Predictions of a thermoviscoelastic constitutive equation for glassy polymers

Dong-Ik Song, Purdue University

Abstract

A nonlinear thermoviscoelastic constitutive model for amorphous polymers developed via the modified rational thermodynamics framework was examined to assess its predictive capabilities in describing nonlinear mechanical properties in the glass transition region. A nonlinear thermoelastic constitutive model was derived from thermoviscoelastic model via pseudo-time-shift invariance and ideal glass assumption. The thermoelastic model acknowledges conditions under which the glassy material was formed, which is important for glassy polymers. Four material functions are contained in the model--the constant-volume heat capacity, the well-known linear viscoelastic shear and bulk moduli, and a new material property related to the thermal expansion. These material functions could be determined from PVT, heat capacity, and dynamic shear modulus data. Material properties were determined from specific single deformations and not adjusted further. The thermoelastic model satisfies all the linear elasticity relations for Hookean solids. Yield in the nonlinear elastic deformation was also predicted assuming that yield occurs when either nonequilibrium entropy or internal energy reaches its corresponding value at glass transition point. The thermoviscoelastic model is able to predict, at least qualitatively, the mechanical responses for an extremely wide range of nonlinear and nonisothermal deformations. The thermoviscoelastic model predicted both isobaric and isothermal volume relaxations. Glass transition behaviors at both atmospheric and higher pressures were described qualitatively. Isothermal aging and volume hysteresis under cyclic process of cooling-aging-heating were also predicted. All the important features of isothermal volume relaxation, including nonlinearity, volume asymmetry, and memory effects for more complex thermal history were also predicted. The constitutive model predicted uniaxial time-dependent deformations, including the stress-strain response for a constant strain rate history, nonlinear stress relaxation, and nonlinear creep. Yield in compression was predicted as well as yield in tension, where the yield is a natural consequence of viscoelastic relaxation especially driven by shear viscoelastic relaxation. The prediction of compressive yield is a significant advance over other existing models. Effects of temperature, strain rate, pressure, and aging time on the nonlinear uniaxial stress-strain and yield behaviors were studied and compared with experimental observations. Tensile stress relaxation was also qualitatively predicted for one- and two-step deformations. Linear and nonlinear tensile creeps were predicted for both single step and creep recovery deformations.

Degree

Ph.D.

Advisors

Caruthers, Purdue University.

Subject Area

Chemical engineering|Materials science

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