Skip to main content
SpringerLink
Log in

Analysis method of collinear cracks subjected to thermo-magneto-electro-elastic loads

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper discussed the fracture analysis of two collinear cracks under a thermo-magnetic-electric-elastic field. Taking advantage of the permeable crack models and the singular integral equation, the analytical solutions of important parameters around two collinear cracks are obtained. An example is used to demonstrate the method provided in this paper. The effects of the dimensionless quantities between the upper and lower crack surfaces, such as heat flux on the crack surface, electric displacement, magnetic induction per unit thickness, and the corresponding intensity factors near the inner and outer crack tips, are shown in the case analysis. It should be emphasized that because the theoretical solution obtained in this paper has an explicit form, it is convenient to solve the stress intensity factor. In particular, it is very convenient to solve the influence of various physical quantities on the stress intensity factor of the crack tip.

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

Similar content being viewed by others

References

  1. Nowacki, W.: Some general theorems of thermo-piezo-electricity. J. Therm. Stress. 1(2), 171–182 (1978)

    Article  Google Scholar 

  2. Bao, G., Suo, Z.: Remarks on crack-bridging concepts. Appl. Mech. Rev. 45(8), 355–366 (1992)

    Article  Google Scholar 

  3. Nan, C.W., Bichurin, M.I., Dong, S., et al.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)

    Article  Google Scholar 

  4. Wu, T.L., Huang, J.H.: Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases. Int. J. Solids Struct. 37, 2981–3009 (2000)

    Article  Google Scholar 

  5. Zhou, Z.G., Wu, L.Z., Wang, B.: The behavior of a crack in functionally graded piezo-electric/piezomagnetic materials under anti-plane shear loading. Arch. Appl. Mech. 74(8), 526–535 (2005)

    Article  Google Scholar 

  6. Tian, W.Y., Gabbert, U.: Multiple crack interaction problem in magneto-electro-elastic solids. Eur. J. Mech. A-Solid 23, 599–614 (2004)

    Article  Google Scholar 

  7. Feng, W.J., Ma, P., Su, R.K.L.: An electrically impermeable and magnetically permeable interface crack with a contact zone in magneto-electro-elastic bi-materials under a thermal flux and magneto-electro-mechanical loads. Int. J. Solids Struct. 49(23–24), 3472–3483 (2012)

    Article  Google Scholar 

  8. Chen, X.: Energy release rate and path-independent integral in dynamic fracture of magneto-electro-thermo-elastic solids. Int. J. Solids Struct. 46(13), 2706–2711 (2019)

    Article  Google Scholar 

  9. Sladek, J., Sladek, V., Zhang, C., et al.: Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG. Comput. Model. Eng. 19(3), 247–262 (2007)

    MathSciNet  Google Scholar 

  10. Kumaravel, A., Ganesan, N., Sethuraman, R.: Steady-state analysis of a three-layered electro-magneto-elastic strip in a thermal environment. Smart Mater. Struct. 16(2), 282–295 (2007)

    Article  Google Scholar 

  11. Chen, W.Q., Yong Lee, K., Ding, H.J.: General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. Int. J. Eng. Sci. 42(13), 1361–1379 (2004)

    Article  Google Scholar 

  12. Sladek, J., Sladek, V., Solek, P., et al.: Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG. Int. J. Solids Struct. 47(10), 1381–1391 (2010)

    Article  Google Scholar 

  13. Gao, C.F., Kessler, H., Balke, H.: Fracture analysis of electromagnetic thermoelastic solids. Eur. J. Mech. A-Solid 22(3), 433–442 (2003)

    Article  Google Scholar 

  14. Ma, P., Feng, W.J., Su, R.K.L.: An electrically impermeable and magnetically permeable interface crack with a contact zone in a magneto-electro-elastic bi-material under uniform magneto-electro-mechanical loads. Eur. J. Mech. A-Solid. 32, 41–51 (2012)

    Article  Google Scholar 

  15. Wang, X., Shen, Y.: The general solution of three-dimensional problems in magneto-electro-elastic media. Int. J. Eng. Sci. 40(10), 1069–1080 (2002)

    Article  Google Scholar 

  16. Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50(9), 6082–6088 (1994)

    Article  Google Scholar 

  17. Gao, C.F., Noda, N.: Thermal-induced interfacial cracking of magneto-electro-elastic material. Int. J. Eng. Sci. 42(13), 1347–1360 (2004)

    Article  Google Scholar 

  18. Heyliger, P.R., Ramirez, F., Pan, E.: Two-dimensional static fields in magneto-electro-elastic laminates. J. Intel. Mater. Syst. Struct. 15(9–10), 689–709 (2004)

    Article  Google Scholar 

  19. Feng, W.J., Li, Y.S., Xu, Z.H.: Transient response of an interfacial crack between dissimilar magneto-electro-elastic layers under magneto-electro-mechanical impact loadings: mode-I problem. Int. J. Solids Struct. 46(18–19), 3346–3356 (2009)

    Article  Google Scholar 

  20. Wang, B.L., Sun, Y.G., Zhang, H.Y.: Analysis of a penny-shaped crack in magneto-electro-elastic materials. J. Appl. Phys. 103(8), 083530–083530 (2008)

    Article  Google Scholar 

  21. Gao, C.F., Tong, P., Zhang, T.Y.: Fracture mechanics for a mode III crack in a magneto-electro-elastic solid. Int. J. Solids Struct. 41, 6613–6629 (2004)

    Article  Google Scholar 

  22. Zhong, X.C.: Closed-form solutions for two collinear dielectric cracks in a magneto-electro-elastic solid. Appl. Math. Model. 35(6), 2930–2944 (2011)

    Article  MathSciNet  Google Scholar 

  23. Rogowski, B.: The analysis of a mode I conducting crack under general applied loads in piezo-electro-magneto-elastic layer. Int. J. Eng. Sci. 75, 11–30 (2014)

    Article  MathSciNet  Google Scholar 

  24. Zhong, X.C., Li, X.F.: Fracture analysis of a magneto-electro-elastic solid with a penny-shaped crack by considering the effects of the opening crack interior. Int. J. Eng. Sci. 46, 374–390 (2008)

    Article  Google Scholar 

  25. Nagai, M., Ikeda, T., Miyazaki, N.: Stress intensity factor analysis of an interface crack between dissimilar anisotropic materials under thermal stress using the finite element analysis. Int. J. Fract. 146(4), 233–248 (2007)

    Article  Google Scholar 

  26. Wang, W., Feng, S.J., Luo, Y.: Modern Electronic Materials and Components. Science Press, Beijing (2012)

    Google Scholar 

  27. Li, X.F., Kang, Y.L.: Fracture analysis of cracked piezoelectric materials. Int. J. Solids Struct. 41(15), 4137–4161 (2004)

    Article  Google Scholar 

  28. Zhong, X.C., Huang, Q.A.: Thermal stress intensity factor for an opening crack in thermo-magneto-electro-elastic solids. J. Therm. Stress. 37(7–9), 928–946 (2014)

    Article  Google Scholar 

  29. Wu, B., Peng, D., Jones, R.: Fracture analysis for a crack in orthotropic material subjected to combined 2i-order symmetrical thermal flux and 2j-order symmetrical mechanical loading. Appl. Mech 2(1), 127–146 (2021)

    Article  Google Scholar 

  30. Pérez-Fernández, L.D., Bravo-Castillero, J., Rodríguez-Ramos, R., et al.: On the constitutive relations and energy potentials of linear thermo-magneto-electro-elasticity. Mech. Res. Commun. 36(3), 343–350 (2009)

    Article  MathSciNet  Google Scholar 

  31. Zhong, X.C., Wu, B., Zhang, K.S.: Thermally conducting collinear cracks engulfed by thermomechanical field in a material with orthotropy. Theor. Appl. Fract. Mech. 65, 61–68 (2013)

    Article  Google Scholar 

  32. Wu, B., Zhu, J.G., Peng, D., et al.: Thermoelastic analysis for two collinear cracks in an orthotropic solid disturbed by anti-symmetrical linear heat flow. Math. Probl. Eng. (2017). https://doi.org/10.1155/2017/5093404

    Article  Google Scholar 

  33. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Elsevier Academic Press, California (2007)

    Google Scholar 

  34. Bing, Wu., Peng, D., Jones, R.: Two collinear cracks under combined quadratic thermo-electro-elastic loading. Acta Mech. 233, 2439–2452 (2022)

    Article  MathSciNet  Google Scholar 

  35. Bing, Wu., Peng, D., Jones, R.: On thermoelastic analysis of two collinear cracks subject to combined quadratic thermo-mechanical load. Appl. Math. Comput. 421, 126905 (2022)

    MathSciNet  Google Scholar 

  36. Wu, B., Peng, D., Jones, R.: On the analysis of cracking under a combined quadratic thermal flux and a quadratic mechanical loading. Appl. Math. Model. 68, 182–197 (2019)

    Article  MathSciNet  Google Scholar 

  37. Wu, B., Peng, D., Singh Raman, R.K., Jones, R.: Negative energy release rate or J-integral for a crack in orthotropic material under thermal-mechanical loading. Int. J. Terrasp. Sci. Technol. 10(2), 42–48 (2018)

    Google Scholar 

  38. Li, Y.: The Study on Three-Dimensional Multi-Field Coupling Crack Problems Considering Thermal Effect. Zhengzhou University, Zhengzhou (2020)

    Google Scholar 

Download references

Acknowledgements

B.W. would like to acknowledge the higher-level talents funding (No: 521100221019) provided by Hebei University Scientific Research Foundation and the China Scholarship Council (No. 202208130086).

Author information

Authors and Affiliations

  1. Co-Technology Innovation Center for Testing and Evaluation in Civil Engineering of Hebei Province, Hebei University, Baoding, 071002, Hebei, China

    B. Wu

  2. Department of Mechanical and Aerospace Engineering, Centre of Expertise Structural Mechanics, Monash University, Clayton, VIC, 3800, Australia

    D. Peng & R. Jones

  3. ARC Industrial Transformation Training Centre on Surface Engineering for Advanced Materials, School of Engineering, Swinburne University of Technology, John Street, Hawthorn, VIC, 3122, Australia

    D. Peng & R. Jones

  4. Department of Civil, Environmental and Mining Engineering, University of Western Australia, Crawley, Australia

    B. Wu

Authors
  1. B. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Peng.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, B., Peng, D. & Jones, R. Analysis method of collinear cracks subjected to thermo-magneto-electro-elastic loads. Arch Appl Mech 94, 99–117 (2024). https://doi.org/10.1007/s00419-023-02511-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-023-02511-3

Keywords

Search

Navigation