Neutral Radius Research Articles

Buckling Analysis of Composite Piezoelectric Cylindrical Shells with Graphene Skin Subjected to the Axial Load

The buckling of new three‐phase composite shells, which include the base material combined with macro fiber composite and reinforced with graphene (MFC‐GP), is investigated in this article. The bifurcation condition of the buckling is obtained by implementing the first‐order shell theory and wave propagation theory in conjunction with the principle of minimum potential energy. The buckling analysis is transformed into a bifurcation problem of equations. Parametric study is conducted to investigate the effects of the GP volume fraction, length, neutral surface radius, and thickness on the critical buckling loads and critical buckling modes. Furthermore, the influences of voltage and temperature change on the critical buckling displacements are explored. Reliable theoretical support for the design and manufacture of the MFC‐GP structures is provided in the results.

Modal analysis of a hydrogen-damaged pipe as shell inhomogeneous on thickness

Hydrogen corrosion of main gas and oil pipelines often leads to accidents. It is necessary to assess the life of hydrogen-weakened pipes. An inner layer with deteriorated mechanical characteristics is formed in them under pressure of hydrogen-containing medium. In the paper the calculation of free vibrations of such a tube taking into account the degradation of its material is performed. The tube is modeled as a bilayer cylindrical shell according to the classical theory. Influence of hydrogen-impacted layer is taken into account when calculating stiffnesses and displacement of neutral line of the shell. Three variants of averaging of parameters determining the stiffness of the shell are considered, numerical experiments are carried out and the natural frequencies of the shell are found. Comparison with calculations using the method of finite elements in the ANSYS software made it possible to estimate the degree of applicability of each version of averaging. The method of averaging Young's modulus over the thickness of the shell does not "feel" asymmetry of layers relative to the neutral line. The method of adding a correction for the neutral line radius of the shell works satisfactorily for axisymmetric and beam modes. The next more accurate approximation is to average the shell stiffnesses over its thickness with the reduced radius. This method allows us to obtain satisfactory results in a wide enough frequency range and for the modes related to the deformation of the shell cross section. A method for the principle reconstruction of the parameters characterizing the stiffness of the shell using three experimentally obtained fixed frequencies has been proposed. On the basis of these studies formulas are proposed which allow to reconstruct parameters of weakening of pipe material, as a result of hydrogen corrosion, both in thickness and in time from the frequency characteristics of the pipe.

Flow Dynamics of a Contra-Rotating Axial Fan Under Windmilling and Locked Conditions

The present work aims to understand the flow dynamics of a low-speed contra-rotating axial fan under windmilling and locked state. To gain a deep understanding of flow behavior, four configurations are evaluated, both experimentally and numerically, in which one of the rotors will be in windmilling or locked mode while the other is in powered mode. The spanwise distribution of the loading coefficient and flow angles at different streamwise positions reveals the details of the flow development across the rotors. The windmilling rotor depicts the existence of a “neutral radius,” where compressor and turbine behaviors coexist. When rotor-2 is windmilling, the neutral radius is identified closer to the tip of the blade. In contrast, when rotor-1 is windmilling, the neutral radius is identified closer to the hub of the blade. The flow coefficient has a significant effect on the position of the neutral radius. Results from numerical simulations imply that the flow separates from the pressure surface in the span regions where the rotor behaves as a turbine and from the suction surface in the span regions where the rotor behaves as a fan.

ЭКСПЕРИМЕНТАЛЬНОЕ ОПРЕДЕЛЕНИЕ РАДИУСА НЕЙТРАЛЬНОЙ ПОВЕРХНОСТИ ПРИ ГИБКЕ МОМЕНТОМ

The paper presents the results of the experimental determination of the neutral surface radius during bending by the moment and their comparison with theoretical values. For this, a method has been developed for determining strains during two-corner bending using the Vic-3D system, which operates on the basis of digital image correlation (DIC). The measurement error and the limitation of the developed technique are determined.

Windmilling Characteristics of a Contra-Rotating Fan

Abstract In the present experimental study, a low aspect ratio, low hub-tip ratio contra-rotating axial fan is investigated to understand its performance under windmilling conditions. Two configurations are tested; in the first configuration (event A), the front rotor of the contra-rotating fan is powered and the rear rotor is allowed to windmill; in the second configuration (event B), the rear rotor of the contra-rotating fan is powered and the front rotor is allowed to windmill. The spanwise distribution of the loading coefficient and the flow angles at different streamwise positions reveal the details of the flow development across the rotors. Though the average total pressure drops across the windmilling rotor for both the events, a small spanwise region behaves as a fan or a stirrer. Thus, a “neutral radius” on the windmilling rotor is identified for both events A and B. The neutral radius appears close to the tip for event A and it appears close to the hub for event B. Thus, the span regions close to the tip behave as a fan for event A and the span regions close to the hub behave as a stirrer for event B. It is also observed that the neutral radius shifts to a lower span location as the flow coefficient reduces. Thus, the flow coefficient is a significant parameter that decides the position of the neutral radius. Further, the unsteady pressure measurements recorded at the casing capture the fundamental phenomena during the stall inception. The paper thus relates the similarities and unveils the contrasting features of the windmilling events A and B. In summary, this paper discusses the performance, flow physics, and stall inception characteristics of a contra-rotating axial fan under windmilling conditions.

Mechanical Characterization of Embedded Serpentine Conductors in Wearable Electronics

Abstract Wearable electronics undergo stretching, flexing, bending, and twisting during the process of being put on and while being worn. In addition, wearable textile electronics also need to survive under cyclic washing. During such processes, it is necessary to ensure that the electronics as well as the conductors and various other supporting materials remain reliable. In this work, mechanical characterization of various materials in a commercially available smart shirt is presented. The serpentine conductor used in the smart shirt has been carefully examined to understand the strain distribution at various locations under stretching. Both analytical formulations and numerical simulations have been carried out to determine the strain distribution in the serpentine structure, and the results from the simulations have been compared against experimental data obtained through two-dimensional digital image correlation (2D DIC). Various design configurations of the semicircular serpentine structure have been studied in this work, and a relationship between width and the neutral line radius of the semicircular serpentine structure has been obtained to reduce maximum strains in the serpentine structure under stretching.

A Finite Element Study of Thermo-Mechanical Fields and Their Relation to Friction Conditions in Al1050 Ring Compression Tests

The most accepted method for determining friction conditions in metal forming is the ring compression test (RCT). At high temperatures, extraction of the friction coefficient, μ, commonly requires numerical analysis due to the coupling between the mechanical and thermal fields. In the current study, compression tests of cylindrical specimens and RCT experiments were conducted on commercially pure aluminium (Al1050) at several temperatures, loading rates, and lubrication conditions. The experiments were used in conjunction with a coupled thermo-mechanical finite element analysis to study the dependence of the friction coefficient on those parameters. It is demonstrated that due to the coupling between friction conditions and material flow stress, both μ and flow stress data should be determined from the cylinder and ring specimens simultaneously and not subsequently. The computed friction conditions are validated using a novel method based on identification of the plastic flow neutral radius. It is shown that, due to heat loss mechanisms, the experimental system preparation stage must be incorporated in the computational analysis. The study also addresses the limitation of the RCT in the presence of high friction conditions. The computational models are finally used to examine the thermo-mechanical fields, which develop during the different processes, with an emphasis on the effect of friction conditions, which were then correlated to the resulting microstructure in the RCTs.

Effect of electropulsing on springback during V-bending of Ti-6Al-4V titanium alloy sheet

Effect of frequency and peak current density of electropulsing on springback behaviors of Ti-6Al-4V titanium alloy was investigated during electrically assisted V-bending tests. The experiments were carried out by controlling variable parameters with a frequency of 0–450 Hz and peak current density of 0–62.5 A/mm2. The results show that springback angle and V-bending load value decrease with increasing frequency and peak current density. Springback can almost be eliminated at 450 Hz and 43.1 A/mm2. Based on neutral layer offset and microstructure analysis, it demonstrates that the reductions of neutral layer radius, bending moment, and residual stress are responsible for the springback reduction. In addition, the refined β phase particles, dissolution of clustered β phase, the reduction of β particle spacing at outer layer, and enhancement of β particle spacing at inner layer contribute to the balance of tensile and compression residual stress, contributing to springback reduction. Effect of peak current densities on the springback behavior under similar RMS current density was carried out and it was found that athermal effect could promote the dislocation motion and unraveling of dislocation pile-ups, further promoting to the springback reduction.

Mathematical model of neutral line on the contact zone in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to determine the relative slip condition between the contact surface of rolling pieces and the roll, the contact boundary curve was proposed by obtaining the radius of flow line and the bite angle of points on the contact boundary based on the flow line method, and then the contact surface was discretized as flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of X-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the three-dimensional rectangular coordinates of points on the neutral line were derived.Based on these mathematical models, the three dimensional geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error is acceptable and the results of the mathematical model is satisfying.

Research on the characteristics of forward slip and backward slip in alloyed bar rolling by the round-oval-round pass sequence

For determining the neutral line on the contact zone to distinguish the forward slip zone and backward slip zone on the contact surface between the deformed pieces and the roll, the contact surface was discretized as finite flow line elements to build a novel analytic model to reconstruct the geometry of contact surface. Moreover, the velocity of flow lines on the contact surface along the direction of x-axis was derived by the condition of steady-state incompressible flow, and the function of neutral line was obtained by determining the neutral radius and the neutral angle of the points on the neutral line. In addition, the forward slip coefficient and backward slip coefficient was derived and the relative slip condition of contact surface between the roll and the rolled pieces was determined. Based on these mathematical models the geometry of contact surface and neutral line were drawn up by mathematical software. The validity of the theoretical model was verified by rolling experiments of alloyed bar and the numerical simulation by rigid-plastic FEM software. Compared with the experimental data and simulation results, the prediction error of the mathematical model is acceptable and results from the mathematical model are satisfying.

Analysis of Ring Compression Test by Upper Bound Theorem as Special Case of Non-symmetric Part

The ring compression test is considered one of the most reliable ways to obtain the friction shear factor existing in a plastic deformation process, particularly in open die forging processes. The test is performed on a ring-shaped specimen, so that the whole workpiece is axisymmetric. The application of the upper bound theorem with a triangular rigid zones model was initially developed with regard to plane strain and symmetrical geometric configurations. In this paper, the application to the ring faces consider that the neutral radius that defines the reversal of the flow of the material establishes two areas of different section and therefore the possibility of addressing the study considering not symmetrical sections.

Radial deformation of a ring gasket under axial compression

The pattern of the radial deformation of an annular component (gasket) is examined during its axial loading. It is demonstrated that as the gasket deforms axially, its outside radius increases, and its inside radius remains essentially constant. Working expressions are derived for determination of the neutral radius, the increase in the outside radius, and the change in the inside radius during axial deformation of the gasket. A device was built to verify the working relationships obtained, and experiments substantiating their practical applicability were conducted. It is recommended that information on tolerances for the diametrical dimensions of the gaskets and annular groves for their seating be incorporated in regulatory materials.

Loading and Deformation Progression during Open Forging of Hollow Cylindrical Blanks

A solution for a hollow cylindrical blank with a velocity field derived from the equations of equilibrium and compatibility conditions is obtained. The solution, accounts for both platen interfacial friction and the blank geometry. The platens were assumed as flat bodies moving normal to the blank surface. The problem is solved by the upper-bound approach, with the assumption of constant shear factor (average coefficient of friction) between platens and blank. The radius of the blank which does not experience deformation during the forging process is referred to as the neutral radius, and was determined by power minimization. The neutral radius as well as the friction coefficient at the blank interface were found to play an important role in determining the average forging pressure and the blank deformation from initial to final configurations. (Extended paper from the ICAT 2008 Conference, Ptuj, Slovenia, 17-18 September 2008.)

Analysis of Strain Neutral Layer Displacement in Tube-bending Process

In the series study of the tube-bending deformation, in order to reveal the deformation mechanism of tube bending and promote the rapid development of accurate tube bending and digital bending technology, the approximate calculation formulae of the strain neutral layer radius and the thickness attenuation of outer-lateral tube-wall are deduced on the basis of the plate-bending theory and under the plane strain conditions, and the changes of the strain neutral layer along radius are analysed with the consideration of the thinning of thickness of outer-lateral tube-wall. Given that the ratio of the strain neutral layer radius and bending radius is smaller than 1, it is proved that the strain neutral layer moves towards the bending center during the process of tube-bending. In addition, it is pointed that the amount of movement towards center of the strain neutral layer is inversely proportional to the relative bending radius. According to the comparison between the tube-bending test and finite element simulation results, the calculation of tube-wall thinning is proved to be relatively accurate, but since it does not include the effects of deformation perpendicular to the direction of the bending plane in material property parameters, the calculated value is on the high side and needs further modification.

A REVIEW OF FORMULAE FOR AVERAGING PHYSICAL QUANTITIES (APPLICATION TO CALCULATION OF THE AVERAGE RADIUS OF TUBES)

A new method for averaging physical quantities is discovered. It is shown that the traditional method of finding the average value of a physical quantity gives the wrong results when calculating the average radius of a tapering tube, the average flow velocity in the tube and the volume of liquid flow through the tapering tube. The new method of averaging gives the correct results. The new formula is applicable to many other processes, for example, for calculating the flow through tubes of arbitrary form or with time-dependent radius. At present, a neutral radius is used which leads to big discrepancies.

Dynamics of neutralizing electrons and the focusability of intense ion beams in HIF accelerating structures

In most of the proposals for HIF reactors, beams propagate ballistically through the containment chamber. To get the required final radius ( ∼ 3 mm ) , the charge of the beam must be neutralized to some extent. Several neutralization schemes are possible, as co-injection of negative-ion beams, inclusion of external sources of electrons, or it can be provided by electrons coming from ionization of the background gas. In this work, we study the role of the electron dynamic on the neutralization and final radius of the beam. This is done by performing fully electromagnetic PIC simulations of the beam ballistic transport using the BPIC code (Nucl. Instr. and Meth. A 464 (2001) 118). In agreement with previous works we found that the evolution of an isolated beam is well described as a bidimensional adiabatic compression, and the beam neutralization degree and final radius can be estimated from the initial electron transversal temperature. When a background gas is present the evolution differs significantly from an adiabatic compression. Even for low gas densities, the continuous electrons flow coming from gas ionization limits efficiently the compressional heating, thus reducing the final radius. Aspects of beam neutralization by background gas ionization are discussed.

Computer aided die design of straight flanging using approximate numerical analysis

Prediction of springback and minimum bending radius without failure are the main issues in die design for straight flanging process. The previously developed analytical and numerical models for sheet bending were observed to be inaccurate for straight flanging with relatively small bending radii. Finite element analysis with 2D models can be used to predict springback, bendability and tool loads accurately, but the analysis can take several hours, and pre- and post-processing are even more time consuming. Alternatively, in this paper, this problem is solved using advanced bending theory, implementing the geometric details of the straight flanging process to a mathematical model and computerized numerical analysis. The proposed method predicts springback and tool loads, particularly the minimum pad force necessary to prevent pad lift by dividing the deformation zone into three segments as pure elastic deflection without contact, elastic–plastic bending without contact and elastic–plastic bending in full contact with the die shoulder. The shift in neutral radius is modeled using an iterative procedure and taking the tool pressure and local thinning into account. The results are compared with limited experimental data as well as finite element simulations.

Transferability of Norm-Conserving Pseudopotentials: Si, Al and Alkali Metal Elements Embedded in a Jellium

Transferability of the first-principle pseudopotentials is tested for a pseudoatom embedded in a jellium. The Hamann's pseudopotential (Phys. Rev. B 40 (1989) 2980) and its separable form are analyzed in this transferability test. Elements examined in this paper are classified into two; the first class is elements in which even pseudopotential without core-correction can assure sufficient transferability, e.g. Al, Si; the second one is elements in which only psedopotential with core-correction can assure sufficient transferability, e.g. alkali metal elements. The neutral sphere radius is the most important parameter for the transferability which is sensibly dependent upon the charge density parameter r s of the jellium. Once the neutral sphere radius is smaller than the core radius of the pseudopotential, sufficient transferability cannot revive even with the core-correction in a pseudoatom-in-jellium model.

Initial/final state interaction in di-jet production off nuclei

Recently claimed [1–3] anomalous nuclear broadening of the out-of-plane transverse momentum in high- p t di-jet production is analyzed in view of multiple interaction of projectile/ejectile partons in nuclear matter. A model-independent relation between A-dependence of the cross section and nuclear broadening of transverse momentum is derived. Comparison with the data shows that initial/final state interaction of partons participating in a high- p t scattering is hard as well. This is a solid argument in favor of smallness of a color neutralization radius of a hadronizing highly virtual quark.

Diffuse plasma effects on the ion-hose instability

The transverse stability of a relativistic electron beam focused by an ion channel in the presence of a diffuse background plasma is investigated. The linear behavior of the ion-hose and electron two-stream instabilities is treated analytically using a spread-mass model for the beam and ion channel and a cold-fluid model for the plasma. The electron two-stream instability is found to be quite weak. As the plasma neutralization radius approaches the beam radius, the ion-hose growth rate is reduced up to 50% before the model’s assumptions break down. Particle-in-cell simulations confirm the linear analytic theory and show that the electron two-stream instability can saturate nonlinearly with little beam emittance growth.