The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.     

Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

Charged defects-controlled conductivity in Ge-ln-Se glasses

The variation of the d.c. electrical conductivity, , with composition and temperature was investigated for glasses of the Ge-In-Se system. The results indicate a decrease in the activation energy for electrical conductivity, E, and an increase in on introduction of indium into Ge-Se glasses. The changes in E and with composition (selenium content in the glasses) are identical for the Ge_x In₅ Se_95–x and Ge_x In₈Se_92–x families. The results have been traced to the conduction controlled by charged defects in these chalcogenide glasses. The changes in E and have been explained by a shift in the Fermi level, being brought by the introduction of indium.     

Effect of shot peening on the fatigue and fracture behaviour of two titanium alloys

The fatigue and fracture behaviour of two titanium alloys, the near-alpha IMI-685 and alpha-beta IMI-318, were studied in the machined and polished (MP) as well as the machined, polished and shot (glass-bead) peened (MPS) conditions. Glass-bead peening reduced the room-temperature as well as the high-temperature (450°C) fatigue life of alloy IMI-685 at high stress amplitudes, _a, approaching the proof stress, _ps, of the material (LCF region). When the applied stress amplitude (0–770 MPa, HCF region) was comparable to the peen-induced peak longitudinal residual stress, _LP, i.e. (_LP/a)=0.92, an improvement in the room-temperature fatigue life of IMI-685 was observed. When the (_LP/a) ratio was less than this value, decreases in the fatigue life were seen. The room-temperature fatigue behaviour of IMI-318 at high stress amplitudes was similar to that of IMI-685. The decrease in the fatigue life of this alloy, at a stress amplitude (770 MPa) where improvement was observed for IMI-685, could be attributed to the higher relaxation of peen-induced residual stresses in IMI-318 compared with IMI-685. Glass-bead peening improved the hightemperature (450°C) fatigue life of IMI-685 at a low stress amplitude (465 MPa; (_a/PS)=0.87). The crack-initiation sites in the MP and the MPS conditions were at the surface for both the alloys. However, fracture in the surface layers of the alloys appeared more brittle in the peened (MPS) rather than in the unpeened (MP) condition.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

On internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.     

On the effects of microstress on macroscopic diffusion processes

Summary The effects of internal microstress fields are neglected in a usual simulation of the diffusion of a small solute trough solid heterogeneous media. However, when a heterogeneous material is used in a structure undergoing external mechanical loading, highly nonuniform stress fields can arise locally due to the variable microstructure. In this paper a simple quasi-Fickian model is studied which employs a spatially variable stress-dependent diffusivity,D . The structure ofD stems from an assumption that the stresses nonuniformly open and close the pores of the material microstructure, thus providing preferential sites for accumulation of the diffusing solute. When =0, the usual stress-free Fickian diffusivity,D ⁰, is recovered. Because of the highly oscillatory stress fields on the micro level, when employing numerical methods, such as the finite element or finite difference method, the distance between discretization nodes must be far smaller than the microstructural oscillations to obtain accurate simulations. This fact makes direct numerical simulations involvingD virtually impossible without computationally intensive, and complicated, special techniques. In this paper upper bounds are developed for the difference between solutions produced when usingD and alternativelyD ⁰ in the body under analysis. The general case, whenD ⁰, and consequentlyD , are spatially variable, is considered. The bounds are a function of onlyD ⁰ and and do not require any knowledge of the stress-dependent solution, and can thus be used as an a-priori check to determine whether potentially expensive computations are necessary.Dedicated to Prof. Dr. Peter Haupt on the occasion of his 60th birthday     

Distribution characteristics of mechanical properties and correlation between the respective properties on S35C carbon steel

Mechanical properties of tensile strength, , upper yield stress, _SU, lower yield stress, _SL elongation, , area reduction, , Vickers hardness, H _v, and impact absorbed energy, E, were examined using 50 specimens of S35C carbon steel, which were machined from two bars supplied from the same charged and heat-treated material. Distribution characteristics of these properties are discussed, and the correlation between each pair of them is investigated from a statistical viewpoint. The main conclusions obtained are summarized as follows; distribution characteristics of _B, _SL, , , H _v and E are well approximated by a normal distribution, but those of asu are not approximated as well by this type of distribution. In the latter case, a Weibull distribution is preferable to represent the distribution pattern. No significant correlation was observed between each pair of the above mechanical properties. Consequently, individual properties have the inherent distribution characteristics independent of the other properties.     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

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.     

A process model for active brazing of ceramics

In the present investigation process modelling techniques have been applied to describe reaction layer growth during active brazing of ceramics. As a starting point, the classical solution for parabolic growth of transformation products is considered. Specific computational features are then explicitly built into the model to allow for transient effects during heating and cooling as well as changes in the growth kinetics due to depletion of the active element during brazing. This approach gives considerable scope for optimization of both process and joint properties through adjustment of the filler metal composition and the temperature-time programme under which brazing takes place. The aptness of the process model is illustrated in an accompanying paper (Part II).Nomenclature A, C B reaction products in diffusion couple - C A ceramic component - C reactive element in braze alloy - C _B concentration of element B at a given position within the reaction layer, C B (mole m^–3) - C _B ^b bulk concentration of element B in ceramic, A B (mole m^–3) - C _B ⁱ (1), C _B ⁱ (2) concentration of element B in reaction layer at C B /A B and braze metal/C B interface, respectively (mole m^–3) - C _C concentration of element C at a given position within the reaction layer, C B (mole m^–3) - C _C ⁰ initial concentration of element C in braze metal (mole m^–3) - C _C ^b bulk concentration of element C in braze metal (mole m^–3) - C _C ⁱ (1), C _C ⁱ (2) concentration of element C in reaction layer at braze metal/C B and C B /A interface, respectively (mole m^–3) - D ₀, D ₀ ^* constants in expression for diffusion coefficient (m² s^–1) - D _B intrinsic diffusivity of B in C B (m² s^–1) - D _C intrinsic diffusivity of C in C B (m² s^–1) - J _B molar flux of element B (mole m^–2 s^–1) - J _C molar flux of element C (mole m^–2 s^–1) - k ₀ constant in expression for k_p (m² s^–1) - k ₀ ^* rate constant referring to infinite diffusion couple analogue (m² s^–1) - k _p parabolic growth rate constant (m² s^–1) - L half width of braze metal zone (m) - m proportionality constant (equal to the ratio between C _C ⁱ (1) and C _C ^b ) - Q _app apparent activation energy for diffusion of C in C B (J mole^–1) - Q _app ^* apparent activation energy for diffusion of B in C B (J mole^–1) - R universal gas constant (8.314 J mole^–1 K^–1) - t time (s) - t ₀ incubation time (s) - t ₁, t ₂ limits of integration (s) - t _i isothermal hold time (s) - t _i time increment used in the numerical integration procedure (s) - T absolute temperature (K or °C) - T _c chosen reference temperature (K or °C) - T _i isothermal hold temperature (K or °C) - X thickness of reaction layer (m) - X _c contribution of the cooling leg of the brazing cycle to the total reaction layer thickness (m) - X _h contribution of the heating leg of the brazing cycle to the total reaction layer thickness (m) - X _i contribution of the isothermal hold period to the total reaction layer thickness (m) - X _lim limiting thickness of reaction layer, C B (m) - X _i increase in reaction layer thickness due to a small time increment t _i (m) - y ₁, y ₂, y ₃ molar partitioning factors - , , , , , ) molar stoichiometric factors - molar volume of reaction product, C B (m³ mole^–1)     

Methodology for the determination of the interfacial properties of brittle matrix composites

The interfacial properties of a glass-ceramic matrix composite (SiC/CAS) were determined from single-fibre push-out tests using the interfacial test system. The coefficient of friction, , the residual clamping stress, _c, and fibre axial residual stress, _z , were extracted by fitting the experimental stress versus fibre-end displacement curves using the models of Hsueh, and Kerans and Parthasarathy. Using Hsueh's model, the intrinsic interfacial frictional stress (=_c) was found to be 11.1±3.2 MPa, whereas by using Kerans-Parthasarathy's model it was found to be 8.2±1.5 MPa. Comparisons between these models are included, together with a discussion of data analysis techniques.Nomenclature _z Axial fibre residual stress (Pa) - ^* Effective clamping stress (Pa) - _c Residual clamping stress (Pa) - _p Poisson's effect-induced clamping stress (Pa) - _d ⁰ Debond stress in the absence of residual stresses (Pa) - _d Experimental debond stress (Pa) - Compressive applied stress (Pa) - Interfacial shear stress (Pa) - u Fibre-end displacement (m) - h Debond length (m) - r Fibre radius (m) - E _f Fibre Young's modulus (Pa) - E _m Matrix Young's modulus (Pa) - v _f Fibre Poisson's ratio (dimensionless) - v _m Matrix Poisson's ratio (dimensionless) - f Fibre volume fraction (dimensionless) - k Parameter (dimensionless) - D Parameter (dimensionless) - Interfacial coefficient of friction (dimensionless) - G _i Interface toughness (J m^–2) - C _m Load-train compliance (m N^–1)     

A boundary layer theory for the end problem of a circular cylinder

Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a mid-surface radius of cylinder - c half-height of cylinder - E, in-plane elastic moduli - E_t, _t, G_t transverse elastic moduli - _z, , _r axial, circumferential, and normal strain - _rz transverse shear strain - h cylinder thickness - _z, , _r axial, circumferential, and normal stress - _rz transverse shear stress - z, r axial and radial coordinates - u_z, u_r axial and normal displacements     

Underpinning of a simple blunt flaw fracture initiation relation

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius . The relation gives the critical elastic flaw-tip peak stress _pcr, and has been derived using a two-extremes procedure, whereby the separate, and indeed exact, solutions for small and large s/ values are blended together to give an all-embracing relation that is valid for all s/ values. _pcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, _pcr essentially depends on only one geometrical parameter . This paper provides underpinning for the general thrust of the two-extremes procedure by appealing to exact results for the complete spectrum of s/ values from analyses of appropriate Mode III models. Results obtained by applying the two-extremes procedure are shown to be in very good agreement with the exact results.