Showing papers in "Journal of Strain Analysis for Engineering Design in 1982"

Crushing analysis of rotationally symmetric plastic shells

Abstract: The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure.

Determination of large strains in metalforming

Abstract: Certain techniques for the experimental determination of large strains in metalforming are discussed. The methods employ a grid pattern marked on the surface of the workpiece before forming and subsequently measured after deformation. The grid method is a surface phenomenon and the strain determination is reduced to a two dimensional problem. Any measurements taken on the initial and final grid configurations only, without knowing the deformation path, are insufficient to determine the strains precisely. Nevertheless, in practice, strains are determined by such a technique, often by using grid circles and by further assuming they deform into ellipses. The deformation process which transforms circles to ellipses and straight lines to straight lines, still does not define the straining path. Under such a deformation mode strain paths can be divided into two main types, those where an initially orthogonal pair of line elements (the principal axes) remain orthogonal throughout the deformation and thos...

An analysis for cylindrical vessels under local loading-application to saddle supported vessel problems:

Abstract: An analysis is presented for unstiffened circular cylindrical vessels subjected to non-rotationally symmetric and/or local loading. The analysis has been employed to develop a rigorous solu...

Exact solutions to some honeycomb sandwich beam, plate, and shell problems

Abstract: A consistent set of equations is given for honeycomb sandwich shells, wherein each layer of the sandwich is treated separately. The theory allows for the effects of thick cores, non-constant core thickness and arbitrary anisotropic faces. Analytical solutions are obtained for constant thickness and tapered beams, a flat plate, and a circular cylinder subjected to simple loading conditions. The principal use of such solutions is in the testing of finite elements which are intended to model honeycomb sandwich construction.

Steady-State stress distributions in circumferentially notched bars subjected to creep

Abstract: Abstract The paper describes a procedure, based on a finite element method, for calculating directly the steady-state stress distribution in circumferentially notched bars subjected to creep without the need for obtaining solutions at intermediate time intervals. Good agreement is obtained with relevant approximate plasticity solutions and with numerical calculations which approach the steady-state over a period of time from the initial elastic stress distribution. Also, the procedure is equally applicable to primary, secondary, and tertiary creep, provided the variables of stress and time are separable in the creep law. Results obtained for a range of notch geometries and values of the stress index, n, are reported. It is found for each profile that a region of approximately constant effective stress, σ, independent of n, is obtained which can be used to characterise the overall behaviour of the notch throat region when a steady-state is reached sufficiently early in life. An approximate method for estimating the maximum equivalent steady-state stress across the notch throat is also presented which does not require a computer solution.

Stresses in horizontal storage vessels - a comparison of theory and experiments

Abstract: This paper presents the salient features of the experimental work carried out on a series of horizontal storage vessels. These include a 3.66 m diameter gas receiver and two smaller vessels...

Plastic collapse loads of cylindrical pressure vessels supported by rigid saddles

Abstract: The plastic collapse of cylindrical pressure or storage vessels supported by rigid saddle supports is examined both experimentally and in an exploratory theoretical manner. Two cases are considered: (1) when the saddle is welded to the vessel, and (2) when the saddle and vessel are not welded.It is found that the load to cause first yield is much smaller than the fully plastic load and thus there exists a considerable reserve strength even when a vessel is stressed up to yield. The object of this investigation is to examine this considerable reserve strength and to provide results which, when taken with previous elastic studies, should help to improve vessel and support design.

End reinforcement and grips for anisotropic tubes

Abstract: A method of gripping and reinforcing the ends of anisotropic tubes for testing under combined axial load and internal pressure is analysed.Edge solutions for long, cylindrical, specially orthotropic shells are considered.The tube, reinforcement, and grips are then modelled as an assembly of short, parallel, multilayered, thin-walled, orthotropic shells.Theoretical results are presented for the stress distribution in a ± 75 degree filament-wound E glass/epoxy resin tube with circumferentially wound glass fibre reinforced ends.

Stresses around large circular holes in uniform circular cylindrical shells

Abstract: An experimental and finite element analysis of a uniform cylindrical shell with a large circular cut-out is presented. In this analysis three hole sizes are considered, namely μ = 2.037, 4.084, and 6.344 (where μ = {[12(1 - y2)]1/4/2} × [a/(Rt)1/2]), for loadings of axial compression, torsion and three point bending. The experimental results are the only ones available for cylindrical shells with large values of μ (except for one graph by Savin (1)†), while for three point bending there is no previously published theoretical or analytical results.Good agreement is found between the calculated and experimental stresses around the holes.

Two and three parameter representations of crack-tip stress fields

Abstract: An analytical technique is developed to determine, from experimental photoelastic data, parameters additional to the stress intensity factor, K, required to provide an adequate representati...

Determination of the flexural stiffness of thin plates from small deflection measurements using optical holography

Abstract: A technique is presented for accurate determination of the flexural stiffness of thin plates using optical holography. Measurements of the interference fringes on thin rhombic plates in anticlastic bending are used to calculate the components of curvature by a simple numerical method Control experiments on a metal plate give good agreement with the results of small deflection bending theory. The method appears ideally suited to the measurement of anisotropic flexural stiffness properties.

Thermal ratchetting of axially loaded tubes operating in the creep range

Abstract: Finite element predictions of ratchetting and creep behaviour are compared with experimental data for axially loaded tubes subjected to axisymmetric cyclic temperature variations.Eleven tubes made of a lead alloy model material which creeps at ambient temperature were tested. Strain gauges were used to measure the ratchet and creep strains.In the finite element calculations it was assumed that no plasticity-creep interactions occur. Reasonably good predictions of ratchet strains were obtained, particularly in the range of most practical interest. Some of the discrepancies between ratchet and creep results can be accounted for by considering the results from a small number of uniaxial plasticity-creep interaction tests.

A rig for creep and thermal ratchet testing of lead alloy models

Abstract: The development and calibration of a rig and an axisymmetric lead alloy component for isothermal creep, non-isothermal creep, and thermal ratchetting testing is described.Steady and variable, axial mechanical loads are applied by a dead weight and lever system. Thermal loads are applied by controlled variations of the temperature of water flowing through the bore and along the outside of the component. Strains and temperature are measured with electrical resistance strain gauges and thermocouples, respectively.

A rig for controlled cyclic strain and temperature testing

Abstract: A servo-hydraulic test rig capable of applying combined temperature and strain or load cycles has been developed and commissioned. The nature of the test has dictated the specimen form as a hollow, hour-glass type.The critical problem of a suitable extensometer for temperature and strain cycling has been solved. The device designed and produced shows negligible transient temperature effects, has a high resolution of better than 0.1 μm, and is mechanically very stable.The heating and cooling is controlled by an induction heating system with grip cooling; additional cooling is available using compressed air passing through the hollow specimen. The system is capable of following a temperature ramp to within 1°C linearity. The thermal strain associated with a temperature cycle is compensated for using a microprocessor system specially developed for the purpose, which also enables a mechanical strain-stress loop to be plotted during a test.Both ‘in-phase’ and ‘out-of-phase’ temperature/strain cycles ha...

Stress concentrations on axially loaded, unsymmetrical projections on flat bars

Abstract: The effects of shape and position of load application on the magnitude and position of the peak stresses in stepped bars and around T-slots are determined from photoelastic models. Stress concentration factors for any practical shape can be quickly determined from the results. Stress concentration factors at these unsymmetrical projections are related to previously published factors for symmetrical projections. Optimum proportions which give the lowest peak stresses for different specified dimensions are also presented.

Elastic stresses due to torque transmitted through the prismatic part of keyed connections part II: Effect of shape with usual fits and friction

Abstract: Models of 25 different shapes of keyed connections have been loaded by a large range of torques, using ordinary and frozen-stress photoelasticity.Empirical formulae have been derived for five contact points where the stresses are concentrated. These formulae give good predictions over the complete shape range of the metric and inch standards. The latter is consistently better than the former.

Elastic stresses due to torque transmitted through the prismatic part of keyed connections part I: Effect of different fits and friction on standard shapes:

Abstract: Photoelastic models of transverse sections through British Standard metric and inch keyed shafts and hubs (outside diameter = 2 × shaft diameter) have been loaded in torsion. Models with five different combinations of fits of shaft in hub, key in shaft, and key in hub, with three different surface conditions have been analysed over a large range of torques.Stress concentrations occurred at the six contact positions where there are discontinuities of profile of the chamfered key or of the shaft. Normalized peak stresses are presented for all tests and the effects of the controlled variables are discussed.

Recommendations for the measurement of R-curves using centre-cracked panels

Abstract: Experimental techniques for obtaining the R-curve, a measure of fracture toughness used for selection and quality assurance of thin-section materials, are discussed in the light of experien...

Pressurized non-circular member—effect of mean-line form

Abstract: Using an energy analysis, it is shown that for each aspect ratio and for a particular family of curves representing the mean-line form, there will be one particular form which ensures that the maximum bending moment acting on the member takes a minimum value.The traditional elliptic mean-line form currently used for some heat exchanger tubes, sluice-value bodies, and some aircraft monocoque stiffening frames, could be improved by using the optimum form which has heat transfer and fluid-flow characteristics similar to those associated with the elliptic profile (sometimes an essential feature of the design).It is shown that when the aspect ratio is equal to two and the elliptic shape is replaced by an optimum form determined by the method described above, the uniform applied pressure can be increased by fifteen and one-half per cent before the maximum stress in the two members becomes equal.

A new technique for coupled plane thermal stress problems

Abstract: It is well known that the thermoelastic coupling term and the inertia term have to be taken into account for a rigorous treatment of a sudden change of temperature in a elastic body It is now well understood that the inertia effect may disappear in pure thermal stress problems on the stress distribution for realistic materials In the present paper, we propose a new technique for the coupled thermoelastic fields by introducing an additive harmonic function Thus, we can obtain exact solution for all the time period The effect of thermoelastic coupling on the temperature and the stress distributions is shown in the numerical example

Predicting the thermal ratchetting and creep behaviour of a component with a stress concentration

Abstract: Finite element and ‘upper bound’ predictions of ratchetting and creep are compared with experimental data from two axially loaded shouldered tubes subjected to axisymmetric cyclic temperature variations.The shouldered tubes were machined from chill-cast bars of a lead alloy material. Electrical resistance strain gauges were used to measure the ratchet and creep strain.The results show that ratchet strains can accumulate significantly faster in stress concentration regions when compared with plain tube regions. Acceptable predictions were obtained for the ratchet strains. The discrepancies between the predicted and measured dwell period strains were due to neglecting the material plasticity-creep interactions. Some simple methods for estimating the strains are suggested.

Experimental theramal ratchetting data for a component with a stres concentration

Abstract: The result from eleven tests of lead alloy model shouldered tubes, subjected to constant axial mechanical loads and cyclic, axisymmetric thermal shocks are described. Dwell periods between 0.5 h and 24 h allowed creep to occur between the thermal shocks. Electrical resistance strain gauges were used to measure ratchet and creep strains.At low mean axial stresses (< 0.94σy), it was found that the ratchet strains increased with load and dwell period. It was also found that the ratchet strains in the fillet region were significantly larger than those in the shank and are induced at lower mechanical loads than those in the shank. For higher stresses, the ratchet strains were found to be relatively insensitive to both load and dwell period. Also, the ratchet strains in the fillet and shank were found to be of the same magnitude.

Araldite models for the study of elastic stability of plates

Abstract: The suitability of Araldite as a model material for the study of plate instability problems is investigated. Model tests on stiffened plates made of Araldite and steel sheeting are reported and the test results are compared with theoretical predictions.The overwhelming advantage in testing Araldite models is due to the large range of material elasticity (extending up to 36 000 microstrain compared with 1200–1600 microstrain for steel). Models made of Araldite are shown to be useful in simulating buckling modes and in obtaining magnified values of the likely plate and stiffener deformations in the serviceability and ultimate limit states. The ultimate capacity predicted from models is, however, significantly lower than the values of the corresponding steel prototypes on account of the early loss of stiffness of the members caused by the large deformations.

Method of fracture toughness determination in sidewall of a pneumatic tyre

Abstract: A method for determining the fracture toughness of a pneumatic tyre sidewall was developed. Conventional methods of fracture toughness determination require the structural material to be tested independently of the structure. the proposed method allows fracture toughness to be measured directly from the type sidewall. Two advantages follow: (i) elimination of the need for duplicating the identical cured sidewall properties in the testpiece, and (ii) avoidance of the buckling inherent in thin sidewall test specimens.The pneumatic tyre chosen for the investigation was a 7.75–14 bias passenger tyre with a two-ply nylon carcass. An artificial crack was created in the tyre sidewall and the cracked tyre was loaded by inflation pressure. The experimental parameters taken from the tyre include the inflation pressure, volume, and crack opening area at different crack lengths. Based on a quasistatic energy analysis, the pressure-volume-crack length diagram was used to graphically determine the sidewall frac...

The stresses induced in reinforced plastic matrix pipes by saddle supports

Abstract: The results of a series of experiments conducted on reinforced plastic matrix pipes show how the peak stresses, occurring in the saddle support region, can be reduced in magnitude by certain design features. Two methods are found of value: (1) to use a flexible medium, such as PVC or rubber, between the saddle and pipe, and (2) to support the pipe on a saddle with a radius greater than the pipe radius. The experimental results are compared with an analytical approach using shell theory making the assumption that the pipe material is isotropic. The agreement between the experimental and analytical results is promising.

Determination of fracture toughness of ductile materials using a reinforced double cantilever beam specimen

Abstract: A method of determining the fracture toughness of ductile material in the form of a reinforced double cantilever beam (RDCB) specimen is presented. The analysis makes use of the Dugdale strip yield model incorporated in the beam-on-elastic foundation model to represent the fractures of a DC3 specimen. Two different foundation models are considered. The first model assumes that one half of the RDCB acts as the elastic foundation for the other half and the second model assumes that the groove acts as the elastic foundation. The results of the groove foundation model are found to be closer to the experimental values based on the crack growth resistance curves than those of the beam foundation model. The results are further verified using a J control integral determination based on a two dimensional elastic-plastic finite element analysis.The material used is 2024-T3, which is moderately ductile, and the proposed method yields fracture toughness values with a reasonable degree of accuracy.

Fracture of aluminum-epoxy layered composites containing cracks

Abstract: The plane problem of a composite plate consisting of two aluminum half-planes bonded together through an epoxy layer and containing two parallel cracks, one in the layer and the other in one of the half-planes was considered. The composite plate was loaded by a uniform uniaxial compressive stress distribution applied along the surfaces of the crack of either the layer or the half-plane. The critical value of the applied stress as well as the corresponding angle for crack extension were determined by using the minimum strain energy density theory. Valuable results governing the dependence of the critical failure stress of the composite plate as well as the angle of crack extension from the more vulnerable crack on the geometry of the plate were derived.

The design and manufacture of supports for horizontal vessels

Abstract: Various types of supports for horizontal cylindrical vessels are reviewed and the use and limitations of BS 5500 examined. Design and manufacturing requirements for saddle supports are discussed and reference made to some in-service problems.

A three-dimensional photoelastic study of the stresses in horizontal, saddle-supported, liquid-filled storage vessels

Abstract: A series of three-dimensional photoelastic models (thickness to diameter ratio 0.009–0.016) have been tested and analysed with the objective of providing detailed experimental stress distributions for examples of this important configuration. Typical results are presented and discussed. The effects of varying the vessel length to diameter ratio, the support spacing to vessel length ratio, and the wall thickness to diameter ratio are examined; the effects of radiusing the edges and horns of the saddle are also studied.

Stress analysis of axial flow cooling fans

Abstract: Tests on automobile radiator cooling fans of three types of construction pressed out from sheets are reported. The blades of the fans are treated as twisted (from tip to root) cantilever beams (fixed at root) for the purpose of analysis. The effects of centrifugal force, driving torque, and the axial thrust over the blade due to air flow are taken into account. Air flow measurements are obtained using a pitot-static probe. The input power for various speeds is also recorded. The stress values are verified with the strain gauge readings taken at the root and at mid span. The effects of twist angle and number of blades are also discussed. The study does not include riveted construction.