Stresses around a cylindrical interface crack under shear

An eigenvalue method was proposed to study the stress intensity factors associated with the oscillating stress singularity for the axisymmetric cylindrical interface crack of the fiber/matrix composites. The fiber is a transversely isotropic material and the matrix is isotropic. Based on the fundamental equations of the spacial axisymmetric problem and the assumption of first-order approximation of the singular stress field, the discrete characteristic equation was derived using the displacement functions in the form of separated variables and the technique of meshless method. The eigenvalue is relative to the order of stress singularity, and the associated eigenvector is with respect to the displacement angular variations. The stress angular variations were derived by introducing the displacement angular variations into the constitutive relations. A finite element fiber/matrix model was used to verify the validation of the proposed eigenvalue method. The numerical results of the order of stress singularity and normalized stress angular variations are in good agreement with those obtained by the eigenvalue method. Based on the order of stress singularity and stress angular variations obtained by the eigenvalue method, as well as the numerical singular stress fields obtained by the finite element method (FEM), the stress intensity factors were determined successfully with the linear extropolation method.

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Heat Concentration around a Cylindrical Interface Crack in a Composite Tube

Advances in Mathematical Physics ◽

10.1155/2020/5849690 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

J. W. Fu ◽

L. F. Qian

Keyword(s):

Heat Flux ◽

Intensity Factor ◽

Interface Crack ◽

Composite Structures ◽

Superposition Method ◽

Liner Material ◽

Composite Tube ◽

Cylindrical Interface ◽

Flux Intensity ◽

Heat Flux Intensity

Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper based on the singular integral equation method. The time variable in the two-dimensional temperature governing equation, derived from the non-Fourier theory, is eliminated using the Laplace transformation technique and then solved exactly in the Laplacian domain by the employment of a superposition method. The heat concentration degree caused by the interface crack is judged quantitatively with the employment of heat flux intensity factor. After restoring the results in the time domain using a numerical Laplace inversion technique, the effects of thermal resistance of crack, liner material, and crack length on the results are analyzed with a numerical case study. It is found that heat flux intensity factor is material-dependent, and steel is the best liner material among the three potential materials used for sustaining transiently high temperature loadings.

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