Pure Polycrystalline Aluminum Research Articles

Strain rate sensitivity: The role of dislocation loop and point defect recovery

The strain rate sensitivity of nominally pure polycrystalline aluminum was precisely measured using a testing system which minimized the machine transient. The strain rate sensitivity vs temperature relation was determined over three decades of strain rate in the temperature range 247–333 K. The scatter in the averaged values was small enough that steps or plateaus in the ascending curve could be detected. The activation energy of 0.53 eV for the initial step is comparable to that of vacancy or divacancy migration. The increasing trend of strain rate sensitivity with temperature and the observed plateaus can be explained if a two obstacle model of discrete barriers is invoked whereby the recovery of the weaker one affects the force-distance relation of the stronger obstacle.

Internal stress measurments during the saturation fatigue of polycrystalline aluminum

The internal stress and the effective stress were measured using stress relaxation techniques for 99.988% purity polycrystalline aluminum containing a well-defined cellular dislocation microstructure characteristic of large amplitude low cycle fatigue. Room temperature stress relaxation measurements were carried out after cyclic saturation at constant plastic strain amplitude and constant total strain rate as a function of location within a particular hysteresis loop. Measurements of stress relaxation at the tensile and compressive hysteresis loop tips show the dependence of internal and effective stress on plastic strain amplitude and strain rate. Both the internal stress and the effective stress were found to exhibit cyclic behavior representable by a hysteresis loop on each strain reversal. The internal stress was insensitive to strain rate while the saturation stress and the effective stress showed significant rate dependences. Both the internal stress and the effective stress increased with strain amplitude. The stress sensitivity exponent of the strain rate was determined from the variation in the effective stress with rate both during a given hysteresis loop and during strain rate changes and was found to decrease with increasing strain amplitude. The findings are discussed in the context of dislocation velocity and mobile dislocation density contributions to the strain rate sensitivity from which it is suggested that the mobile dislocation density decreases with increasing strain amplitude and strain rate. Plastic strain changes during stress relaxation suggest that the mobile density during saturation fatigue is equivalent to one mobile dislocation segment per dislocation cell.

Deformation kinetics of steady-state creep in metals

The phenomenological constitutive equation given below, for uniaxial steady state creep, i.e. ϵ˙=K10e−ϵ0/kTsinhK2(σ−σ0)log16ϵ0kT−logK2(σ−σ0), has been derived from first principles and applied to AISI316 stainless steel, pure polycrystalline aluminum and copper. A single micromechanism has been found sufficient to predict the data throughout the entire test temperature and stress range.The equation above has an intrinsically atomic basis as it has been obtained through the notion of intermal variables in the context of the absolute reaction theory of Eyring. The physical meaning of the internal variables and the foundation of their associated evolution equations are established clearly in terms of averages of atomic motions over the energy barriers, under application of an external stress field. It is this concept that gives one hope that a sound thermodynamic and physical foundation of irreversible thermodynamics with internal variables has been found from microscopic considerations.

Microplastic bases for constitutive relations found in tensile testing

The microplastic model of plastic flow described by Nabarro, Basinski and Holt is extended to the tensile data of nominally pure polycrystalline aluminum at elevated temperatures. Between 0.25 and 0.4 of the melting temperature where the strain rate sensitivity S was found to become a function of the strain rate level and degree of strain rate change as well as temperature, the tensile data beyond 0.04 strain degenerates along a common line linearly relating log ( σ − σ 0) · dσr/ dϵ to log S( σ − σ 0). The implication of this master curve with slope a is that the mean slip distance is a simple function of the mean interobstacle spacing. Consideration of the theory of thermally activated flow leads to the same result that the activation distance is constant in this temperature range permitting the activation volume to be dependent only on the mean segment length. Thus the resultant work hardening law or constitutive relation is given as σ − σ o = KS −(x 2+z)ϵ(1 2−x) Continuous tests were performed over four decades of strain rate at various temperatures to determine S as a function of ϵ. Estimated activation energies coincide quite reasonably with those determined from creep suggesting that microstructural recovery is responsible for the temperature and strain rate dependence of S. Microstructural effects were clearly manifested in the form of extended uniform extension after imposing static recovery or work softening at a lower strain rate.

The stress and temperature dependence of steady-state flow at intermediate temperatures for pure polycrystalline aluminum

Torsion tests to large strains (ϵ = 3–10) in the intermediate temperature range (0.2−0.6 T m where T m is the melting temperature in degrees absolute) have been performed on high purity aluminum. Steady-state was reached at all temperatures except for 0.2 T m . Between 0.29 and 0.48 T m ä the activation energy for steady-state creep ( Q ss ) was found to be equal to about 87 kj mole −1 which corresponds quiteclosely to the activation energy for dislocation pipe diffusion as measured by Volin, Lie and Balluffi using a void shrinkage analysis. The relation between stress, σ ss, and strain rate, ϵ ss , in steady-state has been analyzed using an effective diffusion coefficient, D eff , for creep data over the temperature range 0.21-0.93 T m . The D heff utilized is based on all published diffusion data, namely two different additive lattice self-diffusion coefficients and one dislocation pipe diffusion coefficient. Over 21 orders of magnitude in ϵ ss / D eff , the data fit the equation ϵ ss D eff = B[ sinh(α σ ss E )] n , where α B and n are constants and E is the dynamic unrelaxed average Young's modulus. This Garofalo-type hyperbolic-sine equation is therefore a good representation of the steady-state behavior of pure polycrystalline aluminum. The activation energy for transient deformation, Q trans , was found to be dependent upon the method of testing. Q trans was greater than Q ss when calculated from temperature-change tests but less than Q ss when calculated from constant temperature tensile tests.

アルミニウム多結晶材の疲労過程における転位組織と疲労硬化の関係

Push-pull and plane bending fatigue tests in the high cycle fatigue region were carried out on annealed polycrystalline pure aluminum. The relationship between fatigue-induced dislocation structures and macroscopic hardening (unidirectional and cyclic) was investigated in the whole process of fatigue before the initiation of macro-crack.The stress amplitude σa and the plastic strain range Δεp tended to saturate at the early stage of fatigue in the both strain control- and stress control-tests. On the other hand, the Vickers hardness HV, the dislocation bundle width BW and the dislocation density ρ increased gradually until the initiation of macro-crack. Such behaviors of σa and Δεp can be explained from the dislocation shuttling model for the mobile dislocations, and the behaviors of HV, BW and ρ from the increase of the immobile dislocations. Furthermore, it is shown that the relationship between HV and ρ is expressed asHV-HVO=C3(ρ-ρ0)hwhere HVO and ρ0 are the values of HV and ρ at the annealed state, respectively, and C3 and h are the experimental constants.

Effect of subgrain size on the high temperature strength of polycrystalline aluminium as determined by constant strain rate tests

The influence of subgrain size, λ, on the creep strength, σ. of high purity polycrystalline aluminum was studied by a unique method involving instantaneous strain rate change tests. The results obtained reveal that the strength at a given strain rate increases as the subgrain size decreases following the relation σ ∝ λ − p/ N , where p and N are creep parameters about equal to 3.2 and 7.4 respectively. These values of p and N are in close agreement with those obtained from stress reduction tests in creep experiments. Attention is drawn to the need for new creep models which identify the importance of subgrain boundaries to the creep process.

Effects of temperature on the static and dynamic stress-strain characteristics in torsion of 1100-0 aluminum

A series of tests is described in which tubular specimens of a commercially pure polycrystalline aluminum were loaded in torsion at either of two dynamic rates, 300 and 600 sec −1, up to shear strains of about 2 and 4 per cent, respectively, at temperatures in the range −180 to 250°C. The tests were performed in a torsional split-Hopkinson bar. In the past when this apparatus was employed at an elevated or reduced temperature multiple reflections were encountered along the bars due to the temperature gradients. These reflections required elaborate computational corrections. In the present tests the reflections were eliminated by tapering the Hopkinson bars appropriately so their mechanical impedance in torsion remained constant in spite of the temperature gradients. The results, in the form of stress-strain curves, are compared to the corresponding “static” curves obtained by testing similar specimens in torsion at about 10 −3 sec −1. The influence of strain rate and of temperature is generally as expected, i.e. the flow stress increases with an increase in strain rate or a decrease in temperature. The strain rate sensitivity parameter varies non-linearly with temperature, and has a minimum value in the neighborhood of room temperature.

High-velocity dislocation damping in aluminum

High-velocity compression tests were conducted on pure polycrystalline aluminum. Data obtained at compressive strain rates ranging from 0.4×104 to 12×104 sec−1 could be divided into two regions of interest. For strain rates from 0.7×104 to 1.4×104 sec−1 a linear relationship was found to exist between the applied stress and the strain rate, indicating that the moving dislocations are viscously damped in this region. The values of the damping constant B obtained in this region ranged from 1.9×10−4 to 3.0×104 dyn sec/cm2 and showed good agreement with B determined by other investigators. Beyond these strain rates, the damping reduced at first and then increased, with very high stresses being obtained at the highest strain rates reached. The drop in the damping has been attributed to the reduction in the volume around the cores of the moving dislocations that can exchange energy with the lattice phonons. The rise in the damping at the higher strain rates may be due to relativistic effects as the moving dislocations approach the velocity of sound. Using the expression for the strain field around a fast-moving dislocation in the phonon viscosity theory and the general expression for dislocation damping due to phonon scattering, an expression for the damping constant was obtained embodying these effects. This was found to show good agreement with the data.

Load relaxation studies of polycrystalline high purity aluminium

Load relaxation studies were carried out to test for the existence of a plastic equation of state in high purity polycrystalline aluminium. The tests verified that such an equation of state held at room temperature. The hardness states that were demonstrated were stable against static recovery up to at least 0.45 T m . The hardness curves of stress-strain rate satisfied a scaling relationship with respect to different states of hardness. Accumulated plastic strain is not a good state variable. Transient behavior could be readily distinguished from the time independent state behavior.

アルミニウム多結晶の引張り変形能におよぼすひずみ速度の影響

In a temperature range from −196 to 400°C, a commercially pure polycrystalline aluminium, 2S-Al, was tested in tension to study its ductility as a function of strain rate over a range from about 10−3 to 102/sec. Findings in the present study are given as follows:(1) The total elongation measured in tension at a high strain rate, i.e., an impact tension, became larger than that measured in a quasi-static tension over the temperature range from −78 to 300°C, especially at room temperature to 200°C. This remarkable increase in elongation at a high strain rate may be attributed not to variations in grain boundary behaviours but to changes in behaviours of the matrix itself. The larger total elongation in the impact tension was brought, at least at room temperature, by the increase in both uniform and local elongations.The reduction in area increased gradually with temperature and no dip was observed on the reduction-temperature curves in all cases, though a deep dip around about 100°C was found on the total elongation-temperature curves obtained in tension at lower strain rates.(2) At room temperature, when the specimen was stretched incrementally to fracture, the total elongation was larger than that measured in a continuous tension, i.e., in a tension without unloading. The increase in total elongation due to an incremental deformation became larger in the impact tension and in tensions with larger repeated numbers of incremental deformation and with larger duration of unloading.(3) The total elongation at −196°C decreased abruptly beyond the strain rate of 1/sec. This decrease was due mainly to the decrease of local elongation. Since at −196°C the aluminium specimen has a small value of specific heat and its strength decreases rapidly with increasing temperature, a necked portion of the specimen subjected to a rapid tension at −196°C becomes remakably weakened under the effect of an adiabatic temperature rise, as compared with other portions which are not necked. The necking generated in rapid tension at −196°C is, therefore, restricted within a shorter length of the specimen, showing a local elongation smaller than that observed in a quasistatic tension at the same temperature.

High temperature work softening yield point phenomena in polycrystalline aluminum

Work softening yield points have been studied in high purity polycrystalline aluminum tested in the temperature rangeT2 = 100°to 450°C at constant strain rate subsequent to prestraining in tension at a lower temperature (T1) = room temperature or 350° C) or higher strain rate. The yield drops increase with prestrain as well as with the difference between the flow stresses at the test and prestrain temperature. Reductions in the yield drop caused by annealing atT2 prior to testing indicate that the yield drops are the result of dynamic recovery. It is shown that dynamic recovery is accelerated by concurrent straining.

The influence of quenching temperature on the hardening of pure aluminium quenched to -72 C

The yield stress of pure polycrystalline aluminium quenched from 600°C shows two stages as a function of ageing temperature. A stage Θ1 below a transition temperature θm (≃ -43°C) in which the yield stress after 150 min of ageing increases with increasing temperature, and a stage Θ2 above θm in which the yield stress decreases with increasing temperature.

Effect of vacuum on the fatigue life of aluminum

The effect of vacuum on the fatigue life of aluminum under a constant stress cyclic bending deformation has been studied. Specimens made of commercially pure polycrystalline aluminum, cycled at two frequencies, 49 and 76 c/s, were tested at 9700 psi and 11700 psi at 50°C as a function of pressure. It was found that the fatigue life was not only dependent upon the testing pressure, but it also became frequency dependent in vacuum. A model based on the concept of the surface “debris” layer is proposed to account for the observations obtained in this study.

Acoustic Attenuation in Aluminum due to Electron-Lattice Interaction

The attenuation of sound due to the interaction of electrons with the lattice has been measured in pure polycrystalline aluminum at low temperatures. Measurements from 26 to 130 kc/sec, obtained by recording the decays of the harmonics of a longitudinally resonating bar, were compared with the electrical conductivity of an aluminum wire of identical purity, over a temperature range of 3\ifmmode^\circ\else\textdegree\fi{} to 70\ifmmode^\circ\else\textdegree\fi{}K. The attenuation was proportional to the square of the frequency. A detailed agreement between the shape of the attenuation and conductivity curves was obtained, but the experimental attenuation was 50% greater than could be explained by the present theory.

Ductile fracture in metals

Abstract Cup-and-cone fracture in single-phase ductile metals appears to originate at holes formed by drawing away of material from non-metallic inclusions, as suggested by Tipper. In copper, the holes expand under the triaxial stresses in the neck and coalesce in a macroscopic fissure; in α iron fine cracks are formed by the stress concentrated at the holes. In coarsegrained material shear cracks are formed on the surface of the neck. Pure polycrystalline aluminium separates at the neck of a tensile specimen by slipping-off along a plane of shear. This is thought to be the usual mode of failure in materials in which work-hardening has been exhausted.

Effect of Room Temperature Aging Upon the Internal Friction Versus the Cold-worked Levels Relationship of Commercially Pure Polycrystalline Aluminium

This paper presents the results of investigations of the effect of room temperature annealing upon the internal friction introduced by cold-working versus the cold-working levels relationship of commercially pure aluminium, by means of transverse vibration about 2000 c.p.s. of squars rods. The internal friction versus the cold-working levels curve for the specimens, annealed for about 30 minutes at room temperature, (11°±2°C), before measurement, produced anomalous peaks at around 15 and 55 pct. reductions, respectively. Although the internal friction introduced by cold-working was diminished with annealing time over the entire range of reduction area, the diminution of internal friction was markedly different by the cold-working levels. The first high peak swaged down with annealing time at room temperature and was decayed completely after an annealing for 2\frac12 days at room temperature. The second small peak was not decayed by a room temperature annealing for 41 days. The removal of the internal friction introduced by cold-working for the 15 pct. reduction area followed the (time)2⁄3 law, but in the other specimens it did not followed the (time)2⁄3 law. These observed results were qualitatively discussed.

Viscous creep of aluminum near its melting temperature

The creep of pure polycrystalline aluminum was studied at low stresses, and temperatures near the melting point. It was found that at stresses between 3 and 13 lb/in 2 the secondary creep rate varied linearly with the stress, whereas at slightly higher stresses, the creep rate increased with the fourth power of the stress. The activation energy for creep was determined to be about 35,500 calories per mole over the entire stress range. The low stress creep results in the range of “viscous” creep were analysed from the viewpoint of the Nabarro-Herring model for stress directed self-diffusion of vacancies, and it was found that the experimental creep rates were about one thousandfold greater than those predicted theoretically. This factor plus additional experimental observations on the displacements of markers at grain boundaries, and on creep recovery upon removal of the stress led to the conclusion that the Nabarro-Herring model does not apply to the case of aluminum, and that creep occurs by a dislocation climb mechanism at all stresses considered.

On the representation of rheological results with special reference to creep and relaxation

The remarkable qualitative similarity in the response of solids of widely different structures to applied stresses, particularly in creep and relaxation, is ascribed to relaxation centres all of which, in a given solid, have approximately the same heat of activation, but, on account of variations in their geometry such as shape and size, have different entropies of activation. A normal distribution of entropies of activation is shown to lead to a log-normal spectrum of relaxation times of the type originally proposed by Wiechert on heuristic grounds. Boltzmann's superposition principle and the relation between creep and relaxation derived by Zener are used to show that this distribution yields a form of stress relaxation curve common to many solids, as well as Andrade's t1/3-creep law. Experimental data, given in the literature, on the creep and relaxation in pure polycrystalline aluminium, rubber, polymethylmethacrylate and ceramics are shown to be in good agreement with the theory. The significance of Nutting's law of deformation is discussed.