Eiichiro Tsuchida

On the elastic interaction between two fibers in a continuous fiber composite under thermal loading

Abstract The problem of fiber interaction in unidirectional fiber composites under thermal loading is considered. A pair of fibers is modeled by two inhomogeneities that sustain an eigenstrain loading, proportional to the difference of fiber/matrix thermal expansion coefficients. Utilizing the displacement potential approach, the plane strain problem is solved analytically. The effect of incoherent interfaces is evaluated, in comparison to the case of perfect bonding.

A Spherical Inclusion in an Elastic Half-Space Under Shear

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to its traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclu- sion and the surrounding matrix is either perfectly bonded or is allowed to slip without friction. We obtain an analytical solution to this problem using displacement potentials in the forms of infinite integrals and infinite series. We include numerical examples which give the local elastic fields due to inclusion and traction-free surface. Introduction When an inclusion (inhomogeneity) is present in a matrix and a loading is applied, elastic stress fields are disturbed in the vicinity of the inclusion. These stresses depend on a number of factors which include the shape and location of the inclusion, the .mismatch in the elastic constants of the inclusion and the matrix, the boundary conditions, and the loading. Inclusion problems have been a focus of the micromechanics research for several decades (for a review of literature see, e.g., Mura, 1987). Most of these studies, however, considered the cases when the inclusion is placed in an infinitely extended material and a matrix-inclusion interface is perfectly bonded. In this paper we are interested in the case when the inclusion, with properties distinct from those of the matrix, is embedded near a surface of a half-space and the matrix-inclusion interface is either perfectly bonded or is allowed to slip. In the terminology of Mura (1987) the inclusion denotes a subdomain in the matrix subjected to transformation strains (eigenstrains), while the inhomogeneity is a region with proper- ties distinct from those of the matrix and subjected to a remote stress. In the above two paragraphs and the Abstract we used the term inclusion to denote both cases, for simplicity. In the remaining part of the Introduction we follow the Muras termi- nology for the clarity of presentation. The elasticity problems involving a half-space with a spheri- cal (or spheroidal) inclusion, inhomogeneity or cavity have been studied by several researchers. Among them, Tsuchida and Nakahara (1970, 1972) solved the problem of a semi- infinite elastic body with a spherical cavity subjected to a remote all-around (equal biaxial) tension on the plane boundary or a uniform pressure on the surface of cavity. Tsutsui and Saito ( 1973 ) investigated the problem of a semi-infinite material con- taining a perfectly bonded spherical inhomogeneity under the all-around tension, while Tsuchida and Mura (1983) considered a similar problem involving a spheroidal inhomogeneity. Other

The elastic stress field in a half-space containing a prolate spheroidal inhomogeneity subject to pure shear eigenstrain

Abstract This paper presents an asymmetric elasticity solution for the stresses in a half-space containing a prolate spheroidal inhomogeneity, when it is subjected to a uniform shear eigenstrain. The interface between the inhomogeneity and the surrounding matrix is assumed to be perfect bonding or sliding. Papcovich–Neuber displacement potentials are used in the analysis. Numerical examples are given for some different major semiaxes and shape ratios, and the stress distributions around the inhomogeneity are shown graphically.

The Hemispheroidal Inhomogeneity at the Free Surface of an Elastic Half Space

A series solution is presented. The loading is either all around tension at infinity perpendicular to the axis of symmetry of the inhomogeneity, or uniform, nonshear type eigenstrains sustained by the inhomogeneity

Fracture mechanisms of aluminium cast alloy locally reinforced by SiC particles and Al2O3 whiskers under monotonic and cyclic load

Abstract In the present paper, fracture mechanisms and corresponding stress distributions in aluminium cast alloy locally reinforced by SiC particles and Al2O3 whiskers under monotonic and cyclic load are investigated experimentally and numerically. The material is monotonically and cyclically deformed to failure at room temperature. The fracture origin and the fracture path are investigated on the fracture surfaces. The fracture occurs in the reinforced part under both monotonic and cyclic loads. Scanning electron microscope (SEM) analysis of fracture surface shows that the fatigue fracture is controlled by the fracture of coarse Al2O3 whiskers. The static fracture (monotonic loading) shows that the fracture mechanism is the combination of reinforcing particle fracture and interfacial debonding between reinforcing ceramics and matrix metal. The stress distributions around the boundary between the reinforced part and the unreinforced part are calculated based on an inclusion array model considering the microscopic inhomogeneous effects. Both the experimental results and the finite element simulation show that the critical location for fracture is changed by the external stress level which controls the local stress distribution through plastic constraint between reinforcing particle and matrix alloy.

Spheroidal Sliding Inclusion in an Elastic Half-Space

An analytical elasticity solution for a half-space having a spheroidal sliding inclusion is obtained. The inclusion is subjected to either a uniform plane hydrostatic loading applied at infinity or a uniform transformation strain (eigenstrain). The interface between the inclusion and the surrounding material allows sliding and does not sustain shear tractions. Boussinesq’s displacement potentials in infinite integral form and in infinite series form are used in the analysis. Numerical examples are included.

Asymmetric problem of a semi-infinite body having a hemispherical pit under uniaxial tension

This paper presents an asymmetric solution for the stress distributions around a hemispherical pit at a plane surface of a semi-infinite body under uniaxial tension. In this analysis, eight stress functions were chosen so as to fulfill the boundary conditions automatically, both at the plane surface and at infinity. On the other hand, the remaining boundary conditions at the surface of the pit were satisfied with the aid of the “half-range expansion” technique. Numerical results are given for the variations around the pit and along the z-axis and compared with the corresponding results under biaxial tension.

A Semi-infinite Body Subjected to an Impulsive Torque on a Hemispherical Pit of a Free Surface

By investigating the applications of Saint Venants principle to dynamic problems, the stress wave propagation in a semi-infinite body subjected to an impulsive torque on the surface of a hemispherical pit is analyzed. The effect of the shear force distribution and the force variation in time on the impact stress is studied. The following results are obtained. In the case of a torque applied step-wise, the stress near the wave front is heavily influenced by the distribution of shear force on the surface of a pit. But in some time after the wave front is carried, the stress at a point far from the pit has no relation to the distribution of the shear force. The longer the rise time of the force, the smaller the influence of the distribution of shear force on the impact stress becomes.

The Hemispherical Inhomogeneity Subjected to a Concentrated Force

The presence of two or more different constituents in an elastic material has a substantial effect on its mechanical behavior under thermal or mechanical loading. The overall, as well as the local, properties of such a material may bear little relation to those of the components, even though the components retain their integrity within the composite. Stress fields in composite materials under applied stresses can be simulated by the inclusion problem, when fibers in the composite are replaced by inhomogeneities. A considerable number of problems can be found in the literature involving the determination of the local stress and displacement fields in the vicinity of a single inhomogeneity or impurity, which is embedded in an infinitely extended surrounding material, i.e., the matrix. In the present paper, an analytical solution for the three-dimensional mixed boundary value problem of a hemispherical inhomogeneity is presented. The inhomogeneity is embedded at the surface of an elastic half-space and is subjected to a concentrated force. First, the problem is solved by assuming perfect bonding along the interface between the matrix and the inhomogeneity. Next, the shear-traction-free (sliding) boundary is considered and the two results are compared. For both cases, the elastic field is deduced in a series form, using Boussinesq’s displacement potentials. Several calculations are performed for various combinations of elastic constants. Finally, stresses and displacements along the free surface and the matrixinhomogeneity interface are evaluated for typical situations, in order to assess the significance of inhomogeneities in composite material applications.

On the Elastic Interaction between a Surface Step and an Edge Dislocation

This manuscript addresses the issue of interaction between a surface step and an edge dislocation. It represents the first step in an investigation that will examine dislocation egress in the presence of surface steps. The geometric step introduces an elastic field that is altered by the presence of a dislocation in its vicinity. The complete elastic field is first determined, followed by explicit expressions for the Peach— Koehler force of the interaction. A discussion follows focusing on the possibility that an edge dislocation can be prevented from reaching the surface as a result of the field generated by the surface step. If such an outcome is possible, surface steps may be responsible for a new mechanism of strain hardening. Such a possibility has been recently suggested in the literature.