Tensile Hoop Stress Research Articles

内部補強Ｎｂ３Ｓｎ超伝導線材およびコイルに及ぼす横圧縮応力の効果

Lorentz force is applied to coil windings when the magnet is charged. The coil windings are subjected to huge hoop tensile stress and transverse compressive stress in both the radial and axial directions due to the Lorentz force. The higher the magnetic field and the larger the bore, the larger the Lorentz force applied to the coil windings. Thus, not only the hoop stress, but also transverse compressive stress should be taken into account when designing the magnet. In this paper, we focus on transverse compressive stress, and the influence of this stress on critical current is explored for a standard Nb3Sn wire and a Cu-NbTi-reinforced Nb3Sn wire. It was confirmed that Cu-NbTi sufficiently reinforced the superconducting wire, not only for tensile stress, but also for transverse compressive stress. The effect of reinforcement arrangement in the cross section was also investigated. In the case that Cu-NbTi reinforcement is arranged at the center of the wire, there was less deterioration in superconducting property than in the case of the reinforcement being arranged in the outer part of the wire.

Analytical model of corrosion-induced cracking of concrete considering the stiffness of reinforcement

The structural deterioration of concrete structures due to reinforcement corrosion is a major worldwide problem. Service life of the age-degraded concrete structures is governed by the protective action provided by the cover concrete against the susceptibility of the reinforcement to the corrosive environment. The corrosion of steel would result in the various corrosion products, which depending on the level of the oxidation may have much greater volume than the original iron that gets consumed by the process of corrosion. This volume expansion would be responsible for exerting the expansive radial pressure at the steel-concrete interface resulting in the development of hoop tensile stresses in the surrounding cover concrete. Once the maximum hoop tensile stress exceeds the tensile strength of the concrete, cracking of cover concrete would take place. The cracking begins at the steel-concrete interface and propagates outwards and eventually resulting in the through cracking of the cover concrete. The cover cracking would indicate the loss of the service life for the corrosion-affected structures. In the present paper, analytical models have been developed considering the residual strength of the cracked concrete and the stiffness provided by the combination of the reinforcement and expansive corrosion products. The problem is modeled as a boundary value problem and the governing equations are expressed in terms of the radial displacement. The analytical solutions are presented considering a simple 2-zone model for the cover concrete viz. cracked or uncracked. A sensitivity analysis has also been carried out to show the influence of the various parameters of the proposed models. The time to cover cracking is found to be function of initial material properties of the cover concrete and reinforcement plus corrosion products combine, type of rust products, rate of corrosion and the residual strength of the cover concrete. The calculated cracking times are correlated against the published experimental and analytical reference data.

Optimal response of conical tool semi angle in ductile metal sheets indentation and its governing mechanics

The nonlinear dependence aspect of various conical tool indentation parameters leading to an optimum tool semi angle value for easiest perforation is plotted and discussed explicitly in this work with the conclusion that tool angle has an optimum response towards most of the indentation parameters. Around this optimum angle, the aluminium sheets showed minimum fracture toughness as well as minimum work input to overcome the offered resistance. At the end, the mechanism leading to this phenomenon is presented with the conclusion that plastic flow dominates as the dimple semi cone angle reaches 35 and both pre and post plastic flow perforations lead the tool semi cone angle value towards this dimple cone semi angle of plastic flow initiation for its optimum performance. It is also concluded that specimen material failure is solely under tensile hoop stress and hence results into radial cracks initiation and propagation.

Effects of tooling on the residual stress distribution in an inertia weld

Neutron diffraction residual strain measurements have been made on a tubular structure formed by joining two nickel-based superalloy RR1000 parts by inertia welding. Residual strains in the radial, hoop and axial directions of the tube cross-section have been measured. The corresponding residual stress field has been calculated accounting for the stress-free lattice parameter variations in the region close to the weld line. Tensile residual stresses were observed near the inner diameter of the tube with magnitudes of the order of +500, +1100 and +1300 MPa in the radial, axial and hoop directions, respectively. By comparison near the outer diameter (OD) of the weld the corresponding stresses are of the order of −200, −1000 and 150 MPa. The final stress state reflects the influence of the gripping fixture tooling and thermal gradients during inertia welding. Additional X-ray (at the surface) and hole-drilling (at the near surface) measurements show a steep residual stress gradient in the near surface region. Tensile hoop and axial machining stresses at the surface indicate the potential for improving the inertia weld tooling and the machining parameters used when removing the flash.

A Hollow Cylinder of Functionally Gradient Materials Fabricated by Centrifugal Molding Technique

Hollow cylinders of functionally graded materials (FGMs) composed of low-density alumina and high-density tungsten powders with two kinds of particle size were fabricated using a centrifugal molding technique. Fine and coarse particle sizes of tungsten powders were used to make continuous and gradual variations of their composition. The alumina and tungsten powders were mixed with ethanol solvent, dispersant, and binder, and rotated at 3000 rpm in a steel mold of the centrifugal molding equipment. After casting and drying the slurry, the FGM cake was sintered in a reduced atmosphere of H2/N2 environment at 1600°C for 3 h. Continuously gradient constituents across the thickness of the hollow cylinder were obtained with the range of the slurry viscosity from 100 mPa·s to 300 mPa·s by adjusting the mixture ratio of the two particle sizes of tungsten powders. Residual thermal stresses generated during the cooling process were also analyzed numerically for each fabricated FGM cylinder with different variation of microstructure using a multi-layered technique. The analytical results showed that tensile hoop stresses appeared on the inner surface of the hollow cylinder and compressive stresses on the outer surface, and these residual stresses were released by selecting appropriate gradients with good dispersion of particles.

All in an engineer’s life

All in an engineer’s life

Salt damage in porous materials: how high supersaturations are generated

The current theory of crystal growth in pores has been further developed to include thermodynamics of real solutions for sodium sulfate and sodium chloride. This allows better quantification of the stresses developed by crystallization of these salts inside porous materials such as stone, brick or concrete. Results for sodium sulfate show that dissolution of its anhydrate produces supersaturations with respect to its decahydrate capable of generating tensile hoop stresses on the order of 10–20 MPa, largely in excess of the tensile strength of almost all stones. It also explains why, in the accelerated testing that involves cycles of impregnation and drying, all damage occurs during the impregnation and not the drying step. The situation in which crystallization is driven by evaporation is also discussed in light of understanding why sodium sulfate also induces more damage than sodium chloride during continuous capillary rise experiments. Results suggest that the classification of stone resistance to salt damage can change depending on the mode of supersaturation generation.

Foreign-object damage and high-cycle fatigue of Ti–6Al–4V

Recent high-cycle fatigue (HCF) related failures of gas-turbine jet engines have prompted a re-examination of the design methodologies for HCF-critical components, such as titanium alloy turbine blades. As foreign-object damage (FOD) from ingested debris is a key concern for HCF-related failures of such blades, the current study is focused on the role of simulated high velocity FOD in affecting the initiation and early growth of small surface fatigue cracks in a Ti–6Al–4V alloy, processed for typical blade applications. It is found that resistance to HCF is markedly reduced, primarily due to earlier fatigue crack initiation. The mechanistic effect of FOD on such premature fatigue crack initiation and the subsequent crack growth is discussed in terms of four prominent factors: (i) the presence of small microcracks in the damaged zone; (ii) the stress concentration associated with the FOD indentation; (iii) the localized presence of tensile residual hoop stresses at the base and rim of the indent sites; and (iv) microstructural damage from FOD-induced plastic deformation. In view of the in-service conditions, i.e., small crack sizes, high frequency (>1 kHz) vibratory loading and (depending on the blade span location) high mean stress levels, a damage-tolerant design approach, based on the concept of a threshold for no fatigue-crack growth, appears to offer a preferred solution. It is shown that FOD-initiated cracks that are of a size comparable with microstructural dimensions can propagate at applied stress-intensity ranges on the order of Δ K∼1 MPa√m.

Rigid square inclusion embedded within an epoxy disk: asymptotic stress analysis

Abstract The asymptotically singular stress state found at the tip of a rigid, square inclusion embedded within a thin, linear elastic disk has been determined for both uniform cooling and an externally applied pressure. Since these loadings are symmetric, the singular stress field is characterized by a single stress intensity factor Ka, and the applicable Ka calibration relationship has been determined for both a fully bonded inclusion and an unbonded inclusion with frictionless sliding. A lack of interfacial bonding has a profound effect on inclusion-tip stress fields. When the inclusion is fully bonded, radial compression dominates in the region directly in front of the inclusion tip and there is negligible tensile hoop stress. When the inclusion is unbonded the radial stress at the inclusion tip is again compressive, but now the hoop tensile stress is of equal magnitude. Consequently, an epoxy disk containing an unbonded inclusion appears to be more likely to crack when cooled than a disk containing a fully bonded inclusion. Elastic–plastic calculations show that when the inclusion is unbonded, encapsulant yielding has a significant effect on the inclusion-tip stress state. Yielding relieves stress parallel to the interface and greatly reduces the radial compressive stress in front of the inclusion. As a result, the encapsulant is subjected to a nearly uniaxial tensile stress at the inclusion tip. For a typical high-strength epoxy, the calculated yield zone is embedded within the region dominated by the elastic hoop stress singularity. A limited number of tests have been carried out to determine if encapsulant cracking can be induced by cooling a specimen fabricated by molding a square, steel insert within a thin epoxy disk. Test results are in qualitative agreement with analysis. Cracks developed only in disks with mold-released inserts, and the tendency for cracking increased with inclusion size.

Fatigue and Fracture Mechanisms in Large Rolling Element Bearings

Fatigue in rolling bearings generally results in failure by pit -ting (spoiling). However, large bearings, most particularly those subjected to significant tensile hoop stress, sometimes fail due to more or less radial cracking, which may lead to fracture of the contacting raceways or of the rolling elements. Examples of this type of failure have been reported from a wide range of applications, suggesting that current understanding is imperfect. In the present paper, an analysis of crack initiation and propagation is presented and used to examine the conditions necessary to cause radial cracking and fracture in large bearing components, including rollers. The analysis includes the effects of hoop tensile stress and of fluid entrapment. Results of the analysis are used to demonstrate the significance of Hertz pressure, roller diameter and hoop stress, whether applied or residual. The results provide a reasonable explanation of the difference in the observed behavior between small and large roller bearings. A simple map is proposed in order to predict the failure mode to be expected in roller bearings operating at modest contact pressures. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2000

高温ガス炉直接発電システム用高強度3-D C/Cコンポジット製タービンディスク模擬試験体の回転強度試験(I)

A turbine disk model has been trially fabricated and tested which uses C/C composite material to lighten the turbo machinery rotor for HTGR-GT system. In present study, the design and production of the most large-scale 1/5 reduction turbine disk model (the outside diameter×inside diameter×thickness=φ400 mm×φ300 mm×t30 mm) in the world which enforced three-dimensional structure to the hoop, radius and thickness directions using the high strength carbon fiber has been implemented. As a result of spin tests, following conclusions were obtained.(1) To establish an enforced structure to endure the amount of hoop tensile stress which occurs in spin test in case of design of the 1/5 disk model, 40 vol% carbon fiber containing quantity to the hoop direction in the preform was chosen. Moreover, to endured a compressive force to the thickness direction and prevent the delamination in the aspect of the carbon fiber product layer during spin test, the carbon fibers of 10 vol% and 4 vol% has been added to the thickness and radial directions.Moreover, this preform was experimentally fabricated using the large-scaled carbon fiber weave equipment (the maximum manufacturing possible shape, the diameter×thickness, 1.5 m of φ2 m) and the experimental production of the 1/5 disk model was successfully implemented which is made from the C/C composite which was strengthened in the three dimensions, then graphitized and densified.It is possible to manufacture the full size gas turbine disk of the HTGR-GT system by the application of this manufacturing technology.(2) The ordinary circumferantial speed (∼350 m/s) of the small disk experimental production body has been achieved which is made form two or three dimensional reinforcement C/C composite in the past in case of spin test of the 1/5 reduction disk model.(3) Moreover, in case of the solid disk created in the identical manufacturing condition, it was considered that the specimen can achieve the high rotational speed performance condition of the HTGR-GT system.

Stress Concentration Reduction at a Reinforced Hole Loaded by a Bonded Circular Inclusion

This paper considers analytically the stress concentration in an infinite plane loaded by a circular inclusion, which is bonded to a reinforced hole in the plane. The pulling force of the inclusion is modeled by distributed body force. The infinite plane, the reinforced ring, and the circular inclusion can be of different elastic properties. Airy stress function with body force potential was used to solve the problem analytically. Numerical results show that the maximum tensile hoop stress at the hole boundary in the plane can be reduced to becoming negligible if an optimum stiffness ratio between the plane and the rivet is chosen (normally a harder material for the reinforced ring comparing to the plane is needed). An optimum thickness of the reinforced ring can also be determined to further reduce the hoop stress concentration. Therefore, the results of the present study provide a new theoretical basis for designing a reinforced rivet hole.

Enhancement of tensile stress near a hole in superconducting trapped-field magnets

The mechanical stress caused by flux pinning in a cylindrical superconductor with a concentric hole is investigated theoretically. Exact expressions for the radial and hoop stress are derived using the critical-state model. Stress profiles during a magnetization process often used to activate high-Tc superconductors as strong trapped-field magnets are presented and analyzed in detail. It is shown that due to the hole the tensile hoop stress is enhanced by a factor of 2 or more, depending on the hole diameter. The dramatic increase in cracking probability is emphasized.

A constitutive model and FE simulation for the sintering process of powder compacts

A model for describing the entire sintering process of powder compacts is presented based on the thermal elasto-viscoplastic theory. The predications of shrinkage and stress changes of WC-6%Co powder compacts during sintering process are simulated using the ABAQUS code. It was found that simulation results for displacements are a good fit of the experimental data. In situ measurement technique and simulation for stresses indicate that maximum tensile stresses always arise at the beginning of cooling stage. The tensile hoop stress σ 33 is a major stress, which may cause surface crack in the cylinder specimen in sintering process and is compared with experimental observation.

Role of foreign-object damage on thresholds for high-cycle fatigue in Ti-6Al-4V

The increasing incidence of military aircraft engine failures that can be traced to high-cycle fatigue (HCF) has prompted a reassessment of the design methodologies for HCF-critical components, such as turbine blades and disks. Because of the high-frequency vibratory loading involved, damagetolerant design methodologies based on a threshold for no crack growth offer a preferred approach. As impact damage from ingested debris is a prime source of HCF-related failures, the current study is focused on the role of such foreign-object damage (FOD) in influencing fatigue crack-growth thresholds and early crack growth of both large and small cracks in a fan blade alloy, Ti-6Al-4V. FOD, which was simulated by the high-velocity (200 to 300 m/s) impact of steel spheres on a flat surface, was found to reduce markedly the fatigue strength, primarily due to earlier crack initiation. This is discussed in terms of four salient factors: (1) the stress concentration associated with the FOD indentation, (2) the presence of small microcracks in the damaged zone, (3) the localized presence of tensile residual hoop stresses at the base and rim of the indent sites, and (4) microstructural damage from FOD-induced plastic deformation. It was found that no crack growth occurred from FOD impact sites in this alloy at ΔK values below ∼ 2.9 MPa √m, i.e., over 50 pct higher than the “closure-free”, worst-case threshold value of ΔK TH = 1.9 MPa √m, defined for large cracks in bimodal Ti-6Al-4V alloys at the highest possible load ratio. It is, therefore, concluded that such worst-case, large fatigue crack thresholds can, thus, be used as a practical lower-bound to FOD-initiated cracking in this alloy.

Change in properties of geophysical medium during underground explosions

Mechanisms of strength loss of rocks in a slightly fractured mass during confined explosions are considered. It is shown that, at small depth (H ≤ 400m) beyond the boundary of radial crack zone, local rock failure is possible under the action of hoop tensile stresses during a single explosion and under the action of shear stresses in wave superposition zones during a group explosion. At great depths, local failure and strength loss of rocks in the indicated area are possible by shear failure in zones of blast wave interaction.

New Retainer Material for High Speed and High Temperature Cylindrical Roller Bearing

Cylindrical roller bearings are being developed which can operate over 300°C and greater than three million DN for innovative gas-generators. Under such severe conditions, it is necessary for retainers to be frictionless, lightweight and strong. After preliminary testing, SiC particle reinforced aluminum alloy composite appeared to have good friction and wear properties. It's specific gravity is about one-third of the present material in use, silver-coated SAE4340. In the course of the study, two different friction and wear tests were conducted to investigate the optimum volume fraction of SiC. The results indicated that the most efficient volume fraction was 20vol%. The tensile strength of Al-20vol%SiC was about 140MPa at 300°C. Based on the results of FEM analysis, 140MPa is considered sufficient to endure any stress concentration caused by tensile hoop stresses up to four million DN. Presented at the 54th Annual Meeting Las Vegas, Nevada May 23–27, 1999

An investigation of biphasic failure criteria for impact-induced fissuring of articular cartilage.

Articular cartilage consists of both solid and fluid phases with fissures observed on the surface occurring in the solid portion. In order to determine which of the solid phase stresses provides the best predictor for the initiation of a fissure, elastic stresses from a series of in vitro impact experiments were used to derive stresses in the solid phase of the cartilage. This stress information was then analyzed using a logistic regression to identify the best predictor of fissuring. The mechanical analysis indicated that low-magnitude tensile solid hoop stress develops in the solid phase within the contact zone in impacts involving the two smaller radius interfaces. The logistic regression, however, indicated that maximum shear stress in the solid (which is equal to the shear stress from the elastic analysis) was the best predictor of the occurrence of a fissure. This study helps support the suggestion that in stress fields dominated by compression, the maximum shear stress from an elastic analysis may be used to predict fissure initiation in cartilage.

Analysis of High Speed Axially Symmetric Cutting for Stripping Peripheral Coating

A theory of axially symmetric cutting is used to estimate the resistance to material removal of a composite cylinder undergoing stripping of a peripheral coating. The removal of materials from the surface of the cylindrical workpiece is analyzed using the minimum energy theory of Merchant. It is assumed that the shear surface is oriented at an angle π, such that the total work done at the shear surface by relative sliding and at the rake face due to friction has a minimum value. When the material conditions and the depth of cut are the same for cuttings in the axially symmetric and orthogonal modes, chips removed in axially symmetric cutting will have an additional energy loss due to the tensile hoop stress. The resistance due to the axially symmetric cutting is therefore larger than that arising from orthogonal cutting. The predicted resistance of axially symmetric cutting are in favorable agreement with data of dynamic stripping tests performed at Sandia National Laboratories.

Manufacturing of an alumina liner-steel sleeve under high pressure and temperature

The finite element analysis for a tubular alumina liner, which was shrink-fitted into a heat-treated high-speed steel (HSS) sleeve and subjected to high internal pressure and high temperature, was performed. The parameters for the analysis were the interference between the alumina and the HSS, the temperature, the internal pressure, the coefficient of friction between the alumina, and the taper at the sleeve ends. From the analysis it was found that the tensile hoop stresses decreased when the end parts of the HSS sleeve were tapered or the coefficient of friction between the alumina and the HSS was decreased. Based on the analysis a prototype alumina liner-steel sleeve was manufactured, and it was found that the alumina might be used as the structural liner for high pressures and temperatures when it was shrink-fitted into a heat-treated HSS sleeve.