A theory of failure based on probability for fatigue of ductile materials

The maximum shear stress theory of failure is extended to consider the crystallographic orientation in a polycrystalline material. At a given point, the angular regions, within which the shear stress is higher than the critical shear stress of the crystal, are calculated and the probability of slip for this crystal is obtained. Since there is little plastic flow associated with fatigue, the stresses can be obtained from theory of elasticity. The probability of failure of components are then calculated from the probability of slip of the individual crystals. Using fatigue results for notched specimens, it is concluded that a propagating crack will only form if a number of neighboring crystals are all orientated to slip.

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Zusammenfassung Die maximale Scherkraft Theorie des Bruches ist erweitert um die kristallographische Orientierung in emem aus mehreren Kristallen bestehenden Material zu untersuchen. An einer gegebenen Stelle werden die Winkelbereiche berechnet, in denen die Scherkraft größer ist als die Schubfestigkeit des Kristalles, und die Schiebungswahrscheinlichkeit für diesen Kristall wird erhalten. Da wenig plastische Ausweitung mit Ermüdung verbunden ist, können die Kräfte aus der Elastizitätstheorie erhalten werden. Die Bruchwahrscheinlichkeit der Teile kann dann aus der Schiebungswahrscheinlichkeit der einzelnen Kristallen berechnet werden. Von den Ermüdungsergebnissen für Kerbproben ist zu schließen ein fortschreitender Riß nur entsteht wenn eine Anzahl benachbarter Kristallen alle zur Schiebung orientiert sind.

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Résumé La théorie de la limite critique de l'effort maximum de cisaillement s'étend à l'étude de l'orientation cristallographique d'une matière polycristalline. A un point donné, les parties angulaires où l'effort de cisaillement est plus élevé que l'effort de cisaillement critique du cristal, sont calculées et la probabilité de glissement pour ce cristal est obtenue. Puisqu'un glissement plastique pen important accompagne la fatigue, on peut estimer les efforts d'après la Théorie de l'Elasticité. La probabilité de rupture des composants est alors calculée d'après la probabilité de glissement de chaque cristal. En utilisant les résultats indiquant le degré de fatigue pour des specimens entaillés, on conclue qu'une fissure ne se propage que si un certain nombre de cristaux avoisinants sont tous orientés dans la direction du glissement.

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Nomenclature _x Principal stress in x-direction - _y Principal stress in y-direction - _z Principal stress in z-direction - Angle from x-axis to perpendicular on arbitrary plane - Angle from y-axis to perpendicular on arbitrary plane - Angle from x-axis to perpendicular on arbitrary plane - l cos , direction cosine - m cos , direction cosine - n cos , direction cosine - Direct stress on arbitrary plane - Shear stress on arbitrary plane - P _A Angular probability - _c Critical shear stress for ductile materials ₁ and ₂ are values of at boundary of slip region ₁ and ₂ are values of at boundary of slip region - p ₁ Number of slip planes with lowest critical shear stress - q Number of regions of slip in the hemisphere - I q ₁ dd - V Volume of overstressed material - Average crystal volume - P _n1 Probability of failure of a fatigue specimen - n ₁ Minimum number of neighboring crystals with continuous slip bands required to form a propagating crack - A,B,C Coefficients - m ₁ cos ₁ - m ₂ cos \gB₂ - Angle - M _xx Bending moment on section x–x of fatigue specimen - d Diameter of section x–x - _n Nominal stress - r Notch radius     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

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Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

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Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

On the bending stress distribution at the tip of a stationary crack from Reissner's theory

A general solution is developed for the symmetric bending stress distribution at the tip of a crack in a plate taking shear deformation into account through Reissner's theory. The solution is obtained in terms of polar coordinates at the crack tip and includes the complete class of solutions satisfying all the three boundary conditions along the crack. The solution has arbitrary multiplicative constants and in specific problems, these constants can be determined from conditions on the exterior boundary by well-known numerical techniques such as collocation, successive integration. Results of a numerical solution for a square plate with a central crack subject to uniaxial bending are presented along with a critical discussion of the sensitivity of the numerical solution which is associated with the exponential character of Bessel terms in this higher order analytical solution.

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Résumé On développe une solution générale à la distribution symétrique de contraintes de flexion à l'extrémité d'une entaille dans une plaque soumise à une déformation de cisaillement, en tenant compte de la théorie de Reissner. La solution est obtenue sous forme de coordonnées polaires à l'extrémité de la fissure et comporte l'ensemble des solutions satisfaisant à toutes les conditions de frontières le long de la fissure. La solution comporte des constantes multiplicatives arbitraires et, dans des problèmes spécifiques, ces constantes peuvent être déterminées à partir des conditions de confinement extérieur à l'aide de techniques numériques bien connues telles que la collocation ou l'intégration successive. Les résultats d'une solution numérique dans le cas d'une plaque carrée comportant une fissure centrale soumise à flexion uniaxiale sont présentés en même temps qu'une discussion critique de la sensibilité de la solution numérique associée au caractère exponentiel des termes de Bessel dans cette solution analytique d'une ordre supérieur.

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Nomenclature 2a crack length - h plate thickness - k ² - E Young's Modulus - v Poisson's ratio - D bending rigidity of plate,Eh ³/12(1-v ²) - M ₀ reference bending moment - ₀ extreme fibre stress due toM ₀, 6M ₀/h ² - r, polar coordinates with crack tip as the origin (Fig. 1), r being nondimensionalized with respect toa - W normal displacement, nondimensionalized with respect toM ₀ a ²/D - M _r ,M ,M _r bending and twisting moments per unit length of plate element (Fig. 1), nondimensionalized with respect toM ₀ - _r , transverse shear forces per unit length of plate element (Fig. I), nondimensionalized with respect toM ₀/a - _{r r} stresses on that surface where a positive moment produces tension, nondimensionalized with respect to ₀ - a stress function in Reissner's theory, nondimensionalized with respect toM ₀ - K _(b) bending stress intensity factor - K_(b) Modified Bessel Functions of first and second kinds respectively - (,m) ( + 1)( + 2)...( +m)form5 0 = 1 form = 0 - Gamma function Structures DivisionMaterials Division     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Behavior of a screw dislocation near a partially bonded bimetallic interface

This paper, based upon the isotropic elastic continuum approximation, deals with the forces of interaction between a stationary screw dislocation and a partially bonded bimetallic interface. The complex variable method is used throughout and the closed form solution is obtained. The result indicates that if the material on the other side of the interface is more rigid than that in which the dislocation is present, the bonded region will act as a barrier to the dislocation located in a certain region near the interface and that there is no stable equilibrium position of single dislocation line even in the aforementioned case since the free surface operates an attractive force on it.

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Zusammenfassung Diese Arbeit behandelt die Kraefte der Wechselwirkung zwischen einer stationaeren Schraubenverschiebung und einer teilweisen unfreien zwei-metallischen Zwischenflaeche. Sie beruht auf dem isotropischen, elastischen Kontinuumnaeherungswert. Die Methode der komplexen Veraenderlichen wurde benutzt und die Loesung der geschlossenen Form wurde erhalten.Das Ergebnis zeigt, dass, sollte das Material auf der anderen Seite der Zwischenflaeche haerter sein, als jenes in welchem die Verschiebung stattfindet, das unfreie Gebiet als Barriere zu der Verschiebung, die sich in einem bestimmten Gebiet in der Nahe der Zwischenflaeche befindet, auftritt. Ferner gibt es keine stabile Gleichgewichtsposition von einer einzelnen Verschiebungslinie, selbst in dem erwaehnten Falle nicht, da die frei Oberflaeche Zugkraft ausuebt.

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Résumé Se basant sur l'approximation d'un milieu continu élastique et isotrope, le mémoire est relatif aux forces d'interaction entre une dislocation-vis et l'interface de deux corps métalliques partiellement solidarisés. On utilise la méthode des variables complexes, et l'on obtient une solution particulière et limitée.Les résultats indiquent que si le mátériau qui se trouve de l'autre côte de l'interface est plus rigide que celui dans lequel se trouve la dislocation, la zone de liaison fera office de barrière pour toute dislocation située à une certaine distance de cet interface. Par ailleurs, il n'y a pas de position d'équilibre stable pour une ligne simple de dislocations se trouvent dans le cas susmentionné, puisque la surface libre opère une force d'attraction sur cette ligne.

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Notation a, h location of screw dislocation - b magnitude of Burgers vector of screw dislocation - force acting on the dislocation - F_y y component of - i –1 - i, i unit vectors in x and y directions - half length of bonded segment - L, L bonded segment and traction free one on real axis - S⁺, S^– upper and lower half-planes in z plane - u, v, w carte sian displacement components - x, y, t cartesian coordinates - X(z) (z+)^–1/2(z–)^–1/2 - z x+iy - h+ia - eeⁱ z– - tan^–1 [a/(+h)] - tan^–1 [a/(–h)] - µ^* shear modulus - - _* - _xt, _yt shear stress components - _xt ⁽ⁱ⁾ _yt(¹) shear stress components at the location of dislocation due to the interaction with the interface - (z) complex displacement potential - (z) potential as defined in text On leave from Department of Mechanical Engineering, Tohoku University, Sendai, Japan.     

Absence of Phase-Fluctuation Contribution to the Low-Frequency Optical Conductivity in d-Wave Superconductors at Zero Temperature

The behavior of the low-frequency optical conductivity _reg() in superconducting cuprates is, at the present, an open and interesting issue. In particular, since the zero-temperature and zero-frequency limit of _reg() attains a value much larger than the universal value expected within a self-consistent T-matrix calculation, an intriguing possibility is that the collective mode can also contribute to _reg(). By taking into account the effect of dissipation on the collective mode in a d-wave superconductor, we evaluate the phase-fluctuation contribution to _reg(0) within the formalism of the phase-only action. We show that even though the collective mode contributes to _reg() at finite frequencies, approaching the zero-temperature and zero-frequency regime the corrections at _reg() due to phase fluctuations vanish.     

Determination of the thermophysical characteristics of alternatively freezing and thawing dispersed media by the method of solving inverse problems of heat conduction

The article explains an algorithm for determining the thermophysical characteristics of dispersed media with phase transitions based on the method of solving inverse problems of heat conduction.Notation r space coordinate - time - T temperature of the specimen - T₀ initial temperature - c_i, c_w, c_sk specific heat of ice, water, and of the organic-mineral skeleton, respectively - c_f, c_m, _f, _m specific heat and thermal conductivity in the frozen and melted zones, respectively - c effective heat capacity - thermal conductivity - p density - ₀, _sb bound and strongly bound moisture, respectively - (T) amount of nonfrozen water - R radius of the cylinder - q() heat flux - I functional - u₁(), U₂() measured temperatures of the specimen at the points r = 0 and r = R, respectively, at the instant - ₁, ₂ degree of confidence of the supplementary information - final instant of time - a, b, k, _s positive constants - L specific heat of melting - N number of grid nodes over space - n number of grid nodes over time - h grid step over space - grid step over time - solution of the conjugate system - s number of iteration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 292–297, August, 1980.     

Dynamic emission of dislocations from a crack tip — a computer simulation

The behavior of dynamic emission of dislocations from the tip of a stationary crack under mode II or mode III loading is examined. A critical stress intensity factor, K _D is assumed for dislocation emission. After emission, the dislocation moves with a velocity which varies with the effective shear stress to the third power. The effective shear stress is due to the applied stress , modified by the presence of the crack and all other dislocations minus the lattice friction stress, ^F. The effects of K _D, , and ^F on the rate of emission, the plastic zone strain rate, the plastic zone size, the dislocation distribution, and the dislocation-free zone are reported.

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Résumé On a examiné le comportement d'une émission dynamique de dislocations depuis l'extrémité d'une fissure stationnaire. On suppose que l'émission de dislocations est caractérisée par un facteur critique d'intensité de constrainte K _D. Après son émission, la dislocation se meut avec une vitesse qui varie avec le cube de la constrainte effective de cisaillement. Celle-ci résulte de la constrainte appliquée , modifiée par la présence de la fissure et de toutes les autres dislocations, et sous déduction de la contrainte de friction du réseau, ^F.On étudie les effects de K _D, et ^F sur la vitesse d'émission des dislocations, la vitesse de déformation plastique, la taille de la zone plastique, la distribution des dislocations, et sur la zone qui en est dépourvue.

     

Dielectric properties of chemically treated wood

Dielectric properties along the grain for absolutely dried untreated and seven kinds of chemically treated Sitka spruce (Picea sitchensis Carr.) woods were measured. Cole-Cole's circular arc law was applied to the results of the relaxation due to the motions of methylol groups. The following changes were caused by chemical treatments. In polyethylene glycol (PEG) impregnation, the distribution of relaxation times became very narrow, the generalized relaxation time (_m) was considerably decreased, and the relaxation magnitude (₀ – ) was slightly increased. In acetylation, the distribution of relaxation times became very broad, _m was considerably increased, and (₀ – ) was remarkably decreased. In propylene oxide treatment, the distribution of relaxation times became slightly narrow and _m was decreased. _m was slightly decreased in formalization, phenol-formaldehyde (PF) resin treatment and wood methyl methacrylate (MMA) composite. (₀ – ) was decreased in formalization and PF-resin treatment and was hardly changed in wood-MMA composite and heat treatment. The distribution of relaxation times was almost unchanged in formalization, PF-resin treatment, wood-MMA composite and heat treatment.     

Dependence of helium II viscosity properties on oscillation frequency

The causes of a discrepancy in the results of measurements of He II viscosity below T 1.6 k obtained with different measurement methods are investigated. It is shown that to obtain correct results in oscillation experiments, the condition _ph should obtain, where is the depth of viscous wave penetration and _ph is the phonon free path length. Results of viscosity measurements at different ratios /_ph (by a wire viscometer) are presented. It is shown that for the condition _ph, the results obtained are in good agreement with the results of Andronikashvili (in which /_ph > 100). If the mentioned relation is not satisfied, then, as the value of the ratio /_ph is decreased, the value measured for the viscosity is increasingly lower than the results of Andronikashvili.     

Thermal Conductivity of Sm3S4 System with Mixed Valence Sm Ions

The thermal conductivity () and electrical resistivity () of mixed-valence compound Sm₃S₄ have been measured in the temperature range 5 to 300 K. The present results and those presented previously [1] for the thermal conductivity between 80 to 850 K are interpreted in terms of the temperature-dependent fluctuating valence of Sm ions. Sm₃S₄ crystallizes in the cubic Th₃P₄ structure, and the cations with different valences occupy equivalent lattice sites. Divalent and trivalent Sm ions are randomly distributed in the ratio of 1:2 over all possible crystallographic cation positions (Sm²⁺ ₂Sm³⁺ ₂S^2– ₄). The behavior of the Sm₃S₄ lattice thermal conductivity _ph is extraordinary since valences of Sm ions are fluctuating (Sm³⁺Sm²⁺) with a temperature dependent frequency. In the interval 20 to 50 K (low hopping frequencies), _ph of Sm₃S₄ varies as _ph T ^–1 (it is similar to materials with static distribution of cations with different valences): at 95 to 300 K (average hopping frequencies 10⁷ to 10¹¹ Hz), _ph changes as _ph T ^–0.3 (it is similar to materials with defects). Defects in Sm₃S₄ appear because of local strains in the lattice by the electrons hopping from Sm²⁺ ions (with big ionic radii) to Sm³⁺ ions (with small ionic radii) and back (Sm²⁺Sm³⁺), at T>300 K (high hopping frequencies), _ph becomes similar to materials with homogenous mixed valence states [1].     

Dielectric properties of chemically vapour-deposited Si3N4

The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si₃N₄ were measured in the temperature range from room temperature to 800° C. The a.c. conductivity ( _a.c.) of the amorphous CVD-Si₃N₄ was found to be less than that of the crystalline CVD-Si₃N₄ below 500° C, but became greater than that of the crystalline CVD-Si₃N₄ over 500° C due to the contribution of d.c. conductivity ( _d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si₃N₄ are smaller than those of the crystalline CVD-Si₃N₄ in all of the temperature and frequency ranges examined. The relationships of ^n-1, (- ) ^n-1 and/(- ) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si₃N₄ were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si₃N₄ was smaller than that of the crystalline CVD-Si₃N₄.     

Microstructural and dimensional stabilities of a potential γ/γ′-α(Mo) directionally solidified eutectic superalloy under cyclic thermal exposure to 1000° C

A potential heat-resistant ductile eutectic composite,/-, in the Ni-Al-Mo ternary system has been thermally cycled in the temperature range 200 to 1000° C for up to 1000 cycles in an attempt to examine dimensional as well as microstructural stability of the composite under thermal fatigue conditions. The composite examined has two types of initial microstructure; in one, blocky -Ni₃Al encircles individual-Mo fibres (as-grown condition) whereas in the other, is in the form of fine cuboidal particles uniformly distributed in an Ni-rich fcc matrix (heat-treated condition). Dilatometric measurements upon temperature cycling show that the composite is stable against thermal ratchetting irrespective of initial microstructural conditions. However, the cycling induces microstructural change, which is characterized by segmentation of-Mo fibres or formation of a detrimental brittle phase identified as an intermetallic-NiMo that consumes-Mo fibres whether the fibres are encircled by or not. Post-cycling tensile tests at room temperature show that the fibre damage in the former has no fatal effect on tensile strength and ductility. A beneficial effect of the-encircling configuration is discussed on the basis of the recognition of a peritecto-eutectoid reaction:++ that has been disregarded.     

Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten