Elastostatic interaction of multiple arbitrarily shaped cracks in plane inhomogeneous regions

Abstract A numerical technique has been developed for the determination of stress fields associated with multiple arbitrarily shaped cracks in plane inhomogeneous regions. The procedure allows the elastostatic analysis of cracks interacting with one or more straight bimaterial interfaces; of cracks located near, or emanating from, circular inclusions; and of cracks that emanate from single or multiple origins. The cracks may be branched or blunted, and may be subjected to arbitrarily applied stresses. The technique employs an efficient surface integral method, using distributions of edge dislocations to represent the cracks. The resulting singular integral equations are solved using a Gauss-Chebyshev integration formula; appropriate conditions are developed for closing the set of equations governing cracks intersecting inhomogeneity boundaries, based on a consideration of the stresses and displacements at the points of intersection. Crack-tip stress intensity factor results are presented for several crack configurations. The overall scheme provides a more general, direct, and convenient approach than other available schemes. A computer program has been developed to implement the various formulations in a single framework.

[1]  V. M. Narendran,et al.  Analysis of Growth and Interaction of Multiple Hydraulic Fractures , 1983 .

[2]  Y. Hsu.  The infinite sheet with cracked cylindrical hole under inclined tension or in-plane shear , 1975 .

[3]  N. Ashbaugh.  Stress solution for a crack at an arbitrary angle to an interface , 1975 .

[4]  F. Erdogan,et al.  A half plane and a strip with an arbitrarily located crack , 1975 .

[5]  F. Erdogan,et al.  The inclusion problem with a crack crossing the boundary , 1975 .

[6]  N. Muskhelishvili.  Some basic problems of the mathematical theory of elasticity , 1953 .

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  A. F. GrandtJr..  Stress intensity factors for some through-cracked fastener holes , 1975 .

[9]  F. Erdogan,et al.  On the numerical solution of singular integral equations , 1972 .

[10]  Michael P. Cleary,et al.  Moving singularities in elasto-diffusive solids with applications to fracture propagation , 1978 .

[11]  D. Barr,et al.  Thermoelastic fracture solutions using distributions of singular influence functions—I: Determining crack stress fields from dislocation distributions , 1983 .

[12]  B. Rao.  Infinite elastic plane with a parabolic arc cut , 1964 .

[13]  Paul Segall,et al.  Mechanics of discontinuous faults , 1980 .

[14]  F. Erdogan,et al.  Bonded half planes containing an arbitrarily oriented crack , 1974 .

[15]  Balkrishna S. Annigeri,et al.  Surface integral finite element hybrid (SIFEH) method for fracture mechanics , 1984 .

[16]  G. D. Gupta,et al.  INTERACTION BETWEEN A CIRCULAR INCLUSION AND AN ARBITRARILY ORIENTED CRACK , 1974 .

[17]  G. D. Gupta,et al.  The stress analysis of multi-layered composites with a flaw , 1971 .

[18]  John Dundurs,et al.  Interaction between an edge dislocation and a circular inclusion , 1964 .

[19]  J. Dundurs,et al.  Edge dislocation inside a circular inclusion , 1965 .

[20]  L. Wheeler,et al.  Crack Path Prediction for a Kinked Crack in the Neighborhood of a Circular Inclusion in an Infinite Medium , 1981 .

[21]  J. Rice,et al.  Slightly curved or kinked cracks , 1980 .

[22]  R. D. Bhargava,et al.  Elastic circular inclusion in an infinite plane containing two cracks , 1973 .

[23]  M. P. Cleary.  Primary factors governing hydraulic fractures in heterogeneous stratified porous formations , 1978 .

[24]  Finn Ouchterlony,et al.  Fracture mechanics applied to rock blasting , 1974 .