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Constitutive Equation for Description of Metallic Materials Behavior during Static and Dynamic Loadings Taking into Account Important Gradients of Plastic Deformation

For numerical simulations of rapid forming processes the most used constitutive equations are based on the Johnson-Cook (JC) law and on the Zerilli-Armstrong (ZA) one. Starting from physical points of view, detailed in the first part, the present paper proposes a more general constitutive equation available for both static and dynamic loadings. It is then possible to describe correctly gradients of strain rate, plastic strain and temperature which occur during a complex deformation path of a metal forming process. 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 similar way, the ZA formulation is obtained at small values of strain rates. Application to an aluminum alloy AA5083 will be presented to validate the proposed constitutive equation by a Finite Element Model (FEM) of a rapid upsetting test performed with the Split Hopkinson Pressure Bars.