Journal of Mathematical Sciences

, Volume 198, Issue 1, pp 75–86 | Cite as

Effect of Partial Closure of an Interface Crack with Heat-conducting Filler and Surface Films in the Case of Thermal Loading of a Bimaterial

  • R. V. Goldstein
  • H. S. Kit
  • R. M. Martynyak
  • Kh. I. Serednytska

We formulate the problem of thermoelasticity for a bimaterial body with interface crack with regard for the contact of its faces in the central part under the action of thermal strains caused by a heat flow perpendicular to the interface. The components of the bimaterial have different heat-conduction coefficients and linear coefficients of thermal expansion. The crack is filled with a heat-conducting medium and its faces have thermal resistance caused by the presence of thin surface films. The problem is reduced to a system of nonlinear singular integrodifferential equations for the jump of temperature between the crack faces and the crack opening displacements. For the solution of this problem, we develop an iterative algorithm based on the method of successive approximations. We analyze the influence of heat flow and thermal resistance of the films on the size of the contact region of the crack faces, crack opening displacements, jump of temperature between the crack faces, and the stress intensity factors for interface stresses.


Heat Flow Stress Intensity Factor Thermal Resistance Half Plane Crack Opening Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. O. Andreikiv, “Generalized Griffith problem of shear with regard for the roughness of the crack surfaces,” Fiz.-Khim. Mekh. Mater., 36, No. 2, 49–54 (2000); English translation: Mater. Sci., 36, No. 2, 210–217 (2000).Google Scholar
  2. 2.
    А. V. Balueva and R. V. Goldstein, “Method for the numerical analysis of the kinetics of cracks in a medium with bulk gas release,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 3, 149–159 (1995).Google Scholar
  3. 3.
    А. V. Balueva, R. V. Goldstein, and M. Matchinskii, “Space problem of crack closure near heat sources,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 85–92 (1996).Google Scholar
  4. 4.
    A. A. Evtushenko and G. T. Sulim, “Stress concentration near a cavity filled with a liquid,” Fiz.-Khim. Mekh. Mater., 16, No. 6, 70–73 (1980); English translation: Mater. Sci., 16, No. 6, 210–217 (1980).Google Scholar
  5. 5.
    G. S. Kit and M. G. Krivtsun, Plane Problems of Thermoelasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
  6. 6.
    G. S. Kit, R. M. Martynyak, S. P. Nagalka, and Kh. I. Honchar, “Problem of thermoelasticity for a bimaterial containing an interface crack whose faces are in contact in the central segment,” Teor. Prikl. Mekh., Issue 36, 83–90 (2002).Google Scholar
  7. 7.
    R. M. Martynyak, “Thermal opening of an initially closed interface crack under the conditions of imperfect thermal contact between its lips,” Fiz.-Khim. Mekh. Mater., 35, No. 5, 14–22 (1999); English translation: Mater. Sci., 35, No. 5, 612–622 (1999).Google Scholar
  8. 8.
    R. M. Martynyak, “Thermal stress state of a bimaterial with closed interfacial crack having rough surfaces,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 1, 71–79 (2010); English translation: J. Math. Sci., 176, No. 4, 578–589 (2011).Google Scholar
  9. 9.
    R. M. Martynyak, Kh. I. Honchar, and S. P. Nahalka, “Simulation of thermomechanical closure of an initially open interface crack with heat resistance,” Fiz.-Khim. Mekh. Mater., 39, No. 5, 59–66 (2003); English translation: Mater. Sci., 39, No. 5, 672–681 (2003).Google Scholar
  10. 10.
    R. M. Martynyak and Kh. I. Honchar, “Thermoelastic deformation of a bimaterial with interface defect filled with a heat-conductive medium,” Teor. Prikl. Mekh., Issue 41, 58–62 (2005).Google Scholar
  11. 11.
    R. M. Martynyak and Kh. I. Serednytska, “Thermoelasticity of a piecewise homogeneous body with heat-permeable interface crack,” Teor. Prikl. Mekh., Issue 4 50, 91–98 (2012).Google Scholar
  12. 12.
    Yu. P. Shlykov, E. A. Ganin, and S. N. Tsarevskii, Contact Thermal Resistance [in Russian], Énergiya, Moscow (1977).Google Scholar
  13. 13.
    O. E. Andreikiv, “Mathematical modeling of hydrogen-assisted fracture in metals,” Fiz.-Khim. Mekh. Mater., 33, No. 4, 53–64 (1997); English translation: Mater. Sci., 33, No. 4, 450–464 (1997).Google Scholar
  14. 14.
    J. R. Barber and M. Comninou, “The penny-shaped interface crack with heat flow. Part 2: Imperfect contact,” Trans. ASME. J. Appl. Mech., 50, No. 4a, 770–776 (1983).CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    A. M. Garsia and H. Sehitoglu, “Contact of crack surfaces during fatigue: Part 1. Formulation of the model,” Metal. Mater. Trans. A, 28A, No. 11, 2263–2275 (1997).CrossRefGoogle Scholar
  16. 16.
    G. I. Giannopoulos and N. K. Anifantis, “A BEM analysis for thermomechanical closure of interfacial cracks incorporating friction and thermal resistance,” Comput. Meth. Appl. Mech. Eng., 196, No. 4–6, 1018–1029 (2007).CrossRefzbMATHGoogle Scholar
  17. 17.
    D. Gross and S. Heimer, “Crack closure and crack path prediction for curved cracks under thermal load,” Eng. Fract. Mech., 46, 633–640 (1993).CrossRefGoogle Scholar
  18. 18.
    T. S. Gross and D. A. Mendelsohn, “On the effect of crack face contact and friction due to fracture surface roughness in edge crack subjected to external shear,” Eng. Fract. Mech., 31, No. 3, 405–420 (1988).CrossRefGoogle Scholar
  19. 19.
    L. K. Keppas and N. K. Anifantis, “Boundary element prediction on TBC fracture resistance,” Fatigue Fract. Eng. Mater. Struct., 33, No. 3, 174–182 (2010).CrossRefGoogle Scholar
  20. 20.
    I. V. Kharun and V. V. Loboda, “A thermoelastic problem for interface crack with contact zones,” Int. J. Solids Struct., 41, No. 1, 159–175 (2004).CrossRefzbMATHGoogle Scholar
  21. 21.
    T. Kobayashi and D. A. Shockey, “Fracture surface topography analysis (FRASTA) – Development, accomplishments, and future applications,” Eng. Fract. Mech., 77, No. 12, 2370–2384 (2010).CrossRefGoogle Scholar
  22. 22.
    D. A. Mendelsohn, T. S. Gross, R. U. Goulet, and M. Zhouc, “Experimental-computational estimation of rough fracture surface contact stresses,” Mater. Sci. Eng. A, 249, No. 1–2, 1–6 (1998).CrossRefGoogle Scholar
  23. 23.
    J. A. Newman and R. S. Piascik, “Interactions of plasticity and oxide crack closure mechanisms near the fatigue crack growth threshold,” Int. J. Fatigue, 26, No. 9, 923–927 (2004).CrossRefGoogle Scholar
  24. 24.
    F. O. Riemelmoser and R. Pippan, “Crack closure: a concept of fatigue crack growth under examination,” Fatigue Fract. Eng. Mater. Struct., 20, No. 11, 1529–1540 (1997).CrossRefGoogle Scholar
  25. 25.
    H. Sehitoglu and A. M. Garsia, “Contact of crack surfaces during fatigue: Part 2. Simulations,” Metal. Mater. Trans. A, 28A, No. 11, 2277–2289 (1997).CrossRefGoogle Scholar
  26. 26.
    C. O. A. Semprimoschnig, J. Stampfl, R. Pippan, and O. Kolednik, “A new powerful tool for surveying cleavage fracture surface,” Fatigue Fract. Eng. Mater. Struct., 20, No. 11, 1541–1550 (1997).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • R. V. Goldstein
    • 1
  • H. S. Kit
    • 2
  • R. M. Martynyak
    • 1
  • Kh. I. Serednytska
    • 1
  1. 1.Ishlinskii Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia
  2. 2.Pidstryhach Institute for Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

Personalised recommendations