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.     

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.     

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, .     

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.     

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.     

The activation energy for superplastic flow in Al-6Cu-0.4Zr

A study of the activation energies for superplastic flow in an essentially single phase Al-6Cu-0.4Zr alloy has been made in the temperature range 430 to 490° C. Straight line Arrhenius plots for bothQ and were obtained in Regions I, II and III. In all cases the ratio corresponded well to the average strain rate sensitivity as determined by both change rate testing and from the slope of the In versus In curves. Values ofQ of 35.2, 19.0 and 20.1 kcal mol^–1 were obtained in Regions I, II and III respectively. These values were expected to be close to the true activation energies, and corresponded to the measured lattice and predicted grain boundary diffusion activation energies. These energies, together with microstructural observations made on deformed material, were used to identify possible deformation mechanisms.     

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.     

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     

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.     

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.     

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.     

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).     

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.     

Effects of grain-boundary configuration on the high-temperature creep strength of cobalt-base L-605 alloys

The effects of grain-boundary configuration on the high-temperature creep strength are investigated using commercial cobalt-base L-605 alloys with low carbon content in the temperature range 816 to 1038° C (1500 to 1900° F). Serrated grain boundaries are formed principally by the precipitation of tungsten-rich b c c phase (the same as ₂ phase found in Ni-20Cr-20W alloys) on grain boundaries by a relatively simple heat treatment in these alloys. The creep rupture properties are improved by strengthening of grain boundaries by the precipitation of tungsten-rich bcc (₂) phase. The specimens with serrated grain boundaries have longer rupture lives and higher ductility than those with normal straight grain boundaries under low stress and high-temperature creep conditions, while the rupture lives and the creep ductility of both specimens are almost the same under high stresses below 927° C. The matrix of the alloys is strengthened by the precipitation of carbides at temperatures below 927° C and by the precipitation of tungsten-rich ₂ phase at 1038° C during creep. It is found that there is an orientation relationship between tungsten-rich a2 phase particles and-Co matrix, such that (0 1 1)₂ ¶ (1 1 1) _-Co and [1 1]₂ ¶ [1 0] _-Co. The fracture surface of specimens with serrated grain boundaries is a ductile grain-boundary fracture surface, while typical grain-boundary facets prevailed in specimens with straight grain boundaries.     

Effect of precipitate type and morphology on high-temperature creep and internal stress in Al-Li based alloys

The tensile creep of a series of aluminium-lithium-based alloys, two binary alloys containing precipitate, and the 2090 alloy containing and T₁ precipitate, has been studied over a range of stresses at 150°C. In some cases the internal stress developed during creep has been determined using the strain transient dip test. The results have been compared with similar data previously obtained for the 8090 alloy containing and S precipitates. The solid solution alloy and the binary alloy containing shearable particles exhibited normal Class II behaviour, with the development of sub-grains and a stress dependence of the creep rate given by a single stress exponent,n, between 4 and 5 at all applied stresses. The alloys containing particles not easily sheared by dislocations, coarse , S and T₁, exhibited similar stress dependencies of the creep rate at low stresses but exhibited large values ofn, between 18 and 35 at high stresses. The internal stress, _i, in these alloys was found to be approximately constant at high stresses possibly due to partial shearing of the coarse , T₁, and the S on sub-boundaries. The stress dependence of the minimum creep rate, , could be represented at all applied stresses, _a, by , where (_a–_i) is the effective stress driving dislocations during creep, andn is a single stress exponent of between 5 and 6 for all applied stresses. The internal stress, which increases with applied stress, at least at a low applied stress, arises from inhomogeneity of plastic deformation, due to hard sub-boundaries or hard particles which are Orowan looped. These two types of contribution to the internal stress are of similar magnitude in the alloys containing coarse and T₁ but the majority of the internal stress in the 8090 alloy may arise as a result of the hardening of sub-boundaries by the S precipitate.     

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.     

Rheological behaviour and modelling of semi-solid Sn-15% Pb alloy

The rheological behaviour and modelling of a semi-solid, Sn-15% Pb alloy characterized by a special coaxial-cylinder rheometer over a wide range of process conditions is reported. In particular, the effect of shear rate , volume fraction of solid (f _s), and cooling rate on the apparent viscosity () of the semi-solid Sn-15% Pb alloy under isothermal and various cooling conditions was studied. Based on the experimental data, the shear rate used in preparing the semi-solid alloy as well as the volume fraction of solid have the most dominant effects on the rheological properties of the semi-solid Sn-15% Pb alloy. A viscosity model expressed as is proposed in which f _s ^* is the critical solid fraction at which the apparent viscosity goes to infinity, (F _s) corresponds to the asymptotic viscosity at infinity shear rate, and characterizes the transition shear rate between the power-law and Newtonian regions. finally, measurements with a differential scanning calorimeter were made and used to correlate the temperature and volume fraction of solid which, in turn, was corroborated with available data from the literature.     

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.     

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.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures