The effect of temperature on the fracture of two partially crystalline polymers; polypropylene and nylon

Brittle fractures in polypropylene and nylon were obtained in the temperature range –180 to –10° C and –160 to 20° C, respectively. The fracture toughness results of surface notches and single edge notches showed a remarkable thickness dependence. This effect was explained in terms of a plane strain (K _C1) and a plane stress (K _C2) toughness value using a bi-modal fracture analysis. While K _C1 in both materials was generally insensitive to temperature, K _C1 was temperature dependent showing substantial viscoelastic effects. In polypropylene, the linear relationship between K _C2 and temperature (7) was associated with the and processes over the same temperature range. In nylon, there was a one-to-one correspondence between the K _C2 changes and the tan peaks due to the and relaxation processes. Using a modified crack tip opening displacement (u) equation, i.e. u = ((K_C2 – K _C1 )/ _y )²e_y, where _y and e_y are the yield stress and yield strain respectively, a constant u criterion was found to describe the fracture behaviour of both materials in the temperature ranges of the and processes.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Nonisothermal film flow of a magnetizable liquid

The problem of the flow of a nonisothermal magnetizable liquid with a free surface in a nonuniform magnetic field is formulated and investigated theoretically by considering a specific example.Notation H magnetic field intensity - M magnetization - _o magnetic permeability of vacuum - I current (r, , z), cylindrical coordinates - (, gz) coordinates of free surface - R radius of current-carrying conductor - p pressure - v axial component of velocity - viscosity - R₁, R₂ principal radii of curvature of surface - surface tension - Q flow rate of liquid - G characteristic value of gradient of magnetic field intensity - density - g acceleration due to gravity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 881–885, November, 1979.     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

Relationship between thermal conductivity,speed of sound,and isobaric heat capacity of liquids

Using two liquids-water and toluene — as an example, the author determines the dependence of the coefficient of thermal conductivity on the speed of sound and isobaric molar heat capacity for high state parameters.Notation coefficient of thermal conductivity - u speed of sound - _S same for a saturated liquid - c isobaric molar heat capacity - density - p_s same, for a saturated liquid - p pressure - p_s same, for a saturated liquid - R gas constant - T absolute temperature - x coefficient of thermal activity - x _s same, for a saturated liquid - L, constants in Eqs. (1) and (2) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 311–314, August, 1980.     

Thermal conductivity of Grafoil from 0.2 to 3 K

The thermal conductivity of compressed exfoliated graphite was measured in the directions parallel (K ) and normal (K ) to the rolling plane, in the temperature range of 0.2–3 K. The temperature dependence was determined in both cases. ForK=aT ^b in the temperature range of 0.2–0.7 K we get values forb of 0.95 forK and 1.6 forK ; in the range 0.7–2 K we get 1.6 forK and 2.1 forK ; and in the range 2–3 K we get 1.9 forK . TheK temperature dependence forT<0.7 K is smaller than what would be expected. ForK , evaluations of lattice and electronic contributions show that below 0.7 K the thermal conductivity is basically electronic. Above 2 K, where results are found in the literature, our data are in good agreement with them.     

Deformation approach to the evaluation of the period of initiation and growth of fatigue macrocracks

We performed experimental investigation of the opening displacements of the contours of stress concentrators (notches and cracks) for various amplitudes of cyclic loading. On the basis of experimental results, we propose a new deformation parameter _t which is a function of the notch (crack) tip opening displacement , namely, _t /(+d*), where is the radius of the tip of the notch andd* is the characteristic size of the prefracture zone. It is shown that this parameter uniquely determines the number of cyclesN _l to the initiation of a fatigue macrocrack independently of the geometry of the specimens and stress concentrators in elastic and elastoplastic materials, i.e., the dependence of _t onN ₁ is a characteristic of the material. It is experimentally demonstrated that this dependence enables one to quantitatively describe the process of fatigue fracture both in the stage of initiation of macrocracks and their propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 7–21, September – October, 1995.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

Hole pockets in the doped 2D Hubbard model

The electronic momentum distributionn(k) of the two dimensional Hubbard model is studied for different values of the couplingU/t, electronic density n, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on 8 × 8 clusters shows that features consistent with hole pockets at momentak = (±/2,±/2) appear as the system is doped away from half-filling. Our results are consistent with recent experimental data for the cuprates discussed by Aebi et al. (Phys. Rev. Lett. 72, 5757 (1994)). In the range of couplings studied, the depth of the pockets is maximum at n 0.9,and it increases with decreasing temperature. The apparent absence of hole pockets in previous numerical studies of this model is explained.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

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.     

Scaling and dynamics of an interfacial crack front

We report on in situ observations with a high speed CCD camera of an in-plane crack propagating through a transparent heterogeneous Plexiglas block. The toughness is controlled artificially and fluctuates spatially as a random noise. A stable crack in mode I was monitored by loading the system by an imposed displacement. We show that the movement of the fracture front is controlled by local instabilities triggered by the depinning of asperities even for very slow loading. Development of crack roughness is described in terms of a Family-Vicsek scaling with a roughness exponent =0.60 and a dynamical exponent =1.2. We also study the system numerically using a Green function technique. We find =0.6 and =1.5 in contrast to earlier numerical studies that reported a much smaller roughness exponent 1/3. We discuss this discrepancy.     

Lower bounds for arithmetic networks

We show lower bounds for depth of arithmetic networks over algebraically closed fields, real closed fields and the field of the rationals. The parameters used are either the degree or the number of connected components. These lower bounds allow us to show the inefficiency of arithmetic networks to parallelize several natural problems. For instance, we show a n lower bound for parallel time of the Knapsack problem over the reals and also that the computation of the integer part is not well parallelizable by arithmetic networks. Over the rationals we obtain results of similar order and that the Knapsack has an n lower bound for the parallel time measured by networks. A simply exponential lower bound for the parallel time of quantifier elimination is also shown. Finally, separations among classesP _K andNC _K are available for fieldsK in the above cases.Dedicated to the Memory of Mario RaimondoPartially supported by DGICyT PB 89/0379 and POSSO, ESPRIT-BRA 6846     

On the proximity effect in a superconductive slab bordered by metal

The first Ginzburg-Landau equation for the order parameter in the absence of magnetic fields is solved analytically for a superconducting slab of thickness 2d bordered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f=/ depends only on the transversal spatial coordinate x, normalized with respect to the coherence length of the superconductor, provided the de Gennes boundary condition df/dx=f/b is used. The closed-form solution expresses x as an elliptic integral of f, depending on the normalized parameters d and b. It is predicted theoretically that, for b< and dd_c=arctan(1/b), the proximity effect is so strong that the superconductivity is completely suppressed. In fact, in this case, the first Ginzburg-Landau equation possesses only the trivial solution f0.     

Computational Modeling of the Optical Pumping of Solid‐State Lasers and the Heating of the Active Element with Allowance for Water Cooling

Twodimensional nonstationary models of optical pumping of a solidstate laser in the presence of a reflector and heating of a cylindrical or plane active element with water cooling have been described. The results of calculations of the spacetime dependence of the pumping rate and the temperature in the active element have been given for different versions of a neodymium laser with a crystalline active medium in laserdiode pumping.     

Tests of Predictive Viscosity Models for Pure Liquids

It is of considerable importance to be able to predict accurately the viscosity of liquids over a wide range of conditions. In the present work, the ability of the three-parameter generalized corresponding states principle (GCSP) for the prediction of the viscosity of pure liquids is demonstrated. The viscosity of six different classes of pure liquids, viz., alkanes (19 compounds; 207 data points), cycloalkanes (6 compounds; 74 data points), alkenes (9 compounds; 146 data points), aromatics (4 compounds; 123 data points), alkanols (8 compounds; 89 data points), and esters (4 compounds; 28 data points) have been predicted over a wide range of temperatures using the three-parameter (T _c, P _c, ) GCSP. Five options for the third parameter () were studied, viz., Pitzer's acentric factor , molar mass M, characteristic viscosity *, critical compressibility factor Z _c, and modified acentric factor , in addition to groups Z _c and Z _c being treated as composite third parameters. Pressure effects were neglected. Good agreement between experimental and predicted values of viscosity was obtained, especially with either or * being used as the third parameter. Furthermore, the viscosities of alkanes predicted by the TRAPP method and an empirical, generalized one-parameter model for liquid hydrocarbons provide comparisons with the more accurate GCSP method. The GCSP provides a simple and yet a powerful technique for the correlation and prediction of viscosities of a variety of pure liquids over a wide range of temperatures.     

Radiofrequency size-effect measurements of the electron scattering frequency in cadmium

Precise parallel- and tilted-field radiofrequency size-effect measurements of the temperature dependence of the electron scattering frequency v(T) have been made on symmetric orbits on the first-, second-, and third-band Fermi surface sheets in samples with normals 11\-20 and 10\-10. The limiting point measurements on the third-band lens near 0001 provide the clearest evidence for a T ² contribution to v(T) that is the right order of magnitude for electron-electron scattering in cadmium. In parallel field measurements on orbits on the first and second bands (including a broken orbit) we find v(T) T ² + T ³. On these orbits the values for are 5–20 times larger than for the limiting point and other orbits on the third band. The temperature dependence of v(T\> 2 K) on extremal, limiting point, and open orbits on the second- and third-band Fermi surface sheets can be well accounted for by a simple plane wave model for electron-phonon intersheet scattering. This contribution to v(T) turns on approximately as exp (–T _t /T) above T _t /10, where T _t is the minimum gap temperature on the orbit for intersheet scattering by quasi-transversely polarized phonons. The fitted gap temperatures as well as the other parameters of the plane wave model agree well with the known dimensions of the Fermi surface of cadmium. While clear evidence is lacking, we note that this intersheet scattering model can also be used to explain the large T ² coefficients obtained for the first- and second-band orbits, where, in fact, one has gap temperatures T _t smaller than 1 K.Supported by the Fonds National Suisse de la Recherche Scientifique.     

Numerical Calculation of the Flow Regimes of a Fluid Partially Filling a Horizontal Rotating Heat‐Exchange Cylinder

Consideration is given to a numerical determination of a twodimensional unsteady viscous flow with the free surface in a stationarily rotating horizontal cylinder in which heatexchange processes are carried out. The markerandcell method in a polar coordinate system is used. The features of modeling of the walllayer regime and the circulating flow regime that occur in rapid and slow rotation of the cylinder, respectively, are discussed. Based on the given results of numerical calculations, the influence of the Reynolds number on the character of flow is analyzed.     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.