Thermoelastic problem of curvilinear cracks in bonded dissimilar materials

Within the framework of the linear theory of thermoelasticity, the heterogeneous problem associated with multiple inclusions, circularly cylindrical layered media and plane layered media is considered and solved in this paper. The number of inclusions and layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solutions to heat conduction (or antiplane deformation) and thermoelasticity problems are derived by the heterogenization technique that allows us to write down the solution explicitly in terms of the solution of a corresponding homogeneous problem subjected to the same loading. A rapid convergent series solution for both the temperature (or antiplane displacement) and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations and geometrical configurations on the interfacial stresses.

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“…which is in agreement with the exact solution of the bimaterial one [11]. Downloaded by [McGill University Library] at 07:10 14 October 2014…”

Section: Stress Functionssupporting

confidence: 87%

Heterogeneous Problems in Plane Thermoelasticity

Chao

Chen

2009

Journal of Thermal Stresses

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“…The behavior of f~(z) near the point z = 0 can be found from (7), (8) and (12); it follows that ~2 l~(X + iY) -2nil 1 = -+ a holomorphic function, Izl < 1. f2(z) z2 2n(1 + ~c) z…”

Section: Formulation and Solution Of The Problemsmentioning

confidence: 99%

“…Using the new integral equation and applying the image method, Chen [6,7] further examined the curved crack problem in antiplane elasticity. Based on the Hilbert problem formulation and a special technique of continuation, Chao and Shen [8] recently gave a closed form solution for thermoelastic problem of curvilinear crack in bonded dissimilar media. They showed that the crack surfaces may come into contact with one another for certain combinations of the angle of heat flux approached from infinity and the angle subtended by the arc crack.…”

Section: Introductionmentioning

confidence: 99%

Explicit solutions for the elastic and thermoelastic fields with a rigid circular-arc inclusion

Shen

Chao

1994

Int J Fract

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A general solution to the elastic and thermoelastic problems with a rigid circular-arc inclusion is presented. The proposed analysis is based upon the complex variable theory dealing with sectionally holomorphic functions which is reduced to the solution of the Hilbert problem. It is indicated that both the stress and thermal stress fields near the inclusion tip possess a square-root singularity similar to that for the corresponding crack problem. In analogy to the stress intensity factors defined for crack problem, stress singularity coefficients are introduced in this paper to characterize the near tip fields. Complete stress fields and the corresponding stress singularity coefficients as the circular-arc inclusion are under uniform remote load, concentrated force and uniform heat flux are given. Failure initiation of an infinite plate embedded with a rigid arc inclusion under different loading conditions is also discussed.

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“…Several papers have been published on this subject such as Comninou (1982, 1983); Martin-Moran et al (1983) and Chao and Shen (1993), etc. ; these studies were, however, for isotropic bi-media; Atkinsion and Clements (1983) began to address the thermo-elastic interface crack problem for anisotropic bi-material media consisting of two dissimilar infinite half spaces.…”

Section: Introductionmentioning

confidence: 99%

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

Kardomateas

2006

International Journal of Solids and Structures

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An interface crack or delamination may often branch out of the interface in a laminated composite due to thermal stresses developing around the delamination/crack tip when the media is exposed to heat flow induced by environmental events such as a sudden short-duration fire. In this paper, the thermo-elastic problem of interface crack branching in dissimilar anisotropic bi-media is studied by using the theory of StrohÕs dislocation formalism, extended to thermo-elasticity in matrix notation. Based on the complex variable method and the analytical continuation principle, the thermo-elastic interface crack/delamination problem is examined and a general solution in compact form is derived for dissimilar anisotropic bi-media. A set of GreenÕs functions is proposed for the dislocations (conventional dislocation and thermal dislocation/heat vortex) in anisotropic bi-media. These functions may be more suitable than those which have appeared in the literature on addressing thermo-elastic interface crack branching in dissimilar anisotropic bi-materials. Using the contour integral method, a closed form solution to the interaction between the dislocations and the interface crack is obtained. Within the scope of linear fracture mechanics, the thermo-elastic problem of interface crack branching is then solved by modelling the branched portion as a continuous distribution of dislocations. The influence of thermal loading and thermal properties on the branching behavior is examined, and criteria for predicting interface crack branching are suggested, based on the extensive numerical results from the study of various cases.

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Thermoelastic problem of curvilinear cracks in bonded dissimilar materials

Cited by 10 publications

References 12 publications

Heterogeneous Problems in Plane Thermoelasticity

Heterogeneous Problems in Plane Thermoelasticity

Explicit solutions for the elastic and thermoelastic fields with a rigid circular-arc inclusion

A solution to the thermo-elastic interface crack branching in dissimilar anisotropic bi-material media

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