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

Constitutive Equations of Yield Stress Sensitivity to Strain Rate of Metals: A Comparative Study

“…The modified-Eyring model is developed by El-Qoubaa and Othman [18][19][20] based on the original work of Eyring [23] except that they used an activation volume decreasing with an increasing strain rate. The model works well here with copper and steel over the studied strain rate range ( Figure 6).…”

“…El-Qoubaa and Othman [18,19] have proposed a modified-Eyring equation for polymers yield stress sensitivity to strain rates. This model was successfully applied to several metallic materials in [20].…”

Modeling of the Strain Rate Dependency of Polycarbonate’s Yield Stress: Evaluation of Four Constitutive Equations

“…El-Qoubaa and Othman [40][41][42] pledged for the use of an apparent volume that decreases as the strain rate increases. More precisely, they proposed that the apparent activation volume is given by * = 0 exp (−√̇̇) ,…”

“…Dealing with amorphous polymers, Richeton et al [24] modified the cooperative model [38,39] by using an Arrhenius-type law for the horizontal and vertical shifts. Recently, El-Qoubaa and Othman [40][41][42] modified the one-process Eyring equation [33] by including an activation volume which is decreasing in terms of strain rate. The modified-Eyring equation was used to fit compression yield stress of polyetheretherketone (PEEK).…”