Analysis of an elliptical crack parallel to graded interfacial zone of bonded bi-materials

This paper analyzes an elliptical crack parallel to the functionally graded interfacial zone between two fully bonded solids. The functionally graded interfacial zone is treated as a nonhomogeneous solid layer with its elastic modulus varying in the thickness direction. A generalized Kelvin solution based boundary element method is employed for the calculation of the stress intensity factors associated with the three-dimensional crack problem. The elliptical crack surface is subject to either uniform normal traction or uniform shear traction. The stress intensity factors are examined by taking into account the effects of the nonhomogeneity parameter and thickness of the functionally graded interfacial zone, as well as the crack distance to the zone. The numerical results are in very good agreement with the existing solutions under degenerated conditions. These stress intensity factor values can be further used to predict the crack growth in the functionally graded materials.

[1]  Robert J. Asaro,et al.  Cracks in functionally graded materials , 1997 .

[2]  Murat Ozturk,et al.  Axsiymmetric crack problem in bonded materials with a graded interfacial region , 1996 .

[3]  Zhong Qi Yue,et al.  Generalized Kelvin solution based boundary element method for crack problems in multilayered solids , 2002 .

[4]  J. Watson,et al.  Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics , 1976 .

[5]  Shaker A. Meguid,et al.  On the dynamic propagation of a finite crack in functionally graded materials , 2002 .

[6]  Nao-Aki Noda,et al.  Application of Finite-Part Integrals to Planar Interfacial Fracture Problems in Three-Dimensional Bimaterials , 1999 .

[7]  L. Tham,et al.  Stress intensity factors for penny-shaped cracks perpendicular to graded interfacial zone of bonded bi-materials , 2005 .

[8]  J. Chapa-Cabrera,et al.  Effects of residual stress and geometry on crack kink angles in graded composites , 2002 .

[9]  L. Tham,et al.  Boundary element analysis of crack problems in functionally graded materials , 2003 .

[10]  Hiroshi Tada,et al.  The stress analysis of cracks handbook , 2000 .

[11]  F. Erdogan,et al.  The crack problem for a nonhomogeneous plane , 1983 .

[12]  F. Erdogan,et al.  The crack problem in bonded nonhomogeneous materials , 1991 .

[13]  Z. Yue.  Elastic field for eccentrically loaded rigid plate on multilayered solids , 1996 .

[14]  F. Fischer,et al.  Inhomogeneity effects on the crack driving force in elastic and elastic–plastic materials , 2003 .

[15]  Zhong Qi Yue,et al.  On generalized Kelvin solutions in a multilayered elastic medium , 1995 .

[16]  M. Laura Luchi,et al.  Boundary elements for three‐dimensional elastic crack analysis , 1987 .

[17]  F. Erdogan,et al.  An Axisymmetric Crack in Bonded Materials With a Nonhomogeneous Interfacial Zone Under Torsion , 1995 .

[18]  F. Erdogan,et al.  The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone , 1991 .

[19]  H. Choi.  The problem for bonded half-planes containing a crack at an arbitrary angle to the graded interfacial zone , 2001 .

[20]  Analysis of an elliptical crack parallel to a bimaterial interface under tension , 2003 .

[21]  Glaucio H. Paulino,et al.  Finite Element Investigation of Quasi-Static Crack Growth in Functionally Graded Materials Using a Novel Cohesive Zone Fracture Model , 2002 .

[22]  Glaucio H. Paulino,et al.  Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method , 2002 .