Application of time‐temperature superposition to energy limit of linear viscoelastic behavior

Abstract

ABSTRACT:The energy approach for evaluation of the limits of linear viscoelastic (LVE) behavior is considered. The approach of Foux and Bruller based on the ReinerWeissenberg dynamic theory of strength is developed for the temperature effect. Value of the stored energy at the limit of LVE is considered as the material characteristic independent on loading conditions and temperature. Timetemperature superposition principle is extended for the energy calculations. Curves of the stored energy calculated for different temperatures are shifted to each other in the logarithmic time axes similarly as creep compliance and relaxation modulus curves in creep and tension tests, respectively. Temperature is considered as a factor that accelerates transition form linear to non-LVE at the same stored energy threshold. This is proved by example of polyvinylchloride by comparing temperature dependences of the stress limits of LVE determined in two independent test series: tensile creep and constant strain rate tests.

A method for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition: Energy‐Based Approach

“…The benefit of data representation in this way is that transition from linear to nonlinear viscoelastic behavior is characterized by only one parameter W LVE , i.e., the energy threshold. It has been shown in Ref 9. that W LVE is independent of test type and its value can be determined, for example, in constant rate tests that are less time‐ and energy‐consuming tests compared to creep tests.…”

“…This can essentially reduce a number of tests required for comprehensive characterization of LVE transition region of polymers. For example, the energy threshold W LVE can be determined in three to five creep tests performed under various stresses at room temperature or alternatively from the data of uniaxial tensile tests,9 while three to five creep tests at a fixed stress under various temperatures are needed more for evaluation of the relaxation spectra ( J i , τ i ) and time‐temperature reduction function a T . Thus, for evaluating the stress threshold at any t and T by eq.…”

“…The total energy of linear viscoelastic material at uniaxial creep can be expressed in terms of relaxation spectra by using eqs. (2) and (6)9, 18: …”

“…In this work, the results discussed by the authors in previous studies7–11 are combined and discussed comprehensively. The novelty of this study is related with an application of the energy approach for calculating time‐ and temperature‐dependences of the stress threshold of linear–nonlinear viscoelastic transition.…”

“…An energy‐based approach for determination the threshold of linear–nonlinear viscoelastic transition was used in Refs 5, 8–10…”