-associated flow rule resolves the above-mentioned problems. Moreover, the possible extensions of the proposed yield function are described to include the hydrostatic stress dependence.