Models of thermomechanical behavior of polymeric materials undergoing glass transition

Abstract

The phenomenological models of the thermomechanical behavior of polymeric materials in a temperature range including the relaxation transition from the highly elastic to the glassy state (vitrification) and the reverse transition (softening) are considered. A model based on the interpretation of the glass transition as a process of gradual increase in intermolecular bonds in the polymer network, "freezing" the current strain with decreasing temperature is developed. A scalar parameter is introduced-the "degree of vitrification," to establish the quantitative dependence of the relaxation transition completion by temperature. Constitutive relations of thermomechanical behavior of vitrifying polymers in uniaxial and complicated stress states in the "elastic approximation" simplification are obtained. A system of experiments for the identification of the proposed model material functions and constants is formulated and implemented. Analytical model problems are solved, clearly illustrating the mechanism for generation of technological and residual stresses in glass polymers in non-uniform cooling.

Post-buckled equilibrium state of axially compressed polymeric rod in glass and rubbery transitions

“…To derive the constitutive equations we use the following simplifying hypotheses (Matveenko et al 2012):…”

“…The hypotheses introduced above allow us to construct the constitutive relations capable of describing the behavior of SMPs over a wide range of temperatures including the transition region (Matveenko et al 2012). In case of small strains for the uniaxial stress state they could be defined in the following way:…”

“…According to the accepted hypotheses, every additional bond formed during vitrification is undeformed at its initiation moment, and so it does not affect the stress-strain state of the construction at that moment (Matveenko et al 2012). Therefore, the curvature during cooling under a constant load remains unchanged: χ 2 (s) = χ 1 (s).…”

“…Two formal groups could be derived from the studies: the models of instantaneous elastic relaxation or phase transition (Bartenev and Barteneva 1992, Bugakov 1989, Klychnikov et al 1980) and the models based on the postulates of the non-isothermal viscous elasticity (Bolotin 1972, Il'ushin and Pobedria 1970, Moskvitin 1972. The approach used in the present study (Matveenko et al 2012) occupies an intermediate position between these two.…”

Numerical investigation of isotropic beam crystallization process under nonuniform cooling

“…Many works of this research are based on removing the constitutive relations and numericalexperimental research of the developed mathematical models. For instance in [4], the problem of describing the thermomechanical behavior of polymer materials in conditions of relaxation conversions is considered in detail. It should be noted that modeling the constitutive relations for describing the crystallization process with the relaxation conversions has wide practical application: in mechanical engineering industry [5], aircraft industry [6], metallurgy [7,8], microstructure [9] of materials and etc.…”