Asymptotic stress field at the tip of an inclined crack terminating to an interface

Liviu Marsavina


Department Strength of Materials; Politehnica University of Timisoara; Timisoara; Romania (Romania)
https://orcid.org/0000-0002-5924-0821

Tomasz Sadowski


Department of Solid Mechanics; Faculty of Civil Engineering and Architecture; University of Technology in Lublin (Poland)
http://orcid.org/0000-0001-9212-8340

Abstract

This paper presents the numerical results for the asymptotic stress field and the fracture parameters at the tip of an inclined cracks terminating to a bi-material ceramic interface. The numerical analysis was carried out using FRANC2D/L fracture analysis code. A biaxial specimen was modeled for producing different mixed mode loads and two materials combinations of Al2O3 and ZrO2 were considered. The influence of the material combination and applied mixed mode load on the singularity orders, stress distributions and stress intensity factors is highlighted.


Keywords:

crack, bi-material interface, asymptotic stress field, stress intensity factor

Kaya C., Butler E.G., Lewis M.H., Co-extrusion of Al2O3/ZrO2 bi-phase high temperature ceramics with fine scale aligned microstructures, Journal of the European Ceramic Society 23, (2003), pp. 935-942.
  Google Scholar

Tilbrook M. T., Rozenburg K., Steffler E. D., Rutgers L, Hoffman M., Crack propagation paths in layered, graded composites, Composites: Part B 37, (2006), pp. 490-498.
  Google Scholar

Zak A.R., Williams M.L., Crack point stress singularities at a bi-material interface, J. Appl. Mech, Volume: 30, (1963), pp. 142-143.
  Google Scholar

Cook T.S., Erdogan F., Stress in bonded materials with a crack perpendicular to the interface, Int. J. Eng. Sci., Volume: 10, (1972), pp. 677-697.
  Google Scholar

Erdogan F., Biricikoglu V., Two bonded half planes with a crack going through the interface, Int. J. Engng. Sci., Volume: 11, (1973), pp. 745-766.
  Google Scholar

Bogy D.B., On the plane elastic problem of a loaded crack terminating a material interface, J. Int. Fract., Volume: 38, (1971), pp. 911-918.
  Google Scholar

Wang W.C., Chen J.T., Theoretical and experimental re-examination of a crack at a biomaterial interface, J. Strain Anal., Volume: 28, (1993), pp. 53-61.
  Google Scholar

Lin K.Y., Mar J.W., Finite element analysis of stress intensity factors for crack at a biomaterial interface, Int. J. Fract., Volume: 12, (1976), pp. 451-531.
  Google Scholar

Ahmad J., A micromechanics analysis of cracks in unidirectional fibre composite, J. Appl. Mech., Volume: 58, (1991), pp. 964-972.
  Google Scholar

Tan M., Meguid S.A., Dynamic analysis of cracks perpendicular to bimaterial interfaces using new singular finite element, Finite Elements in Analysis and Design, 22, (1996), pp. 69-83.
  Google Scholar

Chen D.H., A crack normal to and terminating at a bimaterial interface, Engng. Fract. Mech., Volume: 19, (1994), pp. 517-532.
  Google Scholar

Chen S.H., Wang T.C., Kao – Walter S., A crack perpendicular to the bi-material interface in finite solid, Int. J. Solids Struct, 40, (2003), pp. 2731-2755.
  Google Scholar

He M.Y., Hutchinson J.W., Crack deflection at an interface between dissimilar elastic materials, Int. J. Solids Struct., Volume: 25, (1993), pp. 1053-1067.
  Google Scholar

Chang J., Xu J.-Q., The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface, Int. J. Mechanical Sciences, 49, (2007), pp. 888-897.
  Google Scholar

Lin Y.Y., Sung J.C., Singularities of an inclined crack terminating at an anisotropic biomaterial interface, Int. J. Solids Struct, 38, (1997), pp. 3727-3754.
  Google Scholar

Wang T.C., Stahle P., Stress state in front of a crack perpendicular to bi-material interface, Engng. Fract. Mech., Volume: 4, (1998), pp. 471-485.
  Google Scholar

Liu L., Kardomateas G. A., Holmes J. W., Mixed – mode stress intensity factors for a crack in an anisotropic bi-material strip, Int. J. Solids Struct., 41, (2004), pp. 3095-3017.
  Google Scholar

Kaddouri K., Belhouari M., Bachir Bouiadjra B., Serier B., Finite element analysis of crack perpendicular to bi-material interface: Case of couple ceramic-metal, Comput. Mater. Sci., 35, (2006), pp. 53-60.
  Google Scholar

Madani K., Belhouari M., Bachir Bouiadjra B., Serier B., Benguediab M., Crack deflection at an interface of alumina/metal joint: A numerical analysis, Comput. Mater. Sci., 35, (2007), pp. 625-630.
  Google Scholar

Marsavina L., Sadowski T., Fracture parameters at bi-material ceramic interfaces under bi-axial state of stress, Proceedings of IWCMM 17, Paris, 2007, p. 45-46.
  Google Scholar

He M.Y., Hsueh C.H., Becher P.F., Deflection versus penetration of a wedge-load crack: effects of branch-crack length and penetrated-layer width, Composites: Part B, 31, (2000), pp.299-308.
  Google Scholar

Marsavina L., Sadowski T., Effect of biaxial load on crack deflection/penetration at bi-material ceramic interface, Int. J. Fracture (2008), OnLine First, DOI: 10.1007/s10704-008-9181-y.
DOI: https://doi.org/10.1007/s10704-008-9181-y   Google Scholar

Dundurs J., Effect of elastic constants on stress in a composite under plane deformation, J. Compos. Mater., Volume: 1, (1969), pp. 310-322.
  Google Scholar

Zang Z., Suo Z., Split singularities and the competition between crack penetration and debond at a bimaterial interface, Int. J. Solids Struct., 44, (2007), p. 4559-4573.
  Google Scholar

Bold P. E, Brown M. W., Allen R.J., Shear Mode crack growth and rolling contact fatigue, Wear, 144, (1991), pp. 307-317.
  Google Scholar

Iesulauro, E., FRANC2D/L a Crack Propagation simulator for plane layered materials, Cornell University, Ithaca, 2002.
  Google Scholar

Marsavina L., Sadowski T., The influence of the interface on fracture parameters, Proceedings of the AIQ – ICF Conference, Alger 2008 (in press).
DOI: https://doi.org/10.1007/978-90-481-2669-9_26   Google Scholar

Murakami Y., Stress intensity factors handbook, Vol. I, Pergamon Press, Oxford, 1987.
  Google Scholar

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Published
2008-06-11

Cited by

Marsavina, L. . and Sadowski, T. . (2008) “Asymptotic stress field at the tip of an inclined crack terminating to an interface”, Budownictwo i Architektura, 2(1), pp. 111–124. doi: 10.35784/bud-arch.2316.

Authors

Liviu Marsavina 

Department Strength of Materials; Politehnica University of Timisoara; Timisoara; Romania Romania
https://orcid.org/0000-0002-5924-0821

Authors

Tomasz Sadowski 

Department of Solid Mechanics; Faculty of Civil Engineering and Architecture; University of Technology in Lublin Poland
http://orcid.org/0000-0001-9212-8340

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