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.     

Swelling parameter of polypropylene used in household appliances

Samples of unfilled copolymer polypropylene were immersed in various solvents and the equilibrium swelling was recorded. Two-dimensional solubility maps of the Hildebrand parameter, , versus hydrogen bonding parameter, _c, and _h versus _v for polypropylene were plotted. Using the calculated percentage swell values and the solubility maps, the and _h values for detergent were postulated. No changes in the polypropylene backbone were revealed by mid- or far-infrared spectra, showing that the polypropylene polymer, when subjected to a number of different solvents, had not altered substantially.     

hp-version finite elements for the space-time domain

A bilinear formulation of elasto-dynamics is offered which includes, as a special case, Hamilton's law of varying action. However, the more general bilinear formulation has several advantages over Hamilton's law. First, it admits a larger class of initial-value and boundary-value problems. Second, in its variational form, it offers physical insight into the so-called trailing terms of Hamilton's law. Third, numerical applications (i.e., finite elements in time) can be proven to be convergent under correct application of the bilinear formulation, whereas they can be demonstrated to diverge for specific problems under Hamilton's law. Fourth, the bilinear formulation offers automatic convergence of the natural velocity end conditions; while these must be constrained in present applications of Hamilton's law. Fifth, the bilinear formulation can be implemented in terms of a Larange multiplier that gives an order of magnitude improvement in the convergence of velocity. This implies that, in this form, the method is a hybrid finite-element approach.List of symbols b arbitrary constant - A _i, A _i vector of integrals, i = 0, j - A() linear operator on - () Hamilton's form of A - B (u, ) bilinear operator u, - B (u, ) Hamilton's form of B - B _i,j , B _ij , B _ij matrix of integrals - C constant, N/m - c number of floating-point operations per coef. evaluation - f, f(x) force per unit length, N/m - F, F ₀, F _L forces, N - J number of functions in series for û - k spring rate per unit length, N/m² - K spring rate, N/m - K _max maximum value of K - L _a Lagrangian, non-dimensional - L length of beam, m - m mass per unit length, kg/m - M mass, kg - M _max maximum value of M - n number of functions in series for - N number of elements in domain - p momentum density, kg/sec - P, P ₀, P _T momentum, kg-m/sec - q _i generalized coordinates - r _j coefficients of _j - t time, sec - t ₀, t ₁ limits of action integral, Hamilton's law - T end of time period, sec - u solution for displacement, m - û approximation to u, m - u ₀ initial value for u, m - test function, m - limited class of , m - x spatial coordinate, m - flapping angle, rad - Lock number - time increment, sec - Lagrange multiplier - longitudinal stiffness EA, N (Eqs. 1–18) - advance ratio of rotor (Eqs. 33–34 and figures) - _i , _r polynomial functions - non-dimensional time, azimuth angle - () variation of ( ) - W virtual work - ( ) d ( )/dx - ( .) d ( )/dt - (*) d/d - [ ] matrix - { } column vector - row vector     

Effective permittivity of layered dielectric sphere composites

A straightforward model is presented for analysing the effective permittivities of layered dielectric sphere composites. Using the present model, the effective permittivity, _eff, of layered dielectric sphere composites can be deduced using classical two-phase dielectric mixture formulae in two steps: first, the effective permittivity, _incl, of the inclusions is calculated by taking the layered dielectric sphere inclusions as sub-composites; and second, the effective permittivity, eff, of the composites is found by substituting the layered dielectric sphere inclusions with homogeneous spheres whose permittivity is equal to _incl. The present model is applicable to multi-layer sphere composites. Experiments on resin-based hollow bead composites show that the present model accurately predicts the effective permittivity of layered dielectric sphere composites.     

Elastodynamic parameters for dynamic interface fracture mechanics

Summary Dynamic extension of cracks running along curvilinear interfaces of brittle bimaterials subjected to mechanical crack surface loads and superimposed thermal strains acting along the ligament is considered. This paper especially addresses the provision and discussion of elastodynamic interface parameters in order to assess quantitatively the bimaterial fracture in view of the governing physical features: applied mechanical and thermal strain loading, existence of an interface, crack-tip velocity and curvature of the interface contour. By utilizing the linear theory of thermoelasticity and adopting Stroh's method of generalized complex potentials, from the corresponding boundary and continuity conditions vectorial Hilbert problems are derived. It is shown that the parameters of the eigenvalues and of the eigenvectors of the Hilbert problems can be interpreted as elastodynamic interface mechanics parameters reading (,v _p, _Hf , _Hf ). Generalized Dundurs parameters of dynamics (, ) and consequently an associated generalized Dundurs diagram of dynamics are proposed. While the aforementioned elastodynamic interface parameters (, ,v _p, _Hf , _Hf ) do not assume the interface to be damaged, interfaces with running interface cracks generally cause two additional interface parameters, denoted as bimaterial constants (, _Hf ), where the latter is specific to the curvature of the interface in conjunction with the velocity of the interface crack. However, the bimaterial constants (, _Hf ) can be traced back to interface parameters for an uncracked bimaterial, namely to (, _Hf ).     

Interplay of Nuclear Magnetism and Superconductivity

The ratio of nuclear saturation magnetization and superconducting critical field, ₀ M _sat / B _S0*, classifies the strength of mutual influence of nuclear magnetism and superconductivity. In order to investigate the interplay of both phenomena for the three distinct cases 1, 1, and 1 we have measured the ac susceptibility of Al, of the intermetallic compound AuIn ₂ , and of the metal hydride TiH _2.07 at ultralow temperatures, 17 K T 1 K, as function of static field 0 B 15 mT. For Al, the interplay enables an absolute measurement of the nuclear magnetization. For AuIn ₂ , we get a steep decrease of B _S (T) and a broadening of the superconducting transition in its nuclear ferromagnetic phase. Surprisingly, the nuclear ferromagnetic state coexists with type-I superconductivity in AuIn ₂. The metal hydride TiH _2.07 , which is under present investigation, is a good candidate to show reentrant superconductivity.     

Polymorphism in Sr3Fe2O7−x

The compound Sr₃Fe₂O_7–x , with variable iron valence, was investigated by X-ray powder techniques, both at room and at high temperatures. If the material is examined in massive form, a single phase called -Sr₃Fe₂O_7–x appears as previously reported in the literature. This -phase is tetragonal and exhibits the lattice parameters: a=3.874 and c=40.314 Å. Two other phases, called and -Sr₃Fe₂O_7–x , respectively, can be obtained on heating the finely powdered material when laid on a flat platinum support. The form is stable up to 1275° C, while the form is revealed only above 1275° C and changes always into -Sr₃Fe₂O_7–x when quenched. Both and phases are tetragonal, with a=4.001 and c= 58.251 for the form and a=4.013, c=57.092 Å for the form. The transition involves a true phase equilibrium, while the transformation is possible only by means of a suitable mechanical treatment of the material.     

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.     

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

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

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

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.     

Coefficients of mass transfer between a fluidized bed and the surface of a capillary-porous body

Results are presented from a theoretical determination of coefficients of mass transfer between a fluidized bed of porous particles and a capillary-porous body.Notation a particle radius - F area of contact of particles with the surface of the body - f percentage of area of surface of product in contact with the bubble phase - g acceleration due to gravity - i flow of liquid mass from a unit area of the surface - N number of fluidizations - n number of particles coming into contact with a surface of unit area per unit of time - p_p, p_b capillary potentials of particles and product - R₂, R₁ radii of narrow and broad pores inside the product - r radius of capillaries in the particles - S area of the surface being treated - T temperature of the bed - t time of treatment - u percentage content of liquid in the specimen - V volume of the product being treated - v mean square component of the fluctuation velocity of the particles in the direction normal to the surface - , * standard and corrected mass-transfer coefficients determined from (5) and (9) - _b, _b, _p porosities of product determined for all and for only the small pores and the porosity of the material of the particles - _d, _m porosity of the dense phase and the porosity of the bed in the state of minimum fluidization - _b, _p angles of wetting of the materials of the product and particles, respectively, by the liquid binder - , viscosity and density of the liquid - ₀ density of the dry product - surface tension coefficient of the liquid - characteristic time of contact of particles with the surface - Re_m Reynolds number corresponding to particle radius and minimum-bed-fluidization velocity [6] Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 460–465, March, 1981.     

Excess energy in quenchedβ-Cu-Zn-Al alloys: relation to the martensitic transformation

The disorder-induced excess energy,L , of a-Cu_1– x)(ZnAl) _x (0.30 x 0.35) alloy, which shows a martensitic transformation at low temperature, after quenching from different initial temperatures,T _i, is calculated. Ordering-energi-es for the different nearest and next-nearest neighbour atom pairs, obtained by fitting mean field expressions of order-disorder critical temperatures to experimental data, are used. The excess energy is related to the changes of the latent heat of the martensitic transformation,L, observed just after quenching from T_i. It was found that the shift in latent heat correlates linearly with the calculated excess energy of the-phase. Calorimetric measurements justify the results.     

On the number of term orders

By an admissible order on a finite subsetQ of ⁿ we mean the restriction toQ of a linear order on ⁿ compatible with the group structure of ⁿ and such that ⁿ is contained in the positive cone of the order. We first derive upper and lower bounds on the number of admissible orders on a given setQ in terms of the dimensionn and the cardinality ofQ. Better estimates are possible if the setQ enjoys symmetry properties and in the case whereQ is a discrete hyperbox of the form In the latter case, we also give asymptotic results as d _k for fixedn. We finally present algorithms which compute the set of admissible orders that extend a given binary relation onQ and their number. The algorithms are useful in connection with the construction of universal Gröbner bases.AMS Classification: primary 06F20 secondary 06-04, 11N25     

Critical dynamics of a sheared micellar solution

We have investigated the dynamic behavior of a nonionic micellar solution of tetra-ethylene glycoln-decylether (C₁₀ E₄) in water near its critical point in the presence of shear. The non-Newtonian behavior of the viscosity can be represented by * = [ 1 +a(S₄)=]², where* is the viscosity in the absence of shear,S is the shear rate. ₄ is the lifetime of the critical Iluctuations,a is a system-dependent constant, and = 0.02 In addition, we have found that, before attaining a steady state, the sheared mixture undergoing phase separation shows significant shear-dependent rheological effects due to the presence of concentration domains.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24. 1994, Boulder, Colorado, U.S.A.     

The dielectric properties of glass-ceramic-on-metal substrates for microelectronics packaging

The dielectric properties of some glass-ceramic-on-metal substrates have been determined over the frequency range 500 Hz to 5 MHz using a.c. bridge techniques. The substrates consisted of cordierite-based glass-ceramics screen printed on molybdenum. For glass layers of thickness greater than 100 m both the permittivity, and the dielectric loss, , are frequency independent over this frequency range at room temperature giving the value of =6.5 and tan =8×10^–3; the room-temperature data are consistent with the universal law of dielectric response. The variation of permittivity with temperature has also been examined and, below 120 °C, the temperature coefficient [(–1) (+2)]^–1 (/T)_p, was found to be 1.3×10^–5 K^–1. The results are compared with those previously reported for Al₂O₃ and AIN substrates.     

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.     

Singular Band Behavior of the Extended Emery Model for the Superconducting Cuprates

Mean field slave-boson approximation is performed on the extended Emery model for the CuO₂ conducting plane. The model is parameterized by Cu–O charge transfer energy _pd , copper–oxygen overlap t ₀, oxygen–oxygen overlap t', and Coulomb interaction U on the copper site taken as infinite. Special emphasis is placed on the role of t in the renormalization trends of the effective band parameters _pf and t, replacing _pd and t ₀, at small doping . It is shown that small, negative t expands the range of stability of the metallic phase, changing, in the second order of the perturbation theory, the nature of the metal–insulator transition point. In the nonperturbative limit, t modifies strongly the renormalization of _pf , making it saturate at the value of 4t. Finite doping suppresses the insulating state approximately symmetrically with respect to its sign. The regime _pf 4t fits very well the ARPES spectra of Y123, Bi2212, and LSCO and also explans, in the latter case, the evolution of the FS with doping accompanied by the spectral weight-transfer from the oxygen to the resonant band.     

On a nonlinear stefan problem arising in the continuous casting of steel

Summary The continuous casting process employed in the steel industry is a many faceted big industrial problem which has given rise to many sub-problems. Here, we examine the problem involving the determination of the solid-liquid steel interface and we develop and extend a previously proposed model, which incorporates heat transfer through two layers of solid and liquid mould powder and the interface between the solid powder and the mould wall. The problem simplifies to the classical Stefan problem except that the condition on the boundary is nonlinear. Integral formulation procedures are used to establish the normalized pseudo steady state temperature as an upper bound to the normalized actual temperature. The pseudo steady state approximation yields an upper bound on the interface position, which an independent numerical enthalpy scheme confirms to be an extremely accurate approximation for the parameter values occurring in practice. The present work is important since it provides a simple method for the prediction of the solid-liquid steel interface and a bounding procedure which can be used to validate other estimates.List of symbols D flux thickness atz ^*=0 - H enthalpy - L latent heat of steel - M the half thickness of the cast steel - Q heat flux - R interface thermal contact resistance - S _m ^* melting temperature of steel - T ^* temperature - T normalized temperature - T _m ^* melting temperature of mould powder - T ^* temperature of cooling water - T _w ^* temperature on mould wall - T _u ^* temperature of solid flux on its interface with mould wall - T ₀ ^* temperature on casting surfaceT ^*(0,z ^*) - U casting speed - X ^*(z ^*) physical coordinate of the steel phase change boundary - X(z) non-dimensional coordinate of the steel phase change boundary - c specific heat of steel - h(z ^*) thickness of liquid flux layer - k thermal conductivity of steel - ks thermal conductivity of solid flux layer - k _l thermal conductivity of liquid flux layer - m surface heat transfer coefficient - s(z ^*) thickness of solid flux layer - t time - , , positive constants given by (3.2) - constant given by (3.5) - coefficient of linear thermal expansion of steel - angle shown in Figure 2 - positive constant defined by (M-D)/2 - (z) positive parameter - (z ^*) amount of contraction of steel - density - (z) positive parameter used in (5.7) and (5.8)     

Correlation of burst pressure of GRP cylinders with the stress wave factor

Glass fibre-reinforced plastic (GRP) cylinders are increasingly used for highly stressed structural elements. The higher the demands on the materials, the higher are the fault detection requirements to be met by non-destructive materials testing methods. Acousto-ultrasonics is a valuable aid for the non-destructive evaluation of GRP composite materials, because it may be the answer to evaluating effects of subtle defects in composites. The aim of the research is to evaluate the burst pressure of GRP cylinders by acousto-ultrasonics techniques. The theoretical results have been found to be in good agreement with the experimental values. Hence the results strongly suggest that stress wave factor measurements can be exploited successfully to predict burst pressure of GRP cylinders.Nomenclature P Internal pressure, kgf cm^–2 - d Internal diameter, cm - t Thickness of cylinder, cm - (N ,N ,N ) Resultant forces, kgf - (M ,M ,M ) Moments, kg cm - [A] Extensional stiffness matrix - [B] Bending stretching coupling matrix - [D] Flexural stiffness matrix - ( ⁰ , ⁰ , ⁰ ) Midplane strains - (k ,k ,k ) Curvatures - n Number of laminae - Z Distance from midplane, cm - _u Ultimate tensile strength of GRP composite, kg cm^–2 - S _W Stress wave factor - m Material parameter - Filament winding angle