Skip to main content
SpringerLink
Log in

The effect of interfacial thermal resistance on interface crack subjected to remote heat flux

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

We consider the thermoelastic problem of an interface crack between two dissimilar semi-infinite isotropic materials under a uniform remote heat flux in plane deformation. The crack face is assumed to be partially thermopermeable (defined by a partial insulation coefficient of the crack), while the interface is assumed to be perfectly bonded except that a constant thermal resistance is introduced into the interfacial region near the tips of the crack. By using the integral transform method, we obtain the analytic solution for the thermoelastic field in the entire bi-material system. Numerical examples are presented to study the influence of interfacial thermal resistance on the thermal stress intensity factors and the crack opening/sliding displacements. It is shown that the magnitudes of the mode I and mode II TSIFs, as well as the crack opening displacements, increase with the increasing interfacial thermal resistance, while the crack sliding displacement is insensitive to the change of interfacial thermal resistance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Gross, D., Heimer, S.T.: Crack closure and crack path prediction for curved cracks under thermal load. Eng. Fract. Mech. 46, 633–640 (1993)

    Article  Google Scholar 

  2. Petrova, V.E., Herrmann, K.P.: Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source. Int. J. Fract. 128, 49–63 (2004)

    Article  Google Scholar 

  3. Herrmann, K.P., Dong, M., Hauck, T.: Modeling of thermal cracking in elastic and elastoplastic two-phase solids. J. Therm. Stress. 20, 853–904 (2007)

    Article  Google Scholar 

  4. Chen, J.: Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure. Int. J. Fract. 133, 303–328 (2005)

    Article  Google Scholar 

  5. Lee, G.H., Beom, H.G.: Interfacial edge crack between dissimilar orthotropic thermoelastic materials under uniform heat flow. J. Mech. Sci. Technol. 28(8), 3041–3050 (2014)

    Article  Google Scholar 

  6. Powell, B.R., Youngblood, G.E., Hasselman, D.P.H., Bentsen, L.D.: Effect of thermal expansion mismatch on the thermal diffusivity on glass-Ni composites. J. Am. Ceram. Soc. 63(9–10), 581–586 (1980)

    Article  Google Scholar 

  7. Hasselman, D.P.H., Johnson, L.F.: Effective thermal conductivity of composites with interfacial thermal barrier resistance. J. Compos. Mater. 21(6), 508–514 (1987)

    Article  Google Scholar 

  8. Nan, C.W., Birringer, R., Clarke, D.R., Gleiter, H.: Effective thermal conductivity of particulate composites with interfacial thermal resistance. J. Appl. Phys. 81(10), 6692–6699 (1997)

    Article  Google Scholar 

  9. Lee, K.Y.: Thermal stress intensity factors for partially insulated interface crack under uniform heat flow. Eng. Fract. Mech. 50(4), 475–482 (1995)

    Article  MathSciNet  Google Scholar 

  10. Yang, Y.C., Lee, H.L., Hsu, J.C., Chu, S.S.: Thermal stresses in multilayer gun barrel with interlayer thermal contact resistance. J. Therm. Stress. 31, 624–637 (2008)

    Article  Google Scholar 

  11. Jin, Z.H., Tohgo, K., Fujii, T., Shimamura, Y.: Effect of interfacial thermal resistance on surface cracking in a coating layer bonded to a substrate. Mech. Eng. Lett. 2(16), 16-00436 (2016)

    Article  Google Scholar 

  12. Wang, J., Jin, Z.H., Gao, C.F.: A sub-interface thermal crack problem for bonded dissimilar plates with interfacial thermal resistance. J. Therm. Stress. 42(5), 629–642 (2019)

    Article  Google Scholar 

  13. Noda, N., Hetnarski, R.B., Tanigawa, Y.: Thermal Stresses, 2nd edn. Taylor and Francis, New York (2003)

    Google Scholar 

  14. Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook, 3rd edn. ASME Press, New York (2000)

    Book  Google Scholar 

  15. Sun, C.T., Jin, Z.H.: Fracture Mechanics. Academic Press, Cambridge (2012)

    Google Scholar 

Download references

Acknowledgements

The research is supported by the National Natural Science Foundation of China (Nos. 11872203, 11902147) and the Natural Science Foundation of Jiangsu Province (No. BK20190393).

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Jie Wang, Ming Dai & Cun-Fa Gao

Authors
  1. Jie Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cun-Fa Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ming Dai or Cun-Fa Gao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Dai, M. & Gao, CF. The effect of interfacial thermal resistance on interface crack subjected to remote heat flux. Z. Angew. Math. Phys. 71, 12 (2020). https://doi.org/10.1007/s00033-019-1235-7

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00033-019-1235-7

Keywords

Mathematics Subject Classification

Search

Navigation