H.T. Danyluk

Ductile penny-shaped crack in a transversely isotropic cylinder

The problem of a penny-shaped crack contained in a transversely isotropic cylinder of elastic perfectly-plastic material is considered for the case when the crack is extended by an axial load. The problem is reduced to solving numerically a Fredholm integral equation of the second kind for the width of the plastic zone. Graphical results are presented showing the effect of transverse isotropy upon the width of the plastic zone and these are compared with the results for isotropic materials.

A dugdale-type estimation of the plastic zone for a penny-shaped crack in a thick transversely isotropic layer due to radial shear

A penny-shaped crack is considered under the action of radial shear in a thick transversely isotropic elastic layer. The external faces of the layer are stress free. Employing the Dugdale hypothesis and Hankel transform theory, the problem of determining the size of the plastic zone is reduced to the numerical solution of a Fredholm integral equation of the second kind. Graphical results showing the effect of transverse isotropy upon the width of the plastic zone are presented and compared with results obtained for isotropic material.

Thermal stresses in a transversely isotropic elastic solid weakened by an external circular crack

Abstract This paper examines the problem of the steady state thermoelastic behaviour of an external circular crack located in a transversely isotropic elastic medium. The surfaces of the crack are subjected to a symmetric temperature distribution. The mathematical analysis of the problem is approached via a Hankel transform development of the governing equations. Numerical results presented in the paper illustrate the manner in which the thermoelastic stress intensity factors are governed by the elastic and thermal properties of the transversely isotropic elastic solid.

A note on plastic deformation at the tip of an edge crack

SummaryAn integral transform solution is given for the problem of an edgecrack forming at the free boundary of a half-plane. The plastic zone is taken in precisely the form as it appears experimentally in such materials as low-C steels. The method used is a further extension of the work of Sneddon and Das [1]. Using Dugdales hypothesis, the length of plastic zone is obtained. When the plastic zone tends of zero length, the solution of the stretching of an elastic half-plane with an edge crack is obtained.

The Reissner-Sagoci problem for a non-homogeneous half-space with a penny-shaped crack

The present paper examines the elastostatic problem related to the axisymmetric rotation of a rigid circular disc bonded to a non-homogeneous half-space containing a penny-shaped crack. The shear modulus of the half-space is assumed to vary with depth according to the relation μ(z) = μ1(z + c)α, c > 0 and μ1, α are constants. Using Hankel transforms, the solution of the problem is reduced to integral equations and finally to simultaneous Fredholm integral equations of the second kind. By solving numerically the simultaneous Fredholm integral equations, results are obtained which are used to estimate the stress intensity factor at the crack tip and the torque required to rotate the disc through an angle ω0.

A note on the torsion of a non-homogeneous solid by an annular disc

Abstract The present paper examines the elasto-static problem concerning the axisymmetric rotation of a rigid annular circular punch perfectly bonded to the surface of a non-homogeneous isotropic, elastic half-space possessing a shear modulus, μ ( z ), varying with depth according to the relation μ ( z ) = μ 1 ( c + z ) α ,where c , μ 1 and α are constants.

Problem of an infinite solid containing a flat annular crack under torsion

Abstract An analytic method is developed to find the axisymmetric stress distribution in an infinite elastic solid containing a flat annular crack under axial torsion. By use of Hankel transforms, the solution to the problem is reduced to triple-integral equations involving Bessel functions of order 1. Modifying the method discussed by Cooke[Quart. J. Mech. Appl. Math. 16, 193–203 (1963).], the solution of the triple-integral equations is reduced to a pair of Fredholm integral equations of the second kind. Finally, the approximate expressions for the stress intensity factors are obtained by finding the iterative solution of the pair of Fredholm integral equations.

Plastic zone correction in a stretched cylinder with an external circumferential crack

Abstract The Dugdale hypothesis is adapted to the problem of an external circumferential crack in a stretched cylinder. The lateral surface of the cylinder is stress free and restrained from radial displacements. An external circumferential edge crack in the cylinder which is considered elastic-perfectly plastic is envisaged with the assumption that the plastic zone forms a very thin in-plane layer surrounding the crack. The solution of the problem is reduced to the solution of dual Dini series which, in turn, is reduced to a Fredholm integral equation of the second kind. Solving this integral equation numerically and using the boundedness of the axial stress, the size of the plastic zone correction is obtained.

Stress intensity factors for two rectangular cracks in three-dimensions

Abstract In this paper an analytical solution is developed for two three-dimensional coplanar rectangular-shaped cracks embedded in an infinite elastic medium and subjected to normal loading. Employing two-dimensional integral transforms, the solution of the problem is reduced to triple integral equations. Assuming the plane strain solution across the lengths of the narrow cracks, an approximate solution of the triple integral equations for large values of the lengths of the cracks is obtained. Finally, expressions are obtained for the stress intensity factors along the sides of the cracks and these results are given in the form of graphs.

The Reissner–Sagoci Problem for a Non-homogeneous Half-space with a Surface Constraint

This paper deals with the problem of twisting a non-homogeneous, isotropic, half-space by rotating a circular part of its boundary surface (0 ≤ r < a, z = 0) through a given angle. A ring (a < r < b, z = 0) outside the circle is stress-free and the remaining part (r > b, z = 0) is rigidly clamped. The shear modulus is assumed to vary with the cylindrical coordinates, r, z by the relation μ(z) = μ1(c + z)α, c ≠ 0 where μ1, c and α are real constants. Expressions for some quantities of physical importance, such as torque applied at the surface of the disk and stress intensity factors, are obtained. The effects of non-homogeneity on torque and stress intensity factor are illustrated graphically.