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Showing papers in "Journal of Strain Analysis for Engineering Design in 1967"


Journal ArticleDOI
J Bree1
TL;DR: In this article, a simple model of the can is used to show that the plastic strains so produced may cause ratchetting or plastic cycling as the temperature gradient across the can wall cycles because of startup and shutdown of the reactor.
Abstract: A sealed reactor fuel can when subjected to sufficiently high thermal stresses in the presence of an internal pressure will yield plastically. A simple model of the can is used to show that the plastic strains so produced may cause ratchetting or plastic cycling as the temperature gradient across the can wall cycles because of startup and shutdown of the reactor. On the assumption that creep is negligible, approximate criteria are derived for the onset of ratchetting and plastic cycling, simple expressions are obtained for the plastic strains incurred by each cycle, and failure of the can due to the above mechanisms is discussed both for work-hardening and non-work-hardening material. Consideration is then given to the effect of stress relaxation due to creep when the mean temperature of the can is sufficiently high to cause complete relaxation of the thermal stress while the reactor is at power, creep being ignored while the reactor is shut down. Under these conditions, it is found that the crite...

402 citations


Journal ArticleDOI
TL;DR: In this article, a cruciform test specimen and a loading rig are described, by which any combination of biaxial strains can be applied to a specimen and the fatigue life is related to total strain range by Coffin's law.
Abstract: 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 ∊Na = CThe values of α and C are different for different states of strains. Empirical formulae are given to predict results for other states of strains.

99 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown how compatible displacement fields can be used to generate equilibrating formulations in the other problem, which can result in a direct application of existing programmes to a wider range of problems.
Abstract: It is well known that in approximate analysis of elasticity problems lower and upper bounds to the true strain-energy content can be obtained by the alternative assumptions of compatible displacement fields or of equilibrating stress fields. While formulations based on the first are relatively easy to achieve those based on the second present many difficulties. In this paper it is shown how by virtue of the analogy between plane-elasticity and slab-deflection problems compatible-displacement formulations in either one can be used to generate equilibrating formulations in the other. This should result in a direct application of existing programmes to a wider range of problems.

74 citations


Journal ArticleDOI
TL;DR: A review of failure mechanisms of glass-reinforced plastics under single and repeated (fatigue) loading is presented in this paper, where several micrographs and a brief description of the component materials are given.
Abstract: A review of some failure mechanisms of glass-reinforced plastics under single and repeated (fatigue) loading is presented. Published work of both an experimental and an analytical nature is included. There are several micrographs and a brief description of the component materials is given.

37 citations


Journal ArticleDOI
TL;DR: In this article, the mass and stiffness matrices for a general-triangle element and for a right-angled triangle element are derived for both bending and in-plane actions.
Abstract: Mass and stiffness matrices are obtained for a general-triangle element and for a right-angled-triangle element. Both bending and in-plane actions are considered, although no coupling is assumed, and the matrices relating to bending actions are obtained independently of those relating to in-plane actions. Coupling is introduced, unless all the elements lie in a single plane, when the transformation from local to global co-ordinates is made.In deriving the stiffness matrices assumptions have been made about the form of the stress components within, and on the boundaries of, the element, together with assumptions about the form of the displacement components on the boundary of the element only. The commonly made assumptions in the derivation of stiffness matrices relate to the form of the displacement components not only on the boundary but throughout the element.In order to derive satisfactory mass matrices it is necessary to assume the form of the displacement components throughout the element. Fo...

34 citations


Journal ArticleDOI
TL;DR: In this paper, a review of the available literature relevant to the problem of short-life fatigue failures due to a multiaxial stress-strain system is presented, and a new approach is proposed.
Abstract: Most of the short-life fatigue tests have been carried out in push-pull or in reversed bending. Many machine parts and structural elements, however, are subjected to combined rather than uniaxial fatigue loads. This work is intended to demonstrate a possible approach to solving the problem of short-life fatigue failures due to a multiaxial stress-strain system.The paper includes a review of the available literature relevant to the problem. The more important experimental findings are summarized and presented in the form of diagrams. Various approaches toward the solution of the problems are discussed, and a new approach is proposed.It is demonstrated in this paper that the use of an ‘equivalent-strain parameter’ calculated from the Mises law is not suitable in the description of the problem. It was found that when the strain Δ∊ in the direction of the maximum stress is adopted as a strain parameter and a stress-dependent parameter L is introduced, all of the results can be described by the followi...

30 citations


Journal ArticleDOI
TL;DR: In this paper, the theory for the in-plane and out-of-plane bending of a curved pipe is reviewed by considering it as an extension of the theory of symmetrically loaded shells of revolution.
Abstract: The theory for the in-plane and out-of-plane bending of a curved pipe is reviewed by considering it as an extension of the theory for symmetrically loaded shells of revolution. This treatment is adopted with the intention of modifying an existing elastic-plastic programme for shells of revolution so that it can perform the analysis of pipe bends with in-plane bending. Results are presented for elastic and elastic-plastic behaviour of pipe bends with in-plane bending. These results agree with theoretical and experimental results found in the literature.

27 citations


Journal ArticleDOI
TL;DR: In this article, the suitability of the finite element method for studying the stresses in composite materials and the case of a single broken fibre in a matrix has been examined, and it has been found that high stress concentrations occur in the region of the fibre break which increase with decreasing end gap and would cause matrix yielding or fracture at comparatively low overall stresses.
Abstract: An investigation has been made into the suitability of the finite-element method for studying the stresses in composite materials and the case of a single broken fibre in a matrix has been examined. It has been found that high stress concentrations occur in the region of the fibre break which increase with decreasing end gap and would cause matrix yielding or fracture at comparatively low overall stresses. When the end gap is not void but filled with matrix much lower stress concentrations occur which, below a certain value of end gap, actually decrease as the gap is made smaller.

23 citations


Journal ArticleDOI
TL;DR: In this article, a parametric study has been made of the factors affecting the stresses at rigid inclusions and at unreinforced holes of elliptical shape in spherical shells, which makes possible a simple method of representing the results in terms of the stress-concentration factors in flat plates, and a single geometrical variable.
Abstract: In Part 1 shallow-shell equations expressed in elliptic co-ordinates have been solved in terms of Mathieu functions. Boundary conditions for the rigid insert and for the unreinforced hole are discussed in some detail. Results for an unreinforced opening are compared with experiment and satisfactory agreement is obtained.In Part 2 a parametric study has been made of the factors affecting the stresses at rigid inclusions and at unreinforced holes of elliptical shape in spherical shells. This work makes possible a simple method of representing the results in terms of the stress-concentration factors in flat plates, and a single geometrical variable. The results are verified by experiment.On the basis of this study predictions of the stresses at the intersection of non-radial nozzles in pressure vessels have been made. The theoretical results are compared with experimental evidence already available and reasonable agreement is found.

18 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the plastic instability of thin-walled tubes subjected to internal pressure and independent axial load and showed that taking the stress and strain measurements with reference to the central section of the tube wall gives a good approximation.
Abstract: The plastic instability of thin-walled tubes subjected to internal pressure and independent axial load is investigated. Theoretical treatments of the problem are discussed, in particular the plastic straining of tubes under constant ratio of circumferential to axial stress. The concept of a thin-walled tube is an approximation, the accuracy of which varies with stress ratio. It is shown that taking the stress and strain measurements with reference to the central section of the tube wall gives a good approximation. Thick-walled theory is, therefore, necessary to relate the circumferential strains measured at the outer surface to the strains existing at this central section.The material tested was a nickel-chrome steel, S62, under stress ratios of 0, 0.5, 1.0, 2.0, and ∞. Measurements of strains, pressures, and loads were recorded continuously and it was possible to keep a constant ratio of true stress, as opposed to constant ratio of nominal stress which has been more often adopted.Correlation betw...

16 citations


Journal ArticleDOI
TL;DR: In this article, a technique was developed for measuring accurately the strains in a cylindrical compression specimen both on the cylinear surface and on the flat ends of the cylinder.
Abstract: 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 polytetra...

Journal ArticleDOI
TL;DR: In this paper, a theory of wound yarn under tension was developed to determine the stresses within the wound yarn, and the dependence of stress distribution on the degree of anisotropy was investigated.
Abstract: Some synthetic fibres possess considerable transverse anisotropy. When yarn made from such fibres is wound under tension on a tube, the pack of wound yarn exhibits a high degree of anisotropy of the cylindrical type. A simple experiment which demonstrates this property is described.Treating the yarn as elastic and anisotropic, a theory of winding yarn under tension is developed to determine the stresses within the wound yarn. Expressions for the axial strain and the end load of the containing flanged tube are also obtained. Computed results show the dependence of stress distribution on the degree of anisotropy; of particular interest is the large variation of circumferential tension of the yarn, which affects subsequent yarn processing.

Journal ArticleDOI
TL;DR: In this article, three metals were subjected to zig-zag stress paths in the plastic region, and the direction of the plastic strain increments suggested local distortion of the yield surface rather than the formation of a sharp corner.
Abstract: Three metals were subjected to zig-zag stress paths in the plastic region. The direction of the plastic strain increments suggested local distortion of the yield surface rather than the formation of a sharp corner.A stepped stress path with unloading between steps gave strain increments consistent with a distorted but smooth yield surface, rather than one with plane segments.

Journal ArticleDOI
B G Neal1
TL;DR: In this paper, a theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is presented, and it is shown that inextension behaviour is...
Abstract: A theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is first presented. It is shown that inextensional behaviour is ...

Journal ArticleDOI
TL;DR: In this article, the frozen stress photoelastic technique was used to determine the hoop and radial stresses at the hole boundaries of sixty different hole configurations in flat discs, each had one ring of...
Abstract: The frozen stress photoelastic technique was used to determine the hoop and radial stresses at the hole boundaries of sixty different hole configurations in flat discs. Each had one ring of...

Journal ArticleDOI
B G Neal1
TL;DR: In this paper, it is shown that the yarn has isotropic elastic properties and the yarn may behave as an elastic solid, flange pressure being generated by the partial prevention of longitudinal expansion.
Abstract: After manufacture, some synthetic fibres are wound under tension on a flanged cylinder, and a knowledge of the pressures exerted by the yarn on the flanges and on the cylinder is required for design purposes.During winding, the pack of yarn may behave as an elastic solid, flange pressure being generated by the partial prevention of longitudinal expansion. However, it is also possible that the fibres may undergo a relative slipping movement and tend to slide off the ends of the cylinder. Flange pressure would then be developed in order to inhibit further slip.These two possibilities are examined on the assumption that the yarn has isotropic elastic properties. Although it is known that drawn fibres possess considerable anisotropy, these analyses are a prelude to studies of anisotropic behaviour.

Journal ArticleDOI
TL;DR: In this article, the elastic properties and strength of sedimentary rocks in uniaxial and triaxial compression and tensile strength were investigated, and a brief account was given of the application of dimensionless analysis to scale-model roadway tests and of the properties of a scale model material.
Abstract: Investigations on the elastic properties and strength of sedimentary rocks in uniaxial and triaxial compression and on the tensile strength of sedimentary rocks are described. A brief account is given of the application of dimensionless analysis to scale-model roadway tests and of the properties of a scale-model material.

Journal ArticleDOI
M L Meyer1
TL;DR: In this paper, a semi-quantitative formulae capable of reproducing observed magnitudes and systematic changes of gauge factor and cross-sensitivity in foil and wire gauges is presented.
Abstract: Piezo-resistivity, ‘end’ effects, and transverse connections are taken into account in semi-quantitative formulae capable of reproducing observed magnitudes and systematic changes of gauge factor and cross-sensitivity in foil and wire gauges and of suggesting means for reducing cross-sensitivity.

Journal ArticleDOI
F Ellis1
TL;DR: In this article, the properties of discontinuities which meet on an axis of symmetry are investigated and it is shown that solutions exist for reflections of the discontinuity at the axis at angles of π/4 and 3π/4 as well as the angle π 2 hitherto assumed to be the only solution.
Abstract: Statically admissible stress fields consisting of regions of constant stress in a state of incipient plastic flow separated by stress discontinuities form a powerful tool for obtaining lower bound solutions to problems in plane plastic flow.The properties of discontinuities which meet on an axis of symmetry are investigated and it is shown that solutions exist for ‘reflections’ of the discontinuity at the axis at angles of π/4 and 3π/4 as well as the angle π/2 hitherto assumed to be the only solution.The results are used to obtain a lower bound solution for plane-strain extrusion with reduction ratios less than 3:1.

Journal ArticleDOI
TL;DR: In this article, the elastic shell stresses occurring when vertical loads are transmitted through discrete support brackets welded to the lower hemispherical end of a cylindrical pressure vessel having its axis vertical were investigated.
Abstract: The investigation is concerned with the elastic shell stresses occurring when vertical loads are transmitted through discrete support brackets welded to the lower hemispherical end of a cylindrical pressure vessel having its axis vertical. Three sizes of bracket were examined, and the largest was compared with a similar arrangement having an internal bracket continuous with the external one. Strain-gauge results indicated that shell stresses may be calculated by assuming that the radial deflection of the spherical shell is linearly distributed along the line of contact between bracket and shell. Conventional design methods employed in stress calculations tended to underestimate the shell stresses.It is shown that the line of application of the support reaction in relation to the centre line of the bracket is most important.

Journal ArticleDOI
T C Hsu1
TL;DR: In this paper, the relation between the velocity field and the strain-rates and rotations on a deformed grid is discussed, and the connection between finite deformation and rate of deformation is also explained.
Abstract: Grid lines have often been scribed, printed or photographed on metal surfaces for studying plastic deformation. Hitherto, most of them have been used only for qualitative results. It has been shown in a previous paper (2)∗ how quantitative results on finite deformations can be derived from a deformed grid. As a sequel to that paper, a method is presented here for deriving the rates of deformation from deformed grids. The relation between the velocity field on the one hand and the strain-rates and rotations on the other is first discussed. The theory thus developed is then applied to the cases of steady-state and non-steady-state flow, with practical example for the former. The connection between finite deformation and rate of deformation is also explained.

Journal ArticleDOI
TL;DR: In this article, a finite element displacement method is used to solve a number of thermo-elastic plate problems involving different boundary conditions and variations of thickness, and a plane-stress element stiffness matrix and temperature load column matrix are derived on the assumption that thickness and temperature representations within the element are based on corner-point values.
Abstract: The finite-element displacement method is used to solve a number of thermo-elastic plate problems involving different boundary conditions and variations of thickness. A plane-stress element stiffness matrix and temperature-load column matrix are derived on the assumption that thickness and temperature representations within the element are based on corner-point values. Results obtained from different element models are compared with other analytical solutions in order to establish the best element representation.

Journal ArticleDOI
TL;DR: In this paper, a rheological approach to fatigue behavior was extended to the push-pull fatigue of an 11 per cent chromium steel and a nickel-chromium alloy at room temperature and the influence of the direction of first loading stroke has been examined.
Abstract: A rheological approach to fatigue behaviour has been extended to the push-pull fatigue of an 11 per cent chromium steel and a nickel-chromium alloy at room temperature and the influence of the direction of first loading stroke has been examined. At the high stresses involved, strain was shown to accumulate ultimately in a tensile direction in a manner similar to elevated temperature creep and the strain-time curves were shown to have the form ∊ = Σ Cσβtκ where ∊ is strain, σ is stress, t is time, β and κ are discrete exponents, and C is a material constant. The widths of the hysteresis loops (strain amplitudes) were found to be dependent upon time in a manner similar to the cumulative strains and were analysed by a similar expression.The growth of tensile strain occurred irrespective of whether tension or compression was applied first but the application of compression first caused lower values of cumulative strain and longer endurances for similar load limits.

Journal ArticleDOI
C Ruiz1
TL;DR: In this article, Langer's method, based on an elastic-stress analysis, is applied to the fatigue design of pressure vessels, and design curves for the establishment of the acceptable elastic-stress range corresponding to a given fatigue life are proposed.
Abstract: Thin cylindrical specimens, plain and with deep axial grooves, have been tested under pulsating pressure and under static pressure with cyclic axial straining. The test results, together with some supplementary information from other authors, show that Langer's method, based on an elastic-stress analysis, is applicable to the fatigue design of pressure vessels. Design curves for the establishment of the acceptable elastic-stress range corresponding to a given fatigue life are proposed. Attention is drawn to the limitations of Langer's method.

Journal ArticleDOI
TL;DR: In this article, a new method to evaluate distorted grids is proposed, which consists of shifting an image of a distorted grid over another image of the undistorted grid to obtain displacement components, or shifting an output image of one image to another image to obtain the derivative of the displacement components.
Abstract: This paper deals with a new method to evaluate distorted grids. Instead of evaluating point-by-point the new method consists of shifting an image of a distorted grid over another image of the undistorted grid to obtain displacement components, or shifting an image of a distorted grid over another image of the same distorted grid to obtain the derivative of the displacement components. Whole field information is available by connecting grid line intersections.Displacements and their spacial derivatives are given for a circular ring diametrically compressed, using both the Eulerian and the Lagrangian descriptions. The method has applications in plasticity and in elastic finite strain determinations.

Journal ArticleDOI
TL;DR: In this paper, a simple redundant structure subjected to a non-uniform temperature distribution is simulated experimentally by means of two tensile-creep test machines holding specimens of Nimonic Alloy 90 at different temperatures in the range 800-900°C.
Abstract: A simple redundant structure subjected to a non-uniform temperature distribution is simulated experimentally by means of two tensile-creep test machines holding specimens of Nimonic Alloy 90 at different temperatures in the range 800-900°C The machines are linked together so that although the total load applied to the specimens is constant the share of that load taken by each varies owing to dissimilar creep rates, as it would in the structure This redistribution of load is observed for several initial stress conditions and several temperature differences In each case the results are compared with calculations based on creep-strain data obtained from constant-stress tests An important practical feature of the results is the establishment of stable (fully redistributed) stresses These stresses are insensitive to the initial conditions, can be estimated quite simply from constant-stress creep data, and are always more uniform than the thermal stresses appropriate to the same temperature differe

Journal ArticleDOI
TL;DR: In this article, the discontinuity stresses in the vicinity of discrete supports welded to the hemispherical end of a pressure vessel under internal pressure have been measured, and four brackets fabricated from flat plates and three tubular supports were examined.
Abstract: The discontinuity stresses in the vicinity of discrete supports welded to the hemispherical end of a pressure vessel under internal pressure have been measured. Four brackets fabricated from flat plates and three tubular supports were examined. Experimental stresses compared reasonably well with stresses estimated by approximate analytical methods which are suggested as standard design checks.

Journal ArticleDOI
TL;DR: In this paper, the design and performance of a machine for testing sheet material in the plastic range is described, where the material is stressed in uniform biaxial tension by means of the hydrostatic bulge test.
Abstract: The design and performance of a machine for testing sheet material in the plastic range is described. The material is stressed in uniform biaxial tension by means of the hydrostatic bulge test. Test variables are measured by electrical transducers and an analogue unit is employed to permit autographic recording of the diagram relating true stress and natural strain. Closed-loop control of the rate of straining is achieved with an electro-hydraulic actuator; the feedback signal is derived from the analogue unit and the test can be controlled on the basis of a computed parameter such as true stress or natural strain.

Journal ArticleDOI
TL;DR: In this article, a concave mirror is compared with a plano-convex lens of comparable f-number, as a means of producing collimated light, and its advantages are enumerated.
Abstract: A concave mirror is compared with a plano-convex lens of comparable f-number, as a means of producing collimated light, and its advantages are enumerated.

Journal ArticleDOI
TL;DR: An experimental stress analysis has been carried out on three tubular supports welded to the lower hemispherical dome of a cylindrical vessel having its axis vertical and being subjected to vertical loads as mentioned in this paper.
Abstract: An experimental stress analysis has been carried out on three tubular supports welded to the lower hemispherical dome of a cylindrical vessel having its axis vertical and being subjected to vertical loads. A procedure (based an a method previously used for webbed brackets) for calculating shell stresses in the vicinity of the supports was examined and was found to be reliable.