Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints

The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (=), and those having nonparallel water rays ( ). The = categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two = geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.     

Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

Effect of wall conductances on hydromagnetic flow and heat transfer in a rotating channel

Summary Wall conductance effects on the hydromagnetic flow and heat transfer between two parallel plates in a rotating frame of reference has been studied when the liquid is permeated by a transverse magnetic field. An exact solution of the governing equations has been obtained. It is found that the velocity, current density and the temperature depend only on the sum of the wall conductances ₁ + ₂ = but magnetic field depends on the individual values of ₁ and ₂, where ₁ and ₂ are respectively the wall conductance ratios of the upper and lower walls.

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Einfluß der Wandleitfähigkeit auf die hydromagnetische Strömung und den Wärmeübergang in einem rotierenden Kanal

Zusammenfassung In der Arbeit wird der Einfluß der Leitfähigkeit der Wände auf die MHD-Strömung sowie auf den Wärmeübergang untersucht für den Fall, daß sich das zähe Medium zwischen zwei rotierenden Platten befindet und ein Magnetfeld parallel zur Rotationsachse angelegt wird. Es wird eine exakte Lösung des Problems gegeben. Es zeigt sich, daß die Geschwindigkeit, die Stromdichte und die Temperatur nur von der Summe der Leitfähigkeiten der Wände + ₂ = abhängen, dagegen hängt die magnetische Feldstärke von den individuellen Werten ₁ und ₂ ab, wobei ₁ und ₂ die Leitfähigkeiten der oberen bzw. unteren Wand bezeichnen.

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With 5 Figures     

Theoretical estimation of fracture toughness of fibrous composites

A method of estimating the fracture surface energy of fibre-reinforced materials is discussed. The surface work is shown to increase with increasing fibre content, strength and diameter, and decrease with increasing fibre modulus and matrix flow stress (or hardness).Relatively short fibres should be used if high toughness is required, and the maximum toughness that can be achieved is limited by the amount of crack opening that can be permitted. Under certain conditions, incorporation of fibres into a material can lead to embrittlement.Symbols used c half length of crack - d fibre diameter - D average separation of nearest neighbour fibres - E Young's modulus - G shear modulus of matrix - K fracture toughness - L length of fibre on either side of crack - n number of fibres per unit area - P force on fibre - R pressure exerted by matrix on fibres - u displacement - U work - x distance Greek symbols 8 G/d ² E _fr log(2/p 3) - surface energy or work - tensile strain - _fm E _mr/E_fr R - tensile stress - shear stress - coefficient of friction - Poisson's ratio Suffixes c composite - e elastic - f fibre - m matrix     

Rubber toughening of plastics

Creep measurements were made on a series of six ABS blends containing 0 to 20 vol% of 80m glass beads. At small strains, the beads raised the modulus of the ABS. However, debonding of the polymer from the glass resulted in a rapid drop in modulus with increasing strain and bead content, and at strains above 1.0% the order of stiffnesses was reversed. Debonding resulted in an increase in creep rate with, as measured by the time to reach 1% volume strain. Plots of In ^–1 against applied stress were linear, in accordance with the Eyring equation, and provided data for comparing stress concentration factors. The relationship between and fitted approximately to the Ishai Cohen effective area model. It is concluded that debonded glass beads accelerate multiple crazing by increasing average stresses in the ABS matrix, and in that respect resemble rubber particles. However, unlike rubber particles, debonded beads drastically reduce notched Charpy impact strength.     

Mechanical properties of injection moulded styrene maleic anhydride (SMA) Part II Influence of short glass fibres and weldlines

The dependence of the various mechanical and fracture properties on the volume fraction ofshort glass fibres in the styrene maleic anhydride (SMA) polymer was investigated. Special attention has been given to describing the dependence of various mechanical properties on the volume fraction of the glass fibres, f by way of the rule of mixtures. It was found that, strength, elastic modulus and fracture toughness, all follow a simple rule-of-mixtures of the form Qc=Qff+Qm(1–f), where Qc is the measured quantity for the composite, Qm and Qf are the corresponding values for the matrix and the fibre, respectively, and is the overall efficiency of the fibres, taking into account the orientation and the length of the fibres in the composite. It was also found that, while the presence of the weldline had no significant effect upon elastic modulus, its presence significantly reduced tensile strength and the fracture toughness of SMA and its composites. © 1998 Kluwer Academic Publishers     

Effects of mode mix upon fracture behavior of a solder joint

Results of fracture experiments of brass/solder/brass sandwich CTS (Compact Tension-Shear) specimens are presented together with observations of the crack propagation behavior and the fractographs. The fracture behaviors of the interface crack are analyzed by the finite element method with a modified boundary layer formulation. Several fracture mechanisms and the corresponding criteria are examined. And the crack growth behavior and fracture toughness are predicted. As the results various crack growth procedures such as the crack jump to another interface on the opposite side, the nucleation of a new crack far from the initial crack front, and the asymmetric relation of fracture toughness versus mode mix J _c– can be successfully explained. The fractographs, the crack growth behaviors, and stress-strain distribution along the interface are inter-related.     

Semisolid forming of Al-10mass%Mg alloy by blending of elemental powders

By semisolid processing of metals, not only complicated shapes, but also products with a quality close to forged materials can be produced. In this research the forming temperature range, formability and mechanical strength of Al-10mass%Mg alloy formed by elemental blended powders semisolid forming are investigated. The powders used were gas-atomized aluminum as the high melting point powder, and ball-milled Al-20mass%Mg and Al-30mass%Mg powders as the low melting point ones. Differential thermal analysis has been used to determine the forming ability range. Tensile strength of the product has been evaluated by tests performed on 10 × 50 mm specimens. The relation between tensile strength and heat treatment has been also studied. Furthermore, the formability was investigated by forming cup shaped samples (outer diameter 424 × length 50 mm) with a thin wall (1 mm).     

Rheological properties of aqueous silicon nitride suspensions

The effect of surface modification of Si₃N₄ particle on the colloidal behavior and the rheological properties of aqueous Si₃N₄ suspensions under steady and oscillatory conditions are investigated in detail. Due to the decrease of the oxidizing level, the isoelectric point (IEP) of the modified particle shifts to basic region gently. Attempts have been made to apply rheological models to the suspensions with various solid volume fraction (). For the as-received suspensions, the Sisco model provides the best fit in the range of 0.30 while the Casson model in 0.35 0.45. The shear behavior of modified suspensions fits to Sisco model in the range of 0.40 and Casson model in 0.45 0.54. The rheological behavior of modified suspensions is improved efficiently. The critical strain decreases and the linear viscoelastic regime narrows continuously with increasing solid concentration. For the modified suspensions, the linear viscoelastic regime broadens and the corresponding elastic modulus decreases sharply. With increasing solid concentration, the characteristic frequency shifts toward lower frequencies and the suspension transforms from more viscous to more elastic.     

A new application of the reciprocity relations to the study of fluid flows through fixed beds

Creeping flow through an array of spheres with small volume fraction is studied theoretically. It is observed that it can be described macroscopically by Brinkman's equation. A generalized version of the reciprocity relations is used to determine the viscous term up to O(²) for the case of random configuration and up to O(³) for the case of periodic, cubic configurations of the fixed bed.     

Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids

A numerical technique for the dynamical simulation of three-dimensional rigid particles in a Newtonian fluid is presented. The key idea is to satisfy the no-slip boundary condition on the particle surface by a localized force-density distribution in an otherwise force-free suspending fluid. The technique is used to model the sedimentation of prolate spheroids of aspect ratio b/a=5 at Reynolds number 03. For a periodic lattice of single spheroids, the ideas of Hasimoto are extended to obtain an estimate for the finite-size correction to the sedimentation velocity. For a system of several spheroids in periodic arrangement, a maximum of the settling speed is found at the effective volume fraction (b/a)²04, where is the solid-volume fraction. The occurence of a maximum of the settling speed is partially explained by the competition of two effects: (i) a change in the orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small to a more uniform orientation at larger , and (ii) a monotonic decrease of the the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson–Zaki law (1–)⁵⁵ for suspensions of spheres.     

Negative self-inductance in superconducting thin wires and weak links

One of the most promising implications of the phenomenological Ginzburg—Landau (GL) theory of superconductivity is the possible existence of current-carrying metastable states with a negative effective self-inductance. Microscopically this phenomenon can be explained as a result of the depairing mechanism which, when the center-of-mass velocityv _s of the Cooper pairs is sufficiently large, can be so strong that a further increase ofv _s will lead to a decrease of the total current. Using a one-dimensional formulation of the GL theory we investigate the thermodynamic stability of these states for different external constraints and obtain the result that a negative self-inductance can only be stable if the length of the system in the direction of the current is smaller than a critical value comparable to the GL coherence length /. It is an experimental fact that states of negative self-inductance are realized in Josephson junctions and other types of superconducting weak links because the dc supercurrent can be a decreasing function of the phase variable . The thermodynamic stability theory can therefore explain why weak links have to be short, and it also provides us with a unifying point of view by treating the phase and the current as a pair of thermodynamically conjugate variables for arbitrary one-dimensional systems. An important point is the operational phase definition as a thermodynamic parameter that can be controlled by the experimentalist. This requirement is essential for the general validity of the ac Josephson equation and it implies that must depend on the magnetic self-inductance of the system. By applying the GL theory to weak links we can delimit the validity of the usual dc Josephson equationI sin and see that deviations from this functional form are most likely to be found in thin-film bridges of the Anderson-Dayem (AD) type. When the currentI is the controlled variable the conjugate phase variable will fluctuate and the magnitude of these fluctuations depends strongly on the functional formI(). The phase fluctuations for constantI lead to a reduction of the critical current which will be absent when is the controlled variable. The observed microwave enhancement of the critical current in AD bridges, the so-called Dayem effect, can be explained as a result of a switch from current control to phase control, and the fluctuation formulae explain why the effect is negligible in structures exhibiting the classical Josephson sine law for the current-phase relation.     

A new iterative technique of the finite element method for the analysis of the steady state incompressible viscous flow based on the transformation of variables

In this paper the convergence acceleration for solving steady-state incompressible flows, by using iterative solvers, is explored. The variable transformation: u = u – , p = –r, where u and are the rotational velocity and the velocity potential, respectively, is applied to the finite element discretized equations so as to get diagonal-dominant equations. The effectivity of the present techniques is demonstrated on the 2D lid-driven flow and the 3D flow in a disk-cylinder system.     

Kondo Impurity in a Mesoscopic Ring: Charge Persistent Current

We study the influence of a magnetic impurity or ultrasmallquantum dot on the charge persistent current of a mesoscopicring. The system consists of electrons in a one-dimensionalring threaded by spin-dependent Aharonov–Bohm/Casher fluxes,coupled via an antiferromagnetic exchange interaction to alocalized electron. By passing to a basis of electron stateswith definite parities, the problem is mapped onto a Kondomodel for the even-parity channel plus free electrons in theodd-parity channel. The twisted boundary conditionsrepresenting the fluxes couple states of opposite parityunless the twist angles satisfy =f,where f are integers, with spin index=, . For these special values of, the model is solved exactly by a Bethe ansatz.Special cases are investigated in detail. In particular weshow that the charge stiffness in the case= is insensitive to the presenceof the magnetic impurity/quantum dot.     

Asymptotic tensile crack-tip stress fields in elastic-perfectly plastic crystals

For a crack in an elastic-perfectly plastic crystal, there exist more than one asymptotic stress field around the crack tip. The condition governing which field occurs cannot be determined by the asymptotic fields, but depends on external loading conditions. For a plane-strain tensile crack in the (0 1 0) plane and growing in the [1 0 1] direction in a face-centered-cubic (fcc) crystal, there exist three asymptotic stress fields around the crack tip, including a previously established four-sector field and two new families of three-sector fields. The four-sector field gives a large mean stress ahead of the crack, 6.12, where is the critical resolved shear stress for slip systems {1 1 1}1 1 0. The first family of three-sector fields is parameterized by a single parameter p ranging from 0 to 1. In the limit p=0, the field degenerates to uniform tension in the direction parallel to the crack surface. In the other limit p=1, the corresponding field gives the maximum mean stress, 4.90 , in the family. The other family of three-sector fields also has two limits: one corresponds to uniform compression parallel to the crack, and the other provides the maximum mean stress in the family, 2.45 much less than the four-sector field. The stress distributions obtained by the finite element method confirm not only the four-sector field, but also two families of fields.     

Differential-flow-induced instability in a cubic autocatalator system

The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, A + 2B 3B, B C, with the reactant A being replenished by the slow decay of some precursor P via the simple step P A. The reaction is considered in a differential-flow reactor in the form of a ring. It is assumed that the reactant A is immobilised within the reactor and the autocatalyst B is allowed to flow through the reactor with a constant velocity as well as being able to diffuse. The linear stability of the spatially uniform steady state (a, b) = (µ^–1, µ), where a and b are the dimensionless concentrations of the reactant A and autocatalyst B, and µ is a parameter reflecting the initial concentration of the precursor P, is discussed first. It is shown that a necessary condition for the bifurcation of this steady state to stable, spatially non-uniform, flow-generated patterns is that the flow parameter > _c(µ, ) where _c(µ,) is a (strictly positive) critical value of and is the dimensionless diffusion coefficient of the species B and also reflects the size of the system. Values of _c at which these bifurcations occur are derived in terms of µ and . Further information about the nature of the bifurcating branches (close to their bifurcation points) is obtained from a weakly nonlinear analysis. This reveals that both supercritical and subcritical Hopf bifurcations are possible. The bifurcating branches are then followed numerically by means of a path-following method, with the parameter as a bifurcation parameter, for representatives values of µ and . It is found that multiple stable patterns can exist and that it is also possible that any of these can lose stability through secondary Hopf bifurcations. This typically gives rise to spatio-temporal quasiperiodic transients through which the system is ultimately attracted to one of the remaining available stable patterns.     

Neutron diffraction texture study of deformed uranium plates

The texture of two depleted uranium (DU) samples, labelled DUWR and DUWR2, were studied by neutron diffraction. DUWR was prepared by warm rolling of a cast ingot, and DUWR2 was prepared by adding 20% tensile strain to the warm-rolled DUWR. Complete three-dimensional orientation distribution functions were determined using four neutron pole figures for the DUWR, and using six neutron pole figures for the DUWR2 sample, by the WIMV method of the program popLA. The textures of the two samples were essentially identical to each other. They could be described by a twisted helical density tube spiralling continuously along the -axis of the Euler space. The projection of the backbone of the density tube along the -axis cast a linear shadow running parallel to the diagonal of the - plane, which could be defined by a =+90° (and =+270°) relation. The helical tube was confined within narrow -angle limits, from 14° to 30° with the peak orientation at (103) 0 10. The diffraction patterns of the DUWR2 sample were measured from the normal direction to the rolling surface of the sample, up to the scattering angle of 108° using a 0.15 nm neutron beam. The Rietveld profile refinement using the textured diffraction pattern was quite satisfactory when the texture effect to the entire diffraction profile was corrected for by the corresponding pole density from the inverse pole figure.     

A mechanical model of fatigue crack propagation. Report 2

Conclusions The proposed model of fatigue crack propagation based on the solution of the cyclic elastoplastic problem of the stress-strain state [1] makes it possible to take into account the effect of the triaxial stress state on the deformation of the material at the crack tip. The proposed algorithm of calculations of the state of damage on the basis of the principle of linear damage summation and also the agreement between the calculated and experimental data confirm the assumption on the controlling role of low-cycle damage in the mechanics of crack propagation in cyclic loading described from phenomenological positions. The main advantages of the proposed model are:The possibilities of calculating endurance in crack propagation or calculating the crack propagation rate for cases in which the variation of the range of the stress intensity factor along the crack length in structural members takes place at a variable loading asymmetry;the possibilities of describing the effect of loading asymmetry on the fatigue crack-propagation rate using only the strain criterion (Coffin's equation) since the range of the plastic strain intensity at the crack tip is, as shown in [1], a function of not only the range of the stress intensity factor K but also of its maximum value K_max;the possibilities of describing the dependence of K_th on loading asymmetry based on the assumption on the constancy of the size of the structural element for the given material;the possibilities of describing the crack propagation rate in all the three sections of the dL/dN=f(K) diagram, starting with the values K similar to K_th and ending with the value of K at which monotonic quasistatic fracture becomes the controlling process.Translated from Problemy Prochnosti, No. 8, pp. 14–18, August, 1985.     

Comparison of energy and phase relaxation in metallic wires

We have determined the phase coherence time, , frommagnetoresistance measurements of long, narrow wires ofAu, Ag, and Cu, over the temperature range40 mK-6 K. In the Cu and Au wires, saturates at low temperature. In the Ag wire, continues to increase down to the lowesttemperatures measured; moreover, its temperature dependencebelow about 1 K is consistent with theoreticalpredictions of Altshuler, Aronov and Khmelnitskii published in1982. These results cast doubt on recent assertions thatsaturation of at low temperature is a universalphenomenon in metal wires. We compare these results with thoseof recent experiments on energy relaxation in similar metallicwires. The results of the two experiments are stronglycorrelated, suggesting that a single (unknown) mechanism isthe cause of the enhanced phase and energy relaxation observedin some samples.     

Notch sensitivity of thermoset and thermoplastic laminates loaded in tension

Inplane tensile fracture of unnotched and notched thermoset graphite-epoxy and thermoplastic graphite-PEEK composite laminates is examined. Both fibre-dominated quasi-isotropic and matrix dominated ±45 angle-ply layups were investigated.Classical lamination theory predictions of elastic and strength properties of unnotched specimens are compared with experiments. Several notched geometries, i.e. centre-notched, double-edge notched and open-hole specimens subjected to tensile loading to fracture were examined. The notched strength of the quasi-isotropic laminates was analysed by a damage zone model, where damage around the notch is represented by an equivalent crack with cohesive force acting between the crack surfaces.Good agreement between experimental and calculated strength was observed for the graphite-epoxy laminates which failed in a collinear manner. For the graphite-PEEK laminates discrepancies between predicted and experimental strength are related to observed deviations from collinear crack growth. The angle-ply graphite-PEEK laminates showed larger notch sensitivity than the corresponding graphite-epoxy, probably due to less degree of stress relieving damage formation around the notch.