Angular Stress Distributions Research Articles

The singular field at the tip of a wedge-like rigid inclusion in a hardening material under longitudinal shear

The analytical solution of the singular field at the apex of a rigid wedge embedded in a power law hardening material under longitudinal shear is presented. By the use of the hodograph transformation the singularity and angular distribution of stresses and strains are analytically determined. Special cases, such as elastic, perfectly plastic materials, and the problem of rigid flat inclusion, are discussed.

Antiplane problems in composite anisotropic materials with an inclined crack terminating at a bimaterial interface

The antiplane strain problem for bonded dissimilar half planes of general anisotropic material containing an inclined crack terminating at the bimaterial interface is considered. The surfaces of the crack can be subjected to traction-traction, traction-displacement or displacement-displacement boundary conditions. The dependence of the order of the stress singularity on the inclined angle and material constants is studied. If the effective crack angle and the effective material constant are introduced for the anisotropic case, then the characteristic equation which determines the order of the stress singularity has the same functional form as the isotropic case. Explicit solutions for the order of stress singularity are obtained for some special cases. It is found that the order of the stress singularity is always real for all the cases studied in this paper. This is a quite different character from the in-plane case in which the complex type of stress singularity might exist. The angular distribution of stresses near the crack tip and the exact full field stress solutions are also investigated.

Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation

The antiplane strain problem of two dissimilar anisotropic composite wedges of arbitrary angles that are bonded together along a common edge is considered. The surfaces of the wedges can be subjected to traction-traction, traction-displacement or displacement-displacement boundary conditions. The dependence of the order of the stress singularity on the wedge angles and material constants is studied. The angular distribution of stresses at the apex and the exact full field stress solutions are also investigated. Explicit solutions for the order of stress singularity are obtained for some special cases. It is found that the order of the stress singularity is always real for the antiplane dissimilar anisotropic wedge problem. This is quite different from the in-plane case, in which the complex type of stress singularity might exist.

The singular field at a rigid flat inclusion in hardening materials under longitudinal shear

The analytical solution of the field at the tip of a rigid inclusion under longitudinal shear is derived for a power law hardening material. Using the hodograph transformation the singularity and the angular distribution of stresses and strains are determined. A comparison of the fields for a crack tip and for the inclusion shows that the one is a mirror image of the other.

A Finite Element Study of Stable Crack Growth Under Plane Stress Conditions: Part I—Elastic-Perfectly Plastic Solids

A detailed finite element study of stable crack growth in elastic-perfectly plastic solids obeying an incremental plasticity theory and the Huber-Von Mises yield criterion is performed under plane stress, small-scale yielding conditions. A nodal release procedure is used to simulate crack extension under continuously increasing external load. It is found that the asymptotic angular extent of the active plastic zone surrounding the moving crack tip is from θ = 0 deg to about θ = 45 deg. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading is numerically observed. The near-tip angular stress distribution inside the active plastic zone is in good agreement with the variation inside a centered fan, as predicted by a preliminary asymptotic analysis by Rice. It is also observed that the stress components within the plastic zone have a strong radial variation. The nature of the near-tip profile is studied in detail.

Plane-strain crack-tip fields for power-law hardening orthotropic materials

Near-tip stress and strain fields for power-law hardening orthotropic materials under plane-strain conditions are presented. Plastic orthotropy is described by Hill's quadratic yield function. The angular variations of these HRR-type fields depend on a single parameter which specifies the state of plastic orthotropy. Near-tip fields for highly orthotropic materials differ substantially from the fields for isotropic materials. Mode I (symmetric) and mode II (anti-symmetric) solutions for different degrees of plastic orthotropy are given. The angular stress distributions for the low-hardening material agree remarkably well with the plane-strain slip-line fields. Based on the singularity fields, effective stress contours are constructed. The applicability of these fields in the context of a fiber-reinforced composite containing a macroscopic flaw is discussed.

Isochromatic fringe patterns in duplex specimens

A thorough analysis of the isochromatic fringe patterns in duplex specimens with the crack tip on the interface was undertaken. The particular value of the elastic stress singularity (a value differing in general from that of 0·5) and the appropriate angular distribution of the stress field in the vicinity of the crack tip were taken into account. It was found necessary to introduce large correction factors to the usual photoelastic formula for the determination of stress intensity factors ( K) especially where the elastic moduli of the two materials of the specimen differed greatly. It was established that for certain intervals of the polar angle the greatest part of the correction factor is attributed to the stress singularity, while the influence of the particular angular stress distribution is of minor importance. It was concluded that for practical applications and recording data at the above-mentioned polar angle intervals, it suffices to use the usual formula for K determination by introducing the appropriate value of the stress singularity.

Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading

The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks is considered. For the semi-infinite crack the problem is solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses are calculated. For finite cracks the problem is reduced to a pair of integral equations. Numerical results are obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.

Elastodynamic near-tip fields for a rapidly propagating interface crack

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar isotropic elastic solids is investigated. Both anti-plane and in-plane motions are considered. The anti-plane displacements and the in-plane displacement potentials are sought in the separated forms r qF(θ) , r and θ being polar coordinates centered at the moving tip. The mathematical statement of the problem reduces to a second-order linear ordinary differential equation in θ, which can be solved analytically. Formulation of the boundary and interface conditions leads to an eigenvalue problem for the singularity exponent q. For the in-plane problem, root q is found to be complex. Thus, the stresses exhibit violent oscillations within a small region around the crack tip, and the solutions have physical significance only outside this region. The angular stress distributions are plotted for various crack speeds, and it is found that at a high enough speeds the direction θ of maximum stress moves out of the interface. This result indicates that a running interface crack may move into one of the adjoining materials.