On the calculation of derivatives of stress intensity factors for multiple cracks

Abstract In this paper, the work of Lin and Abel [Lin SC, Abel JF. Variational approach for a new direct-integration form of the virtual crack extension method. Int J Fract 1988;38:217–35] is further extended to the general case of multiple crack systems under mixed-mode loading. Analytical expressions are presented for stress intensity factors and their derivatives for a multiply cracked body using the mode decomposition technique. The salient feature of this method is that the stress intensity factors and their derivatives for the multiple crack system are computed in a single analysis. It is shown through two-dimensional numerical examples that the proposed method gives very accurate results for the stress intensity factors and their derivatives. It is also shown that the variation of mode I and II displacements at one crack-tip influence the mode I and II stress intensity factors at any other crack. The computed errors were about 0.4–3% for stress intensity factors, and 2–4% for their first order derivatives for the mesh density used in the examples.

[1]  Leon M Keer,et al.  Unstable growth of thermally induced interacting cracks in brittle solids , 1978 .

[2]  Anthony R. Ingraffea,et al.  Shape prediction and stability analysis of Mode-I planar cracks , 2004 .

[3]  Sharif Rahman,et al.  Probabilistic fracture mechanics by Galerkin meshless methods – part II: reliability analysis , 2002 .

[4]  Surendra P. Shah,et al.  Mode I fracture in concrete using center-cracked plate specimens , 1989 .

[5]  Wieslaw K. Binienda,et al.  Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part I: Theoretical Analysis , 1999 .

[6]  Wieslaw K. Binienda,et al.  Analysis of the Driving Forces for Multiple Cracks in an Infinite Nonhomogeneous Plate, Part II: Numerical Solutions , 1999 .

[7]  Leon M Keer,et al.  A new combined analytical and finite-element solution method for stability analysis of the growth of interacting tension cracks in brittle solids , 1980 .

[8]  Leon M Keer,et al.  Stress-intensity factors for a semi-infinite plane crack with a wavy front , 1984 .

[9]  A. R. Luxmoore,et al.  Proceedings of the third international conference on numerical methods in fracture mechanics , 1984 .

[10]  Z. Bažant.  FRACTURE MECHANICS OF CONCRETE STRUCTURES , 1992 .

[11]  James R. Rice,et al.  First-Order Variation in Elastic Fields Due to Variation in Location of a Planar Crack Front , 1985 .

[12]  S. K. Maiti.  Finite element computation of the strain energy release rate for kinking of a crack , 1990 .

[13]  S. Rahman,et al.  Probabilistic fracture mechanics by Galerkin meshless methods – part I: rates of stress intensity factors , 2002 .

[14]  Zdeněk P. Bazant,et al.  Bifurcation and stability of structures with interacting propagating cracks , 1992, International Journal of Fracture.

[15]  Alain Combescure,et al.  Double virtual crack extension method for crack growth stability assessment , 1992 .

[16]  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 .

[17]  P. C. Paris,et al.  Stress Analysis of Cracks , 1965 .

[18]  Young Ho Park,et al.  Shape sensitivity analysis in mixed-mode fracture mechanics , 2001 .

[19]  John F. Abel,et al.  Variational approach for a new direct-integration form of the virtual crack extension method , 1988, International Journal of Fracture.

[20]  Paul A. Wawrzynek,et al.  Interactive finite element analysis of fracture processes: An integrated approach , 1987 .

[21]  John R. Rice,et al.  A first-order perturbation analysis of crack trapping by arrays of obstacles , 1989 .

[22]  Claude Stolz,et al.  Energy methods in fracture mechanics: stability, bifurcation and second variations , 1990 .

[23]  Z. Bažant,et al.  Stability and post-critical growth of a system of cooling or shrinkage cracks , 1979 .

[24]  Leon M Keer,et al.  Approximate Description of Crack Kinking and Curving , 1981 .

[25]  Paul A. Wawrzynek,et al.  On the virtual crack extension method for calculation of the rates of energy release rate , 1998 .

[26]  Abubakr A. Bazant,et al.  Instability and Spacing of Cooling or Shrinkage Cracks , 1979 .

[27]  Paul A. Wawrzynek,et al.  On the virtual crack extension method for calculating the derivatives of energy release rates for a 3D planar crack of arbitrary shape under mode-I loading , 2001 .