Rigid Circular Inclusion Research Articles

Analysis of Indentation Crack as a Wedge‐Loaded Half‐Penny Crack

Surface cracks produced by indentation with a Vickers indenter were modeled as half‐penny cracks extended by symmetric disk‐shaped wedges. The wedge diameter was assumed to be equal to the hemispherical plastic zone size, and the wedge thickness was calculated by equating the wedge volume to the hardness‐impression volume. The resulting equilibrium relation between the indentation load and the radius of the half‐penny crack is in good quantitative agreement with similar relations obtained from fracture toughness calibration.

A problem of unsymmetrical bending of shear-deformable circular ring plates

The classical solution of the problem of a circular ring plate which is clamped along its outer edge and loaded along its inner edge by the rotation about a diameter of a rigid circular inclusion is generalized so as to account for the effect of transverse shear deformability. Numerical results for overall stiffness, for bending and twisting moments and for transverse shear stress resultants are obtained for several values of the ratio of outer radius r0to inner radius rias a function of a transverse shear deformability parameter λ which for a transversely homogenous plate of thickness h is of the form \(\lambda = \sqrt {20(1 + v)E/G} (r_{{\text{ }}0} - r_{{\text{ }}i} )/h\)

Finite Strain Contact Problem of Cylinder Embedded in Body

The problem studied in this work is that of a uniform, uniaxial tensile load applied to an infinite body with a smooth, circular rigid inclusion. The body surrounding the rigid shaft is a linear elasto‐plastic, work‐hardening material. The aluminum alloy, 2024 T4, is used to characterize the material parameters of the infinite body. The problem of analysis of displacements, stresses, and strains in elements made of this body subject to arbitrarily large deformations under the conditions of plane strain is formulated in terms of the finite element method. The constant strain triangular element is used. The method of solution to this problem may be applied to any other cylindrical shape of the rigid inclusion in the infinite body.

On the expansion of a penny-shaped crack by a rigid circular disc inclusion

This paper examines the problem of the symmetric indentation of a penny-shaped crack by a smoothly embedded rigid circular thin disc inclusion. The analysis of the problem yields a system of triple integral equations which are solved in an approximate manner. An expression for the stress intensity factor at the boundary of the penny-shaped crack is evaluated in the form of a series which involves the ratio of the radius of the rigid circular inclusion to the radius of the penny-shaped crack.

Indentation of Smooth Elastic Interface by Disk Inclusion

This paper examines the problem related to the unilateral interaction between two smoothly precompressed isotropic elastic halfspaces which is caused by the wedging action of a rigid circular inclusion of finite thickness located at the interface. The unilateral nature of the contact leads to the development of a zone of separation between the halfspace regions. This paper discusses a mathematical treatment of the problem and develops an approximate estimate for the radius of the zone of separation. Numerical results presented in the paper illustrate the manner in which the extent of the zone of separation is influenced by the precompression stress and the geometry of the embedded disk inclusion.

A CONCAVE INTERACTION CURVE CORRESPONDING TO DECOHESIVE CARRYING CAPACITY UNDER THERMAL LOADINGS

Abstract The problem of the non-existence of the solution for the limit of carrying capacity for a perfectly elastic-plastic sheet with a rigid circular inclusion, under combined thermal and surface loadings is discussed. The limitation of the continuous solution is caused by the formation of some inadmissible discontinuities. Corresponding loadings are called the decohesive carrying capacity. The problem is solved within the framework of a small-strain theory, as well as a finite-strain theory. In both cases the interaction curves of decohesive carrying capacity exhibit the property of concavity.

Elastic-plastic state of thin-walled structures with stress concentrators in the cases of small and large strains

1. It is best to use pneumatic gauges (to measure strain, curvature, etc.) to study the stress-strain state of cylindrical shells in the case of large or small strains, especially in the region of stress concentrators. 2. A comparison made of theoretical and experimental results for shells with a rigid circular inclusion showed that these results agree satisfactorily. For shells with holes with reinforced contours, it is necessary to consider specific features of the reinforcing elements (covers, flanges, etc.) and their deformation beyond the elastic limit.

Effects of a Rigid Circular Inclusion on States of Twisting and Shearing in Shallow Spherical Shells

Effects of a Rigid Circular Inclusion on States of Twisting and Shearing in Shallow Spherical Shells

Physical Aspects of Fruit Growth

The skin around a lenticel on a soft fruit has been modelled as a thin elastic plate with a rigid circular inclusion and applied tensile loads at the edges. A solution for the stress distribution in the skin has then been found using the linear theory of elasticity. From that solution the severity of the stress concentration and the location and form of initial cuticular failure have been deduced, the latter two being in broad agreement with observed crack initiation in the cuticle of grapes.

The axisymmetric displacement and rotation of an elastically embedded disc inhomogeneity due to the action of external loads

This paper considers the axisymmetric interaction between a rigid circular disc inclusion embedded in bonded contact with an isotropic elastic medium of infinite extent and a concentrated force and a moment which are located at a finite distance from the inclusion. Explicit results are obtained for the displacement and rotation of the disc inclusion.

Erratum: “On the Influence of a Rigid Circular Inclusion on the Twisting and Shearing of a Shallow Spherical Shell” (Journal of Applied Mechanics, 1980, 47, pp. 586–588)

Erratum: “On the Influence of a Rigid Circular Inclusion on the Twisting and Shearing of a Shallow Spherical Shell” (Journal of Applied Mechanics, 1980, 47, pp. 586–588)

Analysis of the stress concentration on circular rigid inclusion in a non-linear viscous material

The stress concentration factor of a circular rigid inclusion buried in a non-linear viscous material described by a power law is obtained for various rate hardening exponents. The medium, under a generalized plane condition, is subjected to a bi-axial tension with identical boundary stresses in the horizontal and vertical axes. The stress concentration factor of a circular hole in a non-linear viscous material under a plane strain condition is compared to the stress concentration under generalized plane strain conditions for various rate hardening exponents. The medium is considered to be subjected to the same boundary stress condition as the circular rigid inclusion. The effect of the interaction between the two inclusions on the stress concentration is discussed in terms of the volumetric fraction of the inclusion.

Rotary oscillations of a rigid disc inclusion embedded in an isotropic elastic infinite space

This paper examines the asymmetric problem related to the harmonic oscillations of a rigid circular disc inclusion embedded in bonded contact with an isotropic elastic medium of infinite extent. The analysis of the problem is reduced to the solution of a single Fredholm integral equation of the second kind which is solved in an appropriate manner. The dynamic rotary stiffnesses are developed for a range of mass ratios and frequencies of practical interest.

Two arc cracks around a circular rigid inclusion

The problem of two symmetric arc cracks lying between a rigid circular inclusion embedded in an infinite matrix under biaxial loading at infinity is considered. By using the complex variable tecnique, the boundary value problem is solved and stress and displacement components are calculated along the inclusion boundary. Moreover, investigating the local stress field, a stress criterion, already proposed by authors, allowing either the crack extension at the interface or its deviation into the matrix to be taken into account, is applied to study the fracture response of the elastic system. The critical applied loads as well as the angle of the incipient crack extension are expressed in terms of the central angle subtended by the crack arcs.

On the Influence of a Rigid Circular Inclusion on the Twisting and Shearing of a Shallow Spherical Shell

Known results for plates with rigid inclusions are complemented by explicit asymptotic solutions of the corresponding problems for sufficiently thin spherical shells. An important element of the analysis is recognition of the fact that in addition to the distinction between interior and edge zone solution contributions there is a significant distinction between near-field and far-field behavior of the interior solution, with the nature of this distinction depending on the nature of the boundary conditions which are prescribed. In the event that near-field behavior is of the membrane type and far-field behavior of the inextensional bending type, or vice versa, much higher stress concentrations occur than without such change in interior solution behavior.

Elastic-plastic state of shells of revolution with a rigid circular inclusion

Elastic-plastic state of shells of revolution with a rigid circular inclusion

Asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic elastic medium of infinite extent

Asymmetric problems related to a penny-shaped rigid inclusion embedded in bonded contact with a transversely isotropic elastic medium are investigated. The asymmetric displacements of the rigid circular inclusion correspond to a rotation about a diametral axis and an in-plane lateral translation. These problems are formulated in terms of Hankel integral transforms and reduced to systems of dual integral equations. The rotational and translational stiffnesses for the embedded rigid circular disc inclusion are obtained in exact closed forms.

Edge reinforced circular elastic inclusions in cylindrical shells

The effect of having an edge reinforcement around a circular elastic inclusion in a cylindrical shell is studied. The influence of various parameters of the reinforcement such as area of cross section and moment of inertia on the stress concentrations around the inclusion is investigated. It is found that for certain inclusion parameters it is possible to get an optimum reinforcement, which gives minimum stress concentration around the inclusion. The effect of moment of inertia of the reinforcement of SCF is found to be negligible. The results are plotted in a non-dimensional form and a comparison with flat plate results is made which show the curvature effect. In the limiting case of a rigid reinforcement the results tend to those of a rigid circular inclusion. Results are also presented for different values of μ e the ratio of extensional rigidity of shell to that of the inclusion.

Pressurized Cylindrical Shell With a Rigid Circular Inclusion

The effect of a rigid circular inclusion on stresses in a cylindrical shell subjected to internal pressure has been studied. The two linear shallow shell equations governing the behavior of a cylindrical shell are converted into a single differential equation involving a curvature parameter and a potential function in nondimensionalized form. The solution in terms of Hankel functions is used to find membrane and bending stressses. Boundary conditions at the inclusion shell junction are expressed in a simple form involving the in-plane strains and change of curvature. Good agreement has been obtained for the limiting case of a flat plate. The shell results are plotted in nondimensional form for ready use.

Radial deformation of a plane sheet containing a circular hole or inclusion

Seth's generalized measure of strain is used in the determination of the deformation field produced by radial forces acting on a thin plane sheet of incompressible isotropic elastic material, containing a circular hole or circular rigid inclusion, at its outer edge. Results calculated are comparable with the experimental results obtained by Rivlin and Thomas, employing a vulcanized natural rubber.