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 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.     

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.     

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.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Growth of aluminium nitride whiskers by sublimation-recrystallization method

Aluminium nitride (AlN) with various morphologies was fabricated through a sublimation-recrystallization method. The influences of type of reactor and temperature gradient were explored, as well as the orientations and growth mechanism of the obtained AlN whiskers. In the early stage of preparation, a vapour-liquid-solid (VLS) mechanism dominated, producing AlN pillars, whiskers and noncrystalline fibres. In the later stage, as the catalyst liquid was removed by volatilization, the pillars and noncrystalline fibres stopped growing, but the growth of AlN whiskers continued through a vapour-solid (VS) mechanism. By Laue method and rotating-crystal method of x-ray diffraction, together with electron diffraction, most of the AlN whiskers were discovered to grow on planes , or , where l=0, 1, 2, 3, along crystal axes , or , where w=0, 1, 2, 3. Oblique grown whiskers also appeared, with a growth direction at an angle of about 54° to the growth plane, .     

Effects of phase fluctuation on a mixture of rotating superfluids

It is shown that if the root-mean-square of the gradient of the phase fluctuation of either of the components exceeds the corresponding inverse of the coherence length or if the chemical potential exceeds ₁ ⁰ or ₂ ⁰ , where is the volume integrals of the interaction function between the components, and ₁ ⁰ , ₂ ⁰ are the densities of the two components, the mixture of two rotating superfluids has an instability.     

Morphological characterization of selectively overgrown GaN via lateral epitaxy

Morphology as well as the dislocation networks in epitaxial GaN thin film, prepared via selectively lateral overgrowth has been characterized using TEM combined with focused ion beam (FIB) tool. The results showed that orientations of the sidewalls dependent on the orientations of mask strips. The sidewalls coincide with the planes that form V type voids when the mask strips aligning along directions and correspond to the planes that result in rectangular voids if the strips arranging along the directions. The dislocations were observed along the plan view direction. The dislocations in the lateral overgrown region mainly developed along the direction perpendicular to the strips. The genetic aspect of such morphologies of GaN films may have very close relation with the change of growing fronts of the epitaxial layer.     

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep =dH _ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln with the slope m/ ln , numerically equal to the relaxation rate m/ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH _ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate with the critical state at some timet _eff after a step change ofH _ext. The values of analyzed in our experiments actually correspond to the critical state at timest _eff between0.04 and4 sec after an imaginary large step change ofH _ext.     

Transmission electron microscope study of a directionally solidified Cu-MgCu2 eutectic

The crystallography and the interface structure of a unidirectionally solidified Cu-MgCu₂ eutectic alloy have been examined by transmission electron microscopy. The microstructure of the eutectic was found to be lamellar and regularly interrupted by faults. The preference of the particular orientation relationship could not be explained by relative atomic densities of the planes comprising the interface. Based on the defect contrast observed and extinction distance calculations, it is suggested that the fine array of defects observed at the interface may be characterized as steps with step vectors parallel to or Dislocations were also observed at the interface but they were rarely regular.     

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.     

Compressive creep of Si3N4/MgO alloys

The compressive creep behaviour of four compositions within the Si₃N₄-Mg₂SiO₄-Si₂N₂O compatibility triangle were studied in air at 1400° C. Strain rate ( ) versus stress () was analysed to determine the stress exponent, n ( ). Cavitation during creep was determined by precise (sink-float) density measurements. Compositions close to the Si₃N₄-Si₂N₂O tie line exhibited no cavitation and had n1, whereas compositions close to the Si₃N₄-Mg₂SiO₂ tie line exhibited extensive cavitation and had n2. Test results are interpreted in terms of the volume fraction of the viscous phase present.     

Polypropylene nucleation on a glass fibre after melt shearing

Thermoplastic composites may exhibit a wide range of crystalline morphologies in the neighbourhood of fibres. It was found that glass fibre shearing of a molten polypropylene at high temperature modifies the subsequent isothermal crystallization (T _c=122°C) under static conditions. The crystallization results have been analysed as a function of the previous high temperature, shear, , shear rate, , and shear stress, . The mechanical parameters at high temperature, , , , have been calculated for two shearing temperatures (T=170, 210°C) and two fibre displacements. An -phase nucleation process took place at the fibre surface after shearing at the higher temperature (T=210°C). The nucleation increased with shear but did not appear for static conditions. A strong nucleation process in phase appeared on the fibre surface after shearing of the polymer at the lower temperature (T=170°C). These strong morphological modifications with shearing temperature have been analysed as a function of mechanical and thermodynamical parameters.     

Relation between processing,microstructure and mechanical properties of rheocast Al-Cu alloys

The role of microstructure in modifying the tensile strength of rheocast Al-10 wt % Cu and Al-4.5 wt % Cu is investigated by modelling these products as particulate composites. The tensile strength of rheocast AI-10 wt %Cu alloy is found to depend on experimentally determinable parameter which is an undefined function of the size distribution of proeutectic -particles. These products, however, possess lower strength than the conventional casting at equal porosity level. The tensile strength of the rheocast AI-4.5wt%Cu alloy shows an inverse square root dependence on the proeutectic -particle size, , and therefore appropriate rheocasting process parameters may be employed to bring about grain refinement in order to produce rheocastings possessing higher strength than the conventional casting at equal porosity level.     

Thermodynamic properties of iron doped beta″-alumina by e.m.f. measurements with beta-alumina electrolytes

Thermodynamic studies of the non-stoichiometric iron doped beta-alumina (ID) phase were carried out by electrochemical measurements coupled with coulometric titration using the cell Na_liq/Li-alumina/ID. Hot pressing and glass sealing techniques were developed and employed to obtain a suitable and stable Li-alumina/ID interface. The equilibrium e.m.f. of the cell was determined as a function of sodium concentration over the temperature range 444 to 523 K. The range of sodium concentrations over which the ID phase is stable was also determined. The relative partial molar thermodynamic quantities of sodium, , , and in ID alumina as a function of sodium concentration were obtained from cell e.m.f. 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.     

Calculation of the optical characteristics of radiation heat transfer in furnace chambers

A software system for calculating the problems of radiation heat transfer in two-phase media is considered. Results of the calculation of a radiation field in the combustion chamber of a specific steam generator are presented.Notation I(x, y, ) spectral intensity of radiation at the point (x, y) in the direction - B(T) spectral intensity of black body radiation at the temperature T=T(x, y) - , spectral coefficients of absorption and scattering of radiation - external normal to the boundary of the region - and T spectral emissivity factor and temperature of the heat-absorbing surface - Q density of the radiation flux incident on the chamber heat-absorbing surface Academic Scientific Complex A. V. Lyukov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 308–312, March, 1993.     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Surface polarity and symmetry in semiconducting compounds

The polarity of the crystallographic surfaces of semiconducting compounds with the sphalerite and wurtzite structures results in gross differences in macroscopic chemical, mechanical and crystal growth behaviour which are reviewed. The asymmetry of the orthogonal 1 1 0 directions in {100} surfaces of sphalerite structure materials is manifested in phenomena arising from {1 1 1}A- B differences. To treat these phenomena the surface polarity index and the singular surface polyhedra for sphalerite- and wurtzite-structure semconducting compounds are introduced.     

Solidification of aluminium-germanium alloys at high cooling rates

Aluminium-germanium alloys, covering the entire composition range, were subjected to rapid solidification by different techniques ranging from the gun technique of splat cooling to simple quenching of the melt in water. The constitution, microstructure and crystal structure of the alloys thus solidified under cooling rates varying from 10³ to 10⁷° C/sec were studied by standard optical, electron- and X-ray metallographic techniques.The solid solubility of Ge in Al could be increased from the equilibrium value of 2.8 at. % to a maximum of 7.2 at. %. In addition, two new non-equilibrium tetragonal phases ₁(a=12.91 to 13.11 Å,c=12.00 to 12.10 Å) and ₂(a=14.98 Å,c= 16.03 Å) could be obtained in alloys containing 15 to 40 and 40 to 80 at. % Ge respectively. In relation to the face-centred cubic solid solution, these appear to be made up of 30 and 52 unit cells, respectively, with the relations , and , .A new non-equilibrium constitution diagram connecting cooling rate with constitution at room temperature has been proposed and seems to explain all observations satisfactorily.