Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

Extrudate distortion studies of polystyrene using an extrusion rheometer

Uncorrected and corrected logarithmic flow-curves for a general purpose polystyrene (MW=261000 and MW/MN=4.4) obtained using a Davenport Extrusion Rheometer are shown for the range 160 to 200° C. The uncorrected flow curves show a change in slope, but at the lower extrusion temperatures this change occurs after the appearance of distorted extrudates. The onset of extrudate distortion obtained from observation does not coincide with the change in slope of the graph. The corrected logarithmic flow curves show no change in slope. Values of and _c from both sets of graphs show that is inversely proportional to _c, and for the higher melt temperatures the corrected _c values increase with temperature. The high value of critical wall stress at 160° C is attributed to the increase in melt elasticity with decreasing temperature being a greater effect than the decrease in elasticity due to a decrease in .     

On the serrated yielding in Cu-14.1 at%AI polycrystals

Cu-14.1 at %Al polycrystals with three different grain sizes (76,113 and 157 m) have been tested for the Portevin-LeChatlier effect under various conditions of temperature (–196 to 200°C) and strain rate (2.78 × 10^–5 to 5.56 × 10³ sec^–1). In the above range of strain rate, serrated yielding was observed in the temperature range 60 to 160° C. The strain rate dependence of the onset of serrations is most probably due to the diffusion of vacancy-solute atom pairs, as indicated by the low value of the activation energy for migration (0.77 eV). The correlation governing the test variables at the onset of serrations appears to be: = (const)₀ ^{2.2 ± 0.2 –0.87 + 0.03}, where , ₀ and are strain rate, critical strain for the onset of serration and grain size, respectively. The onset of serrations is most probably due to dynamic strain ageing, although the possibility of short range ordering is not ruled out.On leave from Mechanical Engineering Department, Ferdowsi University, Mashhad, Iran.     

Effect of phosphorus additions on the spacing between primary silicon particles in a Bridgman solidified hypereutectic Al-Si alloy

The effect of 100 ppm addition of phosphorus on primary silicon particle number density per unit area N _A and corresponding interparticle spacing is reported for a Bridgman solidified Al-20 wt%Si base alloy. The phosphorus (added as Al-Fe-P base or Al-Cu-P alloys) results in a factor of 3 increase in N _A and a factor of 2 reduction in for the range of conditions studied. In its absence the results conform to = 256 ± 24 m (K/s)_1/3 where is cooling rate during solidification in good agreement with earlier data. When published data on the effect of 0.02 to 0.2 wt%P are included the combined results are well represented by = 250 – 215 (wt%P)^0.17 ( in m, in K/s).     

Effect of superplastic deformation on the grain size and tensile properties of Al-6.2Zn-2.5Mg-1.7Cu (7010) alloy sheet

An Al-Zn-Mg alloy (7010) was cold-rolled and annealed to produce a small recrystallized grain size, and superplastically deformed in the temperature range 475 to 520° C at strain rates to 2.8×10^–3 sec^–1. At 500° C and sec^–1 superplastic elongations up to 350% were obtained, but above about 60% elongation the residual room-temperature tensile properties after heat treatment decreased due to increasing grain-boundary cavitation. Grain growth rates were increased by superplastic strain.     

Metadynamic recrystallization of austenitic stainless steel

Interrupted torsion tests were performed in the temperature range of 900–1100°C, strain rate range of 5.0 × 10^–2–5.0 × 10⁰/sec and interpass time range of 0.5–100 seconds to study the characteristics of metadynamic recrystallization (MDRX) for austenitic stainless steel. To compare the MDRX with static recrystallization (SRX), the pass strain was applied above the critical strain (_c) (_c = 2.2 × 10^–3 D^1/2 ₀ Z ^0.089, where Z is Zener-Hollomon parameter, Z = exp((380000 J/mol)/RT) and D ₀ is as-received grain size) to obtain the MDRX during interpass time. It was found that the kinetics of MDRX were dependent of the strain rate and deformation temperature but were nearly independent of the change in pass strain after the peak strain. The time for 50% metadynamic softening, t ₅₀, was determined as follows: t ₅₀ = 1.33 × 10^{–11 –0.41} D ₀ exp((230000 J/mol)/RT) and this calculated value was consistent with the measured value. The Zener-Hollomon parameter was impossible to evaluate the MDRX fraction, because the fractional softening values were different at the same Z values. The new parameter (MDRX parameter) considering deformation temperature, strain rate and interpass time was proposed to evaluate the MDRX fraction. The MDRX-parameter was determined as 3.25 × 10^{–19 0.3} t _i ^0.6 T ¹².     

Load relaxation studies of germanium

A series of compressive load relaxation experiments were conducted on germanium single crystals in the temperature range 400 to 885° C. The curvature of the log-log data obtained from load relaxation tests changes from concave upward to concave downward as the test temperature increases at fixed stress level, or as the strain level increases at fixed temperature. At intermediate temperatures, 600° C, the transition from concave upward to concave downward curvature happens on a single relaxation curve. These observations are consistent with the two-branch rheological model proposed by Hart to explain the deformation behaviour of metals and were analysed in terms of this model. The transition from concave upward to concave downward curvature could be moved to higher temperature by doping germanium with gallium, which decreases the dislocation glide velocity relative to that in pure germanium. The transition could be shifted to lower temperature by compressing samples along [1 1] rather than [1 0] because the [1 1] orientation favours cross-slip while the [1 0] orientation does not. Dislocation dipoles and straight dislocations dominated the microstructure of samples which had concave upward log-log curves, while well-developed dislocation cell structures dominated the microstructure of samples which yielded concave downward curves. The observed changes in the curvature of the load relaxation curves and the dislocation structure both indicate the increased importance of dislocation climb with increasing temperature. When compared through the Orowan equation, the load relaxation results are in good agreement with published stress-dislocation velocity data.     

The influence of antimony-additions on the creep behaviour of a 25wt% Cr-20wt% Ni austenitic stainless steel

The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate, , decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature _a Creep stress in a constant load creep test without stress-drop - _A Initial applied stress in stress-drop tests - Stress decrement - ( _A-) Applied stress after a stress decrement, - t _i Incubation time after stress drop (by the positive creep) - _C Strain-arrest stress - _i Internal stress - _{s s}-component (= _i- _c) - Steady state creep rate (average value) in a constant load creep test - Strain rate at time,t, in a constant load creep test - New steady state creep rate (average value) after stress drop from _A to ( _A-) - Strain rate at time,t, after stress drop.     

Static recrystallization kinetics of 304 stainless steels

Static restoration mechanism during hot interrupted deformation of 304 stainless steel was studied in the temperature range from 900 to 1100°C, various strain rate from 0.05 to 5/sec and pass strain of 0.25–3 times peak strain. It was clarified that the static recrystallization was happened after 3–10 seconds at first deformation. The static restoration was depended on the pass strain, deformation temperature and strain rate and fractional softening (FS) values increased with increasing strain rate, deformation temperature and pass strain. Recystallization kinetics was explained with Avrami equation and Avrami constant was 1.113. This value was independent of deformation variables significantly. The time of 5, 50, 95% recrystallization was evaluated using such equations: t _0.05 = 2.9 × 10^{–12 –1.17 –0.94} D exp(222000 J/mol/RT), t _0.5 = 2.0 × 10^{–10 –1.56 –0.81} D exp(197000 J/mol/RT), t _0.95 = 1.9 × 10^{–8–1.63 –0.76} D exp(173000J/mol/RT). The predicted values by use of upper equations had a good agreement with a measurement.     

The constant stress tensile creep behaviour of a superplastic zirconia-alumina composite

A detailed study was conducted to evaluate the constant stress tensile creep behaviour of a superplastic 3 mol% yttria-stabilized zirconia-20 wt% alumina composite. The comprehensive experimental results indicate that creep deformation may be expressed in the form exp(–585 000/8.3T), where is the steady-state creep rate, is the imposed stress, is the linear intercept grain size andT is the absolute temperature. Microstructural observations revealed that there is very little dislocation activity, or change in grain size or shape. A detailed analysis was conducted to evaluate the possible rate-controlling mechanisms in terms of the experimentally determined mechanical properties and the microstructural observations. Based on the maintenance of an equiaxed microstructure and the strong grain size and stress dependence, it is concluded that creep occurs by a grain-boundary sliding/grain rearrangement process.     

Parafluidity in helium near the λ-transition and the generalized time-dependent Landau theory

A phenomenological theory of parafluidity, i.e., an enhancement of fluidity due to order-parameter fluctuations, is presented for helium near the transition. The generalized time-dependent Landau theory of second-order phase transitions is reviewed in general and is applied to the superfluid transition in helium as a particular example. In helium, it is found that parafluidity is manifested in the divergences of the mass diffusivity , the thermal conductivity , the first-sound amplitude attenuation ||^–1, and the second-sound dampling , which are all consistent with the dynamic scaling hypothesis. Here a characteristic relaxation time ₀ ||^–1 is used, where =(T–T _c )/T _c andT _c is the transition temperature. Although there are not enough experimental data to confirm our formulas, the present approach is seen to agree in order of magnitude with available experiments. Finally, the sound absorption above a ferromagnetic transition is calculated by adding a diffusion term to the generalized time-dependent Landau equation. The result thus obtained agrees in order of magnitude with experiments in nickel.Supported in part by the National Science Foundation and the Horace H. Rackham School of Graduate Studies.     

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.     

Electrical conduction of partially stabilized zirconia Zr0.94Ca0.06O1.94 as a function of temperature and oxygen partial pressure

Partially stabilized zirconia (PSZ), Zr_0.94Ca_0.06O_1.94was prepared by a hot kerosene drying method and a conventional oxide wet-mixing method. The total d.c. conductivities of these zirconia specimens were measured by the three-terminal technique as a function of temperature in the range 1088 to 1285 K and oxygen partial pressure in the range 1 to 10^–24 bar. The specimen prepared by the hot kerosene drying method showed near oxygen ion conduction with four times higher conductivity than the specimen prepared by the conventional mixing method at T=1088–1285 K and bar. The higher oxygen pressure conductivity tended approximately towards a to dependence, indicative of p-type conduction, whereas the lower oxygen pressure conductivity tended to be virtually independent of oxygen pressure, indicative of oxygenion conduction. The activation energy was found to be 130 kJ mol^–1 at T=1088–1285 K, bar (air) for pure electron-hole conduction and 153kJ mol^–1 at T=1088–1285 K for ionic conduction.     

The high temperature creep deformation of Si3N4-6Y2O3-2Al2O3

The creep properties of silicon nitride containing 6 wt % yttria and 2 wt% alumina have been determined in the temperature range 1573 to 1673 K. The stress exponent, n, in the equation ⁿ was determined to be 2.00±0.15 and the true activation energy was found to be 692±25 kJ mol^–1. Transmission electron microscopy studies showed that deformation occurred in the grain boundary glassy phase accompanied by microcrack formation and cavitation. The steady state creep results are consistent with a diffusion controlled creep mechanism involving nitrogen diffusion through the grain boundary glassy phase.     

Anisotropic flow and fracture in beryl [Be3Al2(SiO3)6]

Flow and fracture resulting from Vickers indentation testing on {0 0 0 1} and {10 0 } planar orientations have been examined. Flow characterized by indent shape differentiation was analysed to belong to the slip system with planes of the types { 10 0} and {11 0}. The ensuing fracture paths were resolved to propagate along {1 0 0} and {1 1 } cleavage planes whileK _c values obtained for them were 0.196 and 0.248 MPam^1/2, respectively.     

Grain growth behaviour of the Al-Cu eutectic alloy during superplastic deformation

Grain growth behaviour of the Al-Cu eutectic alloy was investigated as a function of strain (ε), strain rate and deformation temperature (T) over = 10⁻² s⁻¹ and T=400 to 540°C. The grain size increases with increase in strain and temperature. Upon deformation to a fixed strain, the grain growth is generally seen to be more at lower strain rates. The rates of overall grain growth and due to deformation alone , however, increase with increasing strain rate according to and , respectively. The increase in the grain growth rate with strain rate is attributed primarily to the shorter time involved at higher strain rate for reaching a fixed strain. The activation energy for grain growth under superplastic conditions is estimated to be 79 kJ mol⁻¹.     

Heat flux measurement from the temperature field of a heated surface. 2. Inhomogeneous flux

Based on the previously obtained analytical solutions of the three-dimensional space-time problem of recalculating boundary conditions, algorithms are developed and a computational experiment is carried out to reconstruct the heat flux with arbitrary spatial distribution of the temperature field of the heated surface.Notation T(t, ) temperature over the plate surface - q(t ) heat flux to the plate surface - ={x,y} transverse coordinate - t time - k thermal conductivity - a ² thermal diffusivity - L plate thickness - Jacobi theta-function [4] - Fourier parameter - Jacobi theta-function [4] - transversal Laplacian Institute of Atmospheric Optics, Siberian Division, Russian Academy of Sciences, Tomsk, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 622–628, July–August, 1995.     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

Creep and densification during anisotropic sintering of glass powders

The isothermal sintering behaviour of a barium magnesium aluminosilicate glass powder at 930°C was investigated using a heating microscope. The cylindrical samples exhibited a variable shrinkage anisotropy during sintering. The shrinkage anisotropy ratio, defined as the ratio of the relative change of height and diameter, varied linearly between 0.3 and 0.98 with the relative volume shrinkage during densification. Shrinkage anisotropy caused creep deformation of the samples. The creep rate varied exponentially with the densification rate and the ratio of creep to densification rates, , decreased as densification proceeded. This is in disagreement with most previous studies, which show a constant value of during the densification. Overall, the study points out the relevance of variable shrinkage anisotropy and how it affects the densification behaviour of glass powders.     

Structural aspects of α/β transformation in hot deformed CuZn-39Pb3 alloy

Hot compression tests were performed on commercial CuZn39Pb3 alloy deformed at strain rate of 0.0007 s^–1and 0.02 s^–1within temperature range of 923 K–1023 K. Flow stress vs. deformation temperature and strain rate dependence was found to follow the relation: . Both dynamic recovery and dynamic recrystallization have operated in the presence of fine lead particles being responsible for effective flow stress reduction with increasing deformation temperature. Transformation of - to phase above the temperature approx. 1000 K and the following fast cooling of hot deformed samples produced fine, plate-like structure of -grains, within retained -matrix. Moreover, coherent fine Fe-particles were observed within -grains being not detected at any area of -matrix. The last effect was supposed to result from lower solubility of iron in -phase than that for -phase.