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

Abstract

The main focus of this paper is in evaluating four constitutive relations which model the strain rate dependency of polymers yield stress. Namely, the two-term power-law, the Ree-Eyring, the cooperative, and the newly modified-Eyring equations are used to fit tensile and compression yield stresses of polycarbonate, which are obtained from the literature. The four equations give good agreement with the experimental data. Despite using only three material constants, the modified-Eyring equation, which considers a strain rate-dependent activation volume, gives slightly worse fit than the three other equations. The two-term power-law and the cooperative equation predict a progressive increase in the strain rate sensitivity of the yield stress. Oppositely, the Ree-Eyring and the modified-Eyring equations show a clear transition between the low and high strain rate ranges. Namely, they predict a linear dependency of the yield stress in terms of the strain rate at the low strain rate range. Crossing a threshold strain rate, the yield stress sensitivity sharply increases as the strain rate increases. Hence, two different behaviors were observed though the four equations fit well the experimental data. More experimental data, mainly at the intermediate strain rate range, are needed to conclude which, of the two behaviors, is more appropriate for polymers.

Photopolymerized Triazole‐Based Glassy Polymer Networks with Superior Tensile Toughness

“…From this equation, the average activation volume of the T1 system was found to be ≈1.7 nm 3 (see Figure S12, Supporting Information), which is similar to the volume of one network strand between two centers of alkyne molecules covalently linked with one azide molecule, estimated to be ≈1.2 nm 3 . Furthermore, the activation volume obtained for the T1 polymer is comparable to that found for other glassy polymers (i.e., 1.5 nm 3 for anhydride cross-linked epoxy networks, [59] 2 nm 3 for amine-cross-linked epoxy networks, [58] and 1.9 nm 3 for polycarbonates [60] ).…”

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).…”

“…Couque [17] proposed a modified Johnson-Cook equation where the strain rate sensitivity is written in terms of a four-constant equation. 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].…”

Development of Thermal Spray Processes for Depositing Coatings on Thermoplastics

“…These theories have been validated for polymer solutions in the 1950s (Ref 17 , 18 ). In recent years, sophisticated measurement equipment allowed for the adaptation validation of these theories for several thermoplastic melts, i.e., polycarbonate (PC) (Ref 11 , 19 ), poly(methyl methacrylate) (PMMA) (Ref 11 ), polyamide-imide (PAI) (Ref 11 ), PEEK (Ref 20 ) polypropylene (PP) (Ref 21 ) and PA6 (Ref 22 ).…”