The Journal of Strain Analysis for Engineering Design

The paper describes a three-dimensional photoelastic analysis of a series of Araldite models, each containing five or six different offset-oblique holes positioned in such a way that there were no ‘interaction’ effects between neighbouring holes. The geometric parameters defining a hole were varied systematically and the elastic stress distribution around the outer edge of each hole was obtained. The stress data are presented in non-dimensional form in terms of the shear stress in a plain cylinder. The dependence of the maximum stress on the geometric variables is discussed and it is shown that the stress concentrations for a wide range of hole/cylinder parameters can be reasonably well predicted from flat plate data. In some cases the predictions are unconservative.

The criteria of strain energy density and maximum tangential stress have been applied to the entire stress field existing just before the onset of instability to predict the path of extension of both internal and edge cracks. The stress analysis has been carried out by a finite-element scheme employing the quarter point square-root stress singularity elements. In the case of internal cracks, the unstable paths based on both the criteria are in good agreement with the results available in the literature. Theoretical and experimental studies on edge crack extensions during bar shearing of brittle materials have facilitated a comparison, and it appears that, although the maximum tangential stress criterion may be applicable, the strain energy density criterion is unsuitable for this case.

The method of reflected caustics was extended to evaluate the complex stress intensity factors at the roots of re-entrant corners in elastic plates under generalized plane-stress conditions. The plates were considered loaded under a general mode of loading creating asymmetric stress states at the corners and, thus, engendering complex stress intensity factors at these zones.

For the evaluation of the complex stress intensity factors the coordinates of at least two points on the caustics are necessary whose polar coordinates on the respective initial curves on the specimen are defined in advance. These experimental data must be introduced into a system of six equations, four of which are linear and the remaining two non-linear. The solution of this system yields the components of the complex stress intensity factors with a high accuracy, independently of the form and shape of the caustics developed around the roots of the corners. This high accuracy was achieved among others by the fact that two terms in the asymptotic expansion of Muskhelishvili's complex stress function Φ(z) are taken into consideration for the evaluation of stress intensity factors.

The method was applied first to a symmetric notch whose theoretical solution is known, so that the accuracy of the method could be checked, and afterwards to an asymmetrically loaded notch whose theoretical solution does not exist. For this case a recurrent procedure was applied for checking the accuracy of the experimental results.

Experimental results on a mild steel are reported from ballistics tests which gave rise to strain rates of up to 10⁵ s⁻¹. A finite-difference numerical technique which incorporates material inertia, elastic-strain hardening and strain-rate sensitivity is used to establish the strain-rate sensitivity constants p and D in the equation, σ⁴ = σ¹ (1+(∊/D)^1/p). The rate sensitivity established in this study is compared with those reported by other researchers.

The loss of compressive stiffness of a thin square plate buckled in shear is calculated. Two cases are considered, first a perfectly flat plate, and second a plate with an imperfection amplitude equal to 10 per cent of the plate thickness. Changes in shear stiffess are also plotted. The analysis is by a finite-element method. Substantial reductions in compressive stiffness due to shear buckling are found, with further variation in stiffness as the buckling mode develops. The significance of these results in the design of a stiffened shear web is examined. It is shown that, by a suitable design procedure, the corresponding loss of efficiency can be made quite small.

Many components in conventional and nuclear power plant and chemical plant are subjected to steady mechanical and cyclic thermal loads. The life of such components may be governed by the accumulation of inelastic strain and/or deformation (i.e., ratcheting).

Elasto-plastic finite-element results for a circular plate with radially movable, direction fixed edges, subjected to steady membrane loads, steady transverse pressure loads, and cyclic through-thickness thermal loads, are given. A temperature independent, elasticperfectly plastic material model is assumed. Plastic strains are governed by the von-Mises effective stress criterion and the Prandtl-Reuss flow rule. Cyclic hardening (or softening) effects are not considered. The results are compared with the Miller-Bree uniaxial model (1)(2)(3)†

The results have been normalized with respect to the material properties so that they may be applied to plates made from any material which may be represented by the material model.

Thin-walled tubes, having hemi-spherical ends and four symmetrically placed stiffening rings to model a typical road transport tank container, were subjected to a mechanical loading from either: (i) an axial line or point charge of explosive, or (ii) static penetration from the outside by a punch to determine their plastic deformation characteristics.

The vessels were examined when: (a) nominally empty, (b) air pressurized, and (c) almost completely full of water.

Results for a range of tests in which the vessels were not stiffened are also reported and this facilitates useful comparison between the stiffened and unstiffened cases.