Journal of Mechanical Science and Technology

, Volume 25, Issue 2, pp 309–315 | Cite as

Numerical investigation of the stress field near a crack normal to ceramic-metal interface

  • Liviu Marsavina
  • Tomasz Sadowski
  • Nicolae Faur


Ceramic-metal interfaces are often present in composite materials. The presence of cracks has a major impact on the reliability of advanced materials, such as fiber or particle reinforced ceramic composites, ceramic interfaces and laminated ceramics. The understanding of the failure mechanisms is very important, as is as the estimation of fracture parameters at the tip of the crack approaching an interface and crack propagation path. A cracked sandwich plate loaded with axial uniform normal stress was numerically investigated using plane strain Finite Element Analysis. The numerical results for the singularity orders were compared with the analytical solution. The influences of the material combination and crack length on the radial and circumferential stresses and displacement distributions were investigated. The Stress Intensity Factors were determined based on numerical results using a displacement extrapolation method. The results for the non-dimensional stress intensity factors show that at lower crack lengths the influence of material mismatch is lower, but this influence increases with increasing crack length.


Ceramic-metal interface Crack Stress field Stress intensity factor 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. R. Zak and M. L. Williams, Crack point stress singularities at a bi-material interface, J. Appl. Mech., 30 (1963) 142–143.Google Scholar
  2. [2]
    T. S. Cook and F. Erdogan, Stress in bonded materials with a crack perpendicular to the interface, Int. J. Eng. Sci., 10 (1972) 677–697.CrossRefzbMATHGoogle Scholar
  3. [3]
    F. Erdogan and V. Biricikoglu, Two bonded half planes with a crack going through the interface, Int. J. Engng. Sci., 11 (1973) 745–766.CrossRefzbMATHGoogle Scholar
  4. [4]
    D. B. Bogy, On the plane elastic problem of a loaded crack terminating a material interface, J. Int. Fract., 38 (1971) 911–918.zbMATHGoogle Scholar
  5. [5]
    W. C. Wang and J. T. Chen, Theoretical and experimental re-examination of a crack at a bi-material interface, J. Strain Anal., 28 (1993) 53–61.CrossRefGoogle Scholar
  6. [6]
    K. Y. Lin and J. W. Mar, Finite element analysis of stress intensity factors for crack at a bi-material interface, Int. J. Fract., 12 (1976) 451–531.Google Scholar
  7. [7]
    J. Ahmad, A micromechanics analysis of cracks in unidirectional fibre composite, J. Appl. Mech., 58 (1991) 964–972.CrossRefGoogle Scholar
  8. [8]
    M. Tan and S. A. Meguid, Dynamic analysis of cracks perpendicular to bi-material interfaces using new singular finite element, Finite Elements in Analysis and Design, 22 (1996) 69–83.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    D. H. Chen, A crack normal to and terminating at a bimaterial interface, Engng. Fract. Mech., 49 (1994) 517–532.CrossRefGoogle Scholar
  10. [10]
    S. H. Chen, T. C. Wang, S. Kao-Walter, A crack perpendicular to the bi-material interface in finite solid, Int. J. Solids Struct., 40 (2003) 2731–2755.CrossRefzbMATHGoogle Scholar
  11. [11]
    M. Y. He and J. W. Hutchinson, Crack deflection at an interface between dissimilar elastic materials, Int. J. Solids Struct., 25 (1993) 1053–1067.Google Scholar
  12. [12]
    J. Chang and J.-Q. Xu, The singular stress field and stress intensity factors of a crack terminating at a bi-material interface, Int. J. Mechanical Sciences, 49 (2007) 888–897.CrossRefGoogle Scholar
  13. [13]
    Y. Y. Lin and J. C. Sung, Singularities of an inclined crack terminating at an anisotropic biomaterial interface, Int. J. Solids Struct., 38 (1997) 3727–3754.CrossRefGoogle Scholar
  14. [14]
    T. C. Wang and P. Stahle, Stress state in front of a crack perpendicular to bi-material interface, Engng. Fract. Mech., 4 (1998) 471–485.Google Scholar
  15. [15]
    L. Liu, G. A. Kardomateas and J. W. Holmes, Mixed — mode stress intensity factors for a crack in an anisotropic bimaterial strip, Int. J. Solids Struct., 41 (2004) 3095–3017.CrossRefzbMATHGoogle Scholar
  16. [16]
    L. Marsavina and T. Sadowski, Crack — Interface Interaction in Composite Materials, In. Security and Reliability of Damaged Structures and Defective Materials, G. Pluvinage and A. Sedmak eds. (2009) 139–155.Google Scholar
  17. [17]
    L. Marsavina, T. Sadowski and N. Faur, Asymptotic stress field for a crack normal to a ceramic — metal interface, Key Engng. Mater., 417–418 (2010) 489–492.Google Scholar
  18. [18]
    J. H. Chang and D. J. Wu, Calculation of mixed mode stress intensity factors for a crack normal to a bi-material interface using contour integrals, Engng. Fract. Mech., 70 (2001) 1675–1695.CrossRefGoogle Scholar
  19. [19]
    J. Dundurs, Effect of elastic constants on stress in a composite under plane deformation, J. Compos. Mater., 1 (1969) 310–322.Google Scholar
  20. [20]
    ABAQUS CAE Manual, ABAQUS, Inc. (2006).Google Scholar
  21. [21]
    K. Yilan and L. Hua, Investigations of near — tip displacement fields of a crack normal to and terminating at a bimaterial interface under mixed-mode loading, Engng. Fract. Mech., 69 (2002) 2199–2208.CrossRefGoogle Scholar
  22. [22]
    Y. Murakami, Stress intensity factors handbook, Vol. I, Pergamon Press, Oxford (1987) 511–512.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Liviu Marsavina
    • 1
  • Tomasz Sadowski
    • 2
  • Nicolae Faur
    • 1
  1. 1.Faculty of Mechanical EngineeringUniversity Politehnica of TimisoaraTimisoaraRomania
  2. 2.Faculty of Civil and Sanitary EngineeringLublin University of TechnologyLublinPoland

Personalised recommendations