Formation Of Cottrell Atmospheres Research Articles

Plastic Behavior of Aged Mild Steel

To examine the anisotropy of aging under the multiaxial stress state in a mild steel, the strain aged tubular specimens were subjected to combined axial load and torsion. In this paper, mainly the effects of prestrain and aging temperature were examined. The increase in the yield stress due to aging was resolved into two components ; the increase in the lower yield point due to the formation of Cottrell atmosphere and the recovery of elastic limit which was associated with precipitation hardening. By the separation of these two sources of hardening, a quantitative evaluation was made as to the aging effect and the elimination of anisotropy. Furthermore, the yield function containing the third stress invariant, proposed by Edelman and Drucker and partly corrected by the authors, was in good agreement with the experimental results. The direction of the plastic increment vector at the end of yield point elongation was shown to be normal to the yield surface.

The recovery of internal friction in an iron-carbon alloy

Abstract Strain ageing following plastic deformation was studied at the flow stress and at zero stress levels over the temperature range -37° to 24°C in annealed (at 870°C) and in quenched (from 700°C) polycrystalline and in annealed (at 870°C) single crystal specimens of Ferrovac-E iron. The interactions of interstitial carbon and nitrogen with dislocations were derived from the time-dependent changes in the dislocation damping component of the attenuation at 5 MHz frequency, i.e. from the recovery of internal friction. Two stages of strain ageing observed correspond to Snoek rearrangement and to Cottrell atmosphere formation. The activation energy for Snoek rearrangement was found to be 14·8 ± 0·5 kcal/mole by applying the Granato-Hikata-Lücke equation and 14·0 ± 2·3 kcal/mole by the Arrhenius relationship, with an ageing time exponent of 2/3. The activation energy for the second stage was 22·0 ± 2·0 kcal/mole with the ageing time exponent between 1/3 and 1/2. The ageing stress levels, flow stress or zero stress, do not seem to have any effect on either activation energy or kinetics. Mechanical properties associated with strain ageing are, however, a function of the ageing stress levels and this has led some investigators to an erroneous assumption of stress-assisted diffusion of interstitials.

Phonon Scattering by Cottrell Atmospheres. II. Time-Dependent Effects

The formation of Cottrell atmospheres can change the scattering of phonons by dislocations and affect the lattice thermal resistivity due to dislocations. Since diffusion of solute atoms is required to form atmospheres, they are not formed instantaneously. Changes due to annealing are similarly time dependent. The diffusion equation is solved in its Fourier-inverted form, and changes in phonon scattering and lattice thermal conductivity are obtained in a simple form. Changes in lattice thermal conductivity at higher temperatures occur faster, since diffusion through shorter distances is involved. Diffusion coefficients can be determined by studying the time dependence of the lattice thermal conductivity on annealing, and for slow diffusion this method may have advantages.

X-Ray Study on the Hydrogen Charged Steels

In order to account for the embrittled phenomenon in steels charged with hydrogen, several considerations have so far been proposed, such for instance as the rift network theory, the void theory, the formation of cottrell atmosphere, and the interaction of hydrogen in the lattice work and in the stress field. The authors have tried to make an X-ray study of the mechanism of steel getting charged with hydrogen by performing comparative experiments on the polycrystalline material and on the single crystal material, both electrolytically charged with hydrogen. The former has been subjected to analysis of the X-ray diffraction line profiles, and the latter to analysis of its lattice distortion. The results indicate that thus introduced hydrogen gives rise to plastic deformation in the crystal lattice and there is no recovery phenomenon observable after having been subjected to room temperature aging. By annealing treatment of the material at higher temperature, however, the crystal have been recovered in a similar fashion to mechanically deformed crystal.It is believed that the recovery in this case is not due to the diffusion process of hydrogen. In the case of single crystal, the micro-focus X-ray source (30∼20 micron) is employed to take Laue pictures which showed the heavily deformed spots on the films. This is believed to be due to the distortion in the crystal lattice as well as to the existence of void caused by being charged with hydrogen.

Grain-size dependence of discontinuous yielding in strain-aged steels

Recent studies of discontinuous yielding in polycrystalline metals support interpretations of the Hall-Petch relationship which relate k y to the local stress required to spread yielding across grain-boundaries at a yield front. Changes in yield-point behaviour due to strain-ageing can be rationalised on the assumption that the growth of k y provides a measure of the increase in the average value of this local stress. In low-carbon steels, the first phase of ordinary strain-ageing is concerned with Cottrell-atmosphere formation. In test-pieces aged within this first stage, mobile dislocations are almost certainly released by unpinning, but after later stages of ageing the magnitude of the discontinuous yield becomes insensitive to continued solute segregation to dislocations: yield-nucleation by unpinning is then unlikely. After the first stage of ageing it is probable that mobile dislocations are nucleated from grain-boundaries. Thus a reduction in solute segregation at boundaries, by quenching from ~700°C before prestraining, is accompanied by a decrease in the second-stage (“plateau”) values of Luders strain and k y . It is suggested that prestraining causes a reduction in the stress required to generate dislocations from boundaries and that the final slow increase in k y is due to a transfer of interstitial solute from grain interiors to unsaturated grain-boundaries.

Stress-Assisted Diffusion to Dislocations and its Role in Strain Aging

The kinetics of Cottrell atmosphere formation around dislocations is studied numerically. The spirit of the calculation presented here follows closely that presented by Bullough and Newman, although our conclusions about strain aging are different. We have calculated solute distributions for a number of times using the standard dislocation-solute atom interaction potentials, − A/r and − A cos(θ)/r, for screw and edge dislocations, respectively. It is shown that for suitably strong dislocation-solute binding and appropriate dislocation densities, a Harper-type strain aging can be predicted on the basis of stress-assisted-diffusion theory without ascribing any special properties to the dislocation core regions. The place of the Harper law and the Bullough and Newman calculations in the over-all picture of strain aging is discussed.

A note on precipitate formation in quench-aged α-iron

Abstract Thin foil observations have been made on quench-aged α-iron specimens in the polygonized, recrystallized and pre-strained conditions. It was found that the dislocation density had a profound effect on precipitate distribution and the observations could best be interpreted in terms of indirect visual evidence for the formation of Cottrell atmospheres.

Influence of deformation rate on the blue brittleness temperature and dislocation density of carbon steel

The reduction of the plasticity of carbon steel under conditions of static and dynamic elongation obeys the fundamental kinetic law of strain aging and consequently is caused by the diffusion of impurity atoms (C and N2) to dislocations and the resulting pinning of dislocations by formation of Cottrell atmospheres. The dislocation density for dynamic loading in the temperature range of reduced plasticity proves to be one to one and one-half orders higher than for static loading.

Kinetics of snoek ordering and cottrell atmosphere formation in Fe-N single crystals

The return of the yield point in three Fe-N alloys has been studied as a function of aging time at temperatures between −50°C and 25°C. A two-stage aging process was observed at most of the aging temperatures. The value Δσ (stress difference between upper yield point and the flow stress immediately before aging) first increased, then leveled off, and then increased again with aging time. The kinetics of this phenomenon is controlled by nitrogen diffusion in iron. The time corresponding to the leveling-off point is equivalent to that required for a few jumps of a nitrogen atom for the three nitrogen concentrations at all temperatures investigated. It is thus concluded that the first-stage aging process consists of Snoek ordering of nitrogen atoms in the stress fields of dislocations. The kinetics of the second stage was analyzed according to the Cottrell-Bilby model of atmosphere formation around dislocations. This analysis yields an activation energy for diffusion of nitrogen in iron of 16.3 kcal/mole. This value is in good agreement with those of 16.4 ~ 19.0 kcal/mole reported by previous investigators.

Relaxation of stresses associated with peierls dislocations caused by the formation of cottrell atmospheres

Relaxation of stresses associated with peierls dislocations caused by the formation of cottrell atmospheres

The formation of Cottrell atmospheres in the vicinity of Peierls edge dislocations

The formation of Cottrell atmospheres in the vicinity of Peierls edge dislocations

The flow stress of iron and its dependence on impurities

In the stress field of a dislocation an ordering of solute interstitials takes place. By this Snoek-effect dislocations are locked in times which are too short to allow the formation of Cottrell atmospheres. The locking energy and the stress to free the dislocation is calculated for a screw dislocation in α-iron. If the dislocation moves, a frictional force is caused by the Snoek-effect and its magnitude is calculated. It is suggested that this mechanism determines the flow stress of α-iron above room temperature and experimental results are discussed which support this point of view.