Formulation of a new constitutive equation available simultaneously for static and dynamic loadings

Abstract
In the field of material behavior corresponding to high strain rates the most used constitutive laws are Johnson-Cook (JC) and Zerilli-Armstrong (ZA). Many scientific studies use these two laws or other improved formulations in order to analyse numerically different industrial applications such as the high speed metal forming or machining, defense applications or crashworthiness. Starting from physical points of view, the present paper details the formulation of a new constitutive equation available simultaneously for small and high strain rates. It is then possible to correctly describe the gradients of strain rate and plastic strain that occur during real industrial applications. From this new law, the JC formulation can be easily obtained from an asymptotic variation of the proposed law at high values of strain rates and, in a similar way, the ZA constitutive equation is obtained at small values of strain rates. Moreover a detailed analysis of the ZA description shows that this law is only a classical Norton equation not available for high values of the strain rates. Application to an aluminum alloy AA5083 will be presented to validate the proposed constitutive equation and the SHPB inverse analysis approach.