Transition Radii Research Articles

Fatigue crack growth in wheelset axles under bending and torsional loading

In the past, unexpected failures in wheelset axles lead to catastrophic consequences. To avoid those failures inspection intervals must be defined. The definition of the inspection intervals is based on fracture mechanical approaches. In the present work, the railway axle steel 34CrNiMo6 is investigated. For this material fatigue crack growth data have been experimentally determined for a range of different negative and positive stress ratios. Furthermore, the FORMAN/METTU parameters for different probabilities of survival are identified. In wheelset axles different geometry factors influence the crack growth behaviour. Therefore, different shouldered solid shafts with transition radii and a press fit seat are designed and tested under rotating bending. Moreover, the load situation also has an influence on the crack growth. The main bending load is overlapped with torsional loading at special wheel-rail-situations. With the developed mixed mode test rig, the influence of different load situations on wheelset axles are examined.

Innovative component test concept for crankshafts

The crankshaft is a core component of today’s internal combustion engines and during operation is subject to complex mechanical loading. The transition radii of the crankpins to the crankwebs and the outlets of the oil ducts for lubricating the crankshaft journals and pins are the points that are susceptible to fatigue fractures. For this reason, expensive surface strengthening measures are integrated in the production process. IABG has developed a new test concept for crankshafts to examine the effectiveness of these measures in a fatigue strength test under loading conditions that are as realistic as possible.

Influence of Cutout Geometry on Stresses at Welded Rib-to-Diaphragm Connections in Steel Orthotropic Bridge Decks

The geometry of the cutout at the intersection of longitudinal ribs and transverse diaphragm plates in steel orthotropic bridge decks can have a significant impact on the stress in the region of the welded rib-to-diaphragm connections. Many different approaches to detailing this connection have been tried, with mixed success. To provide additional guidance to designers, a finite element parametric study that systematically investigated the effect of altering the geometry of certain variables was performed. Parameters considered included overall cutout shape, cutout depth, diaphragm plate thickness, and deck plate thickness. Results indicate that the suggested cutout geometry shown in the current (2002) AASHTO LRFD Bridge Design Specifications for closed-rib orthotropic bridge decks produces increased stresses on this fatigue-sensitive connection. An improved geometry is proposed to replace that currently presented in the specification. Results of this study indicate that larger cutout geometries offer less resistance to out-of-plane displacements induced by longitudinal rib rotations. As a result, out-of-plane stresses are decreased at the connection. However, cutouts that are excessively deep will increase in-plane stresses at the welded rib-to-diaphragm connection. If the cutout is too shallow, out-of-plane stresses may become prohibitively high owing to restraint of longitudinal rib rotations. Cutouts that are between 1/3 and 1/2 the depth of the rib with transition radii at the top of the cutout of 50 to 75 mm and vertical cuts are most favorable. The cutout geometry shown in the AASHTO LRFD specification results in an overstiff cutout detail. A proposed improved geometry is presented.

Transition radii and sum rules in 238U(e,e'f).

Transition radii and sum rules in 238U(e,e'f).

Inelastic scattering of pions on7Li

The recent experimental results of Gibson and coworkers, for inelastic scattering of pions on7Li, leading to the first five excited states of7Li are analyzed using a shell model description including configuration admixtures and representing the transition nucleon densities following Helm model, used extensively in the context of inelastic scattering of electrons. With the transition radii for protons and neutrons chosen to be 3.9 fm and 4.1 fm respectively, good fits to the experimental cross sections are obtained. In contrast to the distorted wave Born approximation (dwba) calculations using optical model codes, we find the present work is able to reproduce the observed maxima and minima precisely. Moreover this analysis reveals the importance of considering the configuration admixtures especially in the transitions to24 P 5/2 (7.48 MeV) and24 D 7/2 (9.67 MeV) levels.

Stress concentration in the zone of fastening lamellar structures with rods

1. The perturbations caused by the presence of a rod in a plate are attenuated at a distance of one rod diameter. 2. The largest peripheral stresses arise at the points of intersection of the circle along which the plate is joined to the rod with the radius indicating the line of action of the tensile force. 3. In tension and bending of the plate, the stresses in the rod vanish practically completely at a distance from the plate equal to half the thickness of the plate. 4. In the zone of the joint of the plate with the rod the nature of the stress distribution in pure bending of the plate is the same as in tension; on the opposite surface of the plate (next to the rod) a slight increase of the compressive stresses was found. 5. The found stress concentration factors make it possible to select the transition radii in similar structures. 6. The obtained reuslts are in good agreement with the data of reference books for plane structures (the divergence does not exceed 10%) for the most frequently used ratios of the transition radius to the thickness of the structure.

Velocity-and density-dependent forces in hyperspherical formalism

The hyperspherical one-dimensional Schrodinger equation is derived for a velocity- and density-dependent two-body interaction of finite range. Consequences of newly appearing terms are discussed, application to a contact force is carried out and, as a numerical example, Skyrme force III is used in doubly magic nuclei to calculate energies, breathing modes, r.m.s. and transition radii, and densities.

Exchange and aggregation in dispersions of dimyristoyl phosphatidylcholine vesicles containing myristic acid.

Processes occurring in dispersions of dimyristoyl phosphatidylcholine containing myristic acid have been studied by light scattering of dilute dispersions (concn. less than or equal to 1 mg/ml) at temperatures above and below the phase transition temperatures of these dispersions. The transition temperatures increase with increasing mol fraction of myristic acid. Above these temperatures, vesicles with different mol fractions of myristic acid exchange lipid molecules. The exchange process leads to vesicles having phase transition temperatures and radii, which ar both intermediate between the initial transitions and radii, respectively. In contrast with the observations above the phase transitions, it was found that when dimyristoyl phosphatidylcholine/myristic acid vesicles were cooled to a few degrees below the phase transition, larger particles were formed. These observations are consistent with a mechanism consisting of vesicle aggregation followed by fustion of the aggregated vesicles. The aggregation process is of second order in the vesicle concentration, and its rate increases with increasing mol fraction of myristic acid.

Inelastic electron scattering from low-lying states in the nuclei 36Ar and 40Ar

The low-lying level structure of 36Ar and 40Ar has been investigated using the technique of inelastic electron scattering. Data were collected at the National Bureau of Standards Linear Accelerator with incident electron energies between 65 and 115 MeV and scattering angles of 92.5° and 110°. The data span a range of momentum transfer squared between 0.29 and 0.92 fm −2. Tassie model and Helm model analyses have been applied to data for levels at 1.97 and 4.18 MeV in 36Ar and at 1.46, 2.52, 3.21 and 3.68 MeV in 40Ar. A 2 + assignment to the 3.21 MeV state in 40Ar is suggested. Transition strengths, transition radii, and mean lifetimes for these states are computed and compared with results of previous experiments.

Inelastic electron scattering from29Si

The excited states of 29Si up to 8.3 MeV excitation energy have been studied by inelastic electron scattering in the momentum transfer range 0.4 to 1.05 fm-1. Ground-state transition probabilities and transition radii were obtained for the levels excited. At lower excitation energies the transition probabilities agree with previous work. A number of high excitation and high-multipolarity levels are studied for the first time, and several previously tentative spin-parity assignments are confirmed. Transition probabilities for L=2, 3 and 4 are compared with the predictions of the intermediate coupling model and the Nilsson and shell models.

Transition charge densities of low-lying collective states in even Zn isotopes

The inelastic electron scattering cross sections for the quadrupole transitions to the 2 1 + and 2 2 + states in the even Zn isotopes 64Zn, 66Zn and 68Zn and for the hexadecapole transition to the 4 + 1 state in 64Zn have been measured in a momentum transfer range up to q = 2.2 fm −1. In the frame-work of the vibrational model these states are considered as one- and two-quadrupole-phonon states. The measurements are characterized by high statistical accuracy and by an overall resolution of δE/ E 0 = 10 −3 which permitted separation of almost all members of the two-phonon triplet. The measured cross sections are analyzed with phenomenological models as well as with a Fourier-Bessel expansion of the transition charge density. The latter analysis yields realistic error bands for the transition charge densities and model-independent values for the reduced transition probabilities and transition radii.

Inelastic scattering of electrons from 27Al

Electron scattering form factors have been measured for the excitation of 2.21 MeV( 7 2 + ) 2.734 MeV ( 5 2 +) and 3.00 MeV ( 9 2 +) states in 27Al using values of momentum transfer between 0.31 and 1.05 fm −1. Reduced ground-state transition probabilities and transition radii are obtained for the 2.21 and 3.00 MeV states. Intermediate-coupling calculations are shown to reproduce the energy spectrum of 27A1 but not the transition matrix elements and the form factors. Much better agreement is obtained using a large basis shell-model calculation.

Inelastic electron scattering from25Mg

The excited states of 25Mg have been studied by inelastic electron scattering in the momentum transfer range 0.3 to 1.15 fm-1. The reduced transition probabilities and transition radii were measured for seven levels below 4.1 MeV excitation energy and the transition probabilities are shown to be more precise than existing measurements. A search for the hexadecupole strength to the 11/2+ levels in the vicinity of 5-6 MeV excitation energy was also carried out. The applicability of an extended Nilsson-model description for the ground-state band of 25Mg was also investigated by comparison with the known electromagnetic strengths, and, more crucially, by comparison with the measured form factors.

Nuclear matter sizes and isoscalar octupole transition rates of204,206,208Pb from 104 MeV ?-particle scattering

Differential cross sections for elastic and inelastic scattering of 104 MeVα-particles from204,206,208Pb were measured with high angular accuracy. The experimental results were analysed on the basis of a semimicroscopic folding model in order to determine the matter distributions at the nuclear surface and the transition densities. Using phenomenological parametrizations of the densities the analyses of elastic scattering yield rms radii of 〈r 2〉1/2=5.55±0.06 (204Pb), 5.57±0.06 (206Pb), 5.63±0.05 (208Pb) fm. Various sensitivities affecting the results were studied. From the inelastic cross sections for the 3 1 − -states octupole transition probabilities and transition radii were derived by using different methods proposed in literature.

Inelastic scattering of electrons for90Zr

The states of 90Zr up to 5.8 MeV excitation energy have been studied by (e, e') in the momentum transfer range from 0.29 to 1.07 fm-1. Ground state transition probabilities and transition radii were obtained for the levels excited. Previously published electron scattering data on 90Zr are included in the extraction of these parameters. A comparison of results is made with the model independent measurements of the ( gamma , gamma ') reaction for the 2+ states. Wherever possible, the results for the electromagnetic transition rates are compared with the iso-scalar transition rates and those obtained form (p, p') reactions. Theoretical calculations are seen to be inadequate to describe the strength of the transitions observed in the present experiment.

The ground state band of25Mg studied by electron scattering

The members of the ground state band of 25Mg have been studied in the momentum transfer range 0.2 to 1.15 fm-1. The reduced transition probabilities and transition radii were measured for the 1.612 MeV and 3.405 MeV levels. The transition probabilities are shown to be considerably more precise than existing measurements and are compared with various theoretical predictions. The hexadecupole strength to the 11/2+ levels is also discussed.

Excitation ofM1andM2states inNe22by 180° electron scattering

States in $^{22}\mathrm{Ne}$ have been studied by 180\ifmmode^\circ\else\textdegree\fi{} inelastic electron scattering with incident energies of 37, 50, and 60 MeV. Prominent magnetic dipole and quadrupole states are observed below 13 MeV excitation energy. Reduced transition probabilities, transition radii, and spin and parity assignments are presented for these states and compared to shell model calculations.NUCLEAR REACTIONS $^{22}\mathrm{Ne}(e,{e}^{\ensuremath{'}})$, $E=37, 50, \mathrm{and} 60$; measured $\ensuremath{\sigma}(E,180\ifmmode^\circ\else\textdegree\fi{})$; measured $B(M1)$; deduced ${J}^{\ensuremath{\pi}}$; enriched target.

A study of24Mg by inelastic electron scattering

The excited states of 24Mg with excitation energies less than 14.0 MeV were studied by inelastic electron scattering in the momentum transfer range 0.4 to 1.14 fm-1. Ground state transition probabilities and transition radii were deduced for 9 known levels with excitation less than 11 MeV and evidence was obtained for a (2+, 4+) doublet at 10.352+or-0.024 MeV. In the excitation energy region 11.0 to 14.0 MeV three E2 and four E3 transitions were observed and their ground state widths were deduced. The known 2- states at 12.67 MeV and 13.37 MeV were found to have ground state widths of (1.4+or-0.5)*10-2 eV and (4.0+or-1.4)*10-2 eV respectively.

The study of the excited states of26Mg below 11 MeV by inelastic electron scattering

The excited states of 26Mg below 11 MeV excitation energy were studied by inelastic electron scattering in the momentum transfer range 0.4 to 1.05 fm-1. At lower excitation energies, several spin-parity uncertainties were resolved and the spin-parity assignments were extended up to 11 MeV. Ground state reduced transition probabilities and transition radii were measured for 29 levels. The reduced transition probabilities were found to be more accurate than existing experimental results. The form factors and transition probabilities are compared to various theoretical predictions.

Electroexcitation of 16O levels near 10 MeV excitation

The electromagnetic form factors of the 2 + (9.85 MeV) and 4 + (10.34 MeV) states in 16O have been measured for momentum transfers between 0.7 and 1.2 fm −1. The results for the 4 + state are compared with the predictions of the three-component Brown-Green model. The present data and those of a previous electron scattering experiment are interpreted in the framework of a two-component model in order to obtain rough estimates of the β 2 and β 4 deformation parameters. Predictions for the 2 + (9.85 MeV) level form factor, within the context of an axially asymmetric rotor model, are compared with the experimental form factor. It is found that this model gives a poor description of the data. Radiative widths and transition radii have been determined by a Helm model analysis.