R.O. Scattergood

The effect of dislocation self-interaction on the Orowan stress

Abstract The effect of dislocation self-interaction on the Orowan stress was determined for collinear, impenetrable circular obstacles. The line tension approximation was dropped and an appropriate integro-differential equation governing static equilibrium was solved by an algorithm based on curvature adjustments. When the interactions are taken into account, the Orowan stress varies as In where is the harmonic mean of the obstacle size and spacing. In addition, the configuration of a bowing dislocation at the Orowan stress is strongly influenced by the interactions: as the interactions increase in strength, i.e. as the ratio of obstacle size to spacing decreases, the bow-out and area swept are suppressed. The essential features of the interaction can be incorporated into a line tension framework by treating the impenetrable obstacles as if they were penetrable. Based on this line tension analogue, an approximate form for the flow stress of a random distribution of impenetrable obstacles was developed.

The strengthening effect of voids

Abstract The strengthening effect due to voids was calculated using contemporary, computer-based dislocation theory methods that allow dislocation self interaction and elastic anisotropy to be properly taken into account. Void-dislocation interaction was included by using an approximation based on Lothes solution for a dislocation terminating on the boundary of an elastically anisotropic half-space. The results show that voids are very strong obstacles to dislocation motion, and the void bypassing stress approaches the Orowan stress for impenetrable obstacles obtained under similar conditions. A correlation based on the isotropic-elastic, line-tension approximation was developed to describe the void bypassing stresses in quantitative fashion. With an appropriate choice of the several arbitrary parameters in the line tension description, elastic anisotropy and the various interactions can be included. The resistance due to surface-step formation on voids during dislocation penetration was also included in the calculations and the correlation. Limited experimental data available in the literature is in agreement with the quantitative predictions, and supports the fact that voids must be regarded as strong obstacles to dislocation motion.

The Orowan mechanism in anisotropic crystals

Abstract The static equilibrium configurations of a dislocation bypassing a periodic row of impenetrable circular obstacles were obtained for various crystals by means of a self-stress method wherein the elastic anisotropy of the crystal and the dislocation self-interaction could be taken into account. A correlation was developed from the results which related the Orowan stress values to the obstacle size and spacing. This correlation demands two parameters to account for the anisotropy, and these appear as a suitably defined anisotropic shear modulus and Poissons ratio. The self-interactions are taken into account by a single logarithmic parameter which is the harmonic mean of the obstacle size and spacing, and is independent of anisotropy. The shapes of the bowing dislocation loops are strongly influenced by the anisotropy and interactions. The combined effects on shape can bo simply described in the line-tension framework, using the de Wit—Koehler solutions. In particular, the swept areas and overall ...

On the origin of cell walls and of lattice misorientations during deformation

The purpose of this note is to outline a view of the mechanism by which cell walls form during the course of strain hardening and dynamic recovery. This mechanism would lead one to expect that the cell walls are polarized, in the sense that there tends to be an excess of one sign of dislocation on one side of the cell wall, and of the other sign on the other side. The rearrangement of dislocations in such a cell wall into lower-energy configurations by static or further dynamic recovery could eventually lead to a pair of subboundaries of opposite sign. The misorientation between the cell wall interior and the cells on either side should then be larger than between the cells themselves. This mechanism could help explain some inconsistencies between x-ray and TEM observations of misorientations, and could contribute to a theory of “nucleation” for recrystallization. In addition, the polarity of the cell walls may be linked to the Bauschinger effect and should disappear upon subboundary formation.

Short-range order and fermi surface effects in copper-rich copper-aluminum alloys

Abstract The diffuse scattering of X-rays has been measured in single crystals of Cu-Al alloys containing 6, 11 and 16 at. % Al. A pronounced diffuse satellite intensity with a four-fold symmetrical pattern about the normal f.c.c. superlattice positions was observed with the 11 and 16 at. % Al crystals. From the composition dependence of the satellite peak positions determined by other workers and by us, we show that these peaks have their origin in singularities, analogous to Kohn anomalies, which have previously been demonstrated in copper-gold alloys. This composition dependence provides a sensitive measure of the variation of the value of the Fermi wave vector in the 〈110〉 direction. The results agree with a simple scaling of the Fermi surface of copper. This interpretation is supported by measurements of positron annihilation in Cu-Al alloys reported by other investigators. The absence of anomalies and the near-randomness of the atomic arrangements at 6 at. % Al imply the existence of an order-disorder phase boundary, which is indicated by other data.

Symmetric stacking fault nodes in anisotropic crystals

Abstract The equilibrium configurations of symmetric, 3-fold stacking fault nodes in f.c.c. crystals were determined by a linear elastic self-stress method which accounts for the combined effects of dislocation interaction and elastic anisotropy. Based on the results, a set of empirical equations was developed which compactly summarizes the solution to the anisotropic node problem, and which can be used to analyze node measurements. In principle, the stacking fault energy γ and the dislocation core radius r0 can be obtained from node measurements; however, analysis of data for silver displayed too much scatter for both values to be reliably extracted, and a best fit value of γ = 23.5 erg/cm2 was obtained with the assumption of r0 = b. The appropriate choice of the Poisson ratio and shear modulus to obtain an isotropic approximation to the anisotropic node problem was given, and the deviations from isotropy in the node configurations were rationalized, qualitatively, in terms of the line tension of the partial dislocations.

Stress and irradiation induced mass transport

An exact analytical solution to a model problem that elucidates the relative contributions and interplay of mass-diffusion currents induced by displacement-producing irradiation, stress gradients, and differences in normal tractions applied at surfaces is presented. It was found that Nabarro-Herring creep is independent of irradiation-produced defects and depends on stress gradients. With stress gradients present, the total mass flux is not determined by specification of the boundary values of the chemical potentials for diffusion. Details of stress gradients must be accounted for.

Irradiation enhanced diffusional mass transport

A broad analysis of the irradiation enhanced mass transport problem has been given and it appears that the drift terms in the vacancy and interstitial fluxes play a central role. Under steady state conditions (which are probably the most important ones for practical applications), there will be no enhancement without drift terms, whereas with these terms enhancement will normally occur. Under nonsteady state conditions, enhancement can be expected even in the absence of the drift terms.

A method for evaluation of dislocation strain energy and self force

Abstract In this investigation, a new cutoff procedure was developed for the evaluation of the strain energy associated with a general curvilinear dislocation in an infinite homogeneous linear-elastic anisotropic body. When used in conjunction with the geometric-theorem approach for dislocation stress fields, a convenient and self-consistent prescription for the complete infinite-body self force is obtained. This kind of prescription will be needed to determine the true equilibrium shape of a dislocation within the framework of linear-elastic dislocation theory. The present method has the same essential physical features as an earlier approach due to Barnett and Gavazza. In addition, the method allows a simple double-line integral formula for the strain energy to be derived, which may prove useful in applications.

In-situ HVEM recovery annealing of A1 single crystals☆

In-situ annealing experiments were made in a high voltage electron microscope using thin foils prepared from prestrained bulk Al single crystals to characterize the recovery events. Recovery events involve dislocation interaction and migration, which underlie the structural changes accompanying recovery. A comparison of these results with other results reveal the influence of foil free surfaces. (FS)