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.     

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.     

Failure crack orientation at ductile shear fracture of Fe80−x Ni x B20 metallic glass ribbons

Orientation of failure cracks of oblique mode at ductile shear fracture are measured for Fe_80–x Ni _x B₂₀ (x=10, 20, 30, 40, 50, 60) metallic glass ribbons (MGR) uniaxially extended with strain rate from 3.3×10^–6 to 1.25×10^–3 s^–1 at temperatures 300, 77 and 4.2 K. An angle between the failure crack and tension axis is found to depend non-monotonously on nickel concentrationx and strain rate . These dependences are probably due to the presence of dilatancy in shear bands and its variation as a function of concentration, strain rate and temperature.Mean values of quenching stresses in ribbons are estimated by comparing experimentally measured values and those predicted by T. Thomas in 1953.     

The effect of particles on the critical strain associated with the Portevin-LeChatelier effect in aluminium alloys

The effect of particles on the critical strain, _c, associated with the Portevin-LeChatelier (PL) effect of aluminium alloys is studied using Al-Mg-Ni and Al-Si alloys. Al-Mg-Ni and Al-Si alloy matrixes are composed of Al₃Ni and Si particles, respectively. Tensile tests were performed in the temperature range 223–273 K in which the critical strain decreases with increasing temperature, and strain rates between 10^–5 and 10^–2 s^–1 were chosen. According to the apparent activation energies, Q, Mg and Si solute atoms are responsible for the flow instability in Al-Mg-Ni and Al-Si alloys, respectively. The experimental results also show that the critical strain decreases with decreasing particle spacing, d _p. Since the particle spacing is small compared to the corresponding grain size, the decrease in critical strain should be ascribed to the effect of particles. Considering that the dislocation density is increased by the particles, a modified model showing the critical strain, _c, as a function of particle spacing, d _p, is proposed as T ^–1 exp (–Q/kT), in which , T and k are the strain rate, temperature and Boltzmann constant, respectively. Linear fit of the plots of In _c versus In d _p and In _c versus In d _p indicates that this equation is appropriate to rationalize the particle effect on the critical strain.     

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.     

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.     

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.     

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.     

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.     

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.     

Distribution of extension rates of growth fronts along Rosiwal's line in the growing two-dimensional cell model

A growing two-dimensional cell model is defined as follows. In an area there are Poisson-distributed nuclei. Arising from these nuclei, grains start to grow simultaneously. All grains grow circularly with the same constant radial growth rate . During the process of growth no new nuclei are formed. If two grains touch each other, growth is stopped there by formation of a straight grain boundary. We arbitrarily put a straight line, called Rosiwal's line, into the area. While grains are growing many straight grain boundaries and circular growth fronts cross Rosiwal's line. At a fixed fraction transformed, F(=crystallized area/total area), we consider the different extension rates of growth fronts (growing borders) along Rosiwal's line, v( v<), in the left (or right) direction. The number of grains that have a growth front along Rosiwal's line into the left (or right) direction depends on F. Although the number changes with variation of F, we obtained theoretically the surprising result that the distribution density of reduced extension rates V = v/ , w(V), does not depend on F, and is always V ^–2(V ²–1)^–1/2. In order to verify this result we found an experimental possibility to realize the growing two-dimensional cell model.     

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     

Welding of thin steel plates: a new model for thermal analysis

A mathematical model for the transient heat flow analysis in arc-welding processes is proposed, based on a unique set of boundary conditions. The model attempts to make use of the relative advantages of analytical as well as numerical techniques in order to reduce the problem size for providing a quicker solution without sacrificing the accuracy of prediction. The variation of thermo-physical properties with temperature has been incorporated into the model to improve the thermal analysis in the weld and heat-affected zones. The model has been evaluated using a five-point explicit finite difference method for analysing the welding heat flow in thin plates of two different geometric configurations. The temperature distribution closer to the heat source, primarily in the weld zone and the heat-affected zones, are predicted by the numerical technique. The thermal characteristics beyond the heat-affected zone are amenable to standard analytical techniques. The behaviour of the boundary condition in the model has been investigated in detail.Nomenclature q Rate of heat per unit thickness (Wm^–1) - d Plate thickness (m) - v Velocity of source (m s^–1) - t Time (s) - T Temperature value at the desired point (K) - T ₀ Initial temperature (K) - K Thermal conductivity (W m^–1 K^–1) - Density (kg m^–3) - c _p Specific heat (J kg^–1 K^–1) - Thermal diffusivity (m² s^–1) - n - Distance of point considered from the source (=x–vt) (m) - K ₀ Modified Bessel function of second kind and zero order - r Radial distance from the source (r=(x ²+y ²)^1/2) (m) - Model width (m) - a Plate width (m) - Distance from the source =(²+4 ×10^–4)^1/2 (m) - _n      

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.     

A thermally stimulated current technique for measuring the molecular parameters of Pebax,a polyether-block amide copolymer

The primary relaxation peaks of Pebax copolymer having a soft segment, poly (tetramethylene glycol) (PTMG) and a hard segment, polyamide 12 (PA12) are located at –69.5 and 18° C for a raw sample and at –71.5 and 4° C when the sample is recrystallized after fusion using the thermally stimulated current (t.s.c.) method. A comparison is made of rapid and slow cooling t.s.c. on hard-segment molecules. Applying the fractional polarization method, the modes _PTMG and _PA have been analysed. The parameters (such as activation energy and relaxation time) associated with the dipolar relaxation process of Pebax have been calculated. The maximum energy observed for modes _PTMG and _PA is 1.47 eV at – 66° C and 1.34 eV at 1° Q respectively. The elementary processes that constitute the modes _PTMG and _PA obey a compensation law with compensation temperatureT _c = –43° C and compensation relaxation time _c, = 3.4 x 10^–2 sec for mode _PTMG, andT _c = 66° C and _c = 2.8 x 1 0^–4 sec for mode _PA.     

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).     

Creep of (Mg,Fe)O single crystals

The creep behaviour of (Mg, Fe)O single crystals compressed along 1 0 0 has been investigated over the temperature range 1300 to 1500° C, at stresses between 20 and 70 MPa, for oxygen partial pressures between 10^–4 and 10² Pa, and with iron concentrations between 70 and 11 900 p.p.m. Under these conditions, the dependence of the steady-state strain rate on stress, temperature, oxygen partial pressure, and iron concentration can be summarized by the flow law, exp (–445 kJ mol^–1/RT. These results suggest that the steadystate strain rate is controlled by dislocation climb with a jog velocity which is limited by lattice diffusion of oxygen by a vacancy pair mechanism. The activation energy for creep, 445 kJ mol^–1 is larger than that reported for self-diffusion of oxygen, 330 kJ mol^–1, because the formation energy for jogs is relatively large, 115 kJ mol^–1.     

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.     

Oxygen ion conduction in γ-Bi2O3 doped with Sb2O3

Electrical conduction in bcc-Bi₂O₃ doped with Sb₂O₃ was investigated by measuring electrical conductivity, as a function of temperature and oxygen partial pressure , and ionic transference number. The-Bi₂O₃ doped with 1 to 3 mol% Sb₂O₃ was stable up to 550° C and showed an oxygen ionic conduction in the region of 10⁵ to 10^–9 Pa. As the Sb₂O₃ content increased, ionic conductivity increased up to 2.5 mol % Sb₂O₃ (1.8×10^–3–1cm^–1 at 500° C) and then decreased. However, the activation energy for ionic conduction remained almost unchanged. It was proposed that the-Bi₂O₃ contains a lot of oxygen vacancies and incorporated Sb⁵⁺ ions at tetrahedral sites which affect the concentration of oxygen vacancy effective for conduction.     

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.