Modified four-point bending specimen for determining the interface fracture energy for thin, brittle layers

A well-known four-point bending test has been modified such that the critical energy release rate for delaminating cracks propagating at the interface of a thin, brittle layer bonded to a substrate can be measured. The energy release rate required for crack delaminating at those interfaces is obtained by attaching a stiffening layer to the layer system. Another advantage of this modification is that segmentation of the layer and plastic deformation of the substrate during bending are avoided. The interface fracture energy of a plasma sprayed ZrO₂-ceramic layer on a flame sprayed high alloyed steel substrate has been measured. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Smallest Correction of an Inconsistent System of Linear Inequalities

The problem of calculating a point x that satisfies a given system of linear inequalities, A x #x2265; b, arises in many applications. Yet often the system to be solved turns out to be inconsistent due to measurement errors in the data vector, b. In such a case it is useful to find the smallest perturbation of b that recovers feasibility. This motivates our interest in the least correction problem and its properties.Let A x #x2265; b be an inconsistent system of linear inequalities. Then it is always possible to find a correction vector y such that the modified system A x #x2265; b #x2212; y is solvable. The smallest correction vector of this type is obtained by solving the least correction problem Let denote the convex cone which consists of all the points for which the system A x #x2265; u is solvable. Let denote the polar cone of . It is shown that the least correction problem has a simple geometric interpretation which is based on the polar decomposition of into and . A further insight into the least correction concept is gained by exploring the duality relations that characterize such problems.     

The Validity of Using the Microscopic Hyperbolic Heat Conduction Model Under a Harmonic Fluctuating Boundary Heating Source

The validity of using the microscopic hyperbolic heat conduction model under a harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic hyperbolic heat conduction model is essential when . The phase shift between the electron-gas and solid-lattice temperatures is found to be . This phase shift reaches a fixed value of 1.5708 rad at very large values of . It is found that the use of the microscopic hyperbolic heat conduction model is essential when ¯>1×10⁹ rads^–1 for most metallic layers independent of their thickness.     

The Dual-Phase-Lag Heat Conduction Model in Thin Slabs Under a Fluctuating Volumetric Thermal Disturbance

In the present work, the thermal behavior of a thin slab, under the effect of a fluctuating volumetric thermal disturbance described by the dual-phase-lag heat conduction model is investigated. It is found that the use of the dual-phase-lag heat conduction model is essential at large frequencies of the volumetric disturbance. It is found that the hyperbolic wave model deviates from the diffusion model when and the dual-phase-lag model deviates from the diffusion model when . where is the angular velocity of the fluctuating wall temperature, is the phase-lag in the heat flux vector and is the phase-lag in the temperature gradient vector.     

Dynamic crack propagation and unloading behavior of brittle polymers

The method of caustics in combination with a Cranz–Schardin high-speed camera was utilized to study dynamic crack propagation and unloading behavior of epoxy, PMMA and Homalite-100 specimens. Dynamic stress intensity factor K _ID and crack velocity were evaluated in the course of crack propagation. Caustic patterns at the loading points were also recorded to estimate load P applied to the specimen. Unloading rate , the time derivative of P, was determined as a function of time t, and its time correlation with K _ID or was examined. The findings showed that the change in was qualitatively in accord with the change in K _ID or . However, there existed slight differences among the values of t giving the maximum , and K _ID, so that their order was , and K _ID. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonsteady crack and craze behavior in PMMA under cyclical loading: II. Effect of load history on growth rate and fracture morphology

This is the second of three papers devoted to time or frequency effects on crack propagation in PMMA under cyclic loading with high resolution measurements of crack and craze growth in the micron range and with subcycle temporal resolution. It is demonstrated that the breakdown rate of the craze leads to quasi-periodic spurts of propagation and growth retardation in dependence on both the magnitude of the stress intensity factor and on the imposed load frequency. The surface morphology is governed more by the time required to build and deteriorate the craze (process time) than by the amplitude of the stress intensity factor. Three different growth ranges are distinguished: At the highest load levels multiple crazes occur at various distances from the major crack plane which coalesce and give rise to an incoherent surface structure not characterizable in terms of a single craze, although the front of the craze/crack is still represented by a smooth curve; crack advance occurs over domains that are larger than a typical craze length. At lower stress levels the craze breaks at different levels within the craze structure, the spatial breakdown of the craze being limited to dimensions smaller than the craze length but with a correlation or memory effect that generates terraces (on the fracture surface) on a scale larger than the craze length. In a transition between this stage and the lowest stress level considered, both features may exist simultaneously on a fracture surface, one increasing or decreasing relative to the other. Increase/decrease of one phenomenon relative to the other does not occur at a fixed stress intensity range but depends on the past history. When a change in the loading produces a change in the fracture mode, it is possible to associate, during the transition, decreasing crack growth rates with increasing stress intensity factors. At the lowest loading a craze breaks essentially through its center leaving a submicroscopically smooth surface; the associated crack growth and craze break down occurs with more or less periodic increments that are each smaller than the full ‘equilibrium’ craze length. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Experimental Observations and Computational Modeling of Fracturing in an Anisotropic Brittle Crystal (Sapphire)

The commonly used fracture criteria-maximum K_I, zero K_II, maximum hoop-stress, and maximum energy-release rate-predict similar fracture paths in isotropic materials, but not in anisotropic materials. In the general anisotropic case, the fracture path depends on the material-symmetry properties, the nature of the applied loads, and the overall geometry of the specimen. In addition, anisotropy in the material's resistance to fracturing plays a key role in defining crack initiation and its propagation path. Experiments are performed on notched specimens made from sapphire, a microscopically homogeneous and brittle single-crystal solid. The force required for fracture initiation is measured. The experimental measurements/observations are compared with the numerical results of the FEM simulations. A stress-based fracture parameter, is shown to be a good measure of the fracture criterion, where σ and E, respectively, are the tensile stress and Young's modulus in the direction normal to the cleavage plane, with surface energy γ , and R is a characteristic length, e.g., the notch radius. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. More than two-thirds of the notched specimens fractured at the point and along a cleavage plane where A is maximum. The measurements of the applied force made it possible to quantitatively obtain a critical value for parameter A. Finally, experiments show that for the notched sapphire specimens the weakest family of cleavage planes, , are the fracture planes, although a few specimens fractured along non-cleavage planes. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effect of temperature on the electric conductivity property of Bi3Zn2Sb3O14 pyrochlore type phase

The electric conductivity characteristic of ceramics was investigated by impedance spectroscopy in the frequency range from 5 Hz to 13 MHz. Electric measurements were performed at temperatures in the range from 25 to 700 °C. The phase type pyrochlore was synthesized by the polimeric precursors method. Ceramic presenting a relative density of 98% of the theoretical density was prepared. The data were presented in Nyquist diagrams form, from which the electric resistivity was determined. The electric conductivity followed the Arrhenius law with an apparent activation energy of the conduction process equal to 1.37 eV. The electric conductivity at room temperature was determined by extrapolation being equal to . Between 400 and 700 °C, the conductivity values were and , respectively.     

Three-dimensional shape of the Y2BaCuO5 pattern in melt-textured Y–Ba–Cu–O oxide

Crystallographic orientations of the Y211 tracks that were trapped within the melt-textured Y123 domains were determined from the orientation relationship among the Y211 pattern, twin traces and a microcrack. Analysing the orientation of the two-dimensional Y211 patterns that were observed on various crystallographic planes of the Y123, the three-dimensional shape of the Y211 pattern was inferred as follows: only one x-type Y211 pattern was included within one Y123 domain and three sets of diagonal Y211 tracks met with the corners of the Y123 domain. The diagonal Y211 tracks lie on the (1 1 0), ( 1 0), (0 1 1), (0 1), (1 0 1) and (1 0 ) planes of the Y123 domain. The planes where the Y211 tracks are located are considered to be the boundary planes where local growing parts of the Y123 domain impinge upon each other. The formation mechanism of the Y211 pattern is discussed on the basis of anisotropic growth behaviour and the shape of the Y123 domain. This revised version was published online in November 2006 with corrections to the Cover Date.     

Growth of aluminium nitride whiskers by sublimation-recrystallization method

Aluminium nitride (AlN) with various morphologies was fabricated through a sublimation-recrystallization method. The influences of type of reactor and temperature gradient were explored, as well as the orientations and growth mechanism of the obtained AlN whiskers. In the early stage of preparation, a vapour-liquid-solid (VLS) mechanism dominated, producing AlN pillars, whiskers and noncrystalline fibres. In the later stage, as the catalyst liquid was removed by volatilization, the pillars and noncrystalline fibres stopped growing, but the growth of AlN whiskers continued through a vapour-solid (VS) mechanism. By Laue method and rotating-crystal method of x-ray diffraction, together with electron diffraction, most of the AlN whiskers were discovered to grow on planes , or , where l=0, 1, 2, 3, along crystal axes , or , where w=0, 1, 2, 3. Oblique grown whiskers also appeared, with a growth direction at an angle of about 54° to the growth plane, .     

A comparison of strengthening mechanisms in rolled and axisymmetrically deformed Ti-20Y composites

Two Ti-20%Y metal-metal composites were deformation processed: one axisymmetrically and the other by rolling. The microstructures, preferred crystallographic orientations, and tensile strengths of each were measured periodically as the deformation progressed. The axisymmetrically deformed Ti matrix developed a [10 0] fiber texture, and the rolled composite acquired a texture with the <0001> tilted 31° from the sheet normal toward the transverse direction with [10 0] parallel to the rolling direction. The orientations of the {10 0}<11 0> and (0002)<11 0> slip systems in Ti with these textures were used in conjunction with the maximum possible slip distances for dislocation travel in each specimen to demonstrate that the axisymmetrically deformed material should be stronger than the rolled material for composites of equal phase thickness and spacing. The strengths of the two composites measured in this study were compared at similar microstructural phase sizes and spacings, and the axisymmetrically deformed composite was indeed found to be somewhat stronger, although the difference in strengths was not large.     

Computer-aided design of small patch antenna using (Al, Mg)TaO2 ceramics

The microwave dielectric properties of (AMT) ceramics and the design of small coplanar waveguide fed antenna (CPWFA) have been investigated. ( and ( have orthorhombic and tetragonal structure, respectively. As ( concentration increased, AMT ceramics transformed into the tetragonal structure. Specimens having tetragonal single phase could be obtained above x=0.6. As ( concentration increased, the grain size, dielectric constant and quality factor (Q) significantly increased and the temperature coefficient of resonant frequency changed from negative to positive. The of was realized at x=0.65 and the Q · f _O value and for this composition were 112 470 GHz and 26.1, respectively. Newly developed dielectric materials were used for 1.5 GHz band CPWFA design and fabrication. The size of the CPWFA can be reduced by using high dielectric constant AMT ceramics, insetting slits into the patch, and fabricating CPW feed line in the ground plane. The slits play a role in not only lowering a center frequency but also fine tuning for the proposed antenna together with the open stub of CPW feed line. The CPWFA with slits has a lower center frequency than the conventional CPWFA, which suggests that the antenna size can be reduced by as much as 16.3%. The structure simulations of the CPWFAs have been performed to obtain impedance matching and to investigate the effects of slits. Experimental results of the fabricated device were in good agreement with the simulation.     

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.     

Effect of the addition of Y2O3 on the structure, microstructure and piezoelectric properties of PZT(53/47)

In this work, an attempt is made to study system with x=0.0125, 0.025, 0.050, 0.075 and 0.1. It was shown that there is limited solid solubility (0.625 mol %) of or 1.25 mol % of in PZT(53/47). For higher levels of dopant, mainly two other extra second phases were detected. The first was a Zr-rich phase in which some and small amounts of was dissolved. The second one was a Pb solid solution composed of mainly PbO, and which was initially also seen in calcined samples. The formation of Zr-rich phase is thought possibly to originate due to the sublimation of Pb from source during the sintering process. For higher x values, a structural shift towards Ti-rich region of PZT's phase diagram is seen. All piezoelectric parameters of the doped samples such as , are seen to decline sharply compared to that of undoped samples. Increasing the level of dopant gave rise to the increase of conductivity and dielectric loss of sintered samples. The formation of non-ferroelectric extra phases, and the Zr/Ti change of the main formed phase is believed to be responsible for this behavior.     

Microstructural development of Ti-24Al-14Nb-3V-0.5Mo alloy during hot tensile deformation

Microstructure of the Ti-24Al-14Nb-3V-0.5Mo (at.%) alloy deformed from room temperature to 700°C was studied by the H-800 transmission electron microscope (TEM) equipped with a side entry goniometer stage capable of ±45° tilt on the X or Y axis operating under two-beam condition. Especially dislocation types and slip systems of the ₂-phase (D0₁₉) were analyzed in accordance with invisibility criterion. The results indicated that with increasing the deformation temperature from room temperature to 700°C, the slip of -type dislocations on prismatic planes in the ₂-phase was enhanced whereas that on basal plane (0001) with hexagonal networks morphology was suppressed during tensile deformation. Being immobile, the dislocation networks were thought to be mainly responsible for the low ductility at low temperature. When the test temperature was increased to 700°C, the -type dislocation glide on pyramidal planes was also observed, but the hexagonal dislocation networks formed by the slip of -type dislocations on basal planes were hardly seen. During the high temperature deformation microstructural refinement was also observed due to dynamic recovery and recrystallization. This, together with the precipitation of secondary ₂ phase and O phase during deformation all contributed to ductility of the present alloy at high temperature.     

The crystallography and morphology of Mo2C in ferrite

The orientation relationships between hexagonal Mo₂C precipitates (H) in ferrite (B) have been determined by electron diffraction to an accuracy of ±2°. With one exception, the 19 results are consistent with the previously reported Pitsch and Schrader (P/S) orientation relationship. However, these more accurate determinations show clearly that there is a systematic deviation of up to 5.5° from the exact P/S relationship and that this deviation consists of a small rotation about the parallel close packed directions-[100]_B// . The long direction of the Mo₂C needles has been determined unequivocally in terms of the orientation relationship to be [100]_B// . Moiré fringes between precipitate and matrix have been used to improve the accuracy of the orientation relationship results and to determine the lattice parameters of the carbide precipitates investigated. The Moiré fringe analysis has shown small systematic departures from the exact parallelism between [100]_B and along the length of Mo₂C needles and a lowering of the carbide lattice parameter that is consistent with the replacement of Mo by Fe in the carbide. The orientation relationship results, including the observed systematic deviation from the exact P/S relationship, are shown to be consistent with the edge-to-edge model.     

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.