Journal of Mathematical Sciences

, Volume 176, Issue 4, pp 578–589 | Cite as

Thermal stress state of a bimaterial with a closed interfacial crack having rough surfaces

  • R. M. Martynyak

We have formulated the problem of thermoelasticity for a bimaterial whose components differ only in their shear moduli, with a closed interfacial crack having rough surfaces. The bimaterial is subjected to the action of compressive loads and heat flow normal to the interfacial surface. We have taken into account the dependence of thermal conductance of the defect on the contact pressure of its faces and heat conductivity of the medium that fills it. The problem is reduced to a Prandtl-type nonlinear singular integro-differential equation for temperature jump between the crack surfaces. An analytical solution of this problem has been constructed for the case of action of the heat flow only. We have analyzed the dependence of contact pressure of the defect faces, temperature jump between them, and the intensity factor of tangential interfacial stresses on the value of given heat flow, roughness of the surfaces, and ratio between the shear moduli of joined materials.


Heat Flow Contact Pressure Crack Surface Fatigue Crack Growth Interfacial Crack 


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • R. M. Martynyak
    • 1
  1. 1.Pidstryhach Institute for Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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