A discussion of the associated flow rule based on the FAY model and Nakajima tests

Abstract

Constitutive models based on a non-associated flow rule (non-AFR) have received increased attention due to their flexibility in capturing laboratory experiments. On the other hand, the recently proposed Fourier Asymmetric Yield (FAY) model enables the definition of convex yield functions with arbitrary complexity, which can be used in conjunction to an associated flow rule and nevertheless accurately match experimental data. The present contribution aims comparing AFR and non-AFR based approaches with respect to their ability in capturing measured strain fields in controlled Nakajima experiments. It is shown that a sufficiently flexible yield function is able of delivering accurate results without having to renounce to restrictions such as flow rule association or convexity. The analysis is carried out using two common deep drawing materials, namely an AA6016 and a steel grade DC05.