Modern aspects of plastic deformation in metals

After a historical survey of crystal plasticity the rôle of dislocations in plastic deformation of metals is outlined. The theory of plastic deformation in metal single crystals before the impact of transmission electron microscopy is described. Recent experimental results on glide and workhardening in single crystals of b.c.c. metals are reviewed and explained by a simple dissociation model of the screw-dislocation cores. A relative success of this explanation together with calculations of atomic structure of dislocation cores support the conclusion that different structures of screw dislocation cores are responsible for both differences and similarities between plastic behaviour of f.c.c. and b.c.c. metals. Further developments in the field of metal crystal plasticity by modern experimental techniques (transmission electron microscopy of deformed crystals in the stress-applied state, magnetic studies of dislocations in ferromagnetic crystals) and by atomic calculations of defect configurations are discussed.Na Slovance 2, Praha 8, Czechoslovakia.Invited paper presented on a plenary session of the First European Conference on the Physics of Condensed Matter organized by the Board of the Condensed Matter Division of E.P.S., in Florence on 14–17 September 1971 (Chairman: Prof. S. F. Edwards; Schuster Laboratory, University of Manchester).     

Density functional theory studies of screw dislocation core structures in bcc metals

The core structures of d111 screw dislocations in bcc metals are studied using density functional theory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180 rotations around an axis perpendicular to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of nsurfaces and the elastic constants B , C ' and c 44 are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point to symmetric core structures for all the studied metals.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

Analysis of the strain-rate sensitivity of flow stresses in nanocrystalline FCC and BCC metals

The dependence of the strain-rate sensitivity coefficient of flow stresses S = dlnσ/dln\(\dot \varepsilon \) on temperature, strain rate, and grain size in nanocrystalline (NC) metals is analyzed quantitatively in terms of the dislocation-kinetics approach taking into account the properties of grain boundaries as sources, sinks, and barriers for moving dislocations. The interaction of moving dislocations with a dislocation forest in nanograin boundaries is shown to be responsible for the fact that the values of this coefficient in NC fcc metals (Cu, Ni) are an order of magnitude greater than those in coarse-grained metals and for the strong dependence of the coefficient S on the above factors. This dependence is largely caused by the annihilation of lattice dislocations in grain boundaries controlled by the activation energy of grain boundary diffusion. The values of the coefficient S in NC bcc metals (α-Fe) are an order of magnitude lower than those in coarse-grained samples, because dislocations move in a Peierls relief in nanograins     

Flexible Ab initio boundary conditions: simulating isolated dislocations in bcc Mo and Ta

We report the first ab initio density-functional study of the strain field and Peierls stress of isolated <111> screw dislocations in bcc Mo and Ta. The local dislocation strain field is self-consistently coupled to the long-range elastic field using a flexible boundary condition method. This reduces the mesoscopic atomistic calculation to one involving only degrees of freedom near the dislocation core. The predicted equilibrium core for Mo is significantly different from previous atomistic results and the Peierls stress shows significant non-Schmid behavior as expected for the bcc metals.     

Structure and dynamics of the Frenkel-Kontorova dislocations in electroconvection in liquid crystals

The Frenkel-Kontorova instability is studied in a 1D lattice of domains formed during electroconvection in nematic liquid crystals twisted by π/2. It is found that generation of defects by such instability can be observed in this model medium. Among other things, it is shown that several types of defects with singular and nonsingular cores, as well as with a extended core, are formed in the 1D domain structure above the electroconvective instability threshold. The extended cores of dislocations are dissociated into a line, and the entire structure is isomorphic to two partial dislocations spaced by a certain distance, which are not observed in free form. Defects with a nonsingular core (zero topological index) exist owing to spiral hydrodynamic flows in convective rolls and are not observed in layers with a homogeneous orientation of molecules. It is shown that the formation of both types of defects follows the scenario of decay of dislocations with extended cores via detachment of nonsingular defects (i.e., discretely); as a result, a dislocation with a singular core is left. “Breather” defects, which are the result of periodic creation and annihilation of dislocations with a topological index of ±1, are also observed. The effect of defects on the transition from the 1D to 2D structures is considered.     

Resistance to expansion of dislocation loop in fcc metal

In the paper we calculate the strength of dislocation compounds in fcc metals for dislocations of different orientation relative to the Burgers vector. A study is made of the dependence of the coefficient _r, which characterizes the contribution of the reactive component of a dislocation forest to the flow stress, and the probability _r of formation of dislocation compounds on the angle II of orientation of glissile dislocations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 35–38, August, 1982.     

On the mechanism of the electric field effect on dislocation mobility in alkali-halide crystals

The dependence is investigated of the velocity of motion of edge and screw dislocations on the applied shear stress in annealed and quenched NaCl and KC1 crystals with various impurity content under the action of an electric field of up to 50 kV/cm. It is shown that in impure crystals the action of the field is determined by its effect on damping centers, while in pure crystals, by its effect on charged dislocations. The interaction force of an edge dislocation with impurity-vacancy dipoles of various orientation is calculated. The charge density and sign of a dislocation is estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 16–21, May, 1975.     

Description of dislocation cores

In this paper we explore the possibility of describing the dislocation core of a dislocation by a distribution of infinitesimal dislocations smooth enough to remove all singularities. The results may be extended straightforwardly to the case of anisotropic elasticity and can be used to calculate accurately contrast effects. It is shown that precipitation at dislocation cores may induce a glissile to sessile transformation.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.     

Ab initio study of screw dislocations in Mo and ta: A new picture of plasticity in bcc transition metals

We report the first ab initio density-functional study of <111> screw dislocation cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.     

Evolution of the dislocation structure and the hardening mechanisms of multiple slip oriented Ni3Ge single crystals

We studied the evolution of the dislocation structure of Ni₃Ge single crystals deformed by compression at room temperature. It is shown that the distribution of dislocations is spatially uniform in the studied alloy. The uniformity in the dislocation distribution is produced by relatively high amounts of the frictional stresses of the dislocations. On the basis of the obtained values of the dislocation structure parameters, the contributions of the various mechanisms in the dislocation drag are determined. It is shown that the resistance to deformation is determined primarily by overcoming reactive and unreactive forest dislocations, the total contribution of which is 0.9 of the applied stress.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 65–70, March, 1987.     

Structure factors that influence the stability of plastic strain of bcc metals under tensile load

The effect of the Peierls stress on the ultimate tensile stress and uniform strain prior to the formation of a neck during stretching of metals and alloys with bcc structure is theoretically analyzed. The analysis is based on the equation for the variation of the dislocation density with deformation; this equation determines the shape of the work-hardening curve for a bcc material and the effect of the Peierls stress on the parameters of this equation (the annihilation coefficient for screw dislocations). Using the Considére condition for plastic instability of the neck type, the ultimate tensile stress and the magnitude of uniform strain are found theoretically as a function of the Peierls stress at different temperatures below 0.15T _m , where T _m is the melting temperature of the bcc metal. Theoretical results are illustrated with experimental data on the temperature dependences of the annihilation coefficients for screw dislocations and of the magnitude of uniform strain in molybdenum and Armco iron.     

Hydrogen diffusion in the elastic fields of dislocations in iron

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10¹⁴ m^–2 in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉{110}, 〈111〉{112}, 〈100〉{100}, and 〈100〉{110} are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change of the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.     

The role of dislocations in radiation strenghtening of alkali halide crystals

The dependence of activation volume and dislocation start stress in sodium and calcium chloride crystals on-radiation dosage (in the range 10⁴–10⁹rad) is studied. It is established that these functions indicate that the hardening of crystals subjected to radiation is of a dislocation nature. Analysis of data from the literature leads to the conclusion that in the medium and high radiation dose region planar precipitates and surrounding dislocations formed by halogen molecules are responsible for hardening.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 99–103, June, 1976.     

Vibrational properties of straight dislocations in bcc and fcc metals within the harmonic approximation

We calculate the vibrational spectra of straight screw and edge dislocations in several body-centered cubic (bcc) (Mo and Fe) and face-centered cubic (fcc) (Cu and Al) metals within the harmonic approximation. We take advantage of the translational symmetry of straight dislocations to efficiently calculate their phonon eigenstates in the harmonic limit. This allows us to calculate the low-temperature contribution of straight screw and edge dislocations to the heat capacity of each respective metal, and show that the dominant temperature dependence below 5 K is linear. Comparison with heat capacity measurements of heavily cold-worked Cu reveals very good agreement with our calculations. At higher temperatures, the contribution from the non-linear terms becomes significant. As a result, maxima in the straight dislocation heat capacities are observed in the temperature range from 9% to 16% of the Debye temperature. We investigate the appearance of localized and resonance peaks in the vibrational spectra induced by dislocations, and study in detail their spatial spread around the dislocation cores by projecting vibrational eigenstates onto individual atoms. We study the deviation of these atomic-level vibrational free energies from that of the perfect crystal as a function of distance to the dislocation cores, and establish that, similar to the dislocation energy, the vibrational free energy of an isolated dislocation behaves logarithmically in the long-range limit. Finally, we obtain vibrational spectra for propagating waves along the dislocation line and find that the dispersion for these waves is consistent with the notion of kink formation and motion for screw dislocations.     

bcc Fe的刃型位错中氦-空位团的稳定性

 采用周期性原子阵列方法建立bcc Fe中的刃型位错,利用分子动力学计算了0 K时bcc Fe的位错芯里氦-空位团的稳定性,并与理想Fe晶体里氦-空位团的稳定性进行比较发现,位错的作用导致氦-空位团不稳定。点缺陷（He、空位与自间隙Fe原子）与氦-空位团的结合能与团中氦-空位比例密切相关,当氦与空位数之比在3~6时,结合能趋于稳定。