Computation of Energy Release Rates for Kinking Cracks based on Virtual Crack Closure Technique

A numerical method based on the virtual crack closure technique (VCCT) (Rybicki and Kanni- nen (1977)) and in conjunction with the finite element (FE) method is presented to compute strain energy re- leaserates forcracks that kink. Themethod partitionsthe strain energy release rate and provides an efficient means to compute values of the mode I (GI) and mode II (GII ) energy release rate at the tip of a kinking crack. The solution procedure is shown to be computationally effi- cient and operationally simple, involving only the nodal forces and displacements near the crack tip. Example problems with kinking cracks in a homogeneous mate- rial, and a layered two constituent material are presented to illustratethe current approach. keyword: kinking crack, virtual crack closure tech- nique, energy release rate

[1]  I. Raju.  Calculation of strain-energy release rates with higher order and singular finite elements , 1987 .

[2]  Sia Nemat-Nasser,et al.  Energy release rate and crack kinking , 1981 .

[3]  M. Kanninen,et al.  A finite element calculation of stress intensity factors by a modified crack closure integral , 1977 .

[4]  J. Dundurs,et al.  Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading , 1969 .

[5]  Ronald Krueger,et al.  The Virtual Crack Closure Technique : History , Approach and Applications , 2002 .

[6]  K. Shivakumar,et al.  An equivalent domain integral method for three-dimensional mixed-mode fracture problems , 1992 .

[7]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[8]  S. Atluri,et al.  Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics , 1983 .

[9]  T. NISHIOKAt.  ON THE COMPUTATION OF MIXED-MODE K-FACTORS FOR A DYNAMICALLY PROPAGATING CRACK , USING PATH-INDEPENDENT INTEGRALS , 2002 .

[10]  W. G. Knauss,et al.  II – On the Problem of Crack Extension in Brittle Solids Under General Loading , 1978 .

[11]  Satya N. Atluri,et al.  New concepts in meshless methods , 2000 .

[12]  H. Ishikawa,et al.  A finite element analysis of stress intensity factors for combined tensile and shear loading by only a virtual crack extension , 1980 .

[13]  G. R. Irwin,et al.  ONSET OF FAST CRACK PROPAGATION IN HIGH STRENGTH STEEL AND ALUMINUM ALLOYS , 1956 .

[14]  Satya N. Atluri,et al.  On the computation of mixed-mode K-factors for a dynamically propagating crack, using path-independent integrals J'k , 1984 .

[15]  S. Atluri,et al.  The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods , 2002 .

[16]  Robert O. Ritchie,et al.  Finite crack kinking and T-stresses in functionally graded materials , 2001 .

[17]  Anthony G. Evans,et al.  Kinking of a Crack out of an Interface: Role of In‐Plane Stress , 1991 .

[18]  K. N. Shivakumar,et al.  A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies , 1988, International Journal of Fracture.

[19]  S. Nemat-Nasser,et al.  Energy-release rate and crack kinking in anisotropic brittle solids , 1996 .

[20]  G. T. Sha,et al.  Weight function calculations for mixedmode fracture problems with the virtual crack extension technique , 1985 .

[21]  David A. Dillard,et al.  Numerical analysis of directionally unstable crack propagation in adhesively bonded joints , 2001 .