Internal fracture in an elastomer containing a rigid inclusion

Rubber blocks were prepared with thin glass rods in their centres, firmly bonded to the surrounding rubber. A tensile stress applied to the ends of a block in the direction of the rod axis induced the sudden formation of voids in the rubber near the flat ends of the rod. Approximate values of the local stresses have been calculated by FEM, assuming linear elastic behaviour. Voids were found to form when and where the local dilatant stress, –P (negative hydrostatic pressure), exceeded the magnitude of Young's modulus,E, for the rubber. A precursor void in a highly elastic solid would expand indefinitely under these circumstances, so that fracture seems to be the result of an elastic instability. The applied stress at which voids appear was of the same order asE for short rods, or for a butt joint between a rod and a rubber cylinder of the same diameter, but it became extremely small when the rod was thin compared to the block in which it was embedded, and relatively long. Under these circumstances the local dilatant stress is calculated to be à large multiple of the applied tensile stress.[/p]     

Limiting equilibrium and fracture in an orthotropic body containing a thin rigid inclusion

The limiting equilibrium and type of fracture of an orthotropic body containing a linear rigid inclusion in tension at infinity along the axis of the inclusion is studied under the conditions of plane problem. Localized process zones (of weakened contact) develop along the boundary of the inclusion from its ends to the central part. The analytic solution is obtained with the help of complex potentials by reducing the analyzed problem to the problem of conjugation. The influence of loading and the orthotropy of the matrix on the development of the process zones, the distributions of contact stresses and axial forces in the inclusion, and the character of fracture of the composition are investigated. We determine the ultimate loads of possible separation or rupture of the inclusion and compute these quantities for some special cases. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 69–79, March–April, 2006.     

Local fracture of a composition containing an inclusion with hardening in the prefracture bands

We obtain a closed analytic solution of the problem of development of local fracture in a composition containing a rigid inclusion in the form of a fiber. Under the action of the load, near the ends of the inclusion, we observe the development of plastic zones (prefracture bands). These zones are modeled by the discontinuities of tangential displacements on the matrix-inclusion boundary. In the prefracture bands, the material is elastoplastic with hardening. Outside these bands, the material is elastic. The dimensions of the bands are determined. By analogy with the well-known δ-model in the theory of cracks, we use a deformation criterion to find the ultimate load of exfoliation of the fiber. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 27–32, March-April, 2000.     

Plane deformation of a body with rigid cylindrical inclusion

We study the problem of plane deformation of an infinite elastic body with thin rigid cylindrical inclusion with oval cross section. The body is loaded by biaxial uniform tensile forces at infinity. The solution of the problem is reduced to two singular integral equations with Cauchy kernels for the jumps of normal and tangential stresses on the surface of the inclusion. The solutions of these equations are obtained in the closed analytic form and, used to deduce the formulas for the concentration of stresses near the inclusion, for stresses inside the inclusion, and for the angle of rotation of the inclusion as a rigid body. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Ukrainian State University of Forestry Engineering, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 6, pp. 87–92, November–December, 1996.     

Determination of the critical dimension of macrocracks originating at the continuation of a linear rigid inclusion

Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, Lvov. Translated from Problemy Prochnosti, No. 2, pp. 68–71, February, 1989.     

Local heating of a cylinder with an inclusion

Exact and approximate solutions are presented for the stationary heat-conduction problem for a cylinder with a foreign inclusion for a discontinuous boundary condition of the first kind. Limits of applicability are set for the approximate solutions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 4, pp. 648–654, September, 1987.     

Green’s functions for the periodic four-phase elastic space with an interface crack or a linear rigid inclusion

We construct fundamental solutions of the problem of antiplane deformation of an unbounded composite body with interface cut or a linear rigid inclusion subjected to the action of concentrated forces. The periodic cell of the composite contains four different elements with rectangular cross sections. The problem is studied by the method of homogenization with microlocal parameters. The formulas for the stress intensity factors are obtained in the analytic form and investigated. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 25–32, March–April, 2007.     

Microcracks with prefracture zones in the vicinity of a rigid inclusion

We establish general relationships for the analysis of local stress fields induced by small cracklide defects and inclusions in the vicinity of a macroscopic rigid inclusion, determine the asymptotic solutions of the corresponding singular integral equations, and construct an analog of the δ_k-model for small cracks in the vicinity of a macroscopic inclusion or a crack. We also present formulas for the numerical evaluation of the parameters of the δ_k-model for a microcrack perpendicular to the macroscopic inclusion. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34. No. 1, pp. 47–58, January–February, 1998.     

Elliptical hole enlarged by a rigid elliptical inclusion

Summary This note deals with the infinitesimal plane analysis of the displacement and stress field in an infinite block with an elliptical hole which is deformed by a rigid elliptical inclusion.     

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.     

The effect of a rigid elliptical inclusion on a straight crack

The general problem of a straight crack near a rigid elliptical inclusion is solved. Complex potentials presented in a previous paper (Santare and Keer [6]) for the interaction of an edge dislocation with rigid ellipse are used to formulate the Green's function for this problem. The solution is written as a set of singular integral equations for crack opening displacement which are solved numerically. Stress intensity factors are presented for a variety of crack/inclusion geometries.     

On fracture initiation in a material with an ellipsoidal inclusion

Fracture initiation at the interface of an inclusion in a metallic material both at room and elevated temperatures, using the equivalent inclusion method, is discussed theoretically. It is shown that the critical strain for fracture initiation at the interface of the inclusion is strongly affected by shape, size, orientation and rigidity of the inclusion, and by the presence of external stress. Dynamic recovery by diffusion of atoms has a large effect on the decohesion at the inclusion-matrix interface in the high-temperature range. Fracture initiation of a brittle material strengthened with strong fibres is also discussed.     

Bending of a thin plate containing a rigid inclusion and a crack

The bending of a thin infinite plate with a line crack and an arbitrarily shaped rigid inclusion is analyzed. The superposition principle is used to reduce the original formulation to two subsidiary problems. A distribution of dislocation is assumed along the crack line. The solution is obtained in an integral form by using the Green function of a point dislocation. The stress functions for both subsidiary problems are obtained by employing the rational mapping function technique. The stress intensity factors are obtained in terms of the dislocation density function. Numerical results are demonstrated for the plate containing a square rigid inclusion and a line crack.