Non-associative flow in metal plasticity: Consistency and model development

It is well known that polycrystal aggregates obeying Schmid law at grain level have an overall constitutive response defined by an associative flow rule (AFR), i.e., the rate of plastic deformation is along the outward normal of the yield surface. We show that when non-Schmid effects are accounted for, the overall response of the aggregate is non-associative. A minimal condition for the thermodynamic consistency of non-associative (NAFR) phenomenological models is that the gradient of the plastic potential be oriented towards the exterior of the elastic domain. The calibration of anisotropic NARF-models is currently done by fitting independently of each other the yield function and the plastic potential on yielding and deformation data. This increases the indeterminacy already observed for AFR-models, since data is never sufficient, particularly for sheet metal. We propose a rational approach to the calibration of NAFR-models based on the comparison with a best AFR-model. This involves the discovery of the appropriate range of mechanical data via an iterative procedure based on data-driven modeling and finite element simulation. We demonstrate our methodology by modeling the O and T4-tempers of the aluminum alloy AA6016 using hole expansion and cup drawing experiments reported in the literature. • Non-Schmid effects induce a split between the yield function and the plastic potential at macroscopic level (non-associative plasticity). • For thermodynamic consistency, the angle between the gradients of the yield function and of the plastic potential must be less than 90 . • The deviation of the yield function from the plastic potential can be estimated by solving an inverse problem using data-driven modeling and finite element simulations of complex deformation processes. • Results for the aluminum alloy AA6016 suggest that non-Schmid effects may be responsible for up to 20% of the observed thickness strains in stretching/drawing.