Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites

Avery, William B.; Herakovich, Carl T.

doi:10.1115/1.3171854

Cited by 71 publications

(32 citation statements)

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“…It is shown in [1 ] that for 'circumferentially orthotropic' shells (the terminology will be defined in Section 2 here), stress resultants and couples vanish at the origin while for 'radially orthotropic' shells these quantities become infinite at the origin. A similar behavior is observed in [4] in an investigation of orthotropic fiber composites (see also [16]). Such anomalies do not arise when the materials are isotropic.…”

Section: Introductionmentioning

confidence: 48%

“…(6) Such types of anisotropy arise in fibers during manufacture of composites (see e.g. [4], [16] for a discussion). They also occur naturally in the casting of metals where the temperature gradient in the freezing process induces a molecular structure which results in radial orthotropy (see e.g.…”

Section: -Vorl/ro -Vorpromentioning

confidence: 99%

“…Indeed, for certain loadings of circumferentially orthotropic solids, the onset of failure may be precipitated by r~ rather than too (of. [4], where in thermal loading of fibrous composites, the radial stress is shown to dominate for circumferentially orthotropic materials). It is noteworthy that the anisotropic disk would tend to fail along a circumferential ring while in the isotropic case, failure would be initiated at the center.…”

Section: (3) (4) Asmentioning

confidence: 99%

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Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

Horgan

Baxter

1996

J Elasticity

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It has been known for some time that certain radial anisotropies in some linear elasticity problems can give rise to stress singularities which are absent in the corresponding isotropic problems. Recently related issues were examined by other authors in the context of plane strain axisymmetric deformations of a hollow circular cylindrically anisotropic linearly elastic cylinder under uniform external pressure, an anisotropic analog of the classic isotropic Lam6 problem. In the isotropic case, as the external radius increases, the stresses rapidly approach those for a traction-free cavity in an infinite medium under remotely applied uniform compression. However, it has been shown that this does not occur when the cylinder is even slightly anisotropic. In this paper, we provide further elaboration on these issues. For the externally pressurized hollow cylinder (or disk), it is shown that for radially orthotropic materials, the maximum hoop stress occurs always on the inner boundary (as in the isotropic case) but that the stress concentration factor is infinite. For circumferentially orthotropic materials, if the tube is sufficiently thin, the maximum hoop stress always occurs on the inner boundary whereas for sufficiently thick tubes, the maximum hoop stress occurs at the outer boundary. For the case of an internally pressurized tube, the anisotropic problem does not give rise to such radical differences in stress behavior from the isotropic problem. Such differences do, however, arise in the problem of an anisotropic disk, in plane stress, rotating at a constant angular velocity about its center, as well as in the three-dimensional problem governing radially symmetric deformations of anisotropic externally pressurized hollow spheres. The anisotropies of concern here do arise in technological applications such as the processing of fiber composites as well as the casting of metals.Mathematics Subject Classifications (1991): 73C02, 73K20.

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Section: Introductionmentioning

confidence: 48%

Section: -Vorl/ro -Vorpromentioning

confidence: 99%

Section: (3) (4) Asmentioning

confidence: 99%

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Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

Horgan

Baxter

1996

J Elasticity

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“…Polyacrylonitrile (PAN) based fibers generally exhibit circumferential alignment of the graphite basal planes, while pitch-based fibers typically have radial alignment. Random orientation of the graphite basal planes in the transverse plane of the fiber would result in a transversely isotropic fiber, or in a narrow zone of the fiber would result in a transversely isotropic core in the fiber [4,5]. The fibers with such microstructures can be idealized as cylindrically orthotropic fibers with a transversely isotropic core, if any.…”

Section: Introductionmentioning

confidence: 99%

A complex variable solution of two-dimensional heat conduction of composites reinforced with periodic arrays of cylindrically orthotropic fibers

Peng

Jiang

Song

2010

Computational Materials Science

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a b s t r a c tProblems of two-dimensional steady-state heat conduction for composites with doubly periodic arrays of cylindrically orthotropic fibers are dealt with. A new complex variable method is presented by introducing an appropriate coordinate transformation to convert the governing differential equation into a harmonic one, and the eigenfunction expansions of the field variables in a unit cell are derived. Then by using a generalized variational functional which absorbs the periodicity condition, an eigenfunction expansion-variational method based on a unit cell is developed to solve such problems. A convergence analysis and a comparison with finite element calculations are conducted to demonstrate the correctness and efficiency of the present method. A discussion is made about the effects of the cylindrical orthotropy of the fiber and the existence of the isotropic core in the fiber on the effective conductivity of the composite. An engineering equivalent parameter, which reflects the overall influence of the thermal conductivities of the matrix and fibers as well as the interfacial characteristic on the effective thermal conductivity of the composite, is found. It is shown that the present first-order approximation of the effective thermal conductivity of the composite can be written in a unified formula for different microstructural characteristics and possesses a good engineering accuracy.

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“…To gauge the impact of cylindrical orthotropy in graphite fibers on the homogenized moduli and local stress fields in unidirectional graphite/epoxy composites, simplified models based on the concentric cylinder geometry had been employed by several investigators. For instance, Avery and Herakovich (1986) employed the composite cylinder geometry to investigate the impact of graphite fiber's cylindrically orthotropic microstructure on residual stresses that arise during the fabrication process and the potential failure modes in the graphite fiber induced by these stresses. In a follow-up investigation, Knott and Herakovich (1991) calculated four of the fiver transversely isotropic moduli of graphite/epoxy unidirectional composites and related stress fields using the CCA model.…”

Section: Cylindrically Orthotropic Fiber Microstructuresmentioning

confidence: 99%

Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

Wang

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This dissertation describes the construction, validation and applications of a stable and quickly converging elasticity-based locally exact homogenization theory for unidirectionallyreinforced composites. Elasticity-based homogenization approaches offer a number of advantages relative to finite-element, finite-difference or finite-volume homogenization schemes, including extremely fast input data construction, ability to investigate composites with very thin coatings or interphases without experiencing convergence issues common to finite-element analyses, and ability to efficiently accommodate phases with cylindrically orthotropic constituents without much effort. The constructed homogenization theory enables efficient analysis of the elastic and viscoelastic response of unidirectional composite materials with rectangular, square, hexagonal and tetragonal periodic microstructures comprised of isotropic, transversely isotropic, and (cylindrically or circumferentially) orthotropic phase constituents, and third phases such as coatings or interphases.The success of this homogenization theory is rooted in the balanced variational principle which plays a key role in the implementation of non-separable periodic boundary conditions, leading to quickly-converging homogenized moduli and stable local stress distributions. This variational principle, originally proposed by Drago and Pindera (2008) for rectangular unit cell architectures, was extended herein to hexagonal and tetragonal unit cells and demonstrated to produce quickly converging homogenized moduli and local stress fields regardless of phase modulus contrast, orthotropy type or viscoelasticity effects.The constructed homogenization theory has been validated upon comparison with known elasticity solutions and micromechanics models. These include the solution to the Eshelby problem which was used as a benchmark to demonstrate the robustness and stability of the developed unit cell solution approach, and the finite volume direct averaging micromechanics (FVDAM) theory which produces high-fidelity results comparable to the finite-element method.Comparison with the classical composite cylinder assemblage (CCA) and Mori-Tanaka micromechanics models establishes applicability and limitations of these approaches based on simplified geometric representation of composite material microstructures. Selected numerical results are generated to provide insight into the efficiency and robustness of the theory. To demonstrate its advantage, the key component of the theory, namely the balanced variational principle, is compared with recently adopted approaches based on a derivative variational principle proposed originally in the context of locally-exact finite-element solutions. Finally, the elastic problem has been extended to viscoelastic domain via the elastic-viscoelastic correspondence principle, validated at the homogenized and local field levels at different times, and employed to investigate thus-far undocumented features of time-dependent response of polymeric ma...

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Effect of Fiber Anisotropy on Thermal Stresses in Fibrous Composites

Cited by 71 publications

References 0 publications

Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

A complex variable solution of two-dimensional heat conduction of composites reinforced with periodic arrays of cylindrically orthotropic fibers

Generalized Locally Exact Homogenization Theory for Unidirectionally Reinforced Composites

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