Dislocation Ensembles Research Articles

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 3—Taylor–Quinney coefficient, size effects and generalized normality

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 3—Taylor–Quinney coefficient, size effects and generalized normality

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 2—ensemble evolution toward correlation of enthalpy barriers

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 2—ensemble evolution toward correlation of enthalpy barriers

Application of recurrence quantification analysis of acoustic emission time series to analysis of a plastic flow of metals.

As a result of the application of recurrence quantification analysis to acoustic emission time series obtained in uniaxial tensile testing of copper and silver, we detected the existence of a characteristic interval in which the Shannon information entropy (as a parameter of the quantitative analysis of recurrence plots) increased rapidly. Using statistical analysis of the behavior of the dislocation ensemble, we established a relation between the physical parameters of the given interval and the global stability loss parameters of the plastic flow of metals, indicating the predictability of the distinctive point determined long before the critical state was attained.

Narushenie kiral'noy simmetrii i neodnorodnye sostoyaniya v deformirovannykh ferromagnetikakh

The general form of chiral terms associated with deformation of a ferromagnet is determined. The possibility of a transition from the helical state to the vortex state is demonstrated for a ferromagnetic rod subjected to elastic torsional strain. In the case of a single screw dislocation, the formation of the skyrmion state due to elastic strains and the helical distribution of magnetization induced by strains in the dislocation core is indicated. The conditions in which a transition from one chiral magnetization distribution to another distribution in an ensemble of identical dislocations are determined.

Особенности высокоскоростной деформации состаренных сплавов

The sliding of an ensemble of edge dislocations under high-speed deformation (high strain rate deformation) of an aged binary alloy is theoretically analyzed. An analytical expression of the dependence of the dynamic yield strength on the dislocation density is obtained. The conditions under which this dependence is nonmonotonic and has a minimum and maximum are obtained. The minimum occurs during the transition from the dominance of dynamic braking (drag) of dislocations by point defects to the dominance of braking by other dislocations (Taylor hardening). The position of the maximum corresponds to the value of the dislocation density, at which their contribution to the formation of the spectral gap becomes dominant.

KINETIC INSTABILITY IN AN ENSEMBLE OF DISLOCATIONS UNDER PLASTIC DEFORMATION OF METALS

Based on a system of evolutionary equations for an ensemble of edge dislocations, the problem associated with the development of instability of a homogeneous distribution of dislocations is considered. Despite the large number of theoretical studies on this topic, most of them are considered within the framework of reaction-diffusion phenomenological models, which contradicts the mathematical structure of the initial evolutionary equations, which are hyperbolic equations. For the initial system of hyperbolic equations, the case is considered when the process of plastic deformation develops along a given axis. The elastic interaction of dislocations is neglected in order to reveal the instability features of the homogeneous state of the system due to the local kinetics of dislocations. The stability analysis of the homogeneous state was carried out for a system of dislocations of two types differing in mobility. As a result of linearization of the initial system, a system of homogeneous linear algebraic equations is obtained. From the condition of the existence of its nontrivial solutions, a dispersion equation is found, using which, on the basis of the Raut – Hurwitz criterion, the range of parameters of the initial system at which kinetic instability is realized is established. In the instability region, an expression is obtained for the increment of the unstable mode, which determines the behavior of the system beyond the bifurcation point, and an expression for the characteristic scale of the inhomogeneous structure. The region of system parameters where the diffusion dynamics of the system is realized is found. It is shown that the Turing instability for the total dislocation density is realized in this parameter range. Within the framework of the initial system of hyperbolic equations, the dynamics of both total and excess dislocation densities is significant. It is the excess density that leads to disorientation in the formation of heterogeneous dislocation structures. This is a fundamental point, since at the advanced stage of plastic deformation, the dislocation structure is basically a system of disoriented cells and ragged sub-boundaries.

Особенности динамики дислокаций в состаренных сплавах

The high-speed deformation of aged alloys containing alloying elements has been theoretically analyzed. An expression for the contribution of the Guinier-Preston zones to the value of the dynamic yield strength has been obtained. Dynamic effects have a significant influence on the motion of dislocation ensembles. The dynamic yield strength under certain conditions does not depend on the rate of plastic deformation. The concentration dependence of the dynamic yield strength is determined by the competition between the interaction of dislocations with alloying elements and dislocations of the ensemble. If the interaction with alloying elements dominates, the dynamic yield strength decreases with increasing their concentration. If the collective interaction of dislocations dominates, the yield strength decreases as their density increases.

Моделювання явища крихкопластичного переходу методом дислокаційної динаміки

Computer modeling by the DD method is based on the Rice and Thompson model, according to which the force reliefnear the crack tip is created by three forces: an external load, an image force acting on dislocations from the free surfaces, and a resistance force from the crystal lattice. The interaction between dislocations in the plastic zone is calculated step by step. At each step, the stress is calculated for all dislocations in the ensemble and the velocities and corresponding new positions are calculated. Computer calculations make it possible to predict the impact of dislocation ensemble shielding on the current value of the stress intensity factor. The calculated value of crack resistance was determined under the condition of reaching the critical value of the stress intensity coefficient of the brittle material at the crack head. The effect of temperature and strain rate on the viscous-brittle transition in polycrystalline molybdenum was modeled using the dislocation dynamics method. From the results of the calculations, it follows that when the test temperature changes, the size of the plastic zone increases by more than an order of magnitude. As the loading rate decreases, the abnormal increase in crack resistance shifts to smaller grain sizes. This effect is significantly smaller than the effect of temperature. Changing the parameters of the model does not change the general mechanism of the viscous-brittle transition, which is associated with the peculiarities of the interaction of dislocations in the plastic zone with grain boundaries in polycrystalline molybdenum. Regardless of the speed of loading and the temperature of the tests, three characteristic ranges of grain sizes can be distinguished: With large grains, the fracture toughness remains unchanged because the size of the plastic zone is much smaller than the grain size. With the average grain size, a dislocation cluster is formed near the boundary, grain boundary sources begin to work in the neighboring grain, forming a small number of dislocations there, which contributes to a slight increase in crack resistance. With a small grain size, the fracture toughness begins to increase rapidly, since the plastic zone covers several grains. The dislocation cluster moves to the top of the crack and screens its propagation. Keywords: phenomenon of brittle-plastic transition, dislocation clustering, dislocation dynamics.

Prismatic-to-basal plastic slip transition in zirconium

We model three-dimensional dislocation ensembles in Zr pillars using newly developed mobility laws for dislocations on prismatic and basal planes. The effects of the loading orientation and temperature on the micro-scale mechanical response of single crystals are systematically explored. Easy dislocation glide is observed on prismatic planes, while hard glide occurs on basal planes. By selection of sample temperature and loading orientation, we show that the transition from prismatic to basal glide of dislocation ensembles can be controlled. We also show that the presence of dislocation cross-slip strongly promotes prismatic glide as a result of prismatic/basal cross-slip energy asymmetry. Cross-slip does not alter the occurrence of plastic slip transition but only induces a shift towards higher temperatures. The preponderance of plastic slip on basal or prismatic planes is found to be mediated by a transitional dislocation, which is composed of glissile segments on parallel prismatic planes connected by glissile super-jogs on basal planes. These findings provide a mechanistic understanding of experiments and highlight the significance of transitional prismatic-basal dislocations on the macroscopic characteristics of plasticity in HCP crystals.

Dislocation modelling of the plastic relaxation and thermal ratchetting induced by zirconium hydride precipitation

The precipitation of hydrides in zirconium alloys is accompanied by a significant and anisotropic volumetric expansion. Previous literature quantified the misfit both theoretically and experimentally, but these values differ greatly; the experimental values are consistently lower. One possibility is that the experimental measurements include the effect of dislocations generated by the hydride, which relax the transformation stresses. To test this hypothesis, it is important to determine the stress field of a hydride and its associated dislocations, combined. A simple planar dislocation model was developed of the hydride—dislocation ensemble in α-Zr. By capturing details of the dislocation structures given in the literature, it is shown in this study that including the interfacial dislocations largely reconciles the predicted and experimental values. Discrete dislocation plasticity is then used to model the diffuse plastic relaxation associated with hydride formation. The effects of plastic relaxation on the equilibrium hydrogen profile, hence the implications for subsequent hydride precipitation, are discussed. In particular, precipitation–dissolution cycles were simulated to calculate the magnitude of the residual hydrostatic tension, which is argued to be the primary cause of the “memory effect” for the re-precipitation of both γ and δ hydrides.

The restricted random dislocation distribution model to describe ensembles of dislocations with a screw component in ZnO layers with a mosaic structure

By applying the restricted random dislocation distribution model, solved using a discrete Hankel transform approach, it is shown that the shapes and characteristics of the ω-scans of the ZnO 00.2 reflection are mainly determined by the strain field introduced by dislocations with a screw component. On the other hand, no clear evidence of mosaicity or interfacial region contributions is found despite the layers exhibiting a c axis oriented residual columnar structure and a highly defective interface being present. The applied model not only permits a more precise estimation of the densities of dislocations, which present a screw component with respect to methods based on the analysis of the 00.2 peak ω-scan FWHM, but also gives an indication of their distribution characteristics with the extracted values, as well as their homogeneous/quasi-regular spacing, being confirmed by cross-sectional transmission electron microscopy observations.

The modified Williamson-Hall plot and dislocation density evaluation from diffraction peaks

Diffraction peak profiles were calculated numerically for dislocation ensembles with different spatial arrangements and correlations between the Burgers vector signs. The latter property determines the stored elastic energy in the crystal and the width of the diffraction peaks. It is shown that within the approximation of the asymptotic line-profile theory the relationship between peak breadth and the magnitude of the diffraction vector in the modified Williamson-Hall (mWH) plot is linear. The slope of the line is proportional to the arrangement parameter M0.3 and to the square root of the dislocation density. The only rigorous way for determining M is the asymptotic Fourier method. Therefore, the evaluation of the dislocation density from the mWH-plot alone is impossible and should be avoided. The mWH plot however, is very useful in practice. Its linearity indicates a consistent asymptotic line-profile analysis.

A Combined Atomistic-Continuum Study on the Unfaulting of Single and Multi-layer Interstitial Dislocation Loops in Irradiated FCC and HCP Metals

Unfaulting of single and multi-layer interstitial loops in face centered cubic (FCC) and hexagonal close-packed (HCP) metals, with Ni, Al, Mg and Zr as model systems, have been comprehensively studied employing molecular dynamics simulations and continuum modeling. A versatile approach properly accounting for atom insertion/removal and displacement field was developed, able to correctly construct single and multi-layer interstitial loop structures of arbitrary geometries. The unfaulting mechanisms and corresponding dislocation reaction intermediates in different unfaulting scenarios were clarified. Critical conditions necessary for unfaulting have been identified, and an analytical model has been developed to accurately predict these conditions. Particularly for unfaulting in FCC materials, the role of Double Shockley (D-Shockley) partial in unfaulting has been explicitly elucidated, and the mechanisms of unfaulting initiating from periphery of the Frank loop and induced by a moving straight edge dislocation have been clarified. For unfaulting in HCP, despite certain similarity to its FCC counterpart, clear difference in unfaulting behaviors due to the HCP stacking sequence has been demonstrated. A comprehensive mapping of unfaulting routes for double-layer interstitial loops in HCP has been established to reveal the relationships between the various loop morphologies observed in experiments. The present work provides important mechanistic insights to address key knowledge deficits regarding interstitial Frank loop unfaulting, essential for better understanding of deformation and irradiation-induced failure in structural metals. The new modeling techniques and predictive tools offered are expected to be of great merits to not only the study of unfaulting of dislocation loops, but also future investigation of other complex dislocation or defect ensembles.

THE MECHANISM OF THE SHOCK WAVE OF PLASTIC DEFORMATION IN METALS

A problem related to the evolution of the density of edge dislocations based on a system of equations for a dislocation ensemble is considered. Considering that during the evolution of the dislocation ensemble, the perturbations of the total dislocation density are small, an equation is obtained that obeys the evolution of the excess dislocation density (dislocation charge). It is shown that in the resulting equation, the nonlinear term due to the annihilation of dislocations is decisive in the evolution of the dislocation charge, provided that the dimensionless parameter R (similar to the Reynolds number in a viscous medium) is greater than one. Under these conditions, the original equation admits a self-similar solution in the form of a wave front of a dislocation charge I(x,t) running along a certain direction. This solution, however, is physically unstable, due to problematic boundary conditions. Therefore, a more feasible case was analyzed in which the initial evolutionary equation for the dislocation charge is reduced to the Burgers equation. For this equation, for sufficiently large values of R, an asymptotic solution I(x,t) = x/t was obtained in the form of a triangular shock wave, which has an amplitude I(x,t) and a front width dx ~ 1/R at the boundary of the wave x0 (for x > x0, I = 0 must be fulfilled). Estimates show that the propagation of the dislocation charge takes on the character of a shock front (R >> 1) if there are internal prerequisites for such an evolution of the dislocation charge, namely: effective conditions arise for the formation of a sufficient number of clusters of N0 in front of various barriers (it is shown that R ~ N0). Otherwise, the dynamics of the dislocation charge acquires the character of diffusion spreading.

The effect of hydrogen on the mechanical properties of metals under conditions of high-speed deformation

The movement of an ensemble of edge dislocations in metals with a high hydrogen content under conditions of high-speed deformation (high strain rate deformation) is theoretically analyzed. Within the framework of the theory of dynamic interaction of defects (DVD) (DID), an analytical expression is obtained for the dependence of the dynamic yield strength on the concentration of hydrogen atoms. Keywords: dislocations, hydrogen, high-speed deformation, metals.

Violation of the Taylor relation under high-energy external influences

The motion of an edge dislocation ensemble in a binary alloy under high strain rate deformation is theoretically analyzed. Within the framework of the theory of dynamic interaction of defects (DID) an analytical expression for the dependence of the dynamic yield stress on the dislocation density is obtained. The conditions for the violation of the Taylor relation under high-energy external influences are determined. The experimentally observed nonmonotonic dependence of the dynamic yield strength on the dislocation density is explained. The minimum of this dependence is due to the competition between the influence of various structural defects on moving dislocations. This minimum takes place during the transition from the dominance of dynamic drag by one type of defects to the dominance of another type defects. Keywords: dislocations, high strain rate deformation, defects, Guinier-Preston zones, alloys.

Нарушение соотношения Тейлора в условиях высокоэнергетических внешних воздействий

The motion of an edge dislocation ensemble in a binary alloy under high strain rate deformation is theoretically analyzed. Within the framework of the theory of dynamic interaction of defects (DID) an analytical expression for the dependence of the dynamic yield stress on the dislocation density is obtained. The conditions for the violation of the Taylor relation under high-energy external influences are determined. The experimentally observed nonmonotonic dependence of the dynamic yield strength on the dislocation density is explained. The minimum of this dependence is due to the competition between the influence of various structural defects on moving dislocations. This minimum takes place during the transition from the dominance of dynamic drag by one type of defects to the dominance of another type defects.

Dynamics of curved dislocation ensembles

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single slip situation. In order to reduce the complexity of the problem a dipole like approximation for the orientation dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the GND densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

Forming a convex flange by pulsed-magnetic field pressure

A large number of parts used in aircraft are D16AM sheet metal flanged parts. Stress plays a role in reducing damage and improving plasticity. Common to such parts is the necessary shaping to increase rigidity and reduce weight. High strain rate forming is a dynamic shaping process that uses the instantaneous impact pressure generated by suddenly released energy to plastically process metal sheets for the numerical study and simulation of the process of magnetic-pulse forming (MPF) of convex flanging. The LS-DYNA program was used, a universal software multi-purpose system of the finite element complex. A computer simulation technique was developed, which allows, in accordance with the required geometry of the die surface and with the selected loading schemes, to take into account the change in load over the deformable area and set the distribution of the pulsed magnetic field (PMF) pressure intensity, vary the geometric parameters of the blanks and the characteristics of the material. In the case of elastic-plastic deformation of a solid, within the framework of the modern approach, it is a cooperative deformation process caused by correlated motion in an ensemble of crystal lattice dislocations. This causes a change in the volume of a deformable body under load by the pressure of a pulsed magnetic field; when the load is removed, the internal stress is almost completely removed and the volume of the body takes the required shape in our case in the form of a convex flange.