Stress relaxation and strain recovery phenomena during curing and thermomechanical loading: Thermorheologically simple viscoelastic analysis

Abstract

Stress relaxation and strain recovery phenomena during curing and changed thermal conditions are analyzed using a viscoelastic model developed for thermorheologically complex materials (VisCoR). By making several simplifying assumptions regarding the material behavior, the incremental form of the VisCoR model is reformulated to a version describing thermorheologically simple material and presented in one-dimension for simplicity. The model (called VisCoR-simple) is used to analyze material behavior under various conditions, including stress relaxation behavior at varying temperatures and time scales; tensile loading and unloading tests at high temperatures; stress build up and “frozen-in” strains during curing and following cool-down and strain recovery during the next step of heating. Furthermore, the differences between the so-called “path-dependent” model, which is a linear elastic model with different elastic properties in glassy and rubbery regions, and the presented viscoelastic model are studied. The path-dependent model is an extreme case of the viscoelastic model presented. The importance of considering viscoelasticity when considering temperature and curing effects on polymers and the shortcomings of the path-dependent model are revealed and discussed.

Molecular Characterization of Polymer Networks

“…Since the sample is kept under a constant deformation due to the imposed step strain, molecular-level movement rather than macroscopic change dominates the stress relaxation processes. Information about entanglement, chain alignment, cross-linker exchange, and, under more extreme conditions, chain scission under strain can be gleaned from stress relaxation experiments. , Additionally, stress relaxation experiments are industrially important in determining whether stress can be dissipated over accessible time scales in materials for applications that require repetitive strain or in molding and curing processes of polymers and composites . This helps determine the best processing conditions and the working lifetime of a material.…”

On Temperature-Related Shift Factors and Master Curves in Viscoelastic Constitutive Models for Thermoset Polymers

“…These master curves (the Prony coefficients and a temperature-dependent shift factor) were used in the previously developed incremental model [2,3] aimed to simulate the stress development in an arbitrary strain-and temperaturecontrolled regime.…”

“…Viscoplastic effects are not considered. The model was derived similar as in [1] (based on expansion of the Helmholtz free energy), with details given in [2,3]. The constitutive law for a uniaxial loading (1D), which is the case in all the experiments performed, is…”

“…For example, in the branch of thermodynamically consistent linear viscoelasticity models derived using Schapery's approach [1,2], temperature ( T )-dependent parameters appear in front of the heredity integral and under its sign. A temperature dependent function a T ( ) is also present in exponents of the Prony series as a multiplier to relaxation times [2,3,4]. The latter, called the "shift factor," may also depend on the degree of cure a DoC ( ) (in thermoset composites) [3,5,6] and on the load or strain level in the case of nonlinear viscoelasticity, a T DoC ,� ,� ε ( ) [7,8].…”

“…For materials with a thermorheologically simple behavior, the temperature dependence is included only in Prony exponents [2,3]. Thermorheologically simple materials have a very useful property: their relaxation functions (stress as a function of the logarithm of time at a unit of applied strain) recorded at different test temperatures can be shifted "horizontally" (with respect to log t ) to create a master curve corresponding to an arbitrary selected reference T ref .…”