Showing papers in "Journal of Strain Analysis for Engineering Design in 1969"

Finite-element analysis of stresses in shafts due to interference-fit hubs

Abstract: 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.

Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses

Abstract: The von Karman 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.

Triangular finite elements of variable thickness and their application to plate and shell problems

Abstract: Stiffness and mass matrices are discussed for a plane triangle whose thickness is allowed to vary linearly between the nodes. In-plane and bending actions are considered separately, and the formulation makes use of the ‘hybrid’ approach, in which the from of the stresses is assumed inside, and on the boundary of, the triangle, and displacements additionally assumed on the boundary only. In Appendix 1 the hybrid approach is developed in detail for a simple beam element.The allowance of variable thickness carries with it a greater reliance on efficient use of computers, and an opportunity is taken in the paper to reorganize the hybrid approach to achieve this.The accuracy attainable with this new element is assessed by comparison with results obtained by other methods for a flat plate of variable thickness, simply supported along its edges. A similar plate supported at its corners, and containing holes, is also considered, and the finite-element calculations are compared with moire fringe and other ...

Shouldered plates and shats in tension and torsion

Abstract: Room-temperature and frozen-stress photoelastic tests have been carried out to determine the magnitude, position, and extent of the stress concentrations which occur in the blending radii at the junctions of sections of different widths in symmetrical plates subjected to direct loads.An empirical equation has been derived from the flat-plate tests which is also applicable to shafts in tension.Other published data are consisent with the predictions of the empirical equations.Stress concentration factors for shafts in torsion are lower than in tension.

Yield and subsequent flow behaviour of some annealed steels under combined stress

Abstract: Constant-stress-ratio tests under combined tension-torsion have been performed on annealed En 25 and En 24 steels. The sharp yield behaviour of these materials enabled the initial yield locus to be clearly defined and this was close to that predicted by the Tresca criterion. Post-yield behaviour showed marked room-temperature creep of the logarithmic form ∊ = a ln t+c, by both the axial- and shear-strain components. The strain-rate ratios and the strain ratios were normal to the yield locus and remained so for increasing stress.The equivalent-plastic-work hypothesis did not produce satisfactory correlation of the combined-stress results and empirical equivalence of the strains was established by introducing a factor to account for the influence of combined stresses upon the magnitude of the resulting strains. This empirical equivalence also provided good correlation of the creep-strain rates and these results finally led to the complete correlation of the stress-strain-time behaviour of these mate...

Stresses at end-milled keyways in plain shafts subjected to tension, bending, and torsion

Abstract: The frozen-stress photoelastic technique has been used to determine the complete surface stress field in empty keyways of British Standard proportions for rectangular keys. A method is included for the photoelastic analysis of general surface stresses in doubly curved surfaces with one small radius. The ratio of measured stress to stress in the same fibre in a shaft without keyway is the same for bending and tension. Stress indices for combined bending and torsion have been calculated for one fillet-radius ratio. A simple method is presented for obtaining a close upper bound for the peak stress in any B.S. keyway for rectangular keys subjected to any combination of bending and torsion.

Effect of multiaxial stresses on the fracture strength of silicon carbide

Abstract: This work describes the fracture behaviour of silicon-carbide tubular specimens under multi-axial stresses at room temperature. A method of obtaining combinations of stresses in the form of torsion, hoop, axial tension, and compression is described and failure envelopes for silicon carbide are included from the data obtained.Failure theories are reviewed and the results from the work show that the available theories are inadequate to describe both the tension-tension and tension-compression quadrants.For practical purposes a straight-line relation can be used joining axial and hoop tensile strengths and the axial compression strength.

Effects of geometry on stresses in discontinuous composite materials

Abstract: 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.

Residual stresses in rolling contact

Abstract: The paper reports an experimental investigation into the residual strsses induced into cylndrical discs by the action of rolling-contact loads sufficiently high to cause some plastic deformation in the near-surface layers.A general method is first described for finding both circumferential and axial components of residual stress in cylindrical bodies in circumstances where the stresses vary with the radial co-ordinate only. This method is believed to be an improvement on previous methods for separating the two components of residual stress, particularly where only specimens of restricted length are available. For example, the method could be applied to thick-walled tubes.Measurements have been made of the residual stresses due to rolling contact, in pure rolling and in combined rolling and sliding. In all cases both components of residual stress were compressive and reached a maximum value below the surface at about the depth of the maximum Hertz shear stress. The measured residual stresses in the...

A 30 ton biaxial tensile testing machine

Abstract: The machine is intended for a flat-plate testpiece, one face of which has to be unobstucted throughout the test. Plates up to 36 in long, 27 in wide, and 3/4 in thick can be accommodated.Hydraulic rams actuated by air-hydraulic pumps exert completely independent tensions on cruciform test pieces through spherical bushes.Satisfactory direct-load readings were obtained form pressure gauges.

Stress distribution in a tension specimen notched on one edge

Abstract: The stress distribution in a tension specimen notched on one edge was obtained photoelastically for several ratios of notch depth to specimen width. The stress-concentration factors agreed well with corresponding values derived from Neuber's theory of notch stresses. It was also shown that the stress-intensity factor for a tension specimen with a single crack on one edge, obtained by the collocation method, agreed well with that deduced from Neuber's theory.

Stress analysis in viscoelastic bodies using finite elements and a correspondence rule with elasticity

Abstract: It is shown how the finite-element displacement method of analysis using an elastic analogy may be applied to problems in plane stress where the material is viscoelastic. The method allows material non-homogeneity to be taken into account, as it might need to be in some thermo-viscoelastic problems.Some numerical results are given, based on the Maxwell body, and these are supported by a short-time creep experiment on a sheet of perspex. The distribution of stress is found to change slightly during this period of time.

Stresses at keyway ends near shoulders

Abstract: The photoelastic stress analysis of a series of shouldered shafts with keyways in the shanks is described. Direct loading and torsion have been studied. The shoulder-fillet ratio (shoulder-...

A photoelastic examination of the stresses in rolls during rolling

Abstract: The paper describes some experiments to determine the stress distribution in rolls during the rolling of pure lead. The rolls were made from a hard transparent resin and the isochromatics and isoclinics were recorded whilst rolling was in progress. From these recordings the stress distributions were obtained. Particular reference was made to conditions of normal and shear stress at the contacting surfaces. The paper gives results for three roll diameters and for each of these four roll loads were applied. The experiments were carried out for both dry and lubricated conditions.The results of this work show a variation of the shear stress at the surface of contact accompanied by a change of sign at the neutral point. The normal roll-pressure curves are in general agreement with those found by workers using other techniques. The results also indicate a significant variation in the ratio (shear stress/normal pressure) over the contact surface, although this was decreased by lubrication. For a given ro...

Effect of pre-stress on the yield and flow of En 25 steel

Abstract: 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...

Experimental analysis of high-frequency stress waves in a ring

Abstract: This paper deals with the photoelastic analysis of stress waves in a thick ring subjected to transient high-frequency loading. The device used to apply the loading is a piezo-electric transducer which initially produces four cycles of a 31·25 kHz toneburst. The loading pulse can be reproduced with high precision. The ring is illuminated with a flash of approximately 0·5 μs duration which can be delayed in a continuously adjustable manner. Isochromatics and isoclinics can be directly observed as static patterns. Photoelastic data are supplemented by measurements obtained with a capacitance gauge used as a dynamic lateral extensometer. Satisfactory agreement is found between tangential stresses near the free boundary of the ring determined from photoelastic data and those determined from capacitance-gauge measurements. As examples of complete determination of stress distributions, the separated principal stresses are obtained along an axis of symmetry and a vectorial representation of the principal ...

Simply supported plates with corners free to lift

Abstract: The lifting of corners from the supports of laterally loaded plates is discussed. A method of analysing the problem for both the small and the large deflection of plates is described; this method is based on the dynamic-relaxation technique.Comparisons are made with experimental results, and the effect on the stress distribution of a lifting corner is discussed.

Deformations of stacks of thin layers under normal compressive loads

Abstract: Stacks, each consisting of 40 thin metallic layers, were compressed under loads of up to 5000 kg. Measurements of the electrical resistance of the stacks (i.e. for the 39 metal-to-metal contacts in series) revealed four distinct regions of deformation.The extent of these regions was marked by sharp changes in the slope of the curves obtained when load was plotted against electrical conductance. The first change occured at a load of approximately 200 kg, irrespective of layer size, roughness, or hardness. Two further transitions occurred at pressures equal to 2·5 and 22·5 per cent approximately of the surface hardness. Above the upper transition point the bulk properties play a large part in the mechanism of surface deformation.

Bending of normally loaded simply supported rectangular plates in the large-deflection range

Abstract: Means of solving the non-linear differential equations of plate bending are revieweed and a method based on minimizing the corresponding energy integral is selected as offering most advantages. The energy intergral can be approximated either by using finite-difference approximatons or by assuming a form of displacement variation. Two sets of non-linear algebraic equations (in the in-plane and out-of-plane deflections) are thus formed and, by substitution alternately in each set, the resulting linear equations are solved.Results for simply supported rectangular plates have been worked out in some detail; these are compared with tests made on plates of various aspect ratios. Good agreement on maximum values of stress and deflection was obtained.

High-temperature high-elongation resistance strain gauges

Abstract: The paper outlines an investigation undertaken in an attempt to evolve an electrical-resistance strain gauge for the measurement of slowly varying strains in the range ±5 per cent over the temperature interval 20°C-400°C in oxidizing environments. A critical review of published work suggested that few pertinent data existed for plastically strained conductors and that only alloys having a high degree of electrical stability and a strain sensitivity close to 2·0 would be suitable. Two alloys appeared to possess such properties, namely one containing nearly equal molecular proportions of nickel and copper and one approximating to 4(Ni3Cr)Ni3Al.Subsequent tests on long free spcimens revealed that the electrical stability was dictated by metallurgical factors and in some way related to the fatigue ductility. Only the nickel-chromium-aluminium alloy was adequately stable, electrically and metallurgically, over the temperature range of interest, provided it was in the disordered annealed condition. Meas...

Transient stress concentration at an elliptical discontinuity

Abstract: : The purpose of the investigation was to determine experimentally the dynamic-stress concentration factors in a strut loaded by high-velocity impact and containing a symmetrically located elliptical discontinuity. The photoelastic technique was used and the conventional light source with its many inherent problems was replaced with a modulated ruby laser. (Author)

A model for uniaxial creep based on internal-stress redistribution

Abstract: The changes of creep-strain rate associated with primary and tertiary creep are attributed to a process of internal-stress redistribution between the strong and weak portions of material while for each portion the creep rate depends only on its stress. An expression for the primary-creep curve is derived which is shown to be in substantial agreement with the usual empirical (time)1/3 power law. The model describes the changes in creep rate when the stress is constant and implies as a natural extension a method of calculating creep rate when the stress changes because memory effects are attributed solely to changes of internal stress. The calculated rates obtained according to the method show the creep-recovery phenomenon and in this respect are superior to the ‘hardening hypotheses’ which fail to simulate creep recovery but are normally used for stress-redistribution calculations. According to the model the strain during primary creep is dependent on the stress derivative of the secondary creep ra...

Calculation of the elastic deformation of textile beams during yarn winding

Abstract: The problem of winding yarn on beams is examined.A theoretical calculation of the pressures on and the deformation of the beams is developed. In a first approximation the beam is assumed to be completely rigid and in a second approximation the elasticity of the barrel and flanges is taken into account.The results, developed on several types of yarn and on beams of various shapes and forms, are compared with experimental data obtained during a series of tests by the I.D.I. of Turin, Italy, on beams during use.

A photoelastic investigation of contact stresses in equal spheres rolling together with spin

Abstract: Photoelastic tests have been performed to investigate the effect of spin on the contact stresses between rolling bodies. All the tests employed equal spheres, resulting in nominally flat, circular contact areas. The shear-stress distributions on such contact areas have been experimentally determined by the ‘frozen stress’ technique. One set of tests examined the case where no resultant surface force was transmitted between the spheres while they were rolling with spin. Another set of tests allowed a resultant force perpendicular to the rolling direction to be transmitted. The test results are compared with several theories.

Stresses in asymmetric discs

Abstract: The surface stresses in rotating discs of asymmetric profile and the effects of axial deflection, as determined theoretically, are compared with measurements made on photoelastic models by the ‘frozen-stress’ technique.

High-strain low-endurance fatigue behaviour of AISI 1018 steel in reversed torsion:

Abstract: Experiments in repersed torsion of AISI 1018 solid-steel specimens of circular cross-section are reported. Cyclic strain hardening and softening were observed. The relations between shear strain and fatigue life and between cyclic shear strees and strain are presented.

Distortion of metal strip during rolling with rough rolls

Abstract: An experiment simulating the deformation that occurs in hot rolling, by rolling a small specimen of aluminium at room temperature with rough rolls, is described. A rectangular grid incorporated into the body of the specimen allows the determination of the mode of deformation that occurs under conditions of plane strain. The data are anlysed by a computerized method which presents the results in the form of a pattern of directions of maximum shear stress. The pattern obtained agrees substantially with a theoretical slip-line field of the type first proposed by Alexander.

A contribution to the application of photoelasticity to the micromechanics of composite materials

Abstract: Photoelastic-model methods can prove advantageous for the investigation of microstresses in composite materials. Some two-dimensional investigations of this type are discussed and the extension of this work into three dimensions is considered. It is suggested that more than one approach to the three-dimensional problem may be practicable, and special attention is paid to obtaining the maximum amount of information from a sandwiched polariscope by means of light-intensity measurements. A cold-casting technique for the fabrication of composite models is also described.

Pre-attachment matching of resistance strain gauges

Abstract: A technique for pre-attachment selection of strain gauges on a temperature-coefficient basis is proposed in which the gauge is clamped tightly between plates forming a specimen. The response of the gauge when the temperature of the specimen is changed is found to be almost identical with the response of the same gauge when attached and subjected to the same change in temperature.

A method of successive approximation applied to an elastic-plastic deformation theory

Abstract: Elastic-plastic stress and strain concentration factors are derived for a circular hole in an infinite medium under uniform anti-plane shear conditions. The suggested method of solution could be applied also to other problems of interest.