Thermal Stresses in Anisotropic Bodies With a Hole or a Rigid Inclusion

Tarn, Jiann-Quo; Wang, Yung Ming

doi:10.1080/01495739308946240

Cited by 35 publications

(25 citation statements)

References 9 publications

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“…The homogenized composite is subjected to a remote heat fluxq 2 = −1 W/m 2 in the two-direction. Figure 2 shows a comparison between the temperature, heat flux and the induced shear stress along the crack line as predicted by the exact solution of [7] and the present approach. Very good agreement can be observed.…”

Section: Verificationsmentioning

confidence: 99%

“…The material is subjected to a remote heat fluxq, and the crack is traction-free and insulated such that its surface heat flux is equal to zero. With the effective heat conductivity, stiffness and thermal stress tensors, κ * , C * and Γ * , that characterize the considered homogenized anisotropic material, the solution of [7] can be implemented to verify the field variation as predicted by the present analysis. The exact expressions for the temperature and heat flux are given by:…”

Section: Verificationsmentioning

confidence: 99%

“…In [7], an exact solution for the temperature and thermal stresses fields is given for a crack of length 2a embedded within an infinite homogeneous anisotropic material. The material is subjected to a remote heat fluxq, and the crack is traction-free and insulated such that its surface heat flux is equal to zero.…”

Section: Verificationsmentioning

confidence: 99%

“…and µ k are the three roots with the positive imaginary part of a cubic equation that is given together with L and h in [7].…”

Section: Verificationsmentioning

confidence: 99%

“…Examples of some articles in which the effect of heat flow in cracked materials is investigated are: [1][2][3][4][5][6][7][8][9][10][11] and the references cited therein, as well as Chapter 10 in the monograph [12]. The analysis of [13] of the singularities at the tip of interfacial cracks in anisotropic materials subjected to heat flow forms a generalization of the square root singularity that occurs in homogeneous materials.…”

Section: Introductionmentioning

confidence: 99%

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The Induced Stress Field in Cracked Composites by Heat Flow

Aboudi

2017

J. Compos. Sci.

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Abstract:A multiscale (micro-macro) approach is proposed for the establishment of the full thermal and induced stress fields in cracked composites that are subjected to heat flow. Both the temperature and stresses' distributions are determined by the solution of a boundary value problem with one-way coupling. At the micro level and for combined thermomechanical loading, a micromechanical analysis is employed to determine the effective moduli, coefficients of thermal expansion and thermal conductivities of the undamaged composite. At the macro level, the representative cell method is employed according to which the periodic damaged composite region is reduced, in conjunction with the discrete Fourier transform, to a finite domain problem. As a result, a boundary value problem is obtained in the Fourier transform domain, which is appropriately discretized and solved. The inverse transform and an iterative procedure provide the full thermal and stress fields. The proposed method is verified by comparisons with exact solutions. Applications are given for the determination of the thermal and stress fields in cracked fiber-reinforced polymeric composite, cracked porous ceramic material and cracked periodically-layered ceramic composite caused by the application of heat flow. The presented formulation admits however the application of a combined mechanical and heat flux on cracked composites.

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Section: Verificationsmentioning

confidence: 99%

Section: Verificationsmentioning

confidence: 99%

Section: Verificationsmentioning

confidence: 99%

“…and µ k are the three roots with the positive imaginary part of a cubic equation that is given together with L and h in [7].…”

Section: Verificationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Induced Stress Field in Cracked Composites by Heat Flow

Aboudi

2017

J. Compos. Sci.

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Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

et al. 2000

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The two-dimensionM problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat flow direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

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