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.     

Creep behaviour of polyethylene and polypropylene

Tensile creep tests and stress reduction studies during creep have been carried out for polyethylene and polypropylene. The results obtained suggest that a consistent approach for the presentation of creep data for these polymeric materials can be obtained since the creep curves at 293K for polyethylene and polypropylene over a wide stress range can be superimposed by describing the variation of creep strain,, with time,t, as= ₀ + _p [1 – exp (–K t)] + t, where ₀ is the initial strain on loading, _p is the primary creep strain, is the secondary creep rate, andK is a constant.     

Heat flow model of rapid solidification with nonhomogeneous thermal contact

A heat flow model is presented of the solidification process of a thin melt layer on a heat conducting substrate. The model is based on the two-dimensional heat conduction equation, which was solved numerically. The effect of coexisting regions of good and bad thermal contact between foil and substrate is considered. The numerical results for thermal parameters of the Al-Cu eutectic alloy show considerable deviations from one-dimensional solidification models. Except for drastic differences in the magnitude of the solidification rate near the foil-substrate interface, the solidification direction deviates from being perpendicular to the substrate and large lateral temperature gradients occur. Interruption of the thermal contact may lead to back-melting effects. A new quantity, the effective diffusion length, is introduced which allows some conclusions to be drawn concerning the behaviour of the frozen microstructure during subsequent cooling.Nomenclature _i ,a _i Thermal diffusivity _i = _i /c _{i i} ,a _i = _i / ₁ - c _i Specific heat capacity - d Foil thickness - D Solid state diffusion coefficient - e_x, e_z Unit vectors - H Latent heat of fusion - h ,h Foil-substrate heat transfer coefficients - i Index: 1, melt; 2, solidified foil; 3, substrate - _i ,k _i Thermal conductivityk _i = _i / ₁ - n Normal unit vector - Nu ,Nu Nusselt numbers for regions of badNu(x,) and good thermal contact, respectivelyNu =h Nu _d / ₁,,Nu(x, )=h(x,)d/ ₁ - R Universal gas constant - , s Position of the liquid-solid interface ¯s/d=s=s _xe_x+s _ze_z - Local solidification rate /d = s =s _xe_x +s _ze_z - t Real time - T _i Temperature field - T ₀ Ambient temperature - T _f Melting temperature - u _i Dimensionless temperature fieldu _i (x, z,)=T _i (x,z,)/T _f - u ₀ Dimensionless ambient temperatureu ₀=T ₀/T _f - _i Local cooling rate within the foil _i = du _i /d - W Stefan numberW=H/c ₁ T _f - ,x Cartesian coordinate parallel to the foil-substrate interfacex= /d - ₀,x ₀ Lateral extension of foil sectionx ₀= ₀/d - ₁,x ₁ Lateral contact lengthx ₁= ₁/d - ,z Cartesian coordinate perpendicular to the foil-substrate interfacez= /d - ₀,z ₀ Substrate thicknessz ₀= ₀/d - E Activation energy of diffusion - T Initial superheat of the melt - u Dimensionless initial superheat u=T/T _f - (x) Step function - _eff Dimensionless effective diffusion length - _i Mass density - Dimensionless time=t ₁/d ² - _f, _f(x, z) Total and local dimensionless freezing time, respectively     

Size effects and ductile-brittle transition of polypropylene

The influence of specimen width on fracture parameters has been investigated. The range examined was sufficiently large to obtain ductile and brittle fractures. With reference to previously published work, the phenomenology has been analysed by combining BCS model and Carpinteri's brittleness number approach.Nomenclature a crack length - f(a/W) shape function according to ASTM specification [16] - F(a/W) shape function according to Tada Paris notation [21] - E elastic modulus - K _IC plane strain fracture toughness - K _IC ^f fictitious plane strain fracture toughness - K _IC2 plane stress fracture toughness - J _IC ^f J-integral at maximum load - L span - weight average molecular weight - number average molecular weight - polydispersity - P _M maximum load - P _F load of brittle fracture - p _P load of plastic collapse - s brittleness number - V machine cross speed - W specimen width - _y yield stress - strain rate     

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     

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.     

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.     

The activation areas for creep deformation

The activation areas for creep deformation are collected and examined in the light of many material and deformation variables. The activation area is A ^*= (kT/b) ( In /^*) _T where k is Boltzmann's constant, T the absolute temperature, b the Burgers vector, the steady state creep rate, and ^* the effective shear stress. It is found that within a factor of 5, there is a general correlation between activation area and stress for all metals, alloys, semiconductors and ionic crystals. A jog-limited dislocation motion with a distribution of jog spacings is suggested as a possible mechanism for this behaviour. Some limitations for the jog mechanism are discussed.     

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).     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

The laminar stagnation-point flow against a solidifying moving shell

Summary This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.Nomenclature A suction velocity in boundary layer variables - a jet width [m] - c specific heat of the solid metal [J/m³K] - h Newtonian heat transfer coefficient [W/m²K] - k velocity gradient in units ofU/a - m dS ^*/dX ^* local inclination of the solidifying phase - S ^* (L)/L average slope of the solidifying phase - S ^* local thickness of the solidified phase [m] - S, S local thickness of the solidified phase in units ofL and , resp. - T absolute temperature [K] - T _f fusion temperature of metal [K] - T ₀ temperature of cooling water [K] - U jet velocity [m/s] - V belt velocity [m/s] - +i complex velocity potential in units ofUa - x coordinate tangential to the solidifying interface in units ofa - X ^* coordinate tangential to the belt [m] - X, X coordinates tangential to the belt in units ofL and , resp. - y coordinate orthogonal to the solidifying interface in units ofa - Y ^* coordinate orthogonal to the belt [m] - Y, Y coordinates orthogonal to the belt in units ofL and , resp. - z x+iy complex coordinates in units ofa - unit vector along the belt - unit vector orthogonal to the belt - local unit normal vector to the solidifying interface - h _f latent heat of fusion of metal [J/m³] - thermal diffusivity of solid metal [m²/s] - belt velocity in units ofU - { _n }, { _n } asymptotic sequences of the outer and inner expansion, resp. - m suction velocity outer variables - velocity potential in units ofUa - jet inclination relative to the local solidifying interface - coordinate orthogonal to the solidifying interface in units of - x c thermal conductivity of solid metal [W/mK] - displacement thickness in units of - v kimematic viscosity of liquid metal [m ²/s] - arctan (dS ^*/dX ^*) local angle of inclination of the solidifying interface - =(T–T ₀)/(T _f –T ₀) dimensionless temperature - perturbation parameter - coordinate tangential to the solidifying interface in units ofa/k - stream function in units ofUa - magnified stream function valid within the boundary layer - solidification constant Dimensionless parameter P _eL VS ^* (L)/ Peclet number - Q h/(cV) Heat flux number - R Ua/v Reynolds number - St Stefan number     

Study of flow in a smectic liquid crystal in the X-ray Surface Forces Apparatus

We describe the newly invented X-Ray Surface Forces Apparatus (X-SFA) which allows the simultaneous measurement of forces and collective structures of confined complex fluids under static and flow conditions. The structure of the smectic liquid crystal 8CB (4-cyano-4-octylbiphenyl) f confined between two mica surfaces with separation ranging from 4000 to 20,000 A was measured. At small gaps and no shear, the smectic layers take on distinct stable orientations, including the bulk forbidden h orientation. which persist under low shear ( 30 s^–1). However, at higher shear rates 360 s^–1) the shear acts to dramatically order and align the smectic layers into a singlea orientation.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

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     

Effect of non-stoichiometry on the sintering of doped TiO2

The sintering of TiO₂ has been studied with respect to oxygen partial pressure ( ) and doping content. From the microstructural evolution, it is obvious that a decrease of the oxygen pressure promotes the densification with a comparatively smaller grain growth than in air sintering. This fact has been related with the influence of defects on the sintering. Both effects of and tantalum doping have been studied. They are interpreted on the basis of a model involving interstitial titanium, electron holes, titanium vacancies and complexes associating titanium vacancies with tantalum substituted titanium. This latter complex is probable according to previous microscopic studies of defects in TiO_2–x and may be important in highly doped compounds. The formation of such associates reduces the mobile defect concentration, however a decrease of the favour their dissociation. The titanium vacancies which are thus released allow the titanium ions to migrate, a necessary condition for the sintering.     

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.     

The influence of grain size,stress and temperature on the steady state creep of a 25 Cr-20 Ni austenitic stainless steel without precipitates

This work was performed in order to study the steady state creep behaviour of a modified 25 Cr-20 Ni stainless steel which has no precipitates. The test temperature range was 1171 to 1211 K, the stress range 4.9 to 19.6 MPa, and the grain size was 40 to 600m. The steady state creep rate, , decreases with increase in grain size, especially at the lowest stress; is proportional to 1/d ² at 4.9 MPa, whered is a mean grain diameter. The variation of with grain size is smaller in the middle and coarse-grained specimens than in the fine-grained specimens, the stress exponent,n, gradually decreases from ~ 4 to ~ 1.5 with reducing stress, but in the middle- and coarse-grained specimens, a discontinuous point appears on a log versus log plot. The activation energy for the steady state creep of the coarse-grained specimens tends to be larger than that of the fine-grained specimens, and the tendency is remarkable in the higher stress level. It is indicated that the creep mechanisms in the fine-grained specimens are essentially different from those in the coarse-grained specimens, and that the creep at the lowest stresses and smallest grain size is similar to that predicted by a vacancy creep model involving grain-boundary diffusion.     

Tunneling with very long relaxation times in glasses,organic materials,and Nb-Ti-H (D)

The long-time (t=10–200 h) heat release from glasses, from organic materials, and from Nb-Ti-H (D) was measured at 30T70 mK. For Suprasil W glass, Dimethyl-Siloxan, Stycast 1266, Stycast 2850 FT, Vespel, and for Nb-Ti-H (D) with various Ti and D concentrations, we found . Typical values are = 0.05 nW/g for the organic materials and for Nb-Ti-H (D) and = 0.005 nW/g for the glass att=100 h after cooldown from room temperature. For charging temperaturesT _i <5 K, we find the predicted dependence (investigated for Suprasil W glass and for Nb-Ti-D). The observed time and temperature dependences agree with predictions of the conventional two-level tunneling model for amorphous materials even at these very long times. No heat release was observed for Teflon, graphite, and Al₂O₃.     

Structure evolution in the Cu-Fe system during mechanical alloying

High-resolution electron microscopy was used to examine the structure evolution of Cu-60 at % Fe powder mixture during mechanical alloying. Fracture and refinement of particles, the lamellar structure formed by cold-welding, and nanocrystals, were all observed at atomic scale. The X-ray diffraction patterns show that the Bragg peaks from the b c c phase decrease obviously in intensity after 3 h milling and entirely disappear after 5 h milling. Lattice images of the products obtained after 3 h milling reveal that there are Nishiyama-Wasserman orientation relationships between the b c c and f c c phases, i.e. (001)//(110), [1 0]//[1 2] and [110]//[ 11] . It is likely that for a mechanically alloyed iron-rich powder mixture, ball milling induces a reverse martensitic transformation of b c c Fe(Cu) to f c c Fe(Cu) phase. The greatly extended f c c phase range is closely related to this transformation. After 5 h milling, nanocrystals with sizes about 10 nm are formed.     

Higher approximations for supersonic flow past slowly oscillating bodies of revolution

Summary Supersonic flow past slowly oscillating pointed bodies of revolution is studied. Starting from the complete nonlinear potential equation an elementary linearized solution is discussed and it is shown how this solution together with the method of matched asymptotic expansions can be used to derive an elementary second-order slender body theory. This approach is further demonstrated for the oscillating cone and its range of validity is evaluated by comparison with other theoretical methods.

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Zusammenfassung Es wird die Überschallströmung um langsam schwingende spitze Rotationskörper untersucht. Ausgehend von der vollständigen nichtlinearen Potentialgleichung wird zuerst eine elementare linearisierte Lösung besprochen und gezeigt, wie diese Lösung im Verein mit der Method of matched asymptotic expansions zur Herleitung einer elementaren Schlankkörpertheorie zweiter Ordnung verwendet werden kann. Die Theorie wird am Beispiel des schwingenden Kegels näher erläutert und mit anderen Methoden verglichen.

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Symbols a Velocity of sound - c _N Normal force coefficient - Damping coefficient - F _(x) Dipole distribution - k Reduced frequency - M Mach number - R (x) Meridian profile - t Time - x, r, Cylindrical coordinates - - Ratio of specific heats - Amplitude of oscillation - Thickness ratio - Perturbation potential - Zero angle of attack potential - æ - Velocity potential - Out-of-phase potential - - In-phase potential - - Source coordinate With 4 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 .