Elastic Green's function for a composite solid with a planar crack in the interface
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The elastic Green's functions for displacements and stresses have been calculated for a composite solid containing a planar crack in a planar interface using the Green's function derived in a previous paper for a line load parallel to the composite interface. The resulting functions can be used to calculate the stress or displacement at any point in the composite for a variety of elastic singularities. As specific applications, the Mode I stress intensity factor of an interfacial crack was calculated as were the Green's functions for the semi-infinite antiplane strain case. The Mode I case shows the near-crack tip oscillations reported by other authors while the Mode III case does not. The newly devised Green's functions are shown to reproduce the results of other authors in the isotropic limit.
I. INTRODUCTION The interfacial fracture strength of polycrystalline and multiphase solids and also of macroscopic composite materials may be controlled by the properties of cracks embedded in the interfaces in the materials. The mode of fracture, viz., intergranular vs transgranular, is presumably related to the relative fracture toughness of the matrix and the interfaces. The elastic properties of a homogeneous, continuous solid are contained in the elastic Green's function for that continuum. These functions are valuable for solving a variety of elastic boundary value problems that meet the physical compatibility and equilibrium conditions.1'3 For a cracked composite body, similar problems can be solved by means of corresponding Green's functions. It is of interest, therefore, to calculate the Green's function of a composite solid containing a crack in the interface: the object of this paper. A considerable amount of work has already been done on elastic fields of line defects in a cracked body (see, for example, Ref. 4 and other references given therein). The mathematical treatment is generally based upon the formalism developed by Stroh.5 An alternative treatment based upon an integral representation of Stroh's theory was developed by Barnett6 and Barnett and Lothe.7 Excellent reviews of the general theory have been given by Rice8 and Thomson.9 These reviews contain many other references to work on fracture. Interfacial cracks subject to uniform loading of crack surfaces in isotropic solids have been studied by several authors, including England10 and Rice and Sih." The case
Current address: National Institute of Standards and Technology, Fracture and Deformation Division, Boulder, Colorado 80303. b) Current address: Washington State University, Department of Mechanical and Materials Engineering, Pullman, Washington 99164-2920. a)
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J. Mater. Res., Vol. 4, No. 1, Jan/Feb 1989
of anisotropic solids subject to loading of crack surfaces has been discussed by Willis12 and Clements.13 For many practical applications, such as the interaction of dislocations and other defects with cracks, one must calculate the displacement field and the stress distribution in a solid subject to arbitrary loading. The Green's functions
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