Anisotropy of Oriented Polymers

Kao, Sendjaja; Hsiao, C. C.

doi:10.1063/1.1713190

Cited by 14 publications

(2 citation statements)

References 4 publications

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“…Analogous to the spring and dashpot models long used to give a pictorial representation of linear viscoelastic behaviour are the oriented linear spring elements considered by Hsaio (1959) and Kao and Hsaio (1964) in an attempt to deal with fracture and time dependence as well as small-strain elasticity of oriented polymers. Although a polymer is regarded as homogeneous on a macroscopic scale, within small sub-volumes molecular chains and their orientation are taken into account.…”

Section: Spring-element Modelsmentioning

confidence: 99%

Anisotropic and nonlinear viscoelastic behaviour in solid polymers

Hadley¹,

Ward²

1975

Rep. Prog. Phys.

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Two aspects of the mechanical behaviour of solid polymers are reviewed: (i) anisotropic mechanical behaviour of oriented polymers, and (ii) nonlinear viscoelastic behaviour.In the case of anisotropic behaviour, the discussion includes a comprehensive account of progress to date in obtaining experimental data, together with recent attempts at understanding the behaviour in structural terms. The discussion of nonlinear viscoelastic behaviour, on the other hand, is almost entirely at a phenomenological level. Here it is attempted to bring together the many different approaches and to show their common relationships, particularly between the engineering formulations and those based on continuum mechanics.

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Section: Spring-element Modelsmentioning

confidence: 99%

Anisotropic and nonlinear viscoelastic behaviour in solid polymers

Hadley¹,

Ward²

1975

Rep. Prog. Phys.

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“…$ = cos e and li = cos Or, the Euler angles, 6, 8, and v, specify the orientation of the structural unit, O-u1uZu3, with respect to the reference coordinates, O-x1xzx3, and the angles, Oj and +, , are the polar and azimuthal angles which specify the orientation of the j t h axis, r5, with respect to the reference coordinates, as shown in and The orientation of the jth axis r5 with respect to the coordinates O-uluzua can be specified, as shown in Figure 3, by the polar and azimuthal angles, (3, and a,. The two sets of angles O, , cp, and e,, aj referring to the vector r, are related by sin e, cos aj (5) where T(4, 0 , q ) is a linear transformation operator* given by the following (3 X 3) matrix:…”

Section: Mathematical Representation Of Coordinate Transformation Of mentioning

confidence: 99%

General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

Maeda

Hibi

Itoh

et al. 1970

J. Polym. Sci. A‐2 Polym. Phys.

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A mathematical representation of the transformation of an orientation function between two sets of Cartesian coordinates is discussed in terms of a series expansion of the distribution function in generalized spherical harmonics. A general procedure for calculating the mechanical anisotropy of a single‐phase system (a polycrystalline material) from the orientation of its structural units and the intrinsic mechanical anisotropy of the structural unit is discussed in relation to the transformation of the orientation distribution function, i.e., mutual conversion of the coefficients in the expansion of the distribution function between the two sets of Cartesian coordinates. The procedure is extended to a two‐phase systems (semicrystalline polymers) containing structural units composed of crystalline and noncrystalline materials in three different geometrical arrangements.

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A simple relation to estimate the maximum tensile modulus of drawn polymer fibers

Bondì

1965

J of Applied Polymer Sci

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SynopsisThe partial unfolding of folded lamehe crystals is taken as point of departure for the development of a model to describe the elastic properties of colddrawn polymer filaments. The resulting relation sums the van der Waals tensile compliance and the spectroscopic tensile compliance of the polymer backbone chain in proportion to the length of folded and unfolded crystal lamellae, respectively, in the drawn filament. Many reported tensile moduli of drawn filaments of semicrystalline polymers are substantially below the predicted value. However, specially careful drawing experiments are rewarded with tensile moduli which closely approach the magnitude predicted by the relation presented here. Purpose and ScopeThe effect of the draw ratio on the high frequency tensile modulus of cold-drawn polymer filaments is often expressed as a function of the orientation angle 6 between the symmetry axis of the polarizable unit (e.g., the polymer molecule) and the filament axis.1.2 Samuels' recent correlation of this elastic orientation function with optical properties has given further strong support to the soundness of this view.a However, at the high draw ratios used in practice the orientation function approach encounters a serious limitation. The experimental measurement of the orientation angle 6 (by any technique) becomes quite inaccurate in a region where the orientation function sin2 6 (which, according to the theory, determines the tensile modulus) changes extremely rapidly. ' It appears then, that the orientation function ceases to help our understanding of the elastic properties of cold-drawn filaments at draw ratios in excess of about 6, which may also be the end point of the affine deformation of spherulites.The purpose of the present exploratory analysis is therefore to relate the high frequency modulus of highly (cold) drawn filaments to the intrinsic elastic properties of the polymer and to the draw ratio through an alternate model. The very large difference between the tensile moduli parallel and normal to the molecule axis suggested that a fairly primitive analysis would suffice to assess the validity of a particular model for the structure of drawn filament. Hence no attempt was made to refine either the model or the mathematical treatment once an estimate had been produced for the curve relating the maximum attainable modulus to the draw ratio. 3897

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Anisotropy of Oriented Polymers

Cited by 14 publications

References 4 publications

Anisotropic and nonlinear viscoelastic behaviour in solid polymers

Anisotropic and nonlinear viscoelastic behaviour in solid polymers

General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

A simple relation to estimate the maximum tensile modulus of drawn polymer fibers

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