Moving interfacial crack between two dissimilar soft ferromagnetic materials in uniform magnetic field

  • She-Xu Zhao
  • Kang Yong Lee


This paper presents the dynamic magnetoelastic stress intensity factors of a Yoffe-type moving crack at the interface between two dissimilar soft ferromagnetic elastic half-planes. The solids are subjected to a uniform in-plane magnetic field and the crack is opened by internal normal and shear tractions. The problem is considered within the framework of linear magnetoelasticity. By application of the Fourier integral transform, the mixed boundary problem is reduced to a pair of integral equations of the second kind with Cauchy-type singularities. The singular integral equations are solved by means of a Jacobi polynomial expansion method. For a particular case, closed-form solutions are obtained. It is shown that the magnetoelastic stress intensity factors depend on the moving velocity of the crack, the magnetic field and the magnetoelastic properties of the materials.


Soft ferromagnetic material Moving interfacial crack Dynamic magnetoelastic stress intensity factor 


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  1. Asanyan, D. D., Aslanyan, A. A. and Bagdasaryan, G. E., 1988, “Concentrantions of Elastic Stresses and Induced Magnetic Field Caused by an External Magnetic Field Next to a Crack,”Soviet Journal of Contemporary Engineering and Mechanics, (I.A.N.A. SSR Mekhanika), Vol. 41, pp. 10–19.MathSciNetGoogle Scholar
  2. Bagdasarian, G. Y. and Hasanian, D. J., 2000, “Magnetoelastic Interaction Between a Soft Ferromagnetic Elastic Half-plane with a Crack and a Constant magnetic field,”International Journal of Solids and Structures, Vol. 37, NO. 38, pp. 5371–5383.MATHCrossRefGoogle Scholar
  3. Erdogan, F. and Gupta, G. D., 1971, “Layered Composites with an Interface Flaw,”International Journal of Solids and Structures, Vol. 7, No. 8, pp. 1089–1107.MATHCrossRefGoogle Scholar
  4. Erdogan, F., 1984, “Mixed Boundary Value Problems in Mechanics,” In: Nemat, Nasser S. (Ed.),Mechanics Today, Vol. 4, Pergamon Press. Oxford.Google Scholar
  5. Gradshteyn, I. S. and Ryzhik, I. M., 1980,Table of Integrals, Series, and Products, Academic Press, New York.MATHGoogle Scholar
  6. Karpenko, L. N., 1966, “Approximate Solution of a Singular Integral Equation by Means of Jacobi Polynomials,”Journal of Applied Mathematics and Mechanics, Vol. 30, No. 3, pp. 668–675.MATHCrossRefMathSciNetGoogle Scholar
  7. Liang, W., Shen, Y. P. and Zhao, M., 2000, “Magnetoelastic Formulation of Soft Ferromagnetic Elastic Problems with Collinear Cracks: Energy Density Fracture Criterion,”Theoretical and Applied Fracture Mechanics, Vol. 34, No. 1, pp. 49–60.CrossRefGoogle Scholar
  8. Lin, C. B. and Lin, H. M., 2002, “The Magnetoelastic Problem of Cracks in Bonded Dissimilar Materials,”International Journal of Solids and Structures, Vol. 39, No. 10, pp. 2807–2826.MATHCrossRefGoogle Scholar
  9. Lin, C. B. and Yeh, C. S., 2002, “The Magne-toelastic Problem of a Crack in a Soft Ferromagnetic solid,”International Journal of Solids and Structures, Vol. 39, No. l,pp. 1–17.MATHCrossRefMathSciNetGoogle Scholar
  10. Muskhelishvili, N. I., 1953,Singular Integeal Equations, Noordhoff, Groningen, The Netherlands.Google Scholar
  11. Pao, Y. H. and Yeh, C. S., 1973, “A Linear Theory for Soft Ferromagnetic Elastic Solids,”International Journal of Engineering Science, Vol. 11, No. 4, pp. 415–436.MATHCrossRefGoogle Scholar
  12. Sabir, M. and Maugin, G. A., 1996, “On the Frac-ture of Paramagnets and Soft Ferromagnets,”Inter-national Journal of Non-Linear Mechanics. Vol. 31, No. 4, pp. 425–440.MATHCrossRefGoogle Scholar
  13. Shindo, Y., 1977, “The Linear Magnetoelastic Problem for a Soft Ferromagnetic Elastic Solid with a Finite Crack,”ASME Journal of Applied Mechanics, Vol. 44, pp. 47–51.MATHGoogle Scholar
  14. Shindo, Y., 1982, “The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip,”ASME Journal of Applied Mechanics, Vol. 49, pp. 69–74.MATHGoogle Scholar
  15. Shindo, Y., 1983, “Dynamic Singular Stresses for a Riffith Crack in a Soft Ferromagnetic Elastic Solid Subjected to a Uniform Magnetic Field,”ASME Journal of Applied Mechanics, Vol. 50, pp. 50–56.MATHMathSciNetGoogle Scholar
  16. Shindo, Y., 1984, “Diffraction of Waves and Sin-gular Stresses in a Soft Ferromagnetic Elastic Solid with Two Coplanar Griffith Cracks,”Journal of the Acoustical Society of America, Vol. 75, pp. 50–57.MATHCrossRefGoogle Scholar
  17. Yeh, C. S., 1989, “Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane,”ASME Journal of Applied Mechanics, Vol. 56, pp. 89–95.MATHCrossRefGoogle Scholar
  18. Yoffe, E. H., 1951, “The Moving Griffith Crack,”Philosophical Magazine. Vol. 42, pp. 739–750.MATHMathSciNetGoogle Scholar
  19. Zhao, S. X. and Lee, K. Y., 2004, “Eccentric Crack Problem in Soft Ferromagnetic Elastic Strip Under Uniform Magnetic Field,”Archive of Applied Mechanics. Vol. 73, No. 11–12, pp. 799–811.MATHGoogle Scholar
  20. Zhao, S. X. and Lee, K. Y., 2007, “Interfacial Crack Problem in Layered Soft Ferromagnetic Materials in Uniform Magnetic Field,”Mechanics Research Communications. Vol. 34, pp. 19–30.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2007

Authors and Affiliations

  1. 1.Department of Engineering MechanicsShanghai Jiaotong UniversityShanghaiChina
  2. 2.School of Mechanical EngineeringYonsei UniversitySeoulSouth Korea

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