Tensile Hoop Stress Research Articles

A study of stresses in alumina universal heads of femoral prostheses.

Three-dimensional, frozen-stress photoelasticity was used to study the best shape for a proposed alumina universal head loaded on to a Vitallium cone taper spigot with a 30 degrees inclined force, as in vivo. Typical cone taper friction values were reproduced in the photoelastic models. The location of the highest tensile stresses in the Mark I shape with a flat crown was found to be on the inner surface of the crown. Changing to a torispherical surface in the Mark II shape reduced this magnitude. However, the Mark III shape with a hemispherical inner crown surface gave even lower stress there, equal to the maximum value of the hoop stress at the taper, which was measured to be fairly uniform both around and along the taper except at the ends where contact pressure concentrations were found to occur and it became reduced. Lamé axisymmetric cylinder stress predictions were found to be useful approximations to measured values and were generally overestimates of the tensile hoop stress at the head taper surface.

Stress-strain state of a rod-type piezoceramic sensor

1. The finite elements method was used to develop an algorithm for calculating the natural frequencies and modes and the stress-strain state of piezoelectric sensors in an axisymmetric formulation. 2. A study was made of the deformation of a rod-type piezoelectric sensor subjected to preliminary static compression and subsequent vibrational loading by means of electrical harmonic excitation. 3. It was shown that the stress distribution in the piezoelements is nonuniform due to design features of the sensor. 4. It was established that an increase in the stiffness of the intermediate disk between the piezoceramic column and the radial cover plate of the sensor lowers the tensile hoop stresses in the adjacent piezoelement by 15–20%.

Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites

A complete solution is given for a fully or partially bridged straight crack in transversely isotropic elastic materials which may correspond to unidirectionally fiber-reinforced ceramics or other brittle composites. The stiffness of the bridging materials may have an arbitrary variation along the crack, representing partially failed fibers or ligaments. The crack may have any orientation with respect to the axis of the material symmetry. The solution is explicit in terms of the Chebychev polynomials when the bridging-forces are linearly dependent on the crack-opening-displacement. In addition, uniformly valid asymptotic solutions are developed for fully or partially bridging cracks. For the case when the crack is short relative to a length scale which depends on the material properties, the method yields a complete asymptotic solution when the bridging forces are linearly or non-linearly dependent on the crack-opening-displacement (a square-root dependence, corresponding to continuous fibers, is used for illustration). For the case of long cracks, the proposed asymptotic is effective, but the results are not presented in this work. The mechanism of crack kinking is studied for an oblique partially or fully bridged, or unbridged crack in a macroscopically transversely isotropic elastic solid. The crack is assumed to grow in the matrix material (containing unbroken strong fibers) under local driving forces which are calculated on the basis of the overall anisotropic material response. The results of various fracture criteria are studied. It is illustrated that, under far-field tensile forces normal to the crack, the criterion of the maximum opening mode stress intensity factor in the homogenized anisotropic solid (i.e., the orientation for which the strength of the singularity associated with the tensile hoop stress is maximum) produces results which suggest crack growth more or less parallel to the fibers, whereas the results based on the maximum Mode I stress intensity factor in the isotropic matrix material and/or on the local symmetry criterion (again, for the isotropic matrix) predict crack extension more or less normal to the reinforcing fibers.

Design recommendations for reinforced concrete cylindrical storage structures for aqueous materials

The design of cylindrical non-prestressed concrete storage structures in Ontario does not appear governed by any standard or building code. Many aboveground water storage reservoirs in Ontario have deteriorated badly in a relatively short period of use. Many farm silos suffer from problems similar to those of the water storage reservoirs. This paper is concerned with the selection of the wall thickness and the hoop reinforcement for cylindrical storage tanks and silos for liquids or wet materials where tensile cracking of the concrete is to be limited.Three design criteria are presented. The first limits the circumferential tensile stress in the concrete from lateral wall pressure, shrinkage, and temperature gradients in the wall. The second is concerned with the tension in the hoop reinforcement and guards against collapse. The third limits the crack widths of the cracked concrete section. The most important design loads are discussed. Maximum values for hoop tension are provided for liquid pressures. A design temperature gradient of 15 °C is recommended for design in southern Ontario. As well, appropriate values of shrinkage tensile stress are suggested. The collapse limit state criterion must be evaluated for the hoop steel stresses due to the lateral wall loads. The limit state criterion related to the hoop tensile stress in the concrete must be investigated for all possible load combinations of lateral wall load, shrinkage, and temperature gradients. Reasonable load combination factors have been recommended. Recommendations on the tensile strength of concrete and on appropriate strength factors have been made. Key words: cylindrical tank, design criteria, hoop stresses, reinforced concrete, silo, standpipe, storage of liquids, storage of saturated bulk materials.

Stress Redistribution During Local Annealing of a Multi-Pass Butt-Welded Pipe

Stress redistributions during local Post Weld Heat Treatments (PWHT) are numerically studied for a multi-pass butt-welded pipe with mechanically unrestrained ends. The pipe material is a micro-alloyed C-Mn steel. Temperature and stress fields developed during welding and PWHT are determined from a FE-analysis where rotational symmetry is assumed. Use of heaters with a total axial width less than four times the pipe wall thickness is found to result in substantially different final stress fields than those obtained after a uniform (furnace) heat treatment. The tensile axial and hoop stresses on the inner pipe surface near the centre section of the weldment are considerably higher after a local PWHT. The differences were found to arise mainly during the cooling periods of the PWHTs.

Fatigue crack propagation in carburized high alloy bearing steels

Fatigue cracks were propagated through carburized cases in M-50NiL (0.1 C,4 Mo, 4 Cr, 1.3 V, 3.5 Ni) and CBS-1000M (0.1 C, 4.5 Mo, 1 Cr, 0.5 V, 3 Ni) steels at constant stress intensity ranges, ΔK, and at a constant cyclic peak load. Residual compressive stresses of the order of 140 MPa (20 Ksi) were developed in the M-50NiL cases, and in tests carried out at constant ΔK values it was observed that the fatigue crack propagation rates,da/dN, slowed significantly. In some tests, at constant peak loads, cracks were stopped in regions with high compressive stresses. The residual stresses in the cases in CBS-1000M steel were predominantly tensile, probably because of the presence of high retained austenite contents, andda/dN was accelerated in these cases. The effects of residual stress on the fatigue crack propagation rates are interpreted in terms of a pinched clothespin model in which the residual stresses introduce an internal stress intensity, Ki where Ki, = σid i 1/2 (σi = internal stress, di = characteristic distance associated with the internal stress distribution). The effective stress intensity becomes Ke = Ka + Ki where Ka is the applied stress intensity. Values of Ki were calculated as a function of distance from the surface using experimental measurements of σi and a value of di = 11 mm (0.43 inch). The resultant values of Ke were taken to be equivalent to effective ΔK values, andda/dN was determined at each point from experimental measurements of fatigue crack propagation obtained separately for the case and core materials. A reasonably good fit was obtained with data for crack growth at a constant ΔK and at a constant cyclic peak load. The carburized case depths were approximately 4 mm, and the possible effects associated with the propagation of short cracks were considered. The major effects were observed at crack lengths of about 2 mm, but the contributions of short crack phenomena were considered to be small in these experiments, since the two steels were at high strength levels, and short cracks would be expected to be of the order of 10 μm. Also, the two other steels behaved differently and in a way which followed the residual stress patterns. Both M-50NiL and CBS-1000M have a high fracture toughness, with Klc = 50 MPa · m1/2 (45 Ksi · in1/2), and the carburized cases exhibit excellent resistance to rolling contact fatigue. Thus, M-50NiL, carburized, may be useful for bearings where high tensile hoop stresses are developed, since fatigue cracks are slowed in the case by the residual compressive stresses, and fracture is resisted by the relatively tough core.

Interfacial Matrix Stresses in Composites Due to Misfitting Cylindrical Constituents

The constituent phases in composite materials of all types can induce local residual stress due to their differing mechanical responses. Changes in thermal, mechanical, or chemical states, encountered in processing or service applications, will generate these stress fields. Analytical solutions to isolated spherical or cylindrical inclusions exist, but the interaction of stress fields among neighboring constituents has not been examined in detail. The present study examined the matrix stress fields at the interface between the matrix and hexagonal arrays of misfitting cylinders. Stresses were analyzed using the photoelastic method, wherein the matrix was the photoelastic material. As the nearest-neighbor cylindrical inclusions first approach each other, there is a tendency for both radial compression and tensile hoop stress components to increase beyond values predicted for single, isolated inclusions. At nearest-neighbor separations less than 40% of the cylindrical inclusion diameter, however, the contact pressure between reinforcement and matrix decreases. At the same time, the tensile hoop component in creases markedly, less so in the hexagonal array than for two inclusions. The physical positioning and arraying of the reinforcement will clearly determine the local stress in duced by processing, which, in turn, will influence composite response and service endurance.

Simulation test on interactions of zircaloy claddings deforming in fuel assembly under LOCA conditions.

In a hypothetical LOCA of LWR, it is assumed that Zircaloy claddings of fuel assemblies occur ballooning and cause thermal and mechanical interactions among themselves. To investigate the phenomena, burst tests were conducted with a single rod fuel simulator placed in the center of eight non-pressurized external heater pipes. It was found that the deformation and rupture behavior of ballooning cladding which made contact with the pipes depends on the following conditions : (1) temperature difference between cladding and heater pipes; higher temperature in the cladding than in the pipes produces an extended deforma-tion and contact area, (2) internal pressure of cladding, and (3) temperature level at which ballooning takes place.It was observed and analyzed that cladding hoop tensile stress is largest at the inflection points generated in the contact surface of the expanding cladding.

Endurance Tests With Large-Bore Tapered-Roller Bearings to 2.2 Million DN

Endurance life tests were run with standard design and optimized high-speed design 120.65-mm- (4.750-in.-) bore tapered-roller bearings at shaft speeds of 12,500 and 18,500 rpm, respectively. Standard design bearings of vacuum melted AISI 4320 and CBS-1000M, and high-speed design bearings of CBS-1000M and through-hardened AISI M-50 were run under heavy combined radial and thrust load until fatigue failure or until a preset cutoff time of 1100 hours was reached. Standard design bearings made from CBS 1000M material ran to a 10-percent life approximately six times rated catalog life. Twelve identical bearings of AISI 4320 material ran to ten times rated calalog life without failure. Cracking and fracture of the cones of AISI M-50 high-speed design bearings occurred at 18,500 rpm due to high tensile hoop stresses. Four CBS 1000M high-speed design bearings ran to twenty-four times rated catalog life without any spalling, cracking or fracture failures.

The Effects of Texture and Surface Condition on the Iodine Stress Corrosion Cracking Susceptibility of Unirradiated Zircaloy-2

Four lots of stress-relieved Zircaloy-2 tubing were prepared from a single heat of the alloy. Tube reduction parameters were controlled so that each lot had a different crystallographic texture. The tubing with the most radial (least tangential) basal pole intensity was shown to have a Kearns texture number in the radial direction of 0.61, whereas the equivalent value for the tubing with the least radial texture was 0.48. Each lot of tubing was given one of three surface treatments: etched, etched and grit blasted, or lightly etched and shot blasted. The iodine stress corrosion cracking (SCC) susceptibility of the unirradiated tubing was determined by measuring the time to failure in a standard tube pressurization test at about 593 K in which 6 mg of iodine was present for each square centimetre of exposed Zircaloy surface. The results showed that texture has a large effect on SCC susceptibility and that surface condition has a significant but lesser effect. The SCC resistance was lowest in the material with the most tangential basal pole intensity and increased as the texture became more radial. The lightly etched and shot-blasted surface resulted in times to failure that were shorter than the times for the othermore » two surface conditions. However, it seems likely that the influence of surface treatment is quite complex and that SCC susceptibility can change significantly with a seemingly minor change in the surface treatment technique. The effect of texture was interpreted in terms of its influence on strength, on deformation characteristics, and on orientation of SCC susceptible planes with respect to the dominant tensile (hoop) stress. The effect of surface condition was interpreted in terms of its influence on residual stresses, on local texture changes, on local stress concentration, and on chemical activity.« less

Measurement of the stress field created within the resin between fibres in a composite material during cooling from the cure temperature

In a long uniaxial glass fibre/epoxy resin composite that is constrained by a rigid outer shell not to change its overall external dimensions, the transverse components of principal stress generated during cooling from the temperature of cure have been measured at various distances from the specimen ends. The radial (compressive) and hoop (tensile) components of stress in the resin between four fibres whose axes define the edge of a prism with square section are in excess of 6 and 100 MPa, respectively. In an identical specimen, 4 days of exposure to distilled water at 80° C was found to give rise to a tensile hoop stress of magnitude sufficient to cause fracture of the rigid outer shell.

The Axial Distribution of Deformation in the Cladding of Pressurized Water Reactor Fuel Rods in a Loss-of-Coolant Accident

In the event of a loss-of-coolant accident in a pressurized water reactor, the cladding of the fuel rods would undergo a temperature excursion while being subject to tensile hoop stress. The deformation behavior of 470-mm lengths of Zircaloy-4 fuel cladding has been studied experimentally; under a range of stress levels in the high-alpha range of zirconium (600 to 850/sup 0/C), diametral strains of up to 70% were observed over the greater part of their length. A negative-feedback mechanism is suggested, based on the reduction of secondary creep rate following cooling by enhanced heat loss at swelling areas. An approximate analysis based on this mechanism was found to be in reasonable agreement with the experimental results. A computer modeling code is being developed to predict cladding deformation under realistic conditions.

Stress Corrosion Cracking of Zircaloy-2 Cladding in Iodine Vapor

Iodine stress corrosion cracking of Zircaloy-2 cladding under static tensile stress has been studied over the temperature range of 250~450°C. The lowest iodine concentration required to cause cracking was 0.15 mg iodine per cm3 free volume in test ampoule at 300°C, and 1.1 mg/cm' at 350°C. The minimum circumferential plastic strain to cause failure was about 0.4% for specimen tubes possessing high cracking susceptibility. Softer tubes tolerate more circumferential deformation before they failed. This is attributed to greater margin retained for work hardening, rather than to smaller residual tensile hoop stress. Cracking was also inhibited by the presence of oxygen in the iodine atmosphere, the threshold partial pressures being 28 torr at 300°C and 9 torr at 350°C. Scanning electron micrographs of the fractured surfaces revealed brittle transgranular fracture carrying river patterns on part of the cleavage facets.

The effect of force fitting on the magnetic properties of iron-cobalt alloy ring samples

Ring samples of annealed iron-27% cobalt (Fe-27 Co) and iron-cobalt-2% vanadium (FeCo-2V) alloys were subjected to a number of force fitted conditions where the maximum tensile and compressive hoop stresses were varied from 0 to 50 MPa. Various dc and 400 Hz ac magnetic characteristics were determined at each stress level. The dc and 400 Hz ac characteristics of both alloys changed in the force fitted condition, with the compressive hoop stress having more of an effect than the tensile hoop stress on most of the magnetic properties. The most drastic changes were observed in the 400 Hz exciting characteristics at 2.0 T in the FeCo-2V alloy, where the unstressed value of 111 VA/kg was increased to 1700 VA/kg at a calculated maximum compressive hoop stress of -49 MPa. The Fe-27 Co alloy, although having poorer exciting characteristics at the same induction level, changed from 880 VA/kg to 1500 VA/kg at -50 MPa, the conclusion being that the Fe-27 Co alloy is less stress sensitive than the magnetically superior FeCo-2V.

Stress Corrosion Cracking of Zircaloy-2 Cladding in Iodine Vapor

Iodine stress corrosion cracking of Zircaloy-2 cladding under static tensile stress has been studied over the temperature range of 250~450°C. The lowest iodine concentration required to cause cracking was 0.15 mg iodine per cm3 free volume in test ampoule at 300°C, and 1.1 mg/cm' at 350°C. The minimum circumferential plastic strain to cause failure was about 0.4% for specimen tubes possessing high cracking susceptibility. Softer tubes tolerate more circumferential deformation before they failed. This is attributed to greater margin retained for work hardening, rather than to smaller residual tensile hoop stress. Cracking was also inhibited by the presence of oxygen in the iodine atmosphere, the threshold partial pressures being 28 torr at 300°C and 9 torr at 350°C. Scanning electron micrographs of the fractured surfaces revealed brittle transgranular fracture carrying river patterns on part of the cleavage facets.

Stresses in Shallow Elliptical Tunnel

A simple 3-dimensional photoelastic model test was devised that would yield data which is compatible with previously reported unlined elliptical tunnel under line loading. The details are outlined of the three-dimensional photoelastic stress freezing tests that were performed on lightly loaded models in a controlled circulation oven. The studies found that under the action of a concentrated surface load, only a relatively small region of the upper portion of the tunnel is subject to high tensile hoop stresses while the compression hoop stresses are distributed more uniformly with their maximum values at about 45 deg. on both sides of the vertical semi axis. In addition to obvious differences because of the attenuation of the concentrated load effect away from the point of load application, the distribution of hoop stresses in the section directly under the loading was also shown to differ significantly. It is concluded that the stress distribution found from a 2-dimensional physical or numericalmodel under an assumed line loading, can only give a coarse approximation of the true effect of a concentrated point load.

Lateral Buckling of Axially Constrained Pipelines

Introduction Imagine a length of straight uniform pipeline, rigidly attached to a rigid anchor block at each end, and initially unstressed. If an internal pressure is applied, can this pressure cause the pipe to buckle sideways?Although a correct answer to this question follows from a simple argument, it is nevertheless the subject of dispute among pipeline engineers. A simple but misleading argument goes like this: pressure induces a hoop tensile stress around the pipe, and if it were unconstrained it would contract along its length (because Poisson's ratio is positive). Since the anchor blocks resist this contraction, a longitudinal tensile stress is induced. Since the pipe wall is in longitudinal tension, the pipe cannot buckle laterally.It is the final step in this argument that is incorrect. This article sets down reasoning that leads to the correct conclusionthat the pipe can buckleand compares the predicted buckling pressure with experiment. The Critical Pressure An elementary argument shows that the longitudinal stress set up in a straight thin-walled axially constrained pipe by an internal pressure, p, is vpD/2T, where v is Poisson's ratio, D is diameter, and T is wall thickness. The resultant force over a complete cross-section perpendicular to the tube axis is (pi/4)D2p (1 - 2v), compressive since v less than 1/2, the difference between the compressive force (pi/4)D2p carried by the fluid within the pipe and the tensile force (vpD/ 2T) (piDT) carried by the wall of the pipe. The pipe can then be thought of as a column with clamped ends carrying this resultant compressive force, and buckling can be expected to occur when the force reaches the Euler buckling load. If Young's modulus is E, the flexural rigidity is phi ED3T/8; by this argument, buckling will occur when where L is the length of the pipe; that is, when The above argument leads to a correct value for the buckling pressure, but leaves a certain uneasiness in one's mind, because an instinctive feeling that the axial compressive force must "follow" the buckling pipe seems to conflict with the fact that the ends are pipe seems to conflict with the fact that the ends are fixed. An alternative argument avoids this difficulty, and makes clearer what the force pushing the pipe sideways is.In the above argument the pipe wall itself and the contained fluid within it were considered together. Instead, consider them separately. Fig. 1a shows the forces and moments acting on an element ds of the pipe wall, and Fig. 1b shows the forces acting on the pipe wall, and Fig. 1b shows the forces acting on the fluid contained within the element. The resultant force exerted by the contained fluid pressure on the pipe wall is Rds, and psi denotes the inclination of the deflected pipe to its original line. Since the fluid element must be in equilibrium, resolving forces perpendicular to the pipe axis in Fig. 1b, so that In words, the contained fluid exerts a lateral force on a deflected pipe; the magnitude of the force per unit length is the pressure multiplied by the cross-section multiplied by the curvature, and it acts towards the outside of the curve. If one analyzes buckling by examining the pipe deflected from its initial position, one must not forget the existence of this force (which is of course well known in other contexts). JPT P. 1283

Fracture of zirconium alloys in iodine vapour

Zirconium alloy tubing in the cold-worked condition has proved susceptible to short-term brittle transgranular cracking when exposed to iodine vapour over the temperature range 250–510 °C at tensile hoop stresses close to the 0.2% proof level. Thermal annealing reduced the cracking susceptibility of Zircaloy fabricated by cold-drawing but did not completely remove it after 850 °C, 1 h; in contrast a 650 °C, l h anneal was sufficient to prevent cracking in tube-reduced Zircaloy. Textural differences arising from the forming processes are considered to be responsible for this behaviour. Since the failures resulted from metal-gas interactions, the dominant mechanism is suggested to be one of mechanical fracture rather than electrochemical attack, a conclusion supported by results of fractographic examination.

AN INVESTIGATION INTO THE KINETIC FORMING OF TUBULAR AND OTHER THIN-WALLED COMPONENTS FROM SOLID CYLINDRICAL ALUMINIUM AND COPPER BILLETS

SUMMARY Experiments are described in which cylindrical aluminium and copper billets were fired from an industrial stud-driving gun into closed die sets of a variety of cavity forms. Where the forming process commenced with a piercing operation, as in the production of conical or tubular components, the effect of piercer radius upon the flow of billet material was investigated. It is shown how a tendency to rupture during “hoop” expansion of the billet material may be suppressed by elimination of hoop tensile stresses, either by using slightly converging die walls, or by constraining the material to move along a curved path so that heavy inertia stresses are developed in the “thickness” direction. Line diagrams of equipment are provided and photographs and photomacrographs of typical formed components are presented and discussed.

FEM Simulations Of Prosthesis Hip JointImplants

The scope of this report is to present the non-linear finite element method (FEM) calculations for two artificial hip joint implants (system composed of a spigot, head and cup). For the implants the influence of the boundary conditions, the variation of the taper angle difference, the coefficient of friction between the spigot and the head and also the material of spigot and head on the stress distribution in the system are determined. For each of the two implants, based on the designs of the producer Metoxit AG, an axisymmetric FE model was generated. Note that the head of the two implants possesses different bore depths. The geometry of the spigot and cup are similar in both models. The calculations were carried out with ABAQUS/Standard. The results of the analyses show that the boundary conditions of the implant and the variation of the taper angle difference have a strong influence on the tensile hoop stress distribution in the head. In addition, it was found that the variation of coefficient of friction determined by measurements and the different materials considered for the spigot and head have a small effect on the stresses. Moreover, the stresses in the head of the system with the deeper head bore do not necessarily have to be higher than those in the head with the shallow head bore, since the resulting stresses depend on the support conditions and the taper angle difference. The dominant influence of the boundary conditions on the stress distribution in the head raises doubts as to the correctness of the ISO 7206-5 standard; while the in vivo circumstances of the implant are not completely simulated by the test specified in this guideline. Transactions on Engineering Sciences vol 24, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533