Thermodynamic constitutive models for materials with fading memory
Abstract
Nonlinear viscoelastic constitutive models for describing the nonlinear mechanical, glass transition, and melt rheology of amorphous polymers have been developed via the framework of rational thermodynamics, modified so that the dissipation occurs on a material timescale. Two constitutive models were derived from the modified rational thermodynamics framework. The GK model is a rigorous reformulation of an earlier purely mechanical model (R. M. Shay, Jr., M.S.E. Thesis, Purdue University, 1986), where the stress and the other constitutive functions depend upon the deformation history and the current values of the deformation and the temperature. The GKAC model is a more general formulation which also includes an explicit dependence upon the thermal history. For both models the stress and nonequilibrium entropy constitutive equations were derived from the nonequilibrium Helmholtz free energy constitutive equation. The material and laboratory timescales are related by an entropy-dependent shift factor. Versions of the GK and GKAC models were derived for both isotropic solids and fluids. A key feature of the GK models is that they only require the time-independent equilibrium thermodynamic properties and the linear viscoelastic shear and bulk moduli. The GKAC models require two additional viscoelastic properties associated with the temperature history. All the material properties can be evaluated from independent experiments that are qualitatively different from the nonlinear stress-strain and glass transition phenomena to be predicted. The GK Solid model predicts the isobaric specific volume response including the glass transition temperature as a polymer is cooled from the rubber or melt, where there exists an interplay between the equilibrium stress and viscoelastic bulk contributions. The effects of varying the glass formation thermal history on the subsequent mechanical response of the glass were predicted for uniaxial deformations, where the predicted effects of cooling rate and aging time were in agreement with experimental data. The effects of the temperature, strain rate, and thermal history during the glass formation on the nonlinear uniaxial stress-strain and yield predictions are in reasonable agreement with experimental observations. The presence of a maximum in the stress-strain curve and the predicted glass transition temperature strongly depend upon the characteristic bulk relaxation time. The nonlinear stress-strain predictions are also sensitive to the shear modulus magnitude and characteristic relaxation time, and to the shift function relating the material and laboratory timescales. For isothermal deformations, the GK models are very similar to our earlier purely mechanical constitutive equation and can therefore also predict yield in experimentally realizable shear deformations. Additional phenomena which may be described by the GKAC models are discussed.
Degree
Ph.D.
Advisors
Caruthers, Purdue University.
Subject Area
Chemical engineering
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.