The Journal of Strain Analysis for Engineering Design

A testing machine developed for the study of the deformational behaviour of plastics under bending loads complements high-accuracy tensile-creep testing machines and provides a more appropriate means for the testing of brittle fibre-plastics composites and plastics sandwich structures. The machine is suitable for applying constant loads and automatically recording the deflections of specimens at several points over periods of up to three months.

It is often suggested that splitting a specimen and machining grid lines on one of the exposed planes to study flow patterns during plastic deformation interferes with the flow process under investigation. A procedure is described here for flow-function analysis of extrusion specimens in which artificial grid lines are not required. The procedure is restricted to situations in which the microstructure exhibits line segments produced by deforming grains or second-phase particles as they flow through the die. These segments represent partial-flow lines according to the assumptions of flow-function analysis. From numerical analysis of their slopes it is possible to construct the complete flow function. From this, all the kinematic quantities of the deformation can be determined.

A rectangular finite-element model has been developed for thermal-stress analysis of shallow shells. The elemental equations are obtained from a two-field variational principle which employs equilibriating stress fields within the elements and compatible displacement fields along inter-element boundaries. The extremization of the variational functional tends to satisfy the compatibility requirements within the elements and equilibrium conditions along inter-element boundaries. The element is employed for thermal-stress analysis of several examples and the numerical results obtained are compared with some analytical results.

Equations for principal displacements in a uniformly pressurized thin-walled cylinder having an elliptic median line are developed from a knowledge of the expressions for tension and bending moment (1) at a general position in the cylinder wall. Displacements derived from these equations are compared with the simple expressions presented by Bresse (2) and MacAlpine (3).

The results of a detailed experimental study in which displacements were measured by a laser interferometer are used to assess the validity of the new displacement equations and to compare these with the predictions due to Bresse and MacAlpine.

It is shown that the equations developed here give good agreement with experimentally measured displacements and furthermore the predictions made in (2) and (3) grossly overestimate the displacement values and are also very much in error when stating that the minor-diameter expansion is of the same order as the major-diameter contraction. In the investigation reported here (ellipse with mean aspect ratio 1.9509) the expansion of the minor diameter is approximately twice the value obtained for the contraction of the major diameter.

Fracture-toughness tests were conducted on Araldite CT 200, in order to obtain K_1c, the plane-strain, mode 1 critical stress-intensity factor. Two essentially different methods were used, namely the photoelastic method and the quasistatic energy method.

In the photoelastic method, stress fringe patterns were analysed at load intervals up to failure and the stress-intensity coefficients obtained were compared with those from the boundary collocation method. In the energy method, two types of specimen geometry were tested, resulting in stable crack propagation. Good correlation was obtained between the two methods.

A theoretical analysis was carried out to determine the distribution of stresses and radial deflections due to internal pressure in the limpet of a limpet-coil pressure vessel. A computer programme was developed to carry out the complete calculations. Theoretical results for a vessel having the dimensions of a test vessel were compared with the corresponding experimental values obtained from strain-gauge and deflection-gauge measurements on the test vessel itself.

The large deflections of rectangular plates and beams obeying a non-linear stress-strain law are examined. Solutions are obtained by use of dynamic relaxation, a numerical finite-difference technique. Comparisons are made with alternative solutions and experimental results. The effects of varying parameters in the non-linear expressions are considered.

Stresses in a standard metal-to-metal adhesive-bonded lap joint are analysed by a two-dimensional finite-element method and comparisons are made with previous analyses. Particular attention is paid to the stresses at the ends of the adhesive layer. Unlike previous work, which assumes the adhesive to have a square edge, the adhesive spew is treated as a triangular fillet. The highest stresses exist at the adherend corner within the spew. Linear elastic behaviour is assumed throughout.

A rubber model is reported which confirms these results physically.

Good agreement was also obtained between some practical results and the finite-element predictions.

A new experimental technique based on the method of caustics is presented for the measurement of the distance between the lips of a crack near the crack-tip. The two parts of the caustic formed by reflections from the front and rear faces of the specimen lie at a distance from each other. The gap between these parts depends on the total c.o.d. (crack-opening displacement), that is the initial opening and the opening due to loading, as well as on the optical and mechanical characteristics of the material By increasing the external loading of the cracked plate, the gap between the parts of the caustic was changed and this gap measured the instantaneous c.o.d. due to loading. The method was applied to the measurement of small c.o.d.s. due to small-scale loading, with satisfactory results. Therefore it can certainly be used to measure c.o.d.s at large loading steps, up to fracture, because the gap between the parts of the caustic becomes significant and easy to measure. Measurements with cracked plates made of p.m.m.a. (polymethylmethacrylate) and polycarbonate showed that the results obtained are in good agreement with theory. Thus, it has been proved that the method of caustics yields a very sensitive means for measuring c.o.d.s, especially in small-scale deformations, where measurement of c.o.d by conventional methods is inaccurate. A great advantage of the method is that it measures the c.o.d.s at a well defined region, which always remains near to the crack tip.

The Fifth International Conference on Experimental Stress Analysis was held on 27–31 May 1974 at Udine in Italy and was concerned with data processing in stress analysis, applications of stress analysis to materials behaviour, stress analysis in biomechanics, and advanced methods and applications of stress analysis in engineering.