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Summary.The evaluation of the stress intensity factors at the tips of a crack in a homogeneous isotropic and elastic medium may be achieved with higher accuracy and much less computation if the Lobatto-Chebyshev method of numerical solution of the corresponding system of singular integral equations is used instead of the method of Gauss-Chebyshev commonly applied to such problems. Comparison of results obtained by the two numerical methods when applied to the problem of a cruciform crack in an infinite medium proves the potentialities of the new approach.

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The singular stress field at the vicinity of the apex of an elastic plane indenter of various angles compressing an elastic half plane was studied by using a complex variable technique. Three particular cases where the indenter is perfectly bonded, slips or adheres according to the Coulomb’s law of friction, to the half plane were considered. The characteristic equations for the determination of the order of the stress singularity at the vicinity of the apex of the indenter for the above three cases were defined in terms of the angle of the indenter and the two composite material parameters α and β first introduced by Dundurs, depicting the mechanical properties of the two materials. The order of singularity at the vertex of the indenter was determined for all material combinations of the indenter and the half plane. Valuable and interesting results were derived.

SynopsisThe adhesion between matrix and inclusions (fibers or particulates) in a composite material is one of principal factors characterizing the mechanical and physical behavior of the modern composite materials. All theoretical models describing these substances neglect to consider the influence of the boundary layer developed between phases during the preparation of the composite. In this paper, two versions of a theoretical model were introduced for the evaluation of this mesophase layer. It had been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of the mesophase unfold from those of the hard-core fibers to those of the softer matrix. Thus, a multicylinder model was assumed, improving the classical two-cylinder model introduced by Hashin and Rosen for the representative volume element of the composite. Based on thermodynamic phenomena appearing at the glass transition temperatures of the composite and concerning the positions and the sizes of the heat-capacity jumps there, as well as on the experimental values of the longitudinal elastic modulus of the composite, the extent of the mesophase and the mechanical properties of the composite may be accurately evaluated. These versions of model are based on a previous one concerning a multilayer model, but they are considerably improved, in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber-reinforced composites.