An approach to modeling the mechanical behavior of fiber reinforced and unreinforced plastics with an evolving internal state is described. Intrinsic nonlinear viscoelastic and viscoplastic behavior of the resin matrix is taken into account along with growth of damage. The thermodynamic framework of the method is discussed first. The Gibbs free energy is expressed in terms of stresses, internal state variables (ISVs), temperatureand moisture content. Simplifications are introduced based on physical models for evolution of the ISVs and on experimental observations of thedependence of strain state on stress state and its history. These simplifications include use of master creep functions that account for multiaxial stresses, environmental factors and aging in a reduced time and other scalars. An explicit representation of the strains follows, which isthen specialized to provide three-dimensional homogenized constitutiveequations for transversely isotropic, fiber composites. Experimentalsupport for these equations is briefly reviewed. Finally, physicalinterpretation of some of the constitutive functions is discussed usingresults from a microcracking model as well as molecular rate process andfree volume theories. It is shown that the present thermodynamicformulation leads to a generalized rate process theory that accounts for abroad distribution of thermally activated transformations in polymers.

Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics

Non-linear viscoelasticity based on free volume consideration

SUMMARY This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the nite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution. Use is made of a Dirichlet{Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. ? 1997 by John Wiley & Sons, Ltd.

/pdf/a-three-dimensional-finite-element-formulation-for-bvf9spz1bo.pdf

A three-dimensional finite element formulation for thermoviscoelastic orthotropic media

Nonequilibrium thermodynamics, rate-process theory, viscoelastic fracture mechanics and various experimentally-motivated simplifications are used to develop constitutive equations that account for effects of viscoelasticity, viscoplasticity, growing damage and aging Their form is more general than previously developed by the author, and allows for relatively general tensorial effects of damage Some important special cases are then covered, with emphasis on viscoelasticity Evolution equations for the damage expressed in terms of internal state variables (ISVs) are discussed, comparing formulations using scalar ISVs and tensor ISVs Finally, some experimental support for the theory is described An Appendix illustrates the theory for an aging, linear viscoelastic material with growing cracks

Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage

One of the most elementary concepts in elasticity theory is that of a uniform state of stress. Producing such a state of stress in the laboratory, however, is not a trivial task. A common experiment in composite mechanics—the tension test of off-angle composites-is discussed in this paper and the influence of end constraint on the uniform stress field is investigated. Analytical and experimental evidence is presented to show the serious effects caused by con ventional clamping devices.

Pagano and Halpin - Influence of End Constraint in the Testing of Anisotropic Bodies

The nonlinear, viscoelastic behavior of a unidirectional, glass fiber-epoxy composite material is characterized by using isothermal, uniaxial creep and recovery tests together with a constitutive equation based on thermodynamic theory. The nonlinear constitutive equation for uniaxial loading is described first, and then fourth-order tensor transformations relating principal linear viscoelastic creep compli ances, uniaxial creep compliance, and fiber angle are summarized. Following a discussion of experimental aspects, creep and recovery data obtained from several different specimens (each having a differ ent fiber orientation relative to the loading axis) are reduced using a graphical shifting procedure and tensor transformations to evaluate all material properties, including the principal creep compliances. As a check on the constitutive theory, the data are shown to be in ternally consistent. Some simplicity in the analytical representation of the data is found; viz. the nonlinear, uniaxial creep compli...

Y.C. Lou

Papers

Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic