Thermal interface crack problems in dissimilar anisotropic media

Abstract

The fundamental nature of an interface crack between dissimilar anisotropic media under the uniform heat flux is studied. Based on the Hilbert problem formulation and a special technique of analytical continuation, a simple and compact version of general solutions for the thermal field are given. The temperature gradients or heat fluxes are found to possess the characteristic inverse square-root singularity in terms of the radial distance from the crack tip. Due to this singular behavior, the heat flux intensity factor is then introduced to quantify the thermal energy cumulated in the neighborhood of the crack tip. Some numerical examples are given for the application of the final results to the intensity factor of heat flux as well as the full field solutions of temperature. It is very interesting to see that the solutions associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution of their own material properties. In general, the system possesses the symmetric properties of the thermal conductivity coefficients which can make the heat flux intensity factor smaller. Consequently, the thermal energy intensification is diminished.

Analytical Solutions and Numerical Examples for Thermoelastic Interface Crack Problems in Dissimilar Anisotropic Media

“…For the problem of plane strain deformation, it can be treated by a change of compliances and thermal expansion coefficients (15) Without loss of generality, we can present our solutions by the function vector cI>(z) defined as (16) In the present study, both the traction in the y-plane and displacement derivative need to satisfy the corresponding boundary value problem. They are…”

“…Therefore, the Downloaded by [New York University] at 18:11 05 February 2015 temperature function 8 1(z) and 8 2 ( z ) in Eqs. (20) and (21) can be determined independently, that is [15], (22) where k, Ci = 1,2) stands for the compound conductivity coefficients of the upper Ci = 1) and lower Ci"= 2) media defined as k, = (k 12 + p,.k 22 )j' Note that the solutions given in Eq. (22) are only valid for the condition that the heat conductivity coefficients must obey the Onsager reciprocal relations, which might guarantee that the singularities of the thermal stress are exactly the same as those for isothermal elasticity.…”

“…Their results indicated that the types of stress singularity at the crack tip are the same as those for the corresponding problem of isothermal elasticity. The effect of the heat conduction coefficients on singularity of the heat flux between dissimilar anisotropic media was discussed by Chao and Chang [15]. They showed that the types of stress singularity depend on the heat conduction coefficients if the heat conduction coefficients do not obey the Onsager reciprocal relations.…”

Interaction between heat dipole and circular interfacial crack

“…Recently, more and more researchers focus on the investigation of the thermoelastic problems with various defects occurring frequently in most engineering structures. The analysis for thermal interfacial crack problems in dissimilar anisotropic media under the uniform heat flux was provided by Chao and Chang [4] based on the Hilbert theory and the analytical continuation. With the combination of Stroh's formulation, the conformal mapping, the perturbation technique, and the analytical continuation, a general analytical thermoelectroelastic solution for an elliptic piezoelectric inclusion embedded in an infinite piezoelectric matrix was obtained by Qin [5] .…”

A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material

“…Hwu and Lee investigated the singularity order of heat flux of multi-bonded anisotropic wedges by using the Stroh formalism for plane anisotropic thermoelasticity, the general solutions were presented in a simple and compact form [21]. Chao and Chang studied the interface crack between two dissimilar anisotropic materials under uniform heat flux based on the Hilbert problem formulation, a special technique was used to determine the general solutions for thermal fields [22].…”