Maximum Radial Stress Research Articles

Numerical analysis of delamination degradation of epoxy-impregnated superconducting coils wound with REBCO tapes caused by thermal stress

REBa2CuOy (REBCO) superconducting wires are expected to be used in coil applications owing to their excellent magnetic field properties. However, their weak delamination strength may deteriorate the superconducting characteristics of an epoxy-impregnated REBCO coil during cooling. In general, degradation is unlikely to occur if the outer-to-inner diameter ratio is less than 1.4; however, degradation has been reported in single pancake coils with an inner diameter of 560 mm and an outer diameter of 670 mm. A thermal stress analysis study is conducted to investigate the cause of this problem. Considering the non-uniformity of the epoxy resin thickness at the top and bottom of the coil, coil warping during cooling is simulated. When an FRP reinforcement plate is attached to the coil to suppress warpage, a high radial stress generated in the coil owing to the thermal contraction difference between the coil and FRP plate. The maximum local radial stress exerting in the delamination direction is 30 MPa, which is believed to degrade the superconducting characteristics of the REBCO single pancake coils.

Fatigue and static damage in curved woven fabric carbon fiber reinforced polymer laminates

Failure mechanisms of curved cross-ply laminates under static and fatigue loading have been studied extensively, but the examination of fabric laminates which are the most commonly used ply type in curved supports in airplane wing structures is lacking. In this study, unidirectional (UD) and fabric carbon fiber reinforced polymer (CFRP) laminates are examined to elucidate the failure initiation mechanisms of laminated composites under fatigue and static loading. The crucial point of the research is applying the analyses using fabric laminate with a currently used stacking sequence in commercial airplanes. In addition to the fabric laminate, UD laminate is also included in the research to compare the real complex stacking with the simplest stacking. In the experiments, it is observed that both static and fatigue failures initiate roughly at the maximum radial stress location (approximately 35% of the thickness from the inner radius). For UD laminates, there is no visible difference between the failure mechanisms under static and fatigue loadings. However, for fabric laminates, fatigue failure is observed to occur as a single major crack at the maximum radial stress location as in UD laminates, whereas static failure is observed to occur as multiple diffusive cracks at the maximum radial stress location. Additionally, cracks grow mostly as intralaminar cracks connected with regions of occasional interlaminar cracks.

Influence of structure of burned pellets on strength and destruction in static compression tests

The burned pellets must retain the strength from the time they come off the roasting machine until they are loaded into the blast furnace. One indicator of the strength of burned pellets is the compressive strength, i.e., the maximum applied load at which the iron-ore pellet completely collapses. The paper studies the character of destruction of burned iron-ore titanomagnetite pellets of fraction 10 - 16 mm in the static compression test according to the Russian State Standard 24765-81. It is shown that the main type of destruction during the test is the emergence and development of plane cracks passing through the center of the magnetite core, where the maximum radial tensile stresses act or in the immediate vicinity. In some cases, the trajectory of one of the destructive cracks deviates from the above plane and envelopes the magnetite core. Obviously, this is due to the presence of a second area of tensile stress concentration at the boundary of the magnetite core and the hematite shell, formed during cooling of the pellets, due to differences in their mechanical and thermophysical properties. As a result, the final structure of pellets is characterized by the presence of two zones -peripheral hematite and central magnetite. The role of the relative size of the magnetite core on the compressive strength of burned pellets has been determined. It was established that the strength characteristics of the pellet increase with a decrease in relative size of the magnetite core. During the process of magnetite complete oxidation (when the whole volume of the pellet consists of hematite), the maximum level of the pellets compressive strength can be: the maximum destructive force - 3300 N, destructive energy - 0.55 J, mass destructive energy - 0.18 J/g.

Research on thermal and mechanical effects of Al/PTFE reactive materials irradiated by femtosecond pulsed laser

In order to study the temperature distribution and thermal stress of femtosecond pulsed laser interacting with energetic materials, in this paper, a femtosecond pulse laser loading system combined with an infrared thermal imager was used to experimentally study the temperature of the material when the femtosecond pulse laser irradiated Al/PTFE reactive material. Scanning electron microscope (SEM) was used to analyze the ablation morphology of laser ablated Al/PTFE. The theoretical model of the interaction between laser and Al/PTFE reactive material was established and the numerical calculation was carried out. The thermal stress was calculated and analyzed by using the material temperature measured by the experiment according to the thermoelastic theory. The following conclusions are obtained. The material is melted and vaporized under laser irradiation and ablation marks appear. The material temperature and ablation depth in the experiment and numerical simulation have a certain consistency. The heat released by the exothermic reaction in the laser irradiation area of the material has little effect on the surrounding materials. The radial thermal stress generated during laser irradiation is compressive stress, and the circular stress along the radius of the light spot changes from compressive stress to tensile stress. The greater the laser repetition frequency and the longer the laser action time are, the greater the thermal stress is. The maximum radial compression stresses are 2.54 MPa and 4.52 MPa when the laser repetition frequencies are 500 Hz and 1000 Hz, respectively.

On the preliminary shape design of axisymmetric twin-web turbine discs considering the burst speed constraint

In this article, a topology optimization method is proposed to obtain a new preliminary shape design of the twin-web turbine disc considering the burst speed constraint. The burst speed constraint is converted to the constraints on the averaged hoop stress and the maximum averaged radial stress. The linear density filter and Heaviside projection are employed to prevent the mesh dependency and chequerboard pattern and ensure distinct solid/void interfaces in the optimization result. The geometric extraction is easily implemented using the least square fitting with B-spline method. Through illustrative examples, the importance of considering the burst speed constraint in the design of turbine disc is verified, which contributes towards obtaining a safer design at the preliminary design stage. The effectiveness of the proposed method in obtaining a lighter preliminary twin-web turbine disc design is also demonstrated compared with the parametric optimization method.

Swell induced stress in a hydrogel coating

A hydrogel can be coated on various substrates to enable multiple functions. Potential applications include biomedical devices, anti-fouling surfaces and microfluidics. In practical use, hydrogel coatings are often submerged in fluids. The swell of hydrogel coating deteriorates the interfacial bonding with the substrate. This paper presents a stress analysis of a hydrogel coating on a cylindrical metal substrate. We adopt the thermodynamic theory coupling large deformation and water migration and formulate two boundary value problems for the coating–substrate system with and without an interfacial crack. The inhomogeneous stress fields in the hydrogel coating are obtained. The influences of modulus, thickness of the hydrogel coating on the maximum radial stress at the interface are analyzed. These results may guide the design of hydrogel coating to avoid interfacial failure. The swell of a hydrogel coating deteriorates the interfacial bonding with the substrate. This paper presents a stress analysis of a hydrogel coating on a cylindrical metal substrate. We adopt the thermodynamic theory coupling large deformation and water migration, formulate two boundary value problems for the coating–substrate system with and without an interfacial crack, and obtain the inhomogeneous stress fields. These results may guide the design of hydrogel coating in future applications.

Effect of magnetic field on the thermo-elastic response of a rotating FGM Circular disk with non-uniform thickness

In this study, the effect of the magnetic field on the thermo-elastic response of a rotating non-uniform circular disk of functionally graded material (FGM) is investigated for both steady and transient states of temperature. A single second-order ordinary differential equation of motion was developed for an FGM disk and solved along with the boundary conditions using the finite-difference method (FDM). The steady-state and transient heat conduction equations were also solved using the finite-difference method. Numerical results were presented and discussed for an Al/Al2O3 FGM disk of exponentially varying material properties keeping Poisson’s ratio and magnetic permeability uniform. Displacement and stress components were analyzed by increasing the intensity of the magnetic field for different cases of steady and transient states of temperature. The analysis suggests that the magnetic field has a remarkable effect on the displacement and stress distributions. It is also found that, high intensity of the magnetic field changes the nature and location of maximum stress. The transient analysis of magneto-thermo-elastic field suggests that the increase in the intensity of magnetic field results in the increase in stress intensity near the outer region of the disk and maximum radial stress always exceeds maximum circumferential stress. The effects of inner and outer surface radius, thermal gradient between inner and outer surface, and the outer surface thickness were also analyzed in detail. It was found that, with the decrease in outer surface radius and thermal gradient between inner and outer surface, maximum circumferential stress becomes higher than the maximum radial stress. In addition, the soundness and accuracy of the solutions were verified with the results from the standard computational method and analytical solution.

2D and 3D simulations of dynamic delamination in curved unidirectional CFRP laminates subjected to moment/axial combined loading

Dynamic failure of 30-ply curved unidirectional CFRP laminate under quasi-static moment/axial combined loading used in the experiments of Tasdemir (2018) is investigated numerically. 2D and 3D explicit finite element analyses are carried out using cohesive zone elements and contact interactions to simulate progressive delamination. In both analyses, dynamic delamination initiates at the maximum radial stress location. The resultant crack propagation in both 2D and 3D simulations is observed to be intersonic in the arm regions, with lower crack tip speeds observed for the 3D case. In 3D simulations, a non-uniform crack front is observed, with the crack nucleating at the middle of the width, propagating to the edges and both arms at sub-Rayleigh speed before continuing to propagate in the arms at intersonic speeds. Intermittent local contact regions are observed in 2D simulations behind the crack tip, which are also observed in the 3D simulations at the free edge with a continuous contact line reaching the middle of the crack front, emphasizing the three-dimensional nature of the delamination growth. Load-displacement curves of both 2D and 3D simulations show good correlations with experimental results.

The burnup raising feasibility by studying the effects of Th and U contents on the thermophysical and mechanical properties of Th1-xUxO2 solid solutions

A comprehensive molecular dynamics study was carried out to investigate the role of thorium and uranium contents on improving the thermal and mechanical properties of the Th1-xUxO2 nuclear fuels. In this regard, several thermophysical and mechanical properties of the Th1-xUxO2 solid solutions including the lattice parameter, density, thermal expansion coefficient, specific heat capacity, thermal conductivity, thermal diffusivity, linear (heat/power) rating, elastic constants (C11, C12, C44, bulk, shear, Young's moduli, and Poisson's ratio) and the maximum radial thermal stress applied to fuel pellets were numerically investigated in a wide range of temperature and compared with experimental results. The results indicated that the Th1-xUxO2 fuels have a lower density, specific heat capacity, and thermal expansion coefficient than pure UO2 at any temperature. The results also showed that the Th1-xUxO2 fuels could increase or decrease the thermal conductivity, thermal diffusivity, and the linear heat rating of nuclear fuels depending on the uranium content (x). The amount of x in which all of the mentioned parameters can rise calculated in a wide range of temperatures. Maximum radial thermal stress was another important parameter that explicated in this paper. Results demonstrated that the Th1-xUxO2 fuels have lower maximum radial thermal stress, especially at high temperatures. These improved the thermo-mechanical properties provide the possibility of rising the fuel burnup in the thorium-based fuels compared to the uranium-based fuels.

Quench characteristics and mechanical responses during quench propagation in rare earth barium copper oxide pancake coils

Quench and mechanical behaviors are critical issues in high temperature superconducting coils. In this paper, the quench characteristics in the rare earth barium copper oxide (REBCO) pancake coil at 4.2 K are analyzed, and a two-dimensional (2D) axisymmetric electro-magneto-thermal model is presented. The effects of the constituent materials, background field, and coil size are analyzed. An elastoplastic mechanical model is used to study the corresponding mechanical responses during the quench propagation. The variations of the temperature and strain in superconducting layers are compared. The results indicate that the radial strain evolutions can reflect the transverse quench propagation and the tensile hoop and radial stresses in superconducting layers increase with the quench propagation. The possible damages are discussed with the consideration of the effects of the background field and coil size. It is concluded that the high background field significantly increases the maximum tensile hoop and radial stresses in quenching coils and local damage may be caused.

Mechanical Mechanism and Propagation Law of Fissure‐Tip Cracks of Large‐Size Rock Specimens with Two Precut Fissures

The rock is a kind of geological medium with damages of different degrees including fissures, faults, joints, and other structural defects. Many underground rock engineering projects, such as mining and tunnel excavation, can break the three‐dimensional stress balance state of rock mass and make it subject to two‐dimensional or even one‐dimensional stress, thus inducing stress concentration which leads to rapid failure. In order to investigate the failure law of the rock mass with such defects under two‐dimensional stress, based on the similarity theory, we first prepared rocklike specimens with fissures featuring actual mechanical properties and then systematically analyzed the fissure‐tip crack propagation and specimen failure law and mechanical mechanism under two‐dimensional stress in view of the stress field theory. The results demonstrate that with the increase of load, the microcracks developed and propagated gradually, during which a number of branch paths were generated from the fissure tips of the specimens; the upper and lower cracks were connected first due to the main crack propagation, forming a sliding surface which caused the failure of the specimens, and the strengths of the specimens also fluctuated according to the different combinations of the fissure dip angles and rock bridge dip angles. In view of acoustic emission (AE), we calculated and obtained the spatial positions of stress peaks in each direction at the fissure tips; through comparison and analysis, the angle corresponding to the negative angle peak of the maximum circumferential tensile stress and the maximum radial tensile stress is basically the same as the angle of the main crack propagation direction generated from the preexisting fissure; it can be inferred that the tensile stress is the main stress inducing crack initiation and specimen failure, which is consistent with the physical characteristics of rock (resistant to compression but not tension). This may serve as a guidance for judging the direction along which new cracks are generated in a rock mass with double structural planes.

Failure characteristics of surrounding rocks along the radial direction of underground excavations: An experimental study

For the in situ surrounding rocks of underground excavations, the radial stress corresponding to the minimum principal stress σ3 varies with increasing distance away from the excavated boundary. To characterize the rock failure along the radial direction of an excavation, true triaxial compression tests with different σ3 values (0.5, 5, 10, 15, 20, 25, and 30 MPa) were performed. The characteristic stresses (including the crack initiation stress σi, crack damage stress σd, and peak stress σs) and failure mode of the tested specimen under different σ3 conditions were systematically investigated. The experimental results indicate that with increasing σ3, the characteristic stresses increase monotonically and continuously. The increasing rate of the characteristic stresses with σ3 ranging from 0 to 10 MPa is higher than that with σ3 ranging from 10 to 30 MPa, indicating that low σ3 impose a greater effect on the characteristic stresses than high σ3. In addition, the failure mode of the tested specimen changes from tensile-shear failure mode I (with vertical tensile cracks and oblique tensile-shear cracks developing along the σ2 direction) to tensile-shear failure mode II (with oblique tensile-shear cracks developing only along the σ2 direction) to tensile-shear failure mode III (with oblique tensile-shear cracks along both σ2 and σ3 directions) as σ3 increases. Then, the failure characteristic of the surrounding rocks of the underground excavation was characterized based on the obtained experimental results. When maximum radial stress σr encountered near the excavated boundary is much smaller than the axis stress σa, the surrounding rocks will exhibit a “Ternary failure characteristic”, i.e., with an increase in the distance from the excavated boundary along the radial direction, the failure mode of the surrounding rocks after excavation changes from tensile/splitting failure mode to tensile-shear failure mode I and then to tensile-shear failure mode II. When the maximum σr encountered near the excavated boundary approximates the original σa, the surrounding rock masses will exhibit a “Quaternary failure characteristic”. Specifically, the corresponding failure mode along the radial stress direction away from the excavated boundary changes from tensile failure mode to tensile-shear failure mode I then to tensile-shear failure mode II and finally to tensile-shear failure mode III.

Simulation Analysis and Research on Integrated Forming Process of Steam Pipe Nozzle

The FORGE@ numerical simulation was used to analysis and research on the integrated forming nozzle process of the main steam pipe, and then guide sampling test plan and forming process evaluation. The results show that the maximum axial tensile stress appears in the middle of the forming process, which is on the inner surface of the extrusion deformation transition region, and the maximum radial tensile stress and equivalent strain appears at the end of the extrusion nozzle forming process, which is located in the inner surface area of the nozzle mouth, and it is easy to crack. For the weak position, it is necessary to increase the number of samples and test items to verify the overall quality of nozzle.

Installation effects of the post-grouted micropile in marine soft clay

The grouted steel pipe micropile is widely used as structural support and in situ improvement in China. This paper presents measurement of the radial soil stress and excess pore water pressure during the construction processes of the grouted steel pipe micropile (with an enlarged driving shoe) embedded in marine soft clay. Comparative analysis was conducted between the predictions by cavity expansion method (CEM) and maximum stress values in situ. The results show that the existence of the enlarged driving shoe has an effect on the stress change in the surrounding soils during penetration. The maximum radial total stress and excess pore water pressure generated during micropile penetration are approximately 4–6σv0′ and 1.5–2.5σv0′, respectively. The maximum radial total stress and excess pore water pressure, which appeared near the pile wall during the process of post-grouting, are approximately 5–7cu and 4–6cu, respectively. The predictions of CEM for pore water pressure during micropile penetration and post-grouting are in reasonable agreement with the field test data.

Mechanical properties optimization of Si3N4 ceramics by in-situ introduction of core-shell structural W-Fe5Si3

It is one inevitable problem that optimizing properties of Si3N4 ceramics by introducing second phase would produce thermal mismatch stress, which may lead to interfacial bonding and strength deterioration. In this work, a novel strategy for regulating the residual thermal stress and inhibiting the interfacial debonding in Fe5Si3/Si3N4 ceramics was proposed, which results in the simultaneous increase of strength and toughness of Si3N4 ceramics. Instead of Fe5Si3 particle, the core-shell structural W-Fe5Si3 particles were in situ generated in the Si3N4 matrix by introducing a new WSi2/FeSi2 powder directly. The maximum principal stress, residual radial and tangential stress around the core-shell structural W-Fe5Si3 and Fe5Si3 particle were compared by using the finite element method. The W core inhibits the radial contraction of the Fe5Si3 shell during the cooling process and alters the residual thermal stress distribution. Both the Griffith fracture equation and Lange's energy model indicate that the core-shell structural W-Fe5Si3 inhibits the interfacial debonding, which is consistent with the experiment result. As a result, with the increase of WSi2/FeSi2 addition from 0 to 1 wt%, the fracture toughness of Si3N4 ceramics increases from 7.1 to 7.7 MPa m1/2, and the strength improves from 1016 to 1173 MPa.

Electro-Magnetic Design of a 3MJ YBCO Magnet

The electro-magnetic design of two 3 MJ superconducting magnetic energy storage (SMES) magnets with YBCO conductor are presented. One magnet is with solenoidal geometry composed of double pancake coils, and the other one is with toroidal geometry. According to the magnetic field simulation results, the perpendicular componet of the magnetic field of the toroidal magnet could be extremely reduced compared with the solenoidal geometry. Therefore, a lower YBCO conductor requirement could be expected due to the dependence of Jc vs B performance of the YBCO conductor. Besides, the lower leakage magnetic field is important for application. A SMES system of 3 MJ is considered, and the coil is made of multiple identical D-type pancake coils. The critical current of the used YBCO conductor at 30K is 270A under 1 T perpendicular magnetic field. The inner radius of the D-type curve is 500 mm, and the outer radius is 1000 mm. The SMES magnet is made of 96 pancake coils, where the rated operating current is 975 A and the maximum perpendicular and parallel magnetic flux density are 0.5 T and 4.0 T, respectively. Further more, the maximum hoop stress and radial stress are 283 MPa and 78 MPa.

Mechanical effects of acupuncture

Acupuncture, a physiotherapy, has been widely accepted all around the world. This study focuses on the influence of membrane structures and explains the acupuncture sensations from the aspect of mechanical properties. By mathematical modeling and numerical simulation, the scientific meaning of the acupuncture depth is investigated and phenomena and theory of acupuncture are discussed. The simulation results show that (a) the fascial structure is the main contributor to the force on the needle, the axial force will gradually increase before piercing the fascial, and suddenly decrease after piercing the fascial; (b) there is an inverse relationship between the needle radius and the maximum radial stress, which indicates that the needle should not be too sharp to cause local stress concentration and piece the fascia layer; and (c) the simulation results of comprehensively considering the static friction and sliding friction is identical with the experiment results. This study proposes a preliminary study of mechanical effects of acupuncture manipulation, clarifies key factors affecting the stress on the needle, and explains the objective requirement of acupuncture depth to effective treatment.

THE EFFECT OF RESIDUAL STRESS ON THE LOAD BEARING CAPACITY OF PVD COATED SURFACES – PART 2

The article presents the results of modelling tests of the coating-substrate systems subjected to a contact load using a spherical diamond indenter with a 20 μm tip radius. Systems with 1 to 5 μm thick CrN coatings deposited on X5CrNi18-10 austenitic steel substrate were analysed. Systems without residual stress as well as with introduced 2 and 5 GPa compressive residual stresses were analysed. The article presents the effect of coating thickness on substrate deformations at load range up to 1 and 3 N. The evolution of maximum radial stress in the substrate and the range of substrate plastic deformation for the assumed coating thicknesses were also analysed. Modelling results showed a strong relation between maximum critical force and relative coating thickness. The maximum radial stresses in the substrate in a case of systems with a thin 1 μm coating are much smaller than for thicker 5 μm coating, referring to the relative coating thickness. However, the analysis of substrate yielding showed that, for thin 1 and 2 μm coatings, substrates deform plastically at 0.01 and 0.03 N, respectively, while the 5 μm coating prevent plastic deformations up to load 0.32N.

Crack Initiation Criteria and Fracture Simulation for Precracked Sandstones

The friction coefficient, tip curvature, and different-width crack state influence the stress intensity factor (SIF). The maximum circumferential tensile stress (MTS) and minimum strain energy density criterion (S) face challenges in explaining the mode-II fracture propagation of cracks. The maximum radial shear stress (MSS) and modified twin shear stress factor (ITS) criteria are proposed as the brittle mode-II fracture criteria. The experiments and numerical analysis are also performed. The results indicate that the fracture angles of the MSS and ITS were similar and different from the results of MTS and S. The equivalent stress intensity factors (ESIFs) from the mixed mode I-II are proposed to determine the fracture mode. There are different fracture models for different cracks under tensile and compressive stresses. The ratio of the tensile strength to uniaxial compressive strength influenced the fracture angle of ITS. The lateral pressure coefficient (k) had a significant effect on the mode-II fracture angle when the angle between the crack and the vertical direction is less than 40° and the lateral pressure coefficient is more than 0. Because the same fracture mode k (k > 0) can inhibit mode-I fracturing, conversely, it can also promote mode-I fracturing. Experimental results and numerical simulations of fracture propagation under uniaxial compression confirmed that the theoretical results were correct.

Analysis of progressive rupture process in surrounding rock for a deep homogeneous and circular opening

ABSTRACT The failure mode and scope of rock surrounding a rupture zone have important theoretical value for stability analysis and support design of excavated openings. This study uses the Mohr–Coulomb yield criteria to study the general pattern of rupture progress in rock surrounding circular openings by resolving the analytical solution of stress in elasto-plastic mechanics of the circular openings. The results indicate a dynamic rupture process that develops gradually in homogeneous and circular surrounding rock in the mode of circular annuli under conditions of hydrostatic pressure. The concept of a sub-rupture zone in the surrounding rock is also proposed, and the criterion for rupture of the sub-rupture zone is derived. The calculation of radial stress is undertaken for the outer boundary of the sub-rupture zone, and the calculation method of radii in the sub-rupture zone is obtained. The equality of radii of adjacent sub-rupture zones is taken as the criterion of cessation of rupturing in a rupture zone, and is the criterion upon which the analytical solutions of maximum radius and maximum radial stress are deduced based. The analytical solutions are highly consistent with the engineering example and numerical simulation results using FLAC3D™, which reveals the failure mechanism of surrounding rock and validates the accuracy of the theoretical calculations. The results provide a theoretical basis for optimizing support design and safety assessment in underground engineering projects.