bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of a variational theorem for boundary values in shell theory
Authors: Lardner T. J. , Reissner E
Published: July 2007

A variational theorem of three-dimensional linear elasticity, for which the comparison functions satisfy all the differential equations of the problem, and all boundary conditions are Euler equations of the variational equation, is reformulated so as to apply to the two-dimensional theory of thin shallow shells of revolution. This variational equation is then applied to the problem of the approximate determination of the interior solution state of a shallow spherical shell, without consideration of the associated edge zone solution state. Explicit results are obtained for the stress boundary value problem and the displacement boundary value problem, and a proceedure, involving an infinite linear system of ordinary equations, is indicated for a mixed problem with different boundary conditions being prescribed along different portions of the edge of the shell. Additionally, possible further developments of a similar nature are discussed.
Stresses in anisotropic media with particular reference to problems of rock mechanics
Authors: Zienkiewicz O. C. , Cheung Y. K. , Stagg K. G.
Published: July 2007

The recently developed finite element method of numerical stress analysis has been previously applied to the analysis of the stress distribution in isotropically elastic materials and is here extended to deal with a particular form of anisotropy. The case of anisotropy considered is that generally referred to as transverse isotropy, i.e. where the material is isotropic in the yz plane but non-isotropic with respect to directions normal to this plane. The analysis is restricted to the consideration of two-dimensional plane strain problems in the xy plane. The individual element axis orientation may be varied at will with respect to the overall co-ordinate system so that problems may be treated where the direction of isotropy varies from point to point within the material.

It is suggested that this system of anisotropy is particularly relevant to the analysis of stress distributions in stratified rock masses. Previous approaches to this problem are outlined in Appendix 1.

A series of illustrative examples are shown, first, to compare the numerical solution to a problem with a known analytical solution to that analytical solution and, second, to show the application to more complex situations with no known analytical solutions.

It is concluded from the first comparison that the method is capable of giving good accuracy.
Report on the conference on stresses in service
Authors: Cox H L
Published: July 2007

The Conference, which was sponsored by the Joint British Committee for Stress Analysis, was held at the Institution of Civil Engineers on 23rd-25th March 1966, and comprised 20 papers.
Optimization of stress concentrations at holes in rotating discs
Authors: Fessler H , Thorpe T E
Published: July 2007

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 holes, evenly spaced on one pitch circle, concentric with the periphery and bore.

The ratio of radial-hoop hole boundary stress was related to the radial-hoop stress ratio of plain discs, the hole spacing and hole diameter in a manner which permits quick determination of optimum hole spacing for the range of bores, pitch circle and hole diameters used in gas turbine discs. The peak stresses can also be predicted in non-optimum configurations.
The use of an electrical analogue to assess the experimentally observed behaviour of a simple longitudinal fillet weld
Authors: Swannell P
Published: July 2007

A pure resistance electrical analogue is used to assess the elastic toe displacements that occur in a longitudinal fillet weld subjected to a uniform shearing intensity throughout its length. The result is compared with measured values obtained from an experimental investigation of fillet weld deformations. Conclusions are drawn concerning the behaviour of a stiff welded junction.
Force dynamometers for coal- and rock-cutting research
Authors: Dalziel J A , Jordan D W , Whittaker D
Published: July 2007

The design requirements of the ideal force dynamometer are manifold and are difficult to satisfy. The difficulties met in attempting to meet these requirements are discussed and the design and function of a number of dynamometers used at the Mining Research Establishment are described.
General interpretation of moiré patterns in strain analysis
Authors: Košťáuk B
Published: July 2007

A simple theoretical treatment of moiré patterns is given with the use of relations between diagonal systems that have the physical meaning of contour lines of the functions in question. The general approach and knowledge of diagonal-system properties can simplify various problems of strain measurement by the moiré method, and this is demonstrated by the compensation of a moiré pattern and by the method of two-dimensional strain measurement.
Stress concentration caused by an oblique round hole in a flat plate under uniaxial tension
Authors: McKenzie H W , White D J
Published: July 2007

Stress-concentration factors have been determined for oblique holes in flat plates by a method using frozen-stress photoelasticity. The ellipses formed at the intersection of the hole and the plate surfaces had their major axes perpendicular to the direction of application of the load.

The maximum stress-concentration factor was found to increase with increasing angle of obliquity with respect to the normal to the plate but the experimental factors were found to be considerably lower than those predicted from a theory of Ellyin et al.

Graphs are given which enable maximum stress-concentration factors to be obtained for oblique holes having a ratio of hole diameter to plate width of 0.1. It was found that, for the models tested, elliptical hole data gave a reasonable estimate of the maximum stress-concentration factors based on net area.

Removing the feather edge of the hole, by applying various edge radii, did not alter the stress concentration appreciably except in so far as load-carrying area was reduced.
An experimental investigation of the cross-sensitivity of resistance strain gauges
Authors: Shelton A
Published: July 2007

A simple method for measuring the cross-sensitivity of resistance strain gauges has been devised and results are given for nine types of gauge. The apparatus consists of a wide stainless-steel sheet of initially large curvature to which gauges are bonded in both axial and transverse directions. A uniaxial strain field is obtained by closing the gap at the ends of the sheet and the ratio of the resistance changes in the two gauge directions gives the cross-sensitivity in terms of the axial sensitivity. The value of the cross-sensitivity is shown to depend upon the geometry of the gauge grid and the method of winding a wire-resistance gauge. Foil gauges are shown to possess a particularly low value of cross-sensitivity.
Incremental growth due to creep and plastic yielding of thin tubes subjected to internal pressure and cyclic thermal stresses
Authors: Bree J
Published: July 2007

A theoretical investigation is made of incremental growth in a thin pressurized tube when the tube wall is subjected to large cyclic variations of temperature and temperature gradient, the mechanisms of deformation being plastic yielding during application and removal of the temperature gradient and creep during the high temperature part of the cycle. In a previous paper a simple model of the tube was developed and used to determine approximately when the mode of incremental growth known as ratcheting occurs and to estimate the ratchet strain per cycle, both when creep is ignored and when it causes complete relaxation of internal stresses. The above work is extended in the present paper to cases where only partial relaxation of internal stresses occurs and a method of evaluating the ratchet strain per cycle is presented. In addition, the method allows the increased creep strain due to non-linear interaction between internal stresses and the pressure stress to be calculated. This accompanies ratcheting when the relation between creep rate and stress is non-linear.
Centrifugal stresses in rotationally symmetrical gas-turbine discs
Authors: Fessler H , Thorpe T E
Published: July 2007

The frozen-stress photoelastic technique has been used to determine stresses in hubs and diaphragms. Different hub sizes and shapes were studied for a typical shape of flat disc (middle surface plane). Shape and size are related to peak stresses.

Conical discs, with different cone angles but having the same mass, were analysed and shown to be more highly stressed than flat discs.
A contribution to the application of photoelasticity to the micromechanics of composite materials
Authors: Stone D E W
Published: July 2007

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.
A model for uniaxial creep based on internal-stress redistribution
Authors: Clarke J M
Published: July 2007

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 rate. Analysis of results for the aluminium alloy DTD 5070A has helped confirm the model by showing a correlation between these quantities.
Deformations of stacks of thin layers under normal compressive loads
Authors: Howells R I L , Probert S D , Jenkins J H
Published: July 2007

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.
Yield and subsequent flow behaviour of some annealed steels under combined stress
Authors: Rogan J , Shelton A
Published: July 2007

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 materials at room temperature.
A technique of printing gauge marks on round tensile specimens
Authors: Chiang C H
Published: July 2007

A printing technique to replace the usual marking practice of punching dots or scribing lines on a round tensile specimen is described. With this method the specimen surface will not be influenced by marking, hence premature failure can be avoided in high-speed testing. The printing technique is simple to apply. The printed gauge mark can be controlled to an accuracy of ± 0.002 in for a 1.4 in gauge length. The width of the printed lines is about 0.003 in.
Effect of tensile prestrain on the yield locus of 1100-f aluminium
Authors: Williams J F , Svensson N L
Published: July 2007

A series of combined stress tests in torsion-tension space is carried out on thin-walled tubes of 1100-F commercially pure aluminium. One initial and four subsequent yield loci are established to a maximum prestrain level of 14 per cent tensile plastic strain.

The results are analysed in terms of a proposed, rationally based, yield criterion constructed according to statistical reasoning.

It is shown that during prestrain a significant degree of geometrical distortion is undergone by the yield loci, accompanied by a strong Bauschinger effect and a flattening of part of the locus opposite to the loading point.

It is found that the yield locus does not rotate during prestrain and, contrary to the case for torsion prestrain, exhibits evidence of a sharply rounded corner developing at the loading point.

The proposed criterion is shown to fit the experimental results extremely well and the mechanism of distortion is explained in terms of a statistical model for work-hardening materials.
An improved apparatus for biaxial loading of concrete specimens
Authors: Parrott L J
Published: July 2007

The report describes a fluid-loading type of platen which can apply uniform sustained stresses of more than 15 N/mm2 (2200 1b/in2) to rectangular specimens. Four such platens were used in a square configuration to apply uniform biaxial compressive and tensile stresses to a 150 × 150 × 19 mm (6 × 6 × 3/4 in) specimen. Two fluid platens in combination with two rams were used to apply uniform biaxial compressive and tensile stresses to a 150 × 273 × 19 mm (6 × 10 3/4 × 3/4 in) specimen. Tests showed that the fluid platens had negligible transverse stiffness and did not, therefore, restrain the specimen or absorb transverse loads.
Mohr circles for large and small strains in two-dimensional deformations
Authors: Choi C Y , Hsü T C
Published: July 2007

The mathematical apparatus is provided for the analysis of large deformations in two dimensions. Deformations are considered as co-ordinate transformations. For homogeneous deformations, a method of finding the directions and magnitudes of the principal strains is presented. The formulae used may be expressed either in terms of the elements of a transformation matrix or in those of displacement gradients. It is shown that, when the displacements are small, the results are reduced to the familiar formulae for small strains in linear elasticity. The Mohr circles for Green's and Cauchy's deformation tensors are also discussed, and their relations with the Mohr circle for the matrix of pure deformation shown. Examples of Mohr circles are provided for some commonly known types of deformation.
Residual stresses in a large circular disc caused by local heating and cooling at its centre
Authors: Gurney T R
Published: July 2007

By means of a form of finite-element analysis and use of a theoretical, radially symmetrical, temperature distribution, the residual stresses resulting from spot heating at the centre of a large circular plate have been calculated. The investigation was concerned in particular with defining the effect of variations in material yield stress, rate of heat input, and peak temperature on the residual-stress distribution.
Compression of bonded rubber blocks
Authors: Holownia B P
Published: July 2007

An approximate theoretical study of bonded rubber blocks under moderate compressions has been carried out. The study is an extension of an earlier one by Gent and Meinecke wherein thin rubber blocks were considered under compression, bending, and shear with small amounts of strain. Here larger amounts of strain are considered and it is shown that considerable difference exists between the present analysis and that of Gent and Meinecke for strains in excess of 5 per cent. An attempt has also been made to define ‘thin’ rubber blocks by using some of the experimental results available. Within the limit of the definition of a ‘thin’ block it is shown that the amount of strain (tensile) necessary to produce an internal rupture can no longer be neglected as in the work of Gent and Meinecke but must be included in the initial analysis.
Shear and rotation moiré patterns obtained by spatial filtering of diffraction patterns
Authors: Clark J A , Durelli A J , Parks V J
Published: July 2007

Two superposed gratings can produce many other moiré patterns in addition to the pattern commonly observed. They correspond to different forms of the indicial equation employed in parametric descriptions of moiré phenomena. An analysis of the Fraunhofer diffraction pattern of two superposed gratings by the methods of Fourier optics shows that the different moiré patterns can be separately observed by spatial-filtering techniques. Examples of additive and subtractive moiré patterns obtained individually over the whole field of two superposed gratings are presented. This method is combined with a previously developed method for obtaining partial derivatives from deformed gratings as a direct moiré pattern (rather than as moiré of moiré) to determine experimentally the whole field of cartesian shears and rigid rotations. The method is applied to a circular ring subjected to diametral compression.
Stress and flexibility factors for multi-mitred bends subjected to out-of-plane bending
Authors: Bond M P , Kitching R
Published: July 2007

A theoretical analysis has been developed to predict stress distributions and flexibility factors associated with out-of-plane bending of multi-mitred pipe bends. The estimated range of validity of the analysis is sufficient to include most practical multi-mitred pipe bends. Tests on a large-diameter, thin-walled, three-weld right-angled multi-mitred bend were undertaken and the results closely agreed with computations based on the analysis.

Predictions for both flexibility factors and overall maximum-stress ratios from the analysis were almost identical with those given by an in-plane bending theory that had been developed from a similar method of approach.
Transient creep of a block compressed on opposite sides by elastic punches of the same width as the block
Authors: Ohashi Y , Nishitani T , Ishida M
Published: July 2007

A method combining photoelasticity of an elastic body and photo-rheological stress analysis of a plastically flowing body may be applied to the experimental investigation of the contact problems between elastic tool and plastic workpiece which appear very often in plastic working.

The transient creep of a block compressed on opposite sides by elastic punches of the same width as the block is analysed by the above-mentioned method.
Interaction between collinear asymmetric cracks
Authors: Theocaris P S
Published: July 2007

Thin strips made of perspex and containing two collinear internal cracks of different length were subjected to tension. The thickness variation of the strips was depicted by the reflected-shadow method, in which a coherent monochromatic light beam, emitted from a helium-neon gas laser, was partly reflected from the rear surface of the specimen. The light rays emerging from the plate, which were twice refracted along the thickness and reflected on the rear surface of the plate, were retarded according to Favre's and Neumann's law. The retarded light rays were focused on a caustic surface which depicted the boundary between the constrained area surrounding the crack tip and the remainder of the plate. In this paper two asymmetric collinear internal cracks of different lengths were studied and the interaction between these cracks was evaluated by measuring the variation of the diameter and the distortion of the shape of the caustics for various ratios of crack lengths.
Effect of Poisson's ratio on bonded rubber blocks
Authors: Holownia B P
Published: July 2007

A theoretical analysis of bonded rubber blocks with circular cross-section under axial compression is obtained by the use of dynamic-relaxation solutions of classical elastic stress-strain equations. The Poisson's ratio ν for rubber is close to 0.5 which causes difficulties in the analysis because the general stress-strain equations of elasticity contain terms such as ν E/(1 + ν)(1 − 2ν) which approaches infinity when ν approaches a value of 0.5. The range of ν considered varies between 0.45000 and 0.49990 which covers all the natural-rubber compounds used, including pure natural gum which has a ν value of 0.49989 (1)∗.

It is shown that the stress distribution within the block is significantly affected by the value of ν and the shape of the block. When a block of material with ν ∼ 0.5, bonded to its end plates, is thin, the stress developed within the block is high and nearly equal in all three directions, which suggests a hydrostatic type of pressure. Such a pressure would confirm the finding in (2) and (3) based on a semi-empirical analysis. When the block is thick this effect is absent. The present paper confirms that these effects follow from the fundamental assumptions of classical elasticity.

The investigation also confirms that the dynamic-relaxation method converges satisfactorily even when the Poisson's ratio is very close to the value of 0.5000.
A testing rig for cycling at high biaxial strains
Authors: Andrews J M H , Ellison E G
Published: July 2007

There is a scarcity of multiaxial fatigue data available to designers especially in the high-strain régime. This is due in part of the complexity of the test equipment involved. A servo-hydraulic experimental rig has been developed for the application of biaxial high-strain reversed cycles to thin-walled tubular specimens, i.e. under axial tension and compression and internal and external pressure. It is capable of testing over a wide range of strain ratios and is reasonably versatile in that other information pertaining to buckling, Poisson's ratio, and criteria for yielding can be obtained.
Biaxial cyclic high-strain fatigue of aluminum alloy RR58
Authors: Ellison E G , Andrews J M H
Published: July 2007

In the régime of biaxial high-strain fatigue there is a scarcity of data and consequently of information regarding methods of predicting such behaviour from simpler uniaxial tests. An investigation was carried out on the aluminum alloy RR58 in the form of cylindrical specimens subjected to axial tensile/compressive load and internal/external pressures at room temperature and 140°C. Additional tests were also conducted in separate cyclic torsion and uniaxial machines. The results in the range 100–5000 c indicated that the biaxial strain ratio 1/1 was the most severe case, the effect being less severe as the ratio changed to 1/-1. Of the correlation techniques examined the most successful was a von Mises strain function using the concept of a equivalent Poisson's ratio; the method of maximum shear strain showed promise. Comparative tests on the different cyclic test rigs on the same batch of material indicated the need for care when such aspects as specimen shape and definition of failure are considered, as well as the more obvious effects of material variation and anisotropy.
Three-dimensional photoelastic analysis in axially loaded thick plate with hole
Authors: Rubayi N A , Yadava V
Published: July 2007

In this study three-dimensional photoelasticity is used to analyse the stress variation through different layers of a thick plate containing a circular hole and subjected to uniform tensile loading. The effect of the thickness/diameter ratios on the stress concentrations with thickness is investigated. The experimental results are correlated with the existing three-dimensional theoretical solutions.

The data establish, both experimentally and theoretically, the precise location of the maximum-stress layers in plates having different thickness/diameter ratios and thus resolves the discrepancies which existed in previous studies.
Experimental evaluation of the fracture toughness (K1c) of an epoxy resin
Authors: Evans W T , Barr B I G
Published: July 2007

Fracture-toughness tests were conducted on Araldite CT 200, in order to obtain K1c, the plane-strain, mode 1 critical stress-intensity factor. Two essentially different methods were used, namely the photoelastic method and the quasistatic energy method.

In the photoelastic method, stress fringe patterns were analysed at load intervals up to failure and the stress-intensity coefficients obtained were compared with those from the boundary collocation method. In the energy method, two types of specimen geometry were tested, resulting in stable crack propagation. Good correlation was obtained between the two methods.
Determination of crack-opening displacement by the method of caustics
Authors: Theocaris P S
Published: July 2007

A new experimental technique based on the method of caustics is presented for the measurement of the distance between the lips of a crack near the crack-tip. The two parts of the caustic formed by reflections from the front and rear faces of the specimen lie at a distance from each other. The gap between these parts depends on the total c.o.d. (crack-opening displacement), that is the initial opening and the opening due to loading, as well as on the optical and mechanical characteristics of the material By increasing the external loading of the cracked plate, the gap between the parts of the caustic was changed and this gap measured the instantaneous c.o.d. due to loading. The method was applied to the measurement of small c.o.d.s. due to small-scale loading, with satisfactory results. Therefore it can certainly be used to measure c.o.d.s at large loading steps, up to fracture, because the gap between the parts of the caustic becomes significant and easy to measure. Measurements with cracked plates made of p.m.m.a. (polymethylmethacrylate) and polycarbonate showed that the results obtained are in good agreement with theory. Thus, it has been proved that the method of caustics yields a very sensitive means for measuring c.o.d.s, especially in small-scale deformations, where measurement of c.o.d by conventional methods is inaccurate. A great advantage of the method is that it measures the c.o.d.s at a well defined region, which always remains near to the crack tip.
Development of a biaxial fatigue testing rig
Authors: Parsons M W , Pascoe K J
Published: July 2007

A biaxial fatigue testing rig which employs cruciform specimens loaded by four double-acting hydraulic cylinders has been improved by the addition of a closed-loop servo-control system. This system enables the loads or strains in the two principal directions to be varied independently of each other. The paper describes the modifications that were made to the system and the various problems then encountered. Further development work was then necessary before the rig operated satisfactorily. The details are published to be of assistance to others who may wish to construct specialist servo-controlled hydraulic testing equipment.
Tension—compression behaviour of annealed oxygen-free high-conductivity copper after strain cycling in the plastic range
Authors: Oldroyd P W J
Published: July 2007

When copper is cycled between fixed limits of strain it ends towards a settled cyclic state. The two curves which form the tension-compression stress-strain loop will have the same shape but, no matter what point is chosen on the loop for the return to zero stress, the material will not be left with symmetrical tension-compression properties. This is because of the Bauschinger effect. It is demonstrated that the Bauschinger effect can be eliminated by cycling down to zero stress and zero strain using progressively decreasing strain amplitudes. Relatively few cycles suffice and, when the strain range is small, the structural strain-hardening effect is not noticeably reduced. Even with the largest range investigated (± 1 per cent plastic strain) the structural resoftening is slight. The significance of the subsequent tension and compression stress-strain curves is discussed.
Steady-state thermal stresses in an elastic solid containing an insulated penny-shaped crack
Authors: Barber J R
Published: July 2007

A solution is given for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack. The problem is reduced to a mixed-boundary-value problem for the half-space, making use of Green's isothermal solution for the thick elastic plate in complex harmonic potentials and a particular thermoelastic solution due to Williams. In the axisymmetric case, the complex potential reduces to the real harmonic function used by Shail in his solution for the external crack.

To illustrate the use of the method in both axisymmetric and non-axisymmetric problems, complete solutionsare given for (1) a uniform heat flow and (2) a linearly varying heat flow disturbed by an insulated penny-shaped crack.
Stress analysis of configurations involving small fillets
Authors: Freese C E , Bowie O L
Published: July 2007

The stress analysis of cut-outs or notches involving fillets with constant curvature is considered for two-dimensional problems of elasticity. An approach using a continuous representation in the region local to the fillet and a finite-element representation in regions where stress gradients are small is proposed. The plan is shown to be effective in both accuracy of results and computer economy. A square cut-out with filleted corners is examined to illustrate the method. The versatility of the approach is then utilized to examine a class of U-notch (or slot) problems with only trivial changes in programming.
Design data for rectangular segment of cylindrical shell with normal loading
Authors: Kitching R , Hughes J F
Published: July 2007

Rectangular segments of a cylindrical shell having simply supported edges and subjected to normal surface loading have been analysed. Stress resultants and deflections are presented in non-dimensional form for a range of shell parameters.
Influence of overlays on stresses in fillet-welded joints
Authors: Gurney T R
Published: July 2007

Finite-element analyses have been carried out on a specimen with transverse non-load-carrying attachments, to examine the influence of low-modulus overlays consisting either of a layer of uniform thickness over the whole weld or of an infill over the weld toe. The variables studied have included coating thickness and the shape, size and modulus of toe infills. It is shown that substantial reductions in stress concentration can be obtained by such coatings.
Crack propagation with quasistatic energy analysis
Authors: Chow C L , Ngan K M
Published: July 2007

In the application of quasistatic energy analysis, the P-u-A diagram has been found a valuable supplement in illustrating the characteristics of crack propagation. The diagram is useful not only for evaluating fracture toughness under quasistatic conditions, but also for representing important fracture parameters such as stability criteria, crack speed, strain rate, fatigue, environmental effects, etc.

A general method of characterizing these parameters in the form of a P-u-A diagram is presented for both linear and non-linear load-displacement relationships at constant crack area. This was achieved by polynomial representation of the diagram. The analysis was extended to cover crack propagation under multiple-loading conditions. By introducing a complementary strain-energy function, equivalent load and compliance, a method of solution has been devised to avoid the laborious computations which may otherwise be required if the loadings become numerous and complex. The computed values of fracture toughness from the numerically represented P-u-A diagram, and the displacements evaluated with the equivalent compliance concept, compare well with those obtained experimentally.
The experimental determination of trajectories in geometrically similar plastic flows
Authors: Roth R N
Published: July 2007

A new experimental method is presented for determining trajectories of flow for non-steady-state processes which exhibit geometric similarity (quasi-steady-state processes (1)∗). One process that is normally regarded as quasi-steady-state (plane strain wedge indentation) is investigated using this method. It is shown that this process satisfies the requirements of geometric similarity within experimental accuracy. Results are presented for wedge angles of 30°, 60° and 90° and a range of indentation depths up to approximately 3 mm.

Finally, it is suggested how this method can be combined with well-known orthogonal-grid techniques to provide information for the calculation of effective strains throughout the deforming region.
On reflected and transmitted stress waves at an elastic-plastic boundary
Authors: Khan A S
Published: July 2007

A theoretical analysis for the reflected and transmitted waves at an elastic-plastic boundary is presented. The basis of this analysis is the linear elastic wave theory in a hard load-bar and the one-dimensional, strain-rate-independent theory of finite-amplitude plastic waves in a soft specimen. The constitutive relationship during dynamic plastic deformation is an experimentally determined dynamic response function in the soft material. The analysis predicts results that agree very closely with experimental results.
The method of caustics for the determination of normal loads acting on surfaces of elastic bodies
Authors: Theocaris P S , Ioakimidis N I
Published: July 2007

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.
Prediction of the path of unstable extension of internal and edge cracks
Authors: Maiti S K
Published: July 2007

The criteria of strain energy density and maximum tangential stress have been applied to the entire stress field existing just before the onset of instability to predict the path of extension of both internal and edge cracks. The stress analysis has been carried out by a finite-element scheme employing the quarter point square-root stress singularity elements. In the case of internal cracks, the unstable paths based on both the criteria are in good agreement with the results available in the literature. Theoretical and experimental studies on edge crack extensions during bar shearing of brittle materials have facilitated a comparison, and it appears that, although the maximum tangential stress criterion may be applicable, the strain energy density criterion is unsuitable for this case.
On the buckling of thin walled cylinders loaded in axial compression
Authors: Foster C G
Published: July 2007

Collapse loads for thin walled cylinders loaded in axial compression can be estimated by considering the buckling failure of equivalent space frames. These loads are presented in the form of a design chart where the collapse load for any cylinder can be determined provided the radius to thickness ratio of the cylinder and the size of the shape defects in the cylinder are known. It is demonstrated how these defects can be evaluated by an optical examination of a proof loaded cylinder. There is good agreement between estimated collapse loads for cylinders with known shape defects and measured collapse loads.
Determination of large strains in metalforming
Authors: Sowerby R , Chu E , Duncan J L
Published: July 2007

Certain techniques for the experimental determination of large strains in metalforming are discussed. The methods employ a grid pattern marked on the surface of the workpiece before forming and subsequently measured after deformation. The grid method is a surface phenomenon and the strain determination is reduced to a two dimensional problem. Any measurements taken on the initial and final grid configurations only, without knowing the deformation path, are insufficient to determine the strains precisely. Nevertheless, in practice, strains are determined by such a technique, often by using grid circles and by further assuming they deform into ellipses. The deformation process which transforms circles to ellipses and straight lines to straight lines, still does not define the straining path. Under such a deformation mode strain paths can be divided into two main types, those where an initially orthogonal pair of line elements (the principal axes) remain orthogonal throughout the deformation and those where they do not. The same change in shape can be achieved by either type of straining path, but the distinction between each straining mode is discussed and analysed in simple terms. The analysis is performed with reference to a square or quadrilateral grid of lines since automatic image analysis can be most effectively exploited when using coordinate or nodal point measures.
Elastic stresses due to torque transmitted through the prismatic part of keyed connections part I: Effect of different fits and friction on standard shapes
Authors: Fessler H , Eissa M
Published: July 2007

Photoelastic models of transverse sections through British Standard metric and inch keyed shafts and hubs (outside diameter = 2 × shaft diameter) have been loaded in torsion. Models with five different combinations of fits of shaft in hub, key in shaft, and key in hub, with three different surface conditions have been analysed over a large range of torques.

Stress concentrations occurred at the six contact positions where there are discontinuities of profile of the chamfered key or of the shaft. Normalized peak stresses are presented for all tests and the effects of the controlled variables are discussed.
Stress intensity factors for cracks at a double row of holes
Authors: Rooke D P
Published: July 2007

The presence of cracks at more than one fastener hole in a row of fastener holes limits the safe use of a component more than if cracks exist at the edge of one hole only, since the stress intensity factor is greater, the crack growth-rate is faster, and the fatigue lifetime is less. The limitations can be made less severe if the component is made with alternate fastener holes in the row displaced to form another parallel row. The compounding method of evaluating stress intensity factors is used to calculate the stress intensity factor as a function of crack length, hole spacing, and row separation. Fatigue growth-rates are calculated for the particular case of a periodic array of holes with two cracks of equal length at each hole.
Determination of the flexural stiffness of carbon composite plates by holographic interferometry
Authors: Snell M B , Marchant M J
Published: July 2007

A method of measuring the flexural stiffness properties of anisotropic thin plates is presented. Three rhombic plates cut at different orientations from the test sheet are loaded in bi-axial bending, and the resulting deflections are recorded as fringe patterns using optical holography. Curvatures determined in the chosen coordinate system and related to the bending moments are used to calculate the flexural stiffness terms. The results of tests on cross-ply carbon fibre reinforced plastic material are in good agreement with laminated plate theory.
Strain field in straight cylindrical shells due to applied forces on an attached shell. Part I: No hole in the intersection region
Authors: Khan A S , Hsiao C
Published: July 2007

The results of an experimental stress analysis of the intersection region of two straight cylindrical shells are presented. Two models were used; in the first model the two axes were inclined at 30 degrees while for the second case, this angle was 60 degrees. In each case, the main shell was 6.625 in. in diameter and 0.198 in. thick, while the attached shell was 3.5 in. in diameter and 0.226 in. thick. The intersection region was subjected to in-plane and out-plane moments applied to the attached shell and the measurements were made using foil resistance rosette gauges. These measurements demonstrate that the local stress concentration in the intersection region of the main shell increases with the increase of the acute angle between the axes of the two shells; thus for a given moment loading on the attached shell, the stress concentration will be the largest when the two axes are normal to each other.
Experimental and fem study of a cylindrical panel loaded through a pad
Authors: Ucmaklioglu M , Dawe D J
Published: July 2007

The static response of a rectangular curved panel to a central radial loading is examined, both for the panel alone and for the panel when reinforced at its centre by a circular pad containing a concentric hole. The examination comprises tests on a physical model, in which point displacements and strains are measured, and numerical studies using the finite element method with two markedly different types of element in turn. The object is to study the quality of the correlation between the results of the physical experiments and the two types of finite element analysis, and it is demonstrated that such correlation is good. Particular considerations is given to the finite element modelling of the pad/panel combination and it is shown that because of the relatively large rigidity of the pad it is possible to provide viable finite element models for the panel behaviour by eliminating the pad from consideration.
On the determination of the strength parameters in the tensor polynomial failure criterion
Authors: Labossiere P , Neale K W
Published: July 2007

The standard method generally used to determine the strength coefficients in the tensor polynomial failure criterion is re-examined. Alternative methods for calculating these strength parameters are proposed and compared using previously published experimental data for paperboard. For this material it is shown that the proposed alternative methods can lead to better analytical descriptions of the experimentally-determined failure envelopes.
Open cracks at or near free edges
Authors: Nowell D , Hills D A
Published: July 2007

We describe a method for the efficient, rapid determination of stress intensity factors for plane cracks at or near free surfaces, with arbitrary far fields. The basic technique is well established in the United States, but comparatively unknown in the UK, and makes use of distributing edge dislocations along the intended line of the crack. Examples given are uniform tension parallel to the free edge and point loads applied to the crack faces, although it is a simple task to formulate the problem for any nominal stress field, providing the crack remains open.
Bolting and loss of contact between cylindrical flat-flanged joints without gaskets
Authors: Hyde T H , Lewis L V , Fessler H
Published: July 2007

Four bolts of a lightweight, steel, flanged joint were strain-gauged to measure bolt tension and bending. Three-dimensional, finite element analysis was used to determine bolt strains and gaps between the flanges due to axial tension and internal pressure for three different contact conditions.

Two joints were tested. The front faces of the first joint were nominally flat while the second had a small negative cone angle (⋍ 0 degrees 15 minutes) so that flanges initially touched at the outside only. The non-linearity of experimental bolt strain with external load shows that the contact area around the bolts decreases with increasing axial tension. Comparison with the finite element predictions shows the rate at which the contact area diminishes. The finite element results also demonstrate that flange deflection is underestimated when contact area loss is ignored, and the consequences for leakage prediction are explained.
A numerical study of parameters controlling stress redistribution in circular notched specimens during creep
Authors: Eggeler G , Wiesner C
Published: July 2007

In this study, numerical calculations of the creep behaviour of circular notched specimens have been performed with emphasis placed on the role of specimen geometry, material ductility, and the constitutive creep law used for the calculations. In a first order approximation, the calculations performed using primary, secondary, and tertiary-types of constitutive equations result in similar stress distributions for most of the creep life. Therefore, acceptable engineering creep calculations can be performed using a pure Norton-type of constitutive law. In the beginning of creep life, however, there are signifiant differences in calculated stress distributions obtained using primary, secondary, and teriary constitutive laws. Brittle material undergoing primary creep can redistribute stresses faster than a ductile material exhibiting tetriary dominated creep behaviour. Comparing flat plate and cylindrical circular notched specimens it is found that maximum axial stresses are higher for flat plate specimens than for cylindrical specimens. Implications of these results on possible failure mechanisms are discussed.
Friction coefficient in fretting between titanium alloy and stainless steel
Authors: Ouyang Z X , Pan S C , Li Y P , Ouyang N
Published: July 2007

A test of fretting between titanium alloy and stainless steel is conducted, with the concept that the friction coefficient is regarded as a variable rather than a constant. The aim of this experiment is to simulate the real working structure of a dovetail joint commonly used in aeroengine components and other related mechanical engineering applications as well as to calculate its contact parameters by means of the Boundary Element method. One of the most important findings shows that the maximum shear stress is lower than usually considered when taking the friction coefficient as a variable into account, since it behaves naturally.
A new approach for the determination of residual stresses in biaxially stressed plates
Authors: Elsayed M M , Hendy M O , El Soally E E
Published: July 2007

This paper presents a modified hole-drilling technique for measuring residual stresses in a finite width plate subjected to biaxial tensile loading. Instead of using a special strain rosette containing three elements, only two strain gauges are used to determine the values of relaxed strains and hence the residual stresses in a biaxially stressed plate. It also gives a new approach which measures the radial relieved strains in two strain gauges mounted on a plate due to drilling a small central hole and then enlarging it. The corresponding residual stresses and their directions are derived.