The Journal of Strain Analysis for Engineering Design

The problem of an inclined crack centrally placed in a generally orthotropic rectangular plate under tension is investigated. The modified mapping-collocation technique introduced by Bowie and other workers is used in the analysis and the stress-intensity factors are computed for several orientations of cracks and for rectangles of various proportions. The effects of orientation of the principal axes of orthotropy are also considered. The results indicate a fairly strong dependence of the stress field on the orientation of these principal axes of the material and the occasional complexity of the interaction of material anisotropy and the geometry of the specimen.

Comparative tensile and compressive creep behaviour at constant stress has been studied for an 11 per cent chromium steel. No significant differences were observed for stresses and temperatures of engineering relevance, i.e. producing lives greater than 200 h. High stresses, producing shorter tensile lives, caused creep to occur more rapidly under tension owing to an earlier development of tertiary-type deformation. It is suggested that the deformation mechanisms are similar for the two modes of stressing but development of stable cracks under tension produces more rapid creep behaviour during the later stages of life.

An improved method for the flow-function analysis of visioplasticty data is presented in which the use of techniques for the smoothing of raw data is reduced. It is shown theoretically, and experimentally verified, that under the assumptions of flow-function analysis the final axial, radial, and circumferential normal strains in the extruded material are fixed solely by the reduction ratio. Velocity fields computed from analysis of axial grid-line data are shown to predict accurately the experimental positions of corresponding transverse grid lines. From the velocity fields strain rates are computed. Transformation equations are developed relating the deformation in the spatial co-ordinate system to a more easily interpreted material co-ordinate system. By use of these equations excellent agreement is obtained with experimental normal strains by integrating the calculated strain rates through the deformation zone. Very good agreement is also obtained with the final angles between axial and transverse grid lines.

A method of numerically approximating the solutions of plane-stress or plane-strain elasticity problems with boundary conditions consisting of concentrated forces or distributed loads is presented herein. The effect of each concentrated force (commonly termed a point load) that acts on the boundary is represented by a Flamant solution. Usually, the combined effect of these Flamant solutions indicates the presence of distributed loadings or ‘residual stresses’ on some portions of the boundary that are not consistent with the actual boundary conditions. The negatives of these ‘residual stresses’ are used as stress boundary conditions in a singular integral method of numerical analysis that is applicable to plane elasticity problems involving distributed loadings on the boundaries. Since the method presented herein involves only stress boundary conditions, the solutions are valid for both plane stress and plane strain.

The accuracy of this superposition method is demonstrated by consideration of a circular disc or cylinder subjected to diametrically opposed concentrated forces for which accuracy to within 0.2 per cent of the exact solution is obtained. Parametric analyses of rectangular and elliptical compression members subjected to point loads are presented. Results determined herein are found to compare relatively well with those determined in previous numerical and experimental investigations of specific cases. These results make possible the design and analysis of compression members used to evaluate the tensile fracture strength of brittle materials.

Thin strips made of perspex and containing two collinear internal cracks of different length were subjected to tension. The thickness variation of the strips was depicted by the reflected-shadow method, in which a coherent monochromatic light beam, emitted from a helium-neon gas laser, was partly reflected from the rear surface of the specimen. The light rays emerging from the plate, which were twice refracted along the thickness and reflected on the rear surface of the plate, were retarded according to Favre's and Neumann's law. The retarded light rays were focused on a caustic surface which depicted the boundary between the constrained area surrounding the crack tip and the remainder of the plate. In this paper two asymmetric collinear internal cracks of different lengths were studied and the interaction between these cracks was evaluated by measuring the variation of the diameter and the distortion of the shape of the caustics for various ratios of crack lengths.

Experiments have been conducted to observe the relaxation behaviour of fishplate-bolted rail joints in which four different polymeric materials were used for electrical insulation. Static tests were conducted to study the effect of temperature and of different locking sequences for the bolts on a rig which simulated service conditions at a joint. The effect of cyclic loading was considered.

To be able to understand the detailed mechanics of plastic flow and lubrication during hydrostatic extrusion it is very desirable to be able to measure the precise pressure distribution along the length of the die.

In the present work, experiments have been developed which enable this pressure distribution to be measured indirectly with reasonable accuracy and comparison is made between the distribution obtained experimentally during slow-speed hydrostatic extrusion of annealed copper and the distribution predicted by theoretical analysis. Very good agreement was obtained for the single geometry investigated.

An extension of the method of photoviscous analysis is presented which permits quantitative studies of strains associated with steady-state vibrations of immersed structures. Strains can be determined both in the vibrating structure and in the surrounding fluid. The method is applied in an investigation of one form of behaviour of buoy-cable systems loaded by the action of surface waves. Procedures are illustrated for evaluating directly from the strain data parameters useful to the buoy-cable system designer.

The analysis performed is two-dimensional. The cable is modelled by a soft rubber strip, and the buoy by a round can floating on the surface of a birefringent fluid. A payload is simulated by a weight attached to the lower end of the strip. Waves of controllable frequency are produced by a device actuated by a shaker. Strains in the fluid and in the strip are determined from isochromatic and isoclinic data and the possible extension of the experimental results obtained to prototypes by means of scaling laws is suggested.

The interaction between a strain gauge and its substratum is investigated for the special case of a one-dimensional gauge adhesively bonded to a half-plane. The influence on the strain distribution of the properties of the underlying material, of strain-gauge design, and of adhesive properties is demonstrated by numerical examples.

A theoretical analysis of bonded rubber blocks with circular cross-section under axial compression is obtained by the use of dynamic-relaxation solutions of classical elastic stress-strain equations. The Poisson's ratio ν for rubber is close to 0.5 which causes difficulties in the analysis because the general stress-strain equations of elasticity contain terms such as νE/(1 + ν)(1 − 2ν) which approaches infinity when ν approaches a value of 0.5. The range of ν considered varies between 0.45000 and 0.49990 which covers all the natural-rubber compounds used, including pure natural gum which has a ν value of 0.49989 (1)∗.

It is shown that the stress distribution within the block is significantly affected by the value of ν and the shape of the block. When a block of material with ν ∼ 0.5, bonded to its end plates, is thin, the stress developed within the block is high and nearly equal in all three directions, which suggests a hydrostatic type of pressure. Such a pressure would confirm the finding in (2) and (3) based on a semi-empirical analysis. When the block is thick this effect is absent. The present paper confirms that these effects follow from the fundamental assumptions of classical elasticity.

The investigation also confirms that the dynamic-relaxation method converges satisfactorily even when the Poisson's ratio is very close to the value of 0.5000.