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 con- stitutive 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 crash- worthiness. 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 con- stitutive 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 pro- posed constitutive equation and the SHPB inverse analysis approach. The majority of the scientific papers of the DYMAT 2003 and 2006 conferences about numerical simulations or parameter identification of material behavior undergoing severe deformations (high velocities, impact, crash), propose to use the Zerilli-Armstrong law, the Johnson-Cook law or other constitutive equations principally developed from these formulations. This paper proposes a detailed analysis of above rheological laws starting from physical and mathematical points of view. A new constitutive model of metallic material behavior available for industrial applications has been developed where important gradients of strain and strain rates occur during the process. The main idea is to allow the description of both static and dynamic loadings, using a minimal number of parameters. Moreover this new law permits to describe many different shapes of the stress-strain curves.