Elastic Green's function for a composite solid with a planar interface
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The elastic plane-strain Green's function is calculated for a general anisotropic composite solid with a plane interface and a line load parallel to the composite interface. The interface may be between two different solids or between different orientations of the same solid such as a grain boundary. The equations of elastic equilibrium are solved by the Fourier transform method. Analytical expressions are obtained for the Green's function in real as well as Fourier space. These expressions should be useful for calculations of elastic properties of a composite solid containing defects. Two sum rules are also derived for matrices which constitute the Green's function and the stress tensor. These sum rules can serve as numerical checks in detailed computer simulation calculations.
I. INTRODUCTION Many elastic properties of a solid with defects can be calculated from the elastic Green's function of the solid and/or its derivatives and integrals. The main advantage of using the Green's function is that it gives the displacement field and the stress distribution in a solid subject to any arbitrary loading which satisfies all the required compatibility and boundary conditions. The Green's function for a solid can be obtained by solving the equations of elastic equilibrium for a unit force at a point or a line subject to appropriate boundary conditions (for mathematical aspects of Green's functions, see Ref. 1). There is growing interest in the calculation of the elastic fields of cracks and dislocations near interfaces. These are important in establishing a basis for the treatment of a number of cracking problems for composites, including near interface crack propagation, crack blunting, and dislocation emission, as well as those for near interface dislocations, including pileups. All of these can be solved by means of Green's function techniques. The anisotropic elastic Green's function for infinite, uniform (or homogeneous) solids containing point or line defects has been extensively studied.2"6 The Green's function for a solid containing a crack has been calculated by Sinclair and Hirth.7 The elastic fields of line defects residing in the interface of a composite have been recently presented.8 However, the Green's function for the bulk phases in a composite solid containing an interface has not been reported in the literature.
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)
J. Mater. Res., Vol. 4, No. 1, Jan/Feb 1989
In this paper we have calculated the anisotropic elastic Green's function for a line force in a composite solid containing a planar interface. The interface may be between two phases or orientations of the same material such as a phase or a grain boundary or two different materials such as in a fiber composite. The Green's function can be used to calculate various elastic properties of the so
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