Determination of sheet steel formability using wide band electromagnetic-acoustic transducers

An electromagnetic-acoustic transducer (EMAT) system was used in conjunction with a sampled CW signal-processing method to generate, receive, and process longitudinal and shear waves in thin steel sheets. Using the system, swept-frequency measurements were made up to 7.5 MHz. To relate the measurements to sheet steel formability, a dimensionless frequency ratio,K, was computed from the resonant frequencies. From theoretical considerations,K should be related to a measure of steel sheet formability, . This parameter is traditionally measured by plastically deforming uniaxial tension specimens. Good correlation was found betweenK and for a set of steel sheet representative of those typically used to produce automobile body parts.Contribution of NIST; not subject to copyright.NIST Guest Researcher; on leave from Technical University of Plovdiv, Bulgaria.     

Thermopower ofAg_{2 + \delta } S across theα-β transitionacross theα-β transition

Thermopower data of S in both of itsα- andβ-phases are reported and the results are compared with the data on Se. Communication No. 129 from the Solid State and Structural Chemistry Unit.     

Eine Erweiterung der Analogie zwischen der Gasdynamik und Flachwasserströmungen auf rotierende Systeme mit konservativen Massenkräften

Zusammenfassung Die bekannte Analogie zwischen den Theorien reibungsfreier flacher Wasserströmung und der isentropen idealen Gasdynamik wird im zweidimensionalen instationären Fall durch Zulassung rotierender Bezugssysteme und konservativer Massenkraftfelder erweitert. Damit kann man in einem rotierenden Wasserbehälter mit geeignet gestaltetem Boden u. a. atmosphärische Probleme näherungsweise studieren.

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Summary The well known analogy of the theories of nonviscous shallow water flows and isentropic ideal gasdynamics is generalized in the two-dimensional nonstationary case to apply to rotating systems with conservative body forces. This enables one, in particular, to simulate atmospheric problems by use of a rotating water tank with suitable bottom shape.

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Liste der verwendeten Symbole spezifische Wärme des Gases bei konstantem Druck - Fr in (2) definierteFroude-Zahl - Gravitationsbeschleunigung - H ortsabhängige Ruhetiefe bei Drehung des Wassers als starrer Körper - Druck - atmosphärischer Druck auf der freien Wasseroberfläche - Bezugslänge - Zeit - absolute Temperatur - Geschwindigkeitskomponenten parallel zu den Achsen - kartesische Koordinaten - durch Abweichung von der Drehung des Wassers als starrer Körper verursachte orts-und zeitabhängige Änderung der Wassertiefe - Verhältnis der spezifischen Wärmen des Gases - zu gehörende Wellenlänge - Dichte - Winkelgeschwindigkeit Mit 1 Textabbildung1 Boden des Wasserbehälters 2 freie Wasseroberfläche II freie Wasseroberfläche bei einer Drehung des Wassers als starrer KörperEin oberer Querstrich gibt an, daß die betreffende Größe eine physikalische Dimension hat; Größen ohne einen solchen Querstrich sind dimensionsfrei.     

Anisotropic flow and fracture in beryl [Be3Al2(SiO3)6]

Flow and fracture resulting from Vickers indentation testing on {0 0 0 1} and {10 0 } planar orientations have been examined. Flow characterized by indent shape differentiation was analysed to belong to the slip system with planes of the types { 10 0} and {11 0}. The ensuing fracture paths were resolved to propagate along {1 0 0} and {1 1 } cleavage planes whileK _c values obtained for them were 0.196 and 0.248 MPam^1/2, respectively.     

Knoop hardness studies on anthracene single crystals

Knoop microhardness studies were carried out on anthracene single crystals. The hardness vs load plot shows two peaks, one at 5g and another at 17·5 g having hardness values 13·0 kg/mm² and 11·4 kg/mm² respectively. The present observation shows that the dislocations split into partials.     

Détermination des contraintes maximale et minimale en valeur algébrique résultant d'un effort normal et d'un moment de flexion dans une section quelconque d'un profil, à partir de trois mesures de déformations superficielles

Résumé Les contraintes maximale et minimale en valeur algébrique engendrées dans une section quelconque d'un profil, par un effort normal et un moment de flexion quelconque , peuvent être déterminées à partir de trois mesures de déformations superficielles effectuées au niveau de cette section. De plus, il est possible de calculer l'effort normal et le moment de flexion ainsi que ses composantesM _GY ,M _GZ sur les axes principaux d'inertie , et de définir la position de l'axe neutre de flexion ainsi que celle de l'axe neutre de flexion et d'effort normal.

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Summary The determination of the maximum and minimum stresses in algebraic value generated in an arbitrary section of a profile by a normal force and an arbitrary bending moment is an important problem that frequently arises. Before showing that 3 measurements of surface deformations effected on the level of the section studied suffice completely to solve this problem some theoretical considerations are recalled. These concern the establishment of the formula giving the bending stress. For this we can attach to the section either arbitrary central axes or the main central inertia axes; this latter possibility leading to a simpler formula. The formulae needed for the determination of the maximum and minimum stresses due to and are then established, for arbitrary coordinates of measurement points. Simpler formulae may be obtained when it is possible practically to choose simple ratios between the coordinates. Next it is shown that one can compute not only but and its componentsM _GY ,M _GZ , on the main intertia axes , and determine the position of the neutral bending axis as well as that of the neutral bending and normal force axis. Finally, the practical utilization of the method is indicated and a concrete case treated.

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Rigid body translation in the (\bar 211) twin boundary in silicon

The rigid body translation accompanying a ( 11) twin boundary in silicon has been studied by transmission electron microscopy. From a detailed analysis of theα-type fringe systems in the 111, 311 and 2 0 common reflections, the following translation vector is deduced: [011], which is equivalent to [411] in the other crystal element. A slight deviation of this orientation is possible.     

Stability analysis of a low energy vortex configuration

Recent work using the London theory of anisotropic superconductivity has shown that, for small values ofB and large values of the anisotropy, a lattice of vortex lines parallel to is not necessarily the minimum energy configuration. When is not parallel to a symmetry axis, the “double lattice”—a lattice of lines parallel to plus a lattice of lines parallel to —can have a lower energy. The question arises, however, of whether some other configuration can have a yet lower energy. To investigate this question, we perform a stability analysis of the double lattice. We find that its energy can indeed be lowered by certain deformations of the vortex lines.     

On the motion of a curved and twisted rod

Summary In this paper, the equations of motion of a curved and twisted rod are derived from the basic principles of dynamics. The set of equations gives the extensional, flexural and torsional motions of the rod. The coupling among these types of motion due to the curvature and tortuosity of the rod is shown explicitly in the case of a helical spring. By successive simplification of the equations, the equations of motion of a circular ring and those of a straight rod are obtained. In this respect, the derived equations can be considered as a generalization of the elementary theories of rod in extensional, torsional and flexural motion.The dispersion relation of a helical spring is calculated for the two lower frequency modes. It is shown that the frequency-wave length relationship is not monotonically decreasing as in the cases of uncoupled flexural or torsional motion. Finally, frequencies are calculated based on the approximate frequency expression ofLove to show that Love's frequency expression for a helical rod is accurate.

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Zur Bewegung eines gekrümmten und verdrillten Stabes

Zusammenfassung In dieser Arbeit werden die Bewegungsgleichungen eines gekrümmten, verdrillten Stabes von den Grundgleichungen der Dynamik hergeleitet. Dieses System von Gleichungen legt die Bewegung des Stabes durch Längsdehnung, Biegung und Torsion fest. Die Kopplung dieser Bewegunsarten, durch Krümmung und Verdrillung, wird für den Fall einer Spiralfeder explizit gezeigt. Durch Vereinfachung der Gleichungen werden die Bewegungsgleichungen des Kreisringes und die des geraden Stabes erhalten. In dieser Hinsicht können die hergeleiteten Gleichungen als Verallgemeinerung der elementaren Theorein der Bewegung eines Stabes betrachtet werden.Die Dispersionsgleichung der Spiralfeder wird für die beiden niedrigsten Frequenzen berechnet. Es wird gezeigt, daß das Verhältnis Frequenz-Wellenlänge nicht wie in den Fällen der ungekoppelten Biege-oder Torsionsbewegung monoton abnimmt. Abschließend werden die Frequenzen nach dem Loveschen Näherungsausdruck berechnet, um zu zeigen, daß die Genauigkeit dieses Ausdruckes für Spiralfedern gut ist.

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Nomenclature position vector of a point on axis of curved rod - position vector relating any pointB in a plane perpendicular to the axis of the rod to pointP where plane cuts axis of rod - R modulus of - linear momentum vector - density - axial force vector = - axial force vector at origin - transverse shear force vector - transverse shear force vector at origin - moment vector - moment vector at origin - s distance measured along axis of rod - t time - a radius of gyration of rod for circular sections - l total length of spring along axis - A cross-sectional area of rod - s/a — normalized coordinates measured along axis of rod - applied load vector - angular momentum vector - trihedral of space curve-unit vectors in tangential, normal and binormal directions - _t axial rotation - displacement vector - normalized displacement vector= - ₀,₀ curvature and tortuosity of rod - , normalized curvature and tortuosity of rod - , circular frequency and normalized frequency respectively - E, G Young's modulus and shear modulus - v Poisson's ratio - Wave number - pitch angle of helical spring - d wire diameter of helical spring - R coil radius of helical spring - N number of turns of helical spring With 5 Figures     

Ultrasonic measurement of sheet steel texture and formability: Comparison with neutron diffraction and mechanical measurements

Ultrasonic measurements were made on a set of thin steel sheets, using the lowest-order shear horizontal mode (SH₀-mode) and lowest-order symmetric Lambwave mode (S₀-mode). The velocities of these modes were measured as a function of angle relative to the sheet rolling direction. From the data reduction it is, in theory, possible to (1) partially characterize the texture of the sheet, and (2) predict the plastic strain ratio (r-value). The plate texture can be completely characterized by quantities known as orientation distribution coefficients (ODCs). The lowest-order ODCs can be obtained from our measurements; these were compared with ODCs measured by neutron diffraction, with good agreement for the dominant ODC. The r-value is a commonly used measure of sheet formability. It is typically measured mechanically with uniaxial tension specimens subjected to large plastic strain. Therefore, the r-value test is destructive and time consuming. We found a good correlation between S₀-mode velocity measurements and , the average in-plane r-value. Consequently, the use of noncontacting electromagnetic-acoustic transducers (EMATs) may offer an online nondestructive measurement of sheet formability.Contribution of U.S. Department of Commerce, National Institute of Standards and Technology; not subject to copyright.     

Analysis of a family of unstable lattice orientations in (110) channel die compression

Summary The family of f.c.c. crystal orientations defined by loading direction (110) and any channel die constraint direction between ( ) and ( ) is kinematically unstable. We establish that the experimentally observed finite rotation of the lattice about the loading axis, for initial orientations in this range, is uniquely predicted by the constraints and critical slip-system inequalities without regard to particular hardening theory. We further establish that experimental information on the changing constraint stress would serve to distinguish among theories. Predictions of three specific hardening rules, including classical Taylor hardening and the simple theory, are illustrated for initial constraint directions ( ) and ( ). For the first of these orientations the predictions include constraint stress, lattice rotation, active and latent hardening, and overall crystal shearing to a logarithmic compressive strain of 1.0.     

Axialer Verlauf der Geschwindigkeit in Luft-Freistrahlen

Zusammenfassung Die bisher bekannten Beziehungen zur Berechnung des axialen Geschwindigkeitsverlaufs in isothermen Luft-Freistrahlen gelten nur für das Strahlende etwa im Gebiet von x/d>50, in dem die Reynoldszahl keinen Einflu? mehr auf den Geschwindigkeits-oder Impulsabfall hat. In dem Gebiet4<x/d<50 nimmt das Verh?ltnis mit wachsender Reynoldszahl bis zu einer Grenz-Reynoldszahl zu. Durch Definition einer axialen Halbwertl?nge x_0,5 (x_0,5=x bei ) wurde eine Beziehung gefunden, die den Einflu? der Reynoldszahl am Strahlanfang berücksichtigt. Mitteilung aus dem Engler-Bunte-Institut, Bereich Feuerungstechnik, der Universit?t Karlsruhe (TH), Direktor des Instituts: Prof. Dr.-Ing. R. Günther.     

Role of recovery in high temperature constant strain rate deformation

A model based on the three-dimensional distribution of dislocations is used to delineate the role of recovery during high temperature constant strain rate deformation. The model provides a good semi-quantitative explanation for classical work-hardening as well as for high temperature work-softening resulting from rapid recovery. It predicts linear work-hardening, whereby the ratio of the work-hardening rate,H, to the shear modulus,G, is constant when a crystal is tested in the absence of recovery. The slope of the stress-strain curve, θ, for high temperature deformation is related to the low temperature work-hardening rateH; the dislocation annihilation rate , the flow stress a, the free dislocation density ρ, the strain rate , and a parameter which is sensitive to the dislocation distribution. A modified version of the Bailey-Orowan equation for simultaneous work-hardening and recovery during constant strain rate deformation which is derived from the model takes the form

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

Grain growth behaviour of the Al-Cu eutectic alloy during superplastic deformation

Grain growth behaviour of the Al-Cu eutectic alloy was investigated as a function of strain (ε), strain rate and deformation temperature (T) over = 10⁻² s⁻¹ and T=400 to 540°C. The grain size increases with increase in strain and temperature. Upon deformation to a fixed strain, the grain growth is generally seen to be more at lower strain rates. The rates of overall grain growth and due to deformation alone , however, increase with increasing strain rate according to and , respectively. The increase in the grain growth rate with strain rate is attributed primarily to the shorter time involved at higher strain rate for reaching a fixed strain. The activation energy for grain growth under superplastic conditions is estimated to be 79 kJ mol⁻¹.     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

AC long-range phase-coherent effects of S-N-S junctions in the dirty limit

The conductance of a normal metal film (N) in contact with two superconductors (S) is calculated in the presence of a constant and oscillating V_ωcosωt bias voltage between N and S. It is shown that the conductance as a function of has a Shapiro-like step at = ħω/2e. This exists in the case when the spacing between two superconductors largely exceeds the coherence length. It is also shown that the Shapiro step height decreases rapidly when the junction size exceeds the phase breaking length.     

Effect of loading direction and initial imperfections on the development of dynamic shear bands in a FCC single crystal

Summary We study plane strain dynamic thermomechanical deformations of a FCC single crystal deformed at an average strain-rate of 1 000 s^–1 along the crystallographic direction [380] with the plane of deformation parallel to the plane (001) of the single crystal. Four different situations are studied; in the first two there is no initial imperfection assumed in the crystal and it is either compressed or pulled, and in the other two the crystal is compressed but either the initial temperature is nonuniform or a small region around the centroid of the cross-section is misoriented relative to the rest of the cross-section. In each case, all twelve slip systems are assumed to be potentially active, and the crystal material is presumed to exhibit strain hardening, strain-rate hardening, and thermal softening. These effects are modelled by using a simple combined isotropic-kinematic hardening expression for the critical resolved shear stress, proposed by Weng, and modified to incorporate the effect of thermal softening of the material. It is found that each one of the slip systems , and contributes essentially equally to the plastic deformations of the crystal and these slip systems become active soon after the load is applied. The same holds for the slip systems , and except that they are active in a region different from that of the previous one. The remaining four slip systems either stay inactive throughout the deformation process, or become active at late stages of the deformation.     

On the origin of recrystallization textures

The development of recrystallization textures has been debated for the past 50 years. Essentially the rival theories of evolution of recrystallization textures i.e. oriented nucleation (ON) and oriented growth (OG) has been under dispute. In the ON model, it has been argued that a higher frequency of the special orientation (grains) than random occur, thus accounting for the texture. In the OG model, it has been argued that the specially oriented grains have a high mobility boundary and thus can migrate faster and grow to a larger size as compared to random orientations thus contributing to the final recrystallization texture. In FCC metals and alloys like aluminium, cube orientation [(001) 〈100〉] is the recrystallization texture component. In the classic OG model, cube orientation is supposed to be misoriented fromS-orientation [(123) ] which is a deformation texture component by a 40° about 〈111〉 relationship which is supposed to be a high mobility boundary leading to faster growth of cube grains. Stereographic calculations and analytical calculations are presented in this paper to the effect that theS-orientation (123) is not misoriented from cube (100) 〈001〉 by 40° 〈111〉 whereas another deformation texture component (123) which is termed theR-component is misoriented from cube component by 40° 〈111〉,R-component is also seen in deformation textures of aluminium and hence the classic OG model remains valid with respect to theR-component.