The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

Tensile and fatigue strength of hydrogen-treated Ti-6Al-4V alloy

Tensile, fatigue and fractographic data on Ti-6Al-4V microstructures attained through a series of post--annealing treatments which used hydrogen as a temporary alloying element are presented. Hydrogen-alloying treatments break up the continuous grain boundary and colony structure, and produce a homogeneous microstructure consisting of refined -grains in a matrix of discontinuous . These changes in microstructural morphology result in significant increases of the yield strength (974 to 1119 MPa), ultimate strength (1025 to 1152 MPa) and high cycle fatigue strength (643 to 669 MPa) compared to respective values for lamellar microstructures (902, 994, 497 MPa). The strengths are also significantly greater than the strengths of equiaxed microstructures (914, 1000, 590 MPa). The strengths of hydrogen-alloy treated samples are therefore superior to strengths attainable via other thermal cycling techniques.The fatigue fracture surfaces of the hydrogen-alloy treated samples were topographically similar to equiaxed samples. Fatigue crack initiation was characterized by faceted regions. As crack length and K increased, the crack surface changed to a rounded, ductile topology, with microcracks and locally striated regions. Fracture primarily followed the - interfaces. This is rationalized by the fact that hydrogen-alloyed microstructures are very fine Widmanstatten microstructures having reduced aspect ratios, and these microstructures fail along - interfaces.     

Correlation between Superconducting Gap and Pseudogap in High-T c Cuprates

We studied the low-temperature energy gap 2 ₀ on Bi ₂ Sr ₂ CaCu ₂ o ₈₊ (Bi2212) and La _2–x Sr _x CuCO ₄ (La214) systematically over a wide range of doping level p using STS, break junction tunneling spectroscopy, Raman scattering and low-T electronic specific heat data. We have also studied the electronic specific heat of La214 in the normal state at T > T _c , and confirmed that pseudogap behavior appears at around T*, below which the in-plane resistivity and magnetic susceptibility tend to be slightly suppressed. Similar suppression appears in and of Bi2212 below the onset temperature of pseudogap T*. It is pointed out in the present study that 2 ₀ is closely related to T* in both Bi2212 and La214 systems; T* 2 ₀ /4.3k _B . It is also pointed out that 2 ₀ is in almost linear proportion to k _B T _max ( T*), where T _max is the temperature exhibiting a broad peak in –T curves and k _B T _max can be considered to give a measure of the effective antiferromagnetic exchange energy J _eff. The factors in 2 ₀ k _B T _max J _eff are 1 for La214 and 2 for Bi2212, respectively. We also report that in both Bi22l2 and La214 systems T _c roughly scales with p ₀ except in highly doped samples, where T _c 2 ₀ .     

Asymptotic expansions for constant-composition dew-bubble curves near the critical locus

Explicit functional representations are developed for constant-composition dew and bubble curves near critical according to the modified Leung-Griffiths theory. The pressure and temperature incrementsP=P–P _c andT= T–T _c, where c denotes critical, are linearly transformed to new variablesP andT. In the transformed space, the coexistence curves are no longer double-valued and can be expressed as a nonanalytic expansion, where the coefficients are functions of the critical properties and their derivatives. A similar asymptotic expansion is developed forT in terms of the density increment=– _c. In the approximation that the critical exponents=0 and=1/3, the critical point in temperature-density space is shown to be a point of maximum concave upward curvature, rather than an inflection point as previously conjectured.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

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.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Dislocations and faults in some alloys containing copper and aluminum

By using the method of variance of the respective X-ray diffraction line profile, the effective particle size (p) and r.m.s.. strain (S ^21/2) of four alloys containing copper and aluminium (Al-0.08, 4 and 10 wt% Cu and Cu-5.87 wt% Al) at different annealing stages (starting from the cold filed stages) have been determined. From the peak shift of these samples, their average stacking fault probability = – where is the intrinsic stacking fault probability and the corresponding extrinsic stacking fault probability, respectively, were determined. Similarly, from the angular distance between the peak and the centroid of the diffraction profiles, the magnitude of + 4.5, where is the twinning fault probability, was measured. From these, the true particle sizeT, the stacking and twinning fault probabilities , and and the minimum stacking fault widthD _min have been determined. The hardness of alloys at different annealing stages was found to be dependent on the dislocation density and the stored energy in the alloys. The relationT S ^21/2 = constant was found to be valid for the alloys and from this a mechanism of grain growth with annealing has been suggested. With annealing the dislocation density and stored energy per unit volume were found to decrease until finally, in the fully annealed stages, they disappeared. The same was found to be valid for stacking and twinning fault probabilities as well as the minimum stacking fault width. A mechanism for the creation and annihilation of the intrinsic and extrinsic stacking faults has been suggested.     

Experimental evaluation of relative mode parameters in the irregular earth-to-ionosphere waveguide

Conclusions A model for representing the propagation of superlong waves was selected. Certain relative mode parameters ()₁, ()₂, ()₃, (V)₁, (V)₂, (V)₃, C₁, C₂, and C₃ can be used in order to account for the time-measurement error produced as a resuit of the double-mode signal propagation, to determine in a semiempirical manner the ionosphere's effective reflection height at night and in the daytime, to calculate and apply signal-propagation corrections which take into account phase velocity changes due to variations in the ionosphere height from day to day, and to calculate the fields of transition paths.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 75–78, August, 1974.     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

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.     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure     

Precipitation phenomena in the Mg-31 at% Li-1 at% Al alloy

Precipitation phenomena produced in the -phase (b c c) of the Mg-31 at% Li-1 at%Al alloy subjected to different heat treatments have been studied by sensitive single-crystal X-ray diffraction techniques. The variation of the hardness values of specimens quenched and then aged was also examined. It was confirmed that AlLi is a stable phase at room temperature for the examined Al content; AlLi precipitation is only produced for very slow cooling rates from the -field. Phase reactions for specimens quenched and then aged can be summarized as follows: ++ after ageing at room temperature; + ++ AlLi after ageing at 473 K. A considerable increase of the hardness, which attains its maximum value after about 30 h ageing at room temperature, was observed. Neither the -phase nor the AlLi-phase precipitation can account for the observed hardening process. The presence of the -metastable phase when the hardness reaches its maximum value is verified.     

Low endurance fatigue in metals and polymers

The fatigue behaviour of commercially pure aluminium and of nylon under sequentially varying strain amplitudes is compared with a damage law of the type suggested by Miner. Aluminium obeys such a law for both cyclic and uniaxial prestrains but the behaviour of nylon is significantly affected by microcracking, which produces a marked effect of loading sequence.Appendix N Number of strain cycles at a given time - N _f Value of N at failure - True tensile stress - True stress range for a strain cycled specimen - _h Value of at half the life of the specimen - True tensile strain - Total true strain range - _p True plastic strain range (= the breadth of the hysteresis loop at = 0) - _d True diametral strain range - E Young's modulus - Linear strain hardening rate when tested at a particular value of _p - D Damage due to cycling - D _p Damage due to prestrain - _p Prestrain. C, K, K₁, , are constants     

Ultrasonic attenuation study of defects in aluminium under the action of constant stress

In attempting to distinguish the interaction between dislocations and that between dislocations and point defects, the variations of the ultrasonic attenuation, , and strain are measured as a function of action timet of different constant tensile stress for 99.999 Al polycrystalline specimens at room temperature. It is found that the ultrasonic attenuation decreases and the strain increases at the beginning, and then reaches a saturation state with increasing time. The can be divided into two parts. The initial decrease in is due to the interaction between dislocations and point defects and the final equilibrium is caused by an interaction purely between dislocations. When the applied constant tensile stress is lower than 0.9 MPa, there is no dislocation multiplication.     

Activated slip systems during yielding of α-β brass two-phase bicrystals

- brass two-phase bicrystals, consisting of fcc () single crystals and bee () single crystals, which were made by the solid state diffusion couple technique, were tensile-tested at room temperature in order to clarify the role of phase-interface on the deformation. The two-phase bicrystals had small concentration gradients in the- and-phases and satisfied the Kurjumov-Sach's orientation relationships i.e. {1 1 1} {1 1 0} and [1 1 0] [1 1 1] at the interface. The slip traces observed in bicrystals deformed to about 3% plastic strain showed a striking contrast between the- and-phases; the slip traces in the-phase were clear and straight, while those in the-phase were fine and wavy. The slip systems in the bicrystals were attributed to those observed in and single crystals, and were explained by a plastic strain incompatibility mechanism. The slip systems, originating at the interface or propagating from another phase, were observed on matching planes.On leave from Mechanical Engineering Department, Faculty of Engineering, Al-Azhar University, Cairo, Egypt.     

A high-resolution-electron-microscopy study of a γ/γ′-α directionally solidified eutectic alloy

The microstructure of a /- directionally solidified (DS) eutectic alloy with a nominal composition of Ni-30.26Mo-6.08Al-1.43V (wt%) was investigated by means of high-resolution electron microscopy (HREM) and analytical electron microscopy. The -fibres exhibited a typical morphology with a rectangular cross-section and they displayed the Bain orientation relationship (OR) with the / matrix; that is, [001][001] and (110)(010). Misfit dislocations and lattice strain fields existed at the / interface for different habit planes; that is, (110)(010) and (100)(110) were analysed. EDAX (Energy dispersive X-ray) analysis showed that the composition of the -phase was approximately Ni₄(Mo, Al, V); it contained 90° rotational domains of Ni₃(Mo, Al, V) with a DO₂₂ structure and Ni₂(Mo, Al, V) with a Pt₂Mo structure.