Strain-rate sensitivity index of thermoplastics

Abstract

Strain-rate sensitivity index, m, values of several thermoplastics (HDPE, PP, PMMA, PS, PVC, PC, and PA) were determined at ambient temperature by both variable strain-rate and stressrelaxation methods. Specimens were loaded in tension in the elastic portion of the stress-strain curve at various strain rates and the load was recorded as a function of elongation. Index values were determined from the relation $m = [\partial \ln (\sigma )]/[\partial \ln (\dot e)]_{e, T}$. Specimens were also loaded in tension at constant strain rate to the proportional limit, loading was halted, and the load was recorded as a function of time at constant strain. A numerical algorithm was implemented to minimize the root-mean-square difference between an empirical equation and the experimental data, i.e.

$$\Phi (n, \tau ) = \left( {1/N\sum\limits_i {\{ P_o \exp [ - (t_i /\tau )^n ] - P(t_i )\} } ^2 } \right)^{1/2} $$

The characteristic time parameter, (τ), and the rate-of-decay parameter, n, were found when Φ(n,τ) was minimized. Index values were determined from the relation $m = {\text{[}}\partial {\text{ln}} {\text{(}}P{\text{)]/[}}\partial {\text{ln(}} {\text{ - }} \dot P{\text{)]}}_{e,{\text{ }}T}$. A marked difference in index values derived from both experimental methods indicates that different processes are operative in each case. Index values are qualitatively evaluated in terms of cohesive energy density, side-chain group molar volume, and main-chain group flexibility.