Thermal Stresses in Nonlinearly Viscoelastic Solids

Losi, Giancarlo U.; Knauss, W. G.

doi:10.1115/1.2899506

Cited by 17 publications

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“…Knauss and co-workers [16,17,22,23], see also [3], suggested a hypothesis that changes in the free-volume fraction f are proportional to the volume deformation. This means that constants C 1 and C 2 exist such that…”

Section: Substitution Of Eq (88) Into Eq (86) Results Inmentioning

confidence: 96%

“…A conventional approach to designing nonlinear analogs for linear constitutive models consists in the introduction of some material time [20] which governs reformation of polymeric networks. This time is traditionally associated with changes in the speci®c free volume [3,12,14,16,17,18,19,22,23]. The evolution of the speci®c volume of a glass observed in experiments is a result of at least two physical processes: (i) time-dependent dilatation caused by the Poisson relaxation [24] and (ii) changes in the speci®c free volume driven by mechanical factors, the so-called apparent rejuvenation of a polymer [28,30,31,34].…”

Section: Introductionmentioning

confidence: 99%

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Volume changes in glassy polymers

Drozdov¹

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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Constitutive equations are derived for compressible glassy polymers at non-isothermal loading with ®nite strains. The model is based on the theory of temporary networks in its version of adaptive links concept. The stress±strain relations are applied to the analysis of uniaxial extension of a viscoelastic bar. Explicit formulas are developed for time-dependent Young's modulus and Poisson's ratio of the bar at small strains. Results of numerical simulation are compared with experimental data for polycarbonate, polyethylene, and poly(methyl methacrylate). It is demonstrated that (i) longitudinal stresses do not affect the speci®c free volume in the region of linear viscoelasticity at strains up to about 0.2%, and cause substantial changes in the free volume in the region of nonlinear viscoelasticity at strains about 1.0%; (ii) in the latter case, the increment of the free-volume fraction is proportional to the increase in the speci®c volume. IntroductionThe study is concerned with the kinetics of volume relaxation in glassy polymers at ®nite and small strains. This subject has attracted substantial attention in the past decade, see, e.g. [5,7,24,25,29] and the references therein, which may be explained by the following reasons:1. To correctly predict stresses in polymeric materials at three-dimensional loading, adequate constitutive equations are necessary. Even for a linear isotropic viscoelastic medium at small strains, stress±strain relations contain two kernels which characterize the material response in shear and hydrostatic tension±compression. Experimental determination of these kernels requires a complicated testing program, see, e.g. [1,24,25]. On the other hand, conventional simpli®cations of the model, based on the assumption regarding the constancy of Poisson's ratio or the neglect of volume relaxation, entail signi®cant deviations of numerical results from observations. In particular, constitutive equations with a constant Poisson ratio cannot predict nonmonotonic changes in the speci®c volume observed in tensile relaxation tests on polycarbonate and poly(methyl methacrylate) [2, 7], whereas stress±strain relations neglecting volume relaxation fail to describe mechanically induced densi®cation observed in tensile and compressive relaxation tests on polycarbonate [5]. A model is therefore necessary that would imply some relations between relaxation kernels or their analogs, and would thus reduce the number of experimental data to be used. 2. The region of linear viscoelasticity for polymeric glasses is rather narrow (usually, strains should not exceed 0.5% [14]), which implies that most problems of interest in polymer engineering are described by nonlinear stress±strain relations. A conventional approach to designing nonlinear analogs for linear constitutive models consists in the introduction of some material time [20] which governs reformation of polymeric networks. This time is

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Section: Substitution Of Eq (88) Into Eq (86) Results Inmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Volume changes in glassy polymers

Drozdov¹

1998

Archive of Applied Mechanics (Ingenieur Archiv)

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“…A good analytical overview can be found in papers [72,73]. Thermal cycling as a source of damage in material systems has been reported for a wide variety of situations.…”

Section: Reliability Study Of Optical Modulesmentioning

confidence: 99%

Design, characterization and reliability studies of passive aligned optical modules

Priyadarshi.¹

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A model for the non‐isothermal viscoelastic behavior of polymers

Drozdov¹

1997

Polymer Engineering & Sci

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A new constitutive model is derived for the viscoelastic behavior of polymers under non‐isothermal loading. The model extends the Tobolsky concept of adaptive links (entanglements) between polymeric molecules to thermoviscoelastic media. Employing this model, we calculate residual stresses built up in an epoxy resin plate under cooling from the rubber‐glass transition temperature, analyze the effect of material parameters on residual stresses, and compare results of numerical simulation with experimental data.

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Thermal Stresses in Nonlinearly Viscoelastic Solids

Cited by 17 publications

References 0 publications

Volume changes in glassy polymers

Volume changes in glassy polymers

Design, characterization and reliability studies of passive aligned optical modules

A model for the non‐isothermal viscoelastic behavior of polymers

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