Skip to main content
Erschienen in: Archive of Applied Mechanics 1/2024

07.11.2023 | Original

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

verfasst von: B. Wu, D. Peng, R. Jones

Erschienen in: Archive of Applied Mechanics | Ausgabe 1/2024

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Nowacki, W.: Some general theorems of thermo-piezo-electricity. J. Therm. Stress. 1(2), 171–182 (1978)CrossRef Nowacki, W.: Some general theorems of thermo-piezo-electricity. J. Therm. Stress. 1(2), 171–182 (1978)CrossRef
2.
Zurück zum Zitat Bao, G., Suo, Z.: Remarks on crack-bridging concepts. Appl. Mech. Rev. 45(8), 355–366 (1992)CrossRef Bao, G., Suo, Z.: Remarks on crack-bridging concepts. Appl. Mech. Rev. 45(8), 355–366 (1992)CrossRef
3.
Zurück zum Zitat 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)CrossRef 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)CrossRef
4.
Zurück zum Zitat 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)CrossRef 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)CrossRef
5.
Zurück zum Zitat 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)CrossRef 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)CrossRef
6.
Zurück zum Zitat Tian, W.Y., Gabbert, U.: Multiple crack interaction problem in magneto-electro-elastic solids. Eur. J. Mech. A-Solid 23, 599–614 (2004)CrossRef Tian, W.Y., Gabbert, U.: Multiple crack interaction problem in magneto-electro-elastic solids. Eur. J. Mech. A-Solid 23, 599–614 (2004)CrossRef
7.
Zurück zum Zitat 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)CrossRef 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)CrossRef
8.
Zurück zum Zitat 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)CrossRef 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)CrossRef
9.
Zurück zum Zitat 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 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
10.
Zurück zum Zitat 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)CrossRef 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)CrossRef
11.
Zurück zum Zitat 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)CrossRef 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)CrossRef
12.
Zurück zum Zitat 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)CrossRef 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)CrossRef
13.
Zurück zum Zitat Gao, C.F., Kessler, H., Balke, H.: Fracture analysis of electromagnetic thermoelastic solids. Eur. J. Mech. A-Solid 22(3), 433–442 (2003)CrossRef Gao, C.F., Kessler, H., Balke, H.: Fracture analysis of electromagnetic thermoelastic solids. Eur. J. Mech. A-Solid 22(3), 433–442 (2003)CrossRef
14.
Zurück zum Zitat 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)CrossRef 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)CrossRef
15.
Zurück zum Zitat 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)CrossRef 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)CrossRef
16.
Zurück zum Zitat Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50(9), 6082–6088 (1994)CrossRef Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50(9), 6082–6088 (1994)CrossRef
17.
Zurück zum Zitat Gao, C.F., Noda, N.: Thermal-induced interfacial cracking of magneto-electro-elastic material. Int. J. Eng. Sci. 42(13), 1347–1360 (2004)CrossRef Gao, C.F., Noda, N.: Thermal-induced interfacial cracking of magneto-electro-elastic material. Int. J. Eng. Sci. 42(13), 1347–1360 (2004)CrossRef
18.
Zurück zum Zitat 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)CrossRef 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)CrossRef
19.
Zurück zum Zitat 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)CrossRef 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)CrossRef
20.
Zurück zum Zitat 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)CrossRef 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)CrossRef
21.
Zurück zum Zitat 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)CrossRef 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)CrossRef
22.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
23.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
24.
Zurück zum Zitat 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)CrossRef 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)CrossRef
25.
Zurück zum Zitat 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)CrossRef 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)CrossRef
26.
Zurück zum Zitat Wang, W., Feng, S.J., Luo, Y.: Modern Electronic Materials and Components. Science Press, Beijing (2012) Wang, W., Feng, S.J., Luo, Y.: Modern Electronic Materials and Components. Science Press, Beijing (2012)
27.
Zurück zum Zitat Li, X.F., Kang, Y.L.: Fracture analysis of cracked piezoelectric materials. Int. J. Solids Struct. 41(15), 4137–4161 (2004)CrossRef Li, X.F., Kang, Y.L.: Fracture analysis of cracked piezoelectric materials. Int. J. Solids Struct. 41(15), 4137–4161 (2004)CrossRef
28.
Zurück zum Zitat 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)CrossRef 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)CrossRef
29.
Zurück zum Zitat 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)CrossRef 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)CrossRef
30.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
31.
Zurück zum Zitat 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)CrossRef 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)CrossRef
33.
Zurück zum Zitat Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Elsevier Academic Press, California (2007) Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Elsevier Academic Press, California (2007)
34.
Zurück zum Zitat Bing, Wu., Peng, D., Jones, R.: Two collinear cracks under combined quadratic thermo-electro-elastic loading. Acta Mech. 233, 2439–2452 (2022)MathSciNetCrossRef Bing, Wu., Peng, D., Jones, R.: Two collinear cracks under combined quadratic thermo-electro-elastic loading. Acta Mech. 233, 2439–2452 (2022)MathSciNetCrossRef
35.
Zurück zum Zitat 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 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
36.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
37.
Zurück zum Zitat 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) 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)
38.
Zurück zum Zitat Li, Y.: The Study on Three-Dimensional Multi-Field Coupling Crack Problems Considering Thermal Effect. Zhengzhou University, Zhengzhou (2020) Li, Y.: The Study on Three-Dimensional Multi-Field Coupling Crack Problems Considering Thermal Effect. Zhengzhou University, Zhengzhou (2020)
Metadaten
Titel
Analysis method of collinear cracks subjected to thermo-magneto-electro-elastic loads
verfasst von
B. Wu
D. Peng
R. Jones
Publikationsdatum
07.11.2023
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 1/2024
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-023-02511-3

Weitere Artikel der Ausgabe 1/2024

Archive of Applied Mechanics 1/2024 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.