Effect of Grain Size on the Modulus of Elasticity and Strength of Synthetic Graphites

The effect of the grain size of the filler on the mechanical properties (compressive, bending, and tensile strength and modulus of elasticity) of synthetic graphite is analyzed using data for commercial structural graphites. As the mean particle size of the filler (_av) decreases from 3000 to 1 m, the modulus of elasticity increases, on the average, from 10 to 15 GPa, and the compressive, bending, and tensile strength increases by about one order of magnitude. The Griffith equation is used to evaluate the size of defects that initiate fracture (c _c) in different types of graphites. It is shown that the factors determining the critical defect size depend on the particle size of the filler. For _av > 150 m, c _c is comparable to _av or _max. In the range 30 < _av < 150 m, c _c is equal to or greater than _max. In graphites with _av < 30 m, c _c far exceeds _max and, presumably, corresponds to the particle size of the molding powder.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Brittle matrices reinforced with polyalkene films of varying elastic moduli

The inclusion of polyalkene films of different moduli in a cement-based matrix has shown the benefits to be gained, in terms of increased stress at a given strain, from the use of films of high elastic modulus. Further, the concept of load-bearing cracks is used to explain the transition region between the limit of proportionality and the bend-over point on the tensile stress-strain curve, which is found to exist with high film modulus composites. This transition region could be an important factor affecting the choice of film to be used in a commercial composite.Nomenclature E _c uncracked composite modulus - E _m matrix modulus - E _f film modulus - V _m matrix volume-fraction - V _t film volume-fraction - V _f(crit) (E _{c mu})/ _fu - A _c cross-sectional area of composite - (E _m V _m/E _fV_f) - _m matrix strain - _mu matrix cracking strain - _mu average matrix cracking strain, (#x03C3;_co)/E _c - _mc strain at end of multiple cracking - _fu ultimate fibre stress - _cu ultimate composite stress - _co average composite cracking stress (assumed at a strain of _mc/2) - S4 81 draw ratio polypropylene film - S8 181 draw ratio polypropylene film - E3H polyethylene film - LOP limit of proportionality (stress at first crack, assumed to be a departure from linearity of the tensile stress-strain curve of a perfectly straight and uniform test specimen. However, this point cannot be reliably determined from the stress-strain curve because of the clamping strains induced in warped specimens) - BOP bend-over point (stress at which the approximately horizontal portion of multiple cracking region commences. The BOP is generally higher than the LOP and is a much more reliable point to determine experimentally than the LOP)     

Mechanical properties in the initial stage of sintering

Silicon nitride-based ceramics with different compositions were sintered in the 60%–90% range of theoretical density. Linear correlations between the apparent density and the modulus of elasticity, the three- and four-point bend strengths or the Vickers hardness, were observed. The slopes of the straight lines were nearly the same for all compositions. Furthermore, the modulus of elasticity, hardness, fracture toughness and strength were calculated as functions of density by modelling the structure as a random arrangement of spheres as suggested by Fischmeister and Arzt. The relationships obtained have been compared with the measured ones.Nomenclature a average contact area - a _c increase of the area of a crack - A area of the reference plane - b size of the critical defect - c constant in Equation 4 - D density - D ₀ density before shrinkage - D _T theoretical density - e direction of macroscopic strain - E modulus of elasticity - E ₀ modulus of elasticity of the dense material - f force loading a contact - f() projection of force f to e - F force loading the reference plane - g geometry parameter in the Griffiths relationship - H hardness - K _IC fracture toughness - N number of particles in unit volume - N() the fraction of N in a given spherical angle - n() number of particles in the volume around the reference plane - P porosity - R initial particle radius - R particle radius after fictitious growth - R particle radius after redistribution of material - R _SQ shared correlation coefficient - S surface energy of the defect - vector connecting the centres of neighbouring particles - W work necessary for increase the area of a crack - Z average coordination number - Z ₀ initial coordination number - strain - _T strain at theoretical strength - strength - _T theoretical strength (limit of elasticity) - angle between v and e     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

Fatigue properties of pure metals

The report considers the stress fatigue limit _D, the fatigue to tensile strength ratio _D/R_m, and the deformation fatigue limit _D of pure metals. For FCC and some HCP metals there exists a linear correlation between fatigue limit and tensile strength. The fatigue limit and the fatigue ratio _D/R_m depend upon the homologous temperature. The fatigue ratios of BCC metals are higher than the fatigue ratios of other metals at room temperature as is also true for metals with nearly the same homologous temperature. The deformation fatigue limit decreases rapidly when T_h - 0.5 and T_h 1. When T_h = 1 then _D = 0, _D = 0 and _D/R_m = 0. The deformation fatigue limits of metals belonging to the same subgroup of the periodic element system and having, similar homologous temperatures at room temperature are very similar.

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Zusammenfassung Der Artikel behandelt die Dauerfestigkeit _D des Ermuedungskoeffizienten _D/R_m und die Deformation _D, die der Dauerfestigkeit entspricht. Fuer kubisch flachzentrierte Metalle und einige hexagonal Metalle existiert eine lineare Korrelation zwischen Dauerfestigkeit _D and Zugfestigkeit R_m. Die Dauerfestigkeit _D und der Ermuedungskoeffizient _D/R_m koennen als Funktion der homologischen Temperatur betrachtet werden. Der Ermuedungskoeffizient der kubisch raumzentrierten Metalle ist groesser als der der anderen in Raumtemperatur. Dieses stimmt auch fuer Metalle mit aehnlichen hornologischen Temperaturen. Die Deformation _D, die der Dauerfestigkeit entspricht, faellt schnell ab, wenn T_h > 0.5 und T_h 1, Wenn T_h = 1, darn ist _D = 0, _D = 0 und _D/R_m = 0. Die Metalle, die zu derselben Gruppe des periodischen Systems der Elemente gehoeren and aehnliche homologische Temperaturen (in Raumtemperatur) besitzen, haben sehr aehnliche Werte der Deformation _D.

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Résumé L'article parle de la contrainte de la limite de fatigue _D le facteur de fatigue _D/R_m et la déformation _D correspondante à la limite de fatigue des métaux pures. Pour les métaux du système cubique aux faces centrées (c. f. c.) et quelques uns du système hexagonale (hex. c.) il existe une correlation linéare entre la limite de fatigue _D et de la résistance a la fraction R_m. La limite de fatigue _D et le facteur de fatigue _D/R_m dependent de la température homologue. Les facteurs de la fatigue des métaux du système cubique centre (c.c.) sort plus grands que ceux des autres métaux dans la température de chambre, aussi por des métaux qui ont presque la même température homologue. La déformation correspondante à la limite de fatigue tombe rapidement quand T_h > 0.5 et T_h 1. Quand T_h = 1, alors _D = 0, _D = 0 et _D/R_m = 0. Cettes déformations _D pour les métaux du même groupe du système périodique des éléments sont proches si les températures homologues dans la température de chambre sont analogues.

     

Heating of a newtonian liquid when extruded through a matrix

Calculations are carried out of the dynamic forces and viscous heating when a layer of Newtonian liquid at the bottom of a rigid container is extruded through a matrix in the form of a circular opening or a narrow slit.Notation r, z axes of a Cartesian (k=0) or a cylindrical (k=1) system of coordinates - u, v velocity components of the liquid in the directions r and z, respectively - V velocity of the liquid in the opening - p pressure - ₁ and ₂ temperature of the liquid under the die and in the opening - m, n rheological constants of the material - tangential stress - shear velocity - _o, c_p, _o density, heat capacity, and thermal conductivity of the liquid - S, M, w area of the working surface, mass and velocity of motion of the die - r_o,l,a, R linear dimensions of the matrix and the container - F operating force on the instrument - Re, Pe similitude criteria Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 710–715, October, 1980.     

The anomalous thermal boundary resistance in superfluid4He near Tλ

The anomalous thermal boundary resistance R of superfluid⁴He near the lambda point T was studied in a cell with parallel copper faces and with various fluid layer thicknesses. The study was made as a function of the heat current Q and reduced temperature (T — T)/T = . In all cases, R tends to a maximum value R_itmax at T = T. This value is independent of Q, and is reproducible for various experiments. This contrasts with the regular boundary resistance which can vary considerably between successive experiments. Near T, the limiting slope dR/d¦¦ is found to be proportional to Q^–1, and this leads to a scaled representation of the data. This analysis is extended to data of similar experiments with gold plated copper surfaces by Duncan and Ahlers and by Zhong et al. The measurements of R over the whole range of¦¦ where it is observable are discussed and compared with previous experiments.     

Influence of Microstructure on the Strength and Cyclic Crack Resistance of Cast Irons

We study the influence of microstructure of high-strength cast irons of ferritic, ferritic-pearlitic, and pearlitic classes on the characteristics of strength and cyclic crack resistance and establish the relationship between the characteristics of strength and cyclic crack resistance and the chemical composition and microstructural parameters of the matrix and graphite inclusions of high-strength cast irons. Indeed, the ultimate strength _u = 750–850 MPa, fatigue threshold K _th = 8–10 MPa , and cyclic fracture toughness K _fc = 50–60 MPa are guaranteed by the pearlitic matrix and the following parameters of the graphite phase: the content of graphite f _p 10%, the degree of its spheroidization of about 95%, the size of globules d _gl 20–50 m, and the distance between them 40–70 m, obtained in high-strength cast irons containing (wt.%): 3.2–3.5 C, 1.9–2.5 Si, 0.35–0.4 Mn, and 0.05 Mg.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu : Mg ratio alloys the main phases found were , , S and T₁, while fewer T₂ and Al₇Cu₂Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T₁ precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu : Mg ratio alloy the addition of 0.2 wt % Ag resulted in the precipitation of phase simultaneously with , , S and T₁ phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed.     

Study of dielectric and electrical properties of mortar in the early hydration period at microwave frequencies

The dielectric constant, , and electrical conductivity, , of mortars with various sand-cement ratios,s/c, were measured for the first 30 h hydration using microwave techniques in the frequency range 8.2–12.4 GHz. The and of the mortars were found to increase linearly with increasing water-solid ratiow/(s + c), but decrease with increasings/c. It was found that as long as thes/c values were the same, the rate of changes in and of the mortars were the same. It appears that thes/c is the key factor controlling the rates of changes in dielectric and electrical parameters of cement hydration in mortar. The relationship between compressive strength and dielectric and electrical properties of mortars was also discussed.     

Photoplastic effects in Cd0.2Hg0.8Te

We irradiated Cd_0.2Hg_0.8Te samples at room temperature in the plastic range, with a CO₂ laser beam the wavelength of which (=10 500 nm) is 20% longer than the absorption threshold. We observed a positive photoplastic effect (PPE) of the order _PPE/4 to 5%.     

Study of the relationship between J-integral and COD parameters under mixed mode I + II loading in aluminum alloy Ly 12

In this paper, the relationship between the J-integral and COD under mixed mode I+II loading was proposed and investigated. The J-integral was calculated by the Finite Element Method, and COD was defined by Rice`s model and measured by a duplicating method in an aluminum alloy Ly12. The critical values of the J-integral and COD for a stable mixed crack initiation were also determined by a resistance curve. It shows that: (1) the mixed J-integral, J _M, and the mixed COD satisfy the relations of J _M=dn₀CTOD+ds₀CTSD and J _M=d_yieldCOD, where dn, ds and d are coefficients; CTOD and CTSD are the mode I and mode II components of COD, respectively; ₀ and ₀ are the tensile and shear stresses at the crack tip strip, respectively, and (2) the initiation values of the J-integral and COD of mixed stable crack growth increase with an increasing mode II component, the J _IIC value is 2 times greater than that of J _IC, and the COD_i for a pure mode II crack is 6 times greater than that of COD_i for a pure mode I crack.     

Microstructural characterization of cast nickel aluminium bronze

The morphology and chemical analysis of the complex phases present in cast nickel aluminium bronze, of nominal composition 10% aluminium, 5% nickel and 5% iron, have been investigated using optical and electron microscopy techniques and energy dispersive analysis. It has been shown that , and four forms of can exist in the ascast microstructure of this alloy. Heat treatment can lead to the precipitation of a further phase which differs in morphology and chemical composition to those present in ascast structures.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Dielectric Dispersion in Yttrium and Erbium Formate Dihydrate Crystals

The dielectric properties of Y(HCOO)₃ · 2H₂O and Er(HCOO)₃ · 2H₂O are studied. The frequency dependences (0.01 Hz to 20 kHz) of the real () and imaginary () parts of dielectric permittivity ( = – i) are shown to follow a fractal scaling law for the dielectric response of solids. In the tan versus temperature curves, a number of maxima are revealed in a narrow temperature range. The experimental data are used to evaluate the activation energies of relaxation processes. The observed anomalies are assumed to be associated with changes in the dynamics of protons in hydrogen bonds.     

A simple model to explain the geometry dependence of J−Δa-curves

Very different patterns of geometry effects may occur if in a bend type specimen the ligament length is increased at constant specimen thickness. These geometry effects can be explained by a model of the total crack growth resistance R which is defined as the sum of the non-reversible energy which must be put into a body to produce an increment of crack area. The relationship between R and the commonly used J–a-curves is worked out. The model shows that a wider-lower pattern, i.e. the case where an increase of the ligament length causes a flatter J–a-curve, appears for fracture under lefm conditions or for contained yielding where R is independent of the geometry. A wider-no effect or a wider-higher pattern may be observed if the crack extension occurs at the plastic limit load and if either plane strain or plane stress conditions prevail.