bluuebunny/crossref_metadata_2025 huggingface dataset:
Stress analysis of pipe bends subjected to internal fluid pressure using the finite element technique
Authors: Veerappan A R , Shanmugam S
Published: July 2007

Ovality and thinning are the commonly observed shape irregularities that are introduced during the forming process of pipe bends. Pipe bends with ovality and thinning are subjected to higher stresses than pipe bends with perfectly circular cross-sections. The stresses introduced in pipe bends with different ovality and thinning for a particular internal pressure are calculated using the finite element method. The constant allowable pressure ratio for different ovality and thinning is presented at different bend radii. The allowable pressure ratio increases, attains a maximum, and then decreases as the values of ovality and thinning are increased. A mathematical correlation to determine the allowable pressure in terms of bend ratio, pipe ratio, per cent thinning, and per cent ovality is presented.
Investigation into damage nucleation and growth for a free-cutting steel under hot-rolling conditions
Authors: Foster A D , Lin J , Farrugia D. C. J , Dean T. A
Published: July 2007

The spatial variations in the inclusion size and distribution are examined for a free-cutting steel bloom. Chemical analysis has been carried out on the inclusions using energy-dispersive X-ray analysis and the main findings are reported. It has been observed that inclusions are often associated with a lead tail. Thus an assumption is made that the lead layer becomes liquid or gaseous at hot-forming temperatures. Based on this assumption, a micromechanical finite element model is established and used to model the damage evolution process. Microstructure examinations of hot-tensile-tested specimens are used to compare experimentally the observed inclusion shape and void growth features with those obtained from the micromechanical finite element method. It is concluded that there is no significant inclusion debonding process for the material deformed under hot-forming conditions. The damage growth is directly related to the inclusion size and spacing.
Finite element-based life prediction for high-temperature cyclic loading of a large superplastic forming die
Authors: Shang J , Hyde T. H , Leen S. B
Published: July 2007

The thermomechanical, time-dependent, elastic-plastic creep behaviour of a representative tool in a high-temperature superplastic forming press has been simulated using a sequential finite element-based heat transfer and mechanical stress analysis approach. The heating and cooling aspects of the heat transfer model have been previously validated against laboratory measurements. This paper focuses on the prediction of die life based on this model. The determination and modelling of the high-temperature mechanical properties of the materials and die are described for both so-called (a) major cycles, relating to die heat-up and cool-down from and to ambient temperature, and (b) minor cycles, relating to die heat-up and cool-down associated with part removal and blank insertion. A creep-fatigue life prediction method using non-linear damage summation is developed and applied to the die-life problem. Isothermal fatigue and creep-fatigue interaction tests at 700 and 900 °C on 40%Ni-20%Cr die material XN40F are carried out to estimate the required strain-life relationships.
Creep analysis for a functionally graded cylinder subjected to internal and external pressure
Authors: Chen Jian Jun , Tu Shan Tung , Xuan Fu Zhen , Wang Zheng Dong
Published: July 2007

In this paper the creep behaviour of a functionally graded cylinder is considered under both internal and external pressures. When the properties of the graded material are axisymmetric and dependent on the radial coordinate, an asymptotic solution can be derived on the basis of a Taylor expansion series. The approximate solutions calculated from different higher-order terms are compared with the results of finite element (FE) analysis using ABAQUS software. It is shown that, although the use of higher-order terms may help to obtain a more accurate result for the time-dependent behaviour of the cylinder, a fifth-order form has been sufficiently accurate to calculate the creep stress distribution with satisfactory approximation.
Residual stresses in rolled and machined nickel alloy plates: Synchrotron X-ray diffraction measurement and three-dimensional eigenstrain analysis
Authors: Korsunsky A. M , Regino G. M , Latham D. P , Li H. Y , Walsh M. J
Published: July 2007

Most engineering components made from wrought metallic alloys undergo complex sequences of manufacturing operations. These processing steps frequently include extrusion, forging, or rolling, followed by machining and heat treatment. Since such components will be subjected to service loading as part of engineering assemblies, their durability must be assessed using suitably reliable life prediction models. The present study is aimed at the investigation of a combination of experimental and modelling techniques that involves microstructural investigation, diffraction measurement of residual elastic strains, and finite element simulation of residual stress distributions.

Eigenstrain-based modelling approach to the analysis of processing-induced residual stresses has been previously presented in the two-dimensional approximation, i.e. under the assumption that the equivalent permanent plastic strain field induced by processing is equibiaxial. Several different formulations were considered and compared, including plane stress, plane stress, and three-dimensional models. In the present study a further development of the eigenstrain-based analysis approach that incorporates the experimental data obtained from synchrotron X-ray diffraction measurements of residual elastic strains in two complementary cross-sections of a forged and machined nickel superalloy plate is reported. The microstructure was assessed using electron backscattered diffraction, and near-surface residual stresses evaluated using laboratory X-ray diffraction. It is found that the results of fully three-dimensional formulation differ from two-dimensional approximations particularly in the vicinity of machined surfaces, having potentially significant implications for durability assessment and fatigue life models.
The rotating wedge: A method of obtaining strain-free locations in a centrifugal field
Authors: Macduff I. B.
Published: July 2007

In strain measurement on rotating members using electrical resistance strain gauges and slip rings, difficulties associated with slip ring ‘noise’ may be overcome by several means, one of which is to adopt the full rotating bridge. As well as the active, the three inactive gauges of the bridge are mounted on the rotating side, the compensator preferably at a strain-free location. Investigators have adopted several methods of achieving this.

A new method has been devised whereby the inactive gauges are mounted axially on the segmented circumference of a thin disc of the same material as the test member, rotating with it on the same axis. Axial slots, running in depth radially into the disc, divide the circumference into a large number of small segments or ‘teeth’, each of which is virtually the wide end of a narrow rotating wedge.

Experimental evidence has been examined, demonstrating that the only significant stress in the narrow rotating wedge is radial stress. The theoretical solution for the stresses is therefore of the form of Boussinesq's two-dimensional elasticity solution for the stationary wedge symmetrically loaded at the apex. The solution for the narrow rotating wedge has been indicated on this basis.

Subsequent to tests to determine the strain equivalent to slip ring noise in a new commercially produced slip ring unit, an investigation using strain gauges was carried out to verify that the segment locations of a 10 in overall diameter rotating aluminium segmented disc were strain-free to a speed of 2400 rev/min.

The geometry of the segmented disc has been considered in respect of notch depth, nominal circumferential stresses in the body of the rotating disc and stress concentration at the notch roots.

Other means of producing the necessary strain-free ‘platforms’ have been suggested for circumstances in which material is unavailable for manufacture of a segmented disc.

An arrangement of test member, segmented disc and strain gauge circuit has been adopted for a steady-state centrifugal strain investigation on a water turbine.
The unstable behaviour of thin-walled unsymmetrical section beams subjected to combined bending and torsion
Authors: Black M. M.
Published: July 2007

The investigation described in this paper examines the large displacement behaviour of thin-walled un-symmetrical section beams subjected to combined bending and torsion.

The relevant theory is briefly described and a method of theoretical solution is given. The unstable nature of the behaviour is indicated and the requirements and design of a suitable experimental test rig used to verify the theoretical results are discussed.

Typical experimental results are shown and compared with the corresponding theoretical values.
Stresses in torispherical drumheads: A photoelastic investigation
Authors: Fessler H , Stanley P
Published: July 2007

The dependence of the elastic stress distribution on the shape and thickness parameters in a wide range of torispherical drumheads has been examined using the photoelastic frozen-stress method. Peak principal stress indices are presented in the form of two contour systems; they have also been studied in terms of mean and bending stresses. An approximate approach to some of the practical problems of non-uniform stress gradients is suggested. Head distortions have been measured. A stress concentration factor based on the Maxwell-von Mises yield criterion is shown to be approximately equal to the conventional one.
A method of elastic-plastic plane stress and strain analysis
Authors: Tuba I. S.
Published: July 2007

Plane boundary value problems are formulated in terms of an elastic-plastic stress function and the plastic strains. The governing relation is a non-homogeneous biharmonic equation. It is applicable to the total or deformation theories and to the incremental theories. Sample problems illustrate the practicality of the method.
Convergent internal stresses and steady cyclic states of stress
Authors: Frederick C. O. , Armstrong P. J.
Published: July 2007

It is proved that if two structures differing only in their initial internal stresses are subject to the same loading history, the distributions of internal stress will approach one another in regions of creep and plasticity as the loading proceeds. This theorem is used to prove the existence and uniqueness of steady cyclic states of stress. The application of the concept of a steady cyclic state to the analysis of structures under a repeated loading cycle is discussed.
A theory of the yield locus and flow rule of anisotropic materials
Authors: Hsu T. C.
Published: July 2007

A general yield criterion for anisotropic materials is derived from the linear relationship between strain and stress components. The particular forms of the yield criterion for plane stress and for certain types of symmetry are discussed and are compared with available experimental data. The separate effects of the stress ratio and the direction of the stress axes on the yield stress are also determined.
The characteristics of coaxial and non-coaxial strain paths
Authors: Hsu T. C.
Published: July 2007

In manufacturing processes involving large strains, the properties of the material undergoing deformation depend not only on the current total strain but on the previous strain path as well. Strain paths are divided into two major types, those in which the principal axes of strain remain fixed with respect to the material (coaxial strain paths), and those in which they rotate (non-coaxial strain paths). The characteristics of the two types of strain path are explained. Particular types of non-coaxial strain path related to practical applications are discussed in further detail and examples based on actual measurements are given.
Numerical analysis of variable thickness plates
Authors: Harnden C. T. , Rushton K. R.
Published: July 2007

Exact solutions of the full finite difference equation to the deflection of laterally loaded variable thickness plates are obtained by a step-by-step numerical method. A pure-resistance electrical analogue computer is used to perform the calculations. Certain mixed derivative terms which cannot be included conveniently in the analogue equations are represented as a modification to the load. The resultant step-by-step method converges rapidly to give results which differ from analytical values by less than 0.5 per cent. Plates with both simply supported and clamped edges are considered.
Low endurance fatigue behaviour of mild steel beams in reversed bending
Authors: Royles R
Published: July 2007

The behaviour of mild steel under conditions of reversed bending in the inelastic range at relatively slow rates of cycling, falls into the category of the low endurance fatigue problem in metals, where failures occur within 105 cycles.

This investigation is concerned with an examination of material behaviour in reversed bending (i.e. pure bending) at three frequencies——1, 10 and 100 c/min——and strain ranges in the region from 0.5-12 per cent. Axial extension assumed some significance during the tests at the larger strain ranges, as did cyclic heating at the higher frequency. Some adjustments are made to take account of the effects of axial extension in the tests at the two lower frequencies.

A moment-curvature relationship for the material in a cyclic state is established along with a fatigue resistance law for the range of deformations considered; the former being restricted to cyclic operations in the range from 1 to 10 c/min.

An indication is given, supported by some experimental evidence, of how the moment-curvature relationship and fatigue resistance law can be used to predict the behaviour of mild steel structural components subjected to the type of loading under consideration.
A theoretical study of in-plane bending of a single unreinforced mitred-bend
Authors: Jones N , Kitching R
Published: July 2007

It can be shown that an exact analysis of the deformations or stresses in a single mitred-bend would involve some terms which rapidly decay along the pipe axes and others which would have a relatively long damping length. The overall flexibility and radial deformations of a single unreinforced mitred-bend have been estimated by minimizing the strain energy contributed by the long damping length terms in a manner similar to that used by von Kármán for curved pipe-bends. Finally, the short damping length terms are introduced in order to satisfy the equilibrium and compatibility conditions across the oblique intersection of the two pipes forming the mitred-bend.

The theoretical values of overall flexibility, diameter changes, and stresses were found to be in close agreement with experimental values for a single right-angled unreinforced mitred-bend.
Design implications of tests on a large 90° smooth bend
Authors: Poynor J F
Published: July 2007

The paper details the design implications of a site strain gauge test carried out on the 6 ft 6 in diameter reactor outlet ducting of a nuclear power station. The test subjected a portion of the ducting to a horizontal load of 10 ton, and the strain gauge survey was taken on a smooth bend of the ducting which was inherently flexible and did not incorporate the usual bellows units to absorb thermal expansions.

Theoretical stresses in the bend of the test portion were calculated under the horizontal load, and comparison made between experimental and theoretical values. At the design stage of the station a detailed analysis was carried out for the complete system under thermal expansions, and this analysis is briefly described. Using the comparison obtained from the test portion, an estimate is made of the probable stress levels that will exist in the complete duct system under reactor operating conditions.

During fabrication of the smooth bends a dimensional survey was carried out on a complete component, and the tolerances achieved are discussed and compared with tolerances obtained on the more usual smaller diameter welding elbow. The effect of end restraints on the flexibility of smooth bends is also discussed, and the lack of design information on this aspect is emphasized.

It is concluded that the stresses in the bends may be accurately predicted, but a larger error is likely to occur in the prediction of end reactions and the stresses induced in vessels subjected to these reactions.
Elastic stress concentration factors in finite plates under tensile loads
Authors: Ibrahim S M , McCallion H
Published: July 2007

New results for stress concentration factors at notches, fillets and circular holes in plates under uniaxial load are presented. These stress concentration factors have been obtained from numerical solutions of the governing equations for elastic stress distribution and are compared with experimental and theoretical factors published by other workers. The generality of the method used is indicated in the solutions obtained for finite plates with a number of holes and for a plate with a hole and notches.
A study of large deformations by matrix algebra
Authors: Hsu T C
Published: July 2007

The mathematical properties of large deformations such as those occurring in rolling and extrusion are different from those of small deformations dealt with in linear elasticity. These properties are explored by matrix algebra. The relation between pure shear and simple shear, and hence the difference between tension and torsion tests, are explained. For practical investigations, a method is presented of representing large deformations as measured from the deformed grid pattern.
Oblique incidence observations as an aid to three-dimensional stress separation
Authors: Allison I M
Published: July 2007

In the most general case the determination of the separate stresses along a selected line in a three-dimensional photoelastic model requires the evaluation of the shear slopes in two mutually perpendicular planes which intersect in the chosen line. The measurement of one normal and two oblique observations at a series of corresponding points in a set of parallel slices provides an alternative method for determining the shear slopes and yields a complete analysis of the stress distribution without further optical measurements. The method is illustrated by its use to analyse the stresses in a model of a loaded rail supported upon a deep welded plate girder.
The application of moiré rotational mismatch techniques to strain analysis
Authors: Vafiadakis A P , Lamble J H
Published: July 2007

Theoretical and technological aspects of moiré fringe techniques when applied to problems of strain analysis are discussed.

An outline is given of the methods of determination of direct and shear strain distributions of elastic and plastic orders of magnitude from the formation of moiré patterns resulting from the superposition of two gratings of straight parallel lines. The rotational mismatch technique is discussed and shown to give strain directly.

Reference is made to the use of master gratings, to the ‘photo-resist’ and ‘stripping film’ techniques for the reproduction of these gratings and to some of the photographic difficulties encountered.

The advantages of the moiré techniques over conventional methods of strain evaluation employing extensometers, strain gauges and photoelastic materials are discussed and illustrated by results obtained during (1) uni-axial tensile tests on mild steel, brass and aluminium alloy, and (2) diametral compressive tests on cast iron discs.
Bending of uniformly loaded column-supported flat plates
Authors: Gupta K K , Vaughan R C
Published: July 2007

The paper presents a brief outline of an analytical and experimental procedure adopted for the generalized solution of bending of a uniformly loaded infinite flat plate structure, rigidly clamped in regularly spaced rectangular columns to form regular rectangular panels of slab. The complex variable method in conjunction with conformal transformation has been adopted for the analytical solution, the results of which are verified by model testing on the moiré apparatus. The close agreement between the compared theoretical and experimental results indicate that the analysis yields reliable results.
Low cycle fatigue of steels under biaxial straining
Authors: Pascoe K J , de Villiers J W R
Published: July 2007

A cruciform test specimen and a loading rig are described, by which any combination of biaxial strains can be applied to a specimen. With the pressurizing equipment so far available, three states of strains have been investigated for two steels. In the mild steel used, large inclusions oriented in the roll direction aided fracture propagation when a maximum shear plane coincided with the roll direction. When not influenced by inclusions, fatigue life is related to total strain range by Coffin's law

        ∊ N a = C

The values of α and C are different for different states of strains. Empirical formulae are given to predict results for other states of strains.
The elastic behaviour of tube drawing dies subjected to a sinking process
Authors: Kenny B
Published: July 2007

A numerical stress analysis study of a tube drawing die of conical profile is used in conjunction with a theoretical expression predicting die pressures in a sinking process, to obtain hoop strain information for the outer surface of a tube drawing die. The analysis indicates that material strain hardening rate and coefficient of friction both affect the hoop strain distributions, but their separate effects may be measured individually by appropriate positioning of strain gauges on the outer surface of the die.
Creep buckling of columns with lateral restraint
Authors: Freed N H , Alexander J M
Published: July 2007

This problem arises from the use of vertical fuel elements in graphite-moderated types of nuclear reactor. Previous theoretical work based on the tangent rate modulus approach has been extended to cover all phases of creep and elastic deformation for both symmetric and asymmetric single-plane bowing. By introducing a ‘solution time’ parameter, a generalized solution can be derived for any given material and initial shape, which is valid for an arbitrary range of sizes of rod, temperatures, and loads (neglecting elasticity). For ‘Magnox’ at 295°C the theory indicates that elastic deformation is negligible.

It was found from experiments on round ‘Magnox’ rods which were allowed to ‘lay’ against a simulated channel wall (this is the condition described as continuous lateral restraint) that creep bowing seldom occurred in a single plane. Comparison with the theoretical analysis for such cases was therefore difficult, but it was found that the theoretical predictions were generally very conservative, and that by splitting the measured deflections into major and minor planes some correlation could be obtained. By using a specimen of rectangular crosssection having an aspect ratio of 2:1, bowing was confined to a single plane and very good agreement with the theory was obtained, both with respect to the deflected shape itself and to the time required to achieve it.
Plastic deformation in the compression test of pure copper
Authors: Hsu T C , Young A J
Published: July 2007

A technique is developed for measuring accurately the strains in a cylindrical compression specimen both on the cylindrical surface and on the flat ends. It is found that by using polytetrafluorethylene (p.t.f.e.) sheets as lubricants, a bollard-shaped specimen is produced, and that a suitable amount of this lubricant produces deformations very nearly the same as those in the ideal compression test. The deviations from the deformations in the ideal compression test are represented by the strain paths of particles on the surfaces of the specimen. The stress-strain relationship based on the middle section of the specimen with optimum amount of lubricant is considered to be the standard, and comparison is made with corresponding stress-strain relationships in barrel- and bollard-shaped specimens.
Experimental determination of thermal stress: A solid circular cylinder in a transverse flow of hot gas
Authors: McQuillin L A
Published: July 2007

A circular disc in a uniform coplanar flow of hot gas ( Re = 4000) is used to find radial and circumferential stresses for a solid cylinder. Heat transfer is through a boundary layer. Stresses are given for diameters parallel to and across the flow direction. There is some agreement with an approximate analytical solution. A generalization of the principal results is suggested.
Evaluation of stresses and strains in two-dimensional photoplasticity
Authors: Javornický J
Published: July 2007

Analysis of birefringent effects in celluloid during plastic strain shows that stresses and strains can be evaluated independently by observation of fringe order under load, residual fringe order, and birefringent dispersion.
A mathematical model for generating microplastic hysteresis loops
Authors: Esin A , Jones W J D
Published: July 2007

A method is suggested for defining the extent of the microplasticity which can exist in a material at stresses between the ‘true elastic limit’ and the nominal yield point or proportional limit.

The suggested mathematical model makes it possible to extrapolate the macroscopic plastic equation into the elastic region in order to take account of the localized nature of the plastic flow.

This analysis can be used to calculate the microplastic hysteresis energy absorbed per cycle by a material under cyclic loading and with a knowledge of the total energy to fracture can be used to predict the number of fatigue cycles to failure; an example is given.
Soils and model tests
Authors: Roscoe K H
Published: July 2007

Two main uses of model testing in soil mechanics are considered. The first is to examine, usually on only a qualitative basis, at a reduced scale the assumptions that have been made in theoretical analyses of prototype problems, the object being to develop analysis and models side by side with a view to improvement of the former. An outline is then given of current methods of analysis based only on failure conditions and of the use of new methods developed at Cambridge of investigating the behaviour of soils in models at all stress levels. Thereafter attention is confined to the second use of models in which attempts are made to satisfy the conditions of similarity so that prototype behaviour can be predicted from model data. These conditions are derived. Simulation of soils by other media is discussed but is not considered to be a rewarding procedure. It is then shown how the Cambridge approach to the mechanical behaviour of soils has enabled the formulation of a useful law in model testing for work-hardening soils, and similar granular media, at all working loads. This law states the conditions under which the same soil may be used in model and prototype. Finally the potentialities of centrifugal model testing are discussed; they provide an opportunity of satisfying simultaneously this law and the conditions of similitude.
Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses
Authors: Rushton K R
Published: July 2007

The von Kármán equations for the large deflection of plates are solved by the dynamic-relaxation method. Detailed results are presented for square plates having simply supported edges with zero in-plane boundary stresses. The results show that high stresses occur towards the corners of the plates. The mesh effect is investigated and recommendations are made for the optimum mesh spacing.
Finite-element analysis of stresses in shafts due to interference-fit hubs
Authors: White D J , Humpherson J
Published: July 2007

Stress distributions in shafts due to interference-fit hubs are presented for shafts with various hub-seat features. For the calculations axisymmetric finite-element computer programmes were used.

In a plain shaft there is a high local pressure just inside the hub face and a high axial tensile stress just outside it. These stresses are relieved by features, such as fillets or grooves in the shaft, arranged to give a raised or isolated hub seat and, of the two, a raised seat with a transition radius is more effective than a stress-relieving groove. Hubs fitted on either side of a groove reduce the maximum tensile stress compared with a single hub, while overhung hubs produce no significant change compared with flush hubs. Methods of fitting which promote axial constraint between the hub and shaft should be avoided since this leads to an increase in tensile stress in the shaft.
Effects of geometry on stresses in discontinuous composite materials
Authors: Iremonger M J , Wood W G
Published: July 2007

The stresses are examined in a plane unidirectional discontinuous-fibre composite when it is loaded in line with the fibres. A systematic study is presented of the effects of fibre spacing and size and nature of discontinuities. For a fibre/matrix modulus ratio of 5 a total of 18 analyses, obtained by the finite-element method, are discussed. These are for models with fibre-volume fractions of 0·3, 0·5, and 0·67, each with three different distances between fibre ends. Each model is analysed first with the end gap filled with matrix material and then with this space void. Results are confirmed by a photoelastic analysis.
Effect of pre-stress on the yield and flow of En 25 steel
Authors: Rogan J , Shelton A
Published: July 2007

Combined tension-torsion tests have been performed at constant stress ratios on En 25 steel, previously annealed and then subjected to a pre-stress in either tension or torsion.

The post-yield behaviour showed marked room-temperature creep and, in general, both the axial- and the shear-strain components could be expressed by the logarithmic creep equation. The direction of the incremental strain-ratio vector was initially markedly different from that shown in the previous tests on annealed En 25 steel, but rotated towards that direction with increased stress. The yield locus subsequent to each pre-stress was established by fulfilling two requirements: that it must pass through the stress space normal to all the plastic-strain-increment vectors it encounters; that each yield stress should be an extrapolation from the curves of creep coefficient plotted against stress and stress plotted against ‘long time’ strain.

The results show that a pre-stress hardens the material over that half of biaxial stress space bisected by the pre-stress axis and hardens it less or even softens it in the reverse half of that space. The cross-effect of a tensile pre-stress is greater than that of a torsion pre-stress and increasing the degree of pre-stress has a gradually reducing cross-effect.
Design of steam-turbine casing flanges: A two-dimensional photoelastic study
Authors: McKenzie H W , White D J , Snell C
Published: July 2007

Photoelastic tests have been made on two-dimensional models of steam-turbine flanges for various combinations of the flange parameters depth, width, and bolt position. Design curves have been produced which show the relation between these flange parameters and the ratio of bolt force to pressure force necessary to produce a compressive stress at the inner edge of the flange equal to the internal pressure, this being the criterion adopted to ensure steam-tightness.

Comparisons have been made between the experimentally determined stress distributions and distributions calculated by various methods. Of computer-aided methods, the English Electric Kidsgrove structural-analysis programme gave the best correspondence to the experimental results with a relatively simple idealization of the problem. When the depth of a flange exceeds the width and the bolt load acts within the inner half, the stress distribution is reliably predicted if the flange is assumed to behave as an eccentrically loaded column.
Numerical solution of axisymmetric-stress problems by point matching
Authors: Hooke C J
Published: July 2007

In a previous paper the author described the application of the point-matching technique to the solution of plane elastic problems. It was shown that it is possible to produce a single computer programme capable of analysing a wide range of such problems. The technique is extended in this paper to the case of an axisymmetrically loaded elastic body of revolution. The details of the technique are necessarily more complicated in the present instance but it has proved possible to develop a general computer programme for this type of problem.

The application of the method is illustrated for a number of problems for which approximate or experimental results are available. Good agreement between these results and the point-matched stress distribution is obtained in every case.
A method of calculation for thermoforming plastics sheets
Authors: Williams J G
Published: July 2007

Stress-strain data for polymethylmethacrylate at the moulding temperature of 160°C are analysed by a rubber elasticity representation. It is shown that large strain solutions may be obtained for simple geometries with an approximate form of stress-strain relation and examples are given of predictions of profile and thickness variation for blown domes and other axisymmetrical shapes. Forming pressures and loads are predicted by an iteration extension of the simple method together with examples of predictions for shapes formed with conical dies. The comparison of experimental and theoretical values is generally good.
Use of collapsible structural elements as impact isolators, with special references to automotive applications
Authors: Postlethwaite H E , Mills B
Published: July 2007

Part 1: Simple struts have been impacted between travelling and stationary masses and the collapse found to consist of two distinct phases. The pre-failure phase, being primarily an elastic region, has been analysed by stability criteria and the post-failure phase by consideration of the plastic collapse of the strut. Associated with the pre-failure phase is a large transient deceleration which is found, among other parameters, to be a function of the strut shape.

Part 2: A series of sheet-metal structures have been impacted and, like struts, the collapse found to consist of pre- and post-failure phases of separate identities. The pre-failure phase is again associated with the shape of the structure and may give rise to a large transient deceleration. This analysis has led to the consideration of more complex elements, such as might be found in an automobile frontal structure, and finally to a complete automobile analogue. Conclusions are drawn about the structural parameters required to bring about specific deceleration characteristics in a vehicle crash.
Grey cast irons for thermal-stress applications
Authors: Bertodo R
Published: July 2007

Pearlitic flake-graphite grey cast irons have long been widely used for the manufacture of diesel-engine combustion-chamber components. Nonetheless, very few pertinent high-temperature data are to be found in published work. The investigation described attempts to enlarge current knowledge on the high-temperature behaviour of grey cast irons in view of requirements highlighted by high thermal ratings. A general consideration of the problem showed that the often quoted Eichelberg material-quality factor is largely irrelevant and an alternative assessment formula is proposed. This is broadly confirmed by a systematic examination of the mechanical and physical properties of 166 plain and alloyed cast irons and a limited number of engine components.

Different engine components impose different demands upon the material properties but for economic reasons a single cast-iron melt capable of meeting most of the requirements of all components is needed. It is shown that this situation is best met with an alloyed iron containing 1.3 per cent of copper-nickel and 0.4 per cent of molybdenum. The scatter in properties obtained from production casts was found to be typical for such irons. For components having safety factors of 2 or less, a prerequisite of economic engineering design, the service reliability is crucially dependent upon the scatter of material properties. Thus, there are advantages in reducing this scatter and it is shown that this can be achieved by attention to the cleanliness of the matrix and tight control of the chemistry of the melt.

In general, the absolute values of mechanical and physical properties of flake-graphite cast irons appear to be governed mainly by the form and size of the graphite flakes and the chemistry of the matrix (i.e. CEV and alloying additions). Regression analysis of the results permitted the derivation of empirical formulae for the prediction of the iron properties. The general findings are used to suggest possible ways of improving the thermal resistance.
Stress-concentration factors in u-shaped and semi-elliptical edge notches
Authors: Baratta F I , Neal D M
Published: July 2007

Stress-concentration factors are analytically determined for relatively deep U-shaped edge notches of constant radii in a semi-infinite sheet with uniaxial tension applied parallel to the sheet edge. Because a strong geometric similarity exists between a U-notch and a semi-elliptical notch of the same tip radius, a comparison of such analytical data is effected. Stress-concentration factors for U-notches in a semi-infinite sheet are also compared with other comparable analytical and experimental data available in the literature.

Finite-width correction factors are applied to the results of the semi-infinite-sheet analysis to provide practical design data. These data are compared with experimental results provided by a number of investigators.
Equipment for creep testing at variable load and temperature
Authors: Smith E M , Grant C , Booth J M
Published: July 2007

A creep laboratory for variable-load and variable-temperature testing in uniaxial tension has been established at the University of Newcastle upon Tyne. The philosophy behind the specification and design of the equipment is described, considerable attention having been paid to accurate control of the test environment. The method of processing experimental data, obtained with a data acquisition system, is outlined.
An experimental linear cumulative-damage law
Authors: Miller K J
Published: July 2007

An hypothesis of cumulative damage is presented that may be expressed mathematically as Σn÷Nf = constant where n is the number of cycles performed at a constant strain range and strain rate and Nf is the number of cycles to failure at the same strain range and strain rate.

An initial experimental investigation at room temperature shows that, under constant strain-rate conditions, the load-sequence effect is removed, but the value of the constant is dependent on the definition of failure. If failure is defined as complete rupture the summation term is less than unity whatever the sequence of loading. Should failure be defined as the termination of the steady-state period, that is at the point of crack growth instability, then the summation term is greater than unity. This latter definition therefore leads to a linear law of cumulative damage that gives a doubly cautious prediction of life that is of obvious advantage to engineers.
Experimental determination of adhesion and slip areas in rolling contact
Authors: Ollerton E , Pigott R
Published: July 2007

An experimental technique has been developed to allow the rapid determination of adhesion and slip areas in steady-state rolling contact.

The technique consists in rolling solid black-rubber toroids on a ground-glass plate under carefully controlled conditions. It enables the division of the contact area into slip and adhesion areas to be observed and photographed whilst rolling is taking place.

A loading frame was devised to enable rolling with longitudinal shearing traction, rolling with transverse creep, and rolling with spin to be investigated either separately or in combinations.

The results of the experiments have been compared with existing theories, and some conclusions as to the accuracy of the theories have been made.
Photothermoelastic analysis of thermal stresses in discs with eccentric holes
Authors: Ajovalasit A
Published: July 2007

The paper deals with thermal stresses that arise in discs with eccentric holes, such as are employed in the rotors of multi-stage gas turbines. The stress distribution was analysed by the photothermoelastic method. CR 39 sheets were used as the material and dry ice as the refrigerant.

The effect of several geometric parameters on stress distribution, especially the influence of adjacent holes, was investigated by testing 32 configurations of discs.

Curves that allow the determination of the peak stresses and optimum spacing of holes are given.
Effect of unidirectional and reversed torsion on the strength and ductility of 2024 aluminium
Authors: Nypan L J
Published: July 2007

Experiments on the tensile yield and ultimate strength and elongation behaviour of 2024-T4 aluminium after torsional prestrain are reported. Tensile strengths were observed to increase with torsional prestrain up to 0.325 in/in, beyond which strengths decreased.
Cruciform specimens for biaxial fatigue tests: An investigation using finite-element analysis and photoelastic-coating techniques
Authors: Wilson I H , White D J
Published: July 2007

The results are presented of investigations made on four cruciform biaxial fatigue specimens, each of which had a differently designed central region. This central region consisted of a reduced section of uniform thickness t over a circular area of diameter d which was connected by a transition radius to the full thickness of the cruciform. Equal tensile and compressive forces were applied alternately along one pair of arms only and the distribution of surface strain was studied by photoelastic-coating techniques after elastic cycling and then plastic cycling. To assess the fatigue performance of the specimens further cycling was carried out until cracks developed. Under elastic conditions, strains uniform over the thickness were calculated by finite-element techniques.

For conventional fatigue tests in the high-endurance range the specimen with d/t = 12.5 is recommended. For high-strain low-endurance fatigue investigations the specimen with d/t = 5 is preferred. The recommended designs are free from problems of buckling and are such that an area of uniform strain is produced at the centre of the specimen.
Pressure distribution over the flat end surfaces of compressed solid-rubber cylinders
Authors: Hall M M
Published: July 2007

The shapes of the pressure distributions over the flat end surfaces of compressed solid-rubber cylinders have been determined. The cylinders were compressed between metal end plates. The pressure distribution for compressive strains of less than 3 per cent is approximately parabolic. It is unaffected by the strains set up in the rubber by the differential thermal contraction of the rubber and bonded-metal end plates. A method of extending these measurements to large compressive strains, and a possible future programme of work, is outlined.
Approximate creep analysis for thermoplastic beams and struts
Authors: Benham P P , McCammond D
Published: July 2007

Creep deformation up to 106 s has been measured for beams subjected to pure and three-point bending and for buckling struts made from polymethyl methacrylate, polyvinyl chloride and polypropylene. Of the analytical methods considered for predicting creep, the most accurate was that in which the isochronous stress-strain curves in tension and compression were used in conjunction with equilibrium and strain displacement equations. However, this involved more computation than the other two methods which simply substituted a secant-modulus value from the isochronous curves (1) at the expected maximum stress and (2) at a limit of 1 per cent strain in the established linear elastic formulae for the components. In (1) there was only slight over-estimation of experimental deformations but in (2) there were quite serious differences, particularly at longer times, and small strains.
New stress-analysis procedures using the method of shear-stress differences
Authors: Bednár J
Published: July 2007

The use of logarithmic scales, adaptation of the polariscope, and the principles of the moiré method and the method of constant spacing between two lines are discussed.
Computation of stresses and flexibilities for multi-mitred pipe bends under in-plane bending
Authors: Bond M P , Kitching R
Published: July 2007

The analysis developed is a refinement and generalization of an existing theory. The extensions incorporated are necessary for the accurate theoretical prediction of stress distributions and flexibility factors for multimitred pipe bends of low pipe factor. A method of approach that renders computation of the analysis more practicable has been introduced and a programme has been developed for the production of design information.

Flexibility factor and stress distributions calculated in this way have been compared with experimental results for a 30-inch-diameter, three-weld right-angled mitred bend of low pipe factor (0·0246).
Strain localization in beams under cyclic plastic straining at room and elevated temperature
Authors: Horwood G P , White D J
Published: July 2007

Deflection-controlled tests have been conducted on beams subjected to uniform bending and two forms of non-uniform bending in which strain localization occurs. The materials tested were mild steel to B.S. 1501–161 Grade 28A at room temperature and 350°C and stainless steel En 58J at room temperature and 650°C.

For materials which show a settled cyclic stress-strain relation (the cyclic semi-range of strain and the corresponding cyclic semi-range of stress) estimates may be made of life in deflection cycling for beams under strain-localization conditions if the strains are calculated from the cyclic relations and the corresponding endurances are obtained from strain-cycling tests in uniform bending. On the basis of the present and previous results, it is believed that this procedure will give predictions which are on the side of safety. In the present work the predictions were often unduly safe. For materials which strain-harden severely, an elastic analysis may sometimes be adequate for an assessment of the strains involved. However, with such an analysis the predicted endurances may be unsafe and should be reduced by a suitable factor to allow for uncertainties.
Design of cams to reduce maximum stress in a longitudinally reciprocated bar
Authors: Beddoe B
Published: July 2007

There is a lower limit to the maximum stress in a bar that is moved longitudinally at constant velocity and reversed at one end in a finite time, the other end being free. The lowest possible value of the maximum bar stress during a single reversal is determined for the general case and equations to define cams that achieve it are established. These cams have the disadvantage of giving much higher stresses when run above or below the speed for which they were designed.

Another type of cam without this disadvantage is obtained by reversing through two parabolic arcs which are selected to minimize the maximum bar stress. Proof that the selection is the best obtainable from two parabolas is derived from solutions in terms of progressive stress waves with consideration for light damping. Specification of this type of cam and measurements of the stresses in ‘traverse bars’ reciprocated by such cams on machines for winding yarn are included.