A Modified Eyring Equation for Modeling Yield and Flow Stresses of Metals at Strain Rates Ranging from 10−5 to 5 × 104 s−1

Abstract

In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5 to 5 × 104 s−1). This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.