A constitutive Equation for Thermoviscoelastic
Behavior of Polymeric Materials
Suri
Ganeriwala
SpectraQuest Inc., 8201 Hermitage Road, Richmond, VA 23228
Published: October 2004
Abstract
With increasing uses of polymeric materials for
providing viscoelastic damping in many mechanical systems and
structures, it has become necessary to develop appropriate
constitutive equations. Conventional constitutive theories and
master curves do not provide a sufficient representation of the
linear thermoviscoelastic properties needed for a sound engineering
analysis and design. this paper presents a new scheme that yields a
complete constitutive equation suitable for analysis of complex
problems. the model is based on postulates of generally observed
temperature and frequency (or time) dependent behavior of polymeric
materials and our recent development of a new model of the glass
transition phenomenon. An important part of the derivation is a new
description of the glass transition behavior of polymers. The model
is internally consistent and makes remarkable predictions. the
time-temperature principle is an integral part of this model. An
initial test of the new approach was carried out with two different
classes of polymers with good results. It is adaptable to most
computer systems.
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Introduction
Viscoelastic material are valuable for isolation
and control of sound and vibration because of their ability to
dissipate energy. the damping ability of these materials is
increasingly utilized to develop advanced composite materials such
as high strength low weight aircraft structures and other
engineering components. A distinguishing feature of viscoelastic
materials is strong dependence of mechanical properties on
temperature and frequency (or time). For an optimum design, dynamic
analysis of viscoelastically damped structures must be performed at
a design phase. Such engineering analysis requires a constitutive
equation for the material viscoelastic behavior.
A Coupled theory of thermoelasticity which
includes the effects of both temperature as well as strain histories
on the mechanical material functions is not well developed yet.
Furthermore, a constitutive theory provides a general form of
material functions. the exact constitutive equation has to be
derived from studies of mechanical properties over wide ranges of
frequency (or time) and temperature. many dynamic mechanical
property studies have been reported but appropriate constitutive
equations defined over a wide ranges of temperature and frequency
have been elusive.
The mechanical behavior of most polymers and
amorphous materials can be adequately represented by the theory of
viscoelasticity. A broad classes of materials form a disordered
solid structure when cooled from the molten state; polymers are just
a one class from the list. But because of wide uses of polymers,
viscoelasticity is generally associated with polymers only. In This
paper, Polymers and polymeric materials will be synchronously used
to designate viscoelastic materials.
Fig 1:
Temperature dependence of properties of glassy
materials. notice rate effect, asymmetry, nonlinearity, and
hysterisis.
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