Dislocation Segment Length Research Articles

Static Unified Inelastic Model: pre- and post-yield dislocation-mediated deformation

Modelling dislocation glide over the initial part of a stress–strain curve of metals received little attention up to now. However, dislocation glide is essential to ones understanding of the fundamental relationship between inelastic deformation and the evolution of the dislocation network structure. Therefore, we present a model of dislocation-driven deformation under static loading conditions.We reproduce repeated cyclic uniaxial tensile tests on Interstitial-Free and Low-Alloy steels. The elastic mechanical behaviour is described by isotropic linear elasticity, pre-yield anelastic mechanical behaviour by a dislocation bow-out model with dissipation, and the post-yield evolution of dislocation network structure by a statistical storage model. We hypothesise that when the local anelastic compliance is lower than the global plastic compliance, deformation is mechanically recoverable, and vice versa. This hypothesis is corroborated with the classical Taylor relation. We report the relation between stable and unstable dislocation glide using this prototypical modelling framework.We find four structural variables, that are based on dislocation physics, to describe the stress–strain curve: total dislocation density, average dislocation segment length, dislocation junction formation rate, and average dislocation junction length. Firstly, we quantify the dislocation network evolution during uniaxial monotonic loading, and verify work-hardening by dislocation junction formation and a Taylor-type equation for flow. Finally, we present a semi-empirical relation for the evolution of the dislocation network structure. Which allows us to: refine the physical interpretation of the Taylor relationship, and rationalise experimental observations on apparent modulus degradation by thermomechanical processing. Both these findings circumvent the limitations of current, physics-based hardening models.

Nonlocality of Dynamic Characteristics for Edge Dislocation Segment, Elastic Interaction of Dislocation with Pinning Points, and their Effect on Dislocation AIIF

In the present work, we studied dislocation amplitude-independent internal friction (AIIF) for segment of edge dislocation. Results obtained were compared with results of the Koehler-Granato-Lücke string model. Expression for dislocation effective rigidity and effective mass, obtained earlier by applying generalized susceptibility of dislocation, is used. Dependences of dislocation effective rigidity on dislocation segment length, dislocation effective mass on frequency and segment length, internal friction on for various values of frequency and segment length are plotted. Case of elastic interaction of the dislocation segment with pinning points is also investigated. It was found that main effect of elastic interaction the dislocation with the pinning points is reduces to influence in the effective rigidity. Plots of internal friction dependence on frequency for various values of distance between the dislocation and the pinning points are constructed.

A Mesh-Independent Brute-Force Approach for Traction-Free Corrections in Dislocation Problems

Simulation of dislocation dynamics opens the opportunity for researchers and scientists to observe in-depth many plastic deformation phenomena. In 2D or 3D media, modeling of physical boundary conditions accurately is one of the keys to the success of dislocation dynamics (DD) simulations. The scope of analytical solutions is restricted and applies to specific configurations only. But in dynamics simulations, the dislocations’ shape and orientation change over time thus limiting the use of analytical solutions. The authors of this article present a mesh-based generalized numerical approach based on the collocation point method. The method is applicable to any number of dislocations of any shape/orientation and to different computational domain shapes. Several verifications of the method are provided and successful implementation of the method in 3D DD simulations have been incorporated. Also, the effect of free surfaces on the Peach-Koehler force has been computed. Lastly, the effect of free surfaces on the flow stress of the material has been studied. The results clearly showed a higher force with increased closeness to the free surface and with increased dislocation segment length. The simulations’ results also show a softening effect on the flow stress results due to the effect of the free surfaces.

Statistical mechanics of kinks on a gliding screw dislocation

The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.

Size dependence of the dislocation segment vibration spectrum for various types of dislocations

The vibration spectra of the edge, mixed and screw dislocations, depending on the dislocation segment length, are considered. The value of Poisson’s ratio 1/3 is assumed. The normalized values of the eigenfrequencies and damping coefficients for different frequency numbers by equating the inverse matrix of dislocation oscillators generalized susceptibilities to zero were found. It is seen from the dependences obtained that in the case of a screw dislocation, the transformation of the dislocation oscillators generalized susceptibility poles occurs. For edge and mixed dislocations the transformation of the poles was not observed. This agrees with the results of the vibration spectrum orientation dependence study. The authors suggest that these differences are due to the presence of a screw dislocation quasilocal vibration branches.

Effect of Si and Zn doping on surface defects in AlGaInAs compositionally graded buffer by MOCVD

The influence of Zn and Si atoms on AlGaInAs compositionally graded buffers (CGBs) was studied using the approaches of optical microscopy, reciprocal space mapping, Raman spectroscopy and cathodoluminescence imaging. CGBs with Zn or Si doping could achieve good relaxation of about 90%, while Si but not Zn doping significantly impacted the tilt angle. Ribbon-like scratches along the 〈1–10〉 direction were observed in samples with Si doping. Sharp increases in threading dislocation density (TDD) and dislocation pile-up were observed along the scratches. In contrast, CGBs with Zn doping featured smooth surfaces and lower TDDs, contributing to improved chip performance. Based on these results, we conclude that Si atoms decrease the glide length of misfit dislocation segments and cause dislocation nucleation multiplication and dislocation pile-up and eventually increase surface roughness and TDD, while Zn could serve as a surface surfactant medium.

Dislocation content in random high angle grain boundaries

The dislocation content of high angle grain boundaries in a random FCC polycrystal was determined through large-scale molecular dynamics modeling and the dislocation extraction algorithm for detecting dislocations. This method provides a means of calculating grain boundary dislocation content in atomistic samples from relaxed atomic positions. It was found that a large fraction of the boundaries studied contained significant densities of lattice and partial dislocations as part of their structure. The observed dislocation content varied widely depending on the boundary’s specific geometrical parameters. The average grain boundary dislocation segment length observed is of the order of the grain boundary thickness, as calculated from the simulation data. The dislocation densities changed significantly during virtual tensile straining of the samples, as dislocations are emitted from and absorbed at grain boundaries. These results are discussed in the context of the role of the multiplicity of possible grain boundary structures on the deformation response of polycrystalline materials.

К РАСЧЕТУ ВНУТРЕННИХ НАПРЯЖЕНИЙ ОТ МЕЗОДЕФЕКТОВ, НАКАПЛИВАЮЩИХСЯ НА ГРАНИЦАХ РАЗДЕЛА ПРИ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ ТВЕРДЫХ ТЕЛ

A new method of calculation of elastic stress fields from internal interfaces (intergranular and interphase boundaries) of plastically deformed polycrystals is proposed. As elementary sources of stress fields, rectangular boundary segments containing uniformly distributed segments of dislocation families accumulating on these segments during plastic deformation are considered. It is shown that the elastic stresses field from a segment with arbitrary geometry of plastic flow and segment orientation can be represented as a superposition of fields from four families of continually distributed dislocation segments with tangential and normal components of the Burgers vector. Analytical expressions for the elastic stress tensor components from each of the four families are obtained. In the limiting case, when the length of dislocation segments tends to infinity, the resulting expressions for the components of the elastic stress field transform known expressions for rotational and shear mesodefects. If dislocation segments have a normal burgers vector, then the stress field is equivalent to the stress field from the biaxial dipole of wedge disclinations. In the case of tangential components of the burgers vector, the field is equivalent to the stress field of the planar mesodefect. As an example of the method application, the calculation of internal stress fields in the plastically deformed crystal containing uniformly distributed cubic particles of the second phase is given. It is shown that the intensity of internal stresses at a given value of strain increases with increasing volume fraction of particles. It is found that for a given volume fraction of the second phase, the internal stresses does not depend on their size.

Two modes of screw dislocation glide in fcc single-phase concentrated alloys

Concentrated solid solution alloys (CSSAs), including medium- and high-entropy alloys, are currently being considered as prospective materials in many applications. The behavior of CSSAs under different conditions, including mechanical loading, differs from that of conventional alloys and has been the subject of intensive study by different techniques. In many cases, their behavior is treated by modifying solid solution hardening models, which, in principle, does not reflect many important features of CSSAs where the distinction between solute and solvent atoms is not clear. In this work, we report the results of an atomic-scale study of ½<110>{111} screw dislocation motion in an fcc equiatomic Ni-Fe alloy. Molecular dynamics simulations demonstrate that the dislocation has two distinctive modes for glide. At lower stress, dislocations move in a very rough manner that cannot be described as continuous glide but rather as jerky motion through a set of obstacles. At high stress, they glide in a manner similar to lattice friction-controlled conditions in single component systems. The stress for the transition between modes depends on the dislocation segment length and temperature. At 300 K, the flow stress saturates at ∼130 MPa for lengths above ∼140 |b| (b is the Burgers vector).

Molecular dynamics study of defect and dislocation behaviors during tensile deformation of copper-silver core-shell nanowires with varying core diameter and shell thickness

Core-shell type nanostructures have drawn much attention among material researchers as they exhibit exceptional properties due to their unique structure. Among different core-shell nanostructures, copper-silver core-shell nanostructures are widely investigated in recent days for exhibiting different unique properties like very high mechanical strength. Molecular dynamics simulations were carried out to investigate the underlying deformation mechanism during tensile testing of copper-silver core-shell nanowires with varying core diameter and shell thickness. The Wigner-Seitz defect analysis was used to calculate the total number of point defects like vacancies and interstitials during the entire deformation process. The type, number, and total length of dislocation segments were thoroughly investigated throughout the different stages of deformation. The effects of varying core diameter and shell thickness on the defect and dislocation configurations were also studied. Thus, this study helps us to understand the underlying mechanisms or factors that contribute to the ultra-high strength and mechanical properties of Cu-Ag core-shell nanowires with varying core diameter and shell thickness.

Interaction Length for Dislocations in Compositionally-Graded Heterostructures

Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length Lint. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.

Cross-slip of long dislocations in FCC solid solutions

Cross-slip of screw dislocations is a dislocation process involved in dislocation structuring, work hardening, and fatigue. Cross-slip nucleation in FCC solid solution alloys has recently been shown to be strongly influenced by local fluctuations in spatial arrangement of solutes, leading to a statistical distribution of cross-slip nucleation barriers. For cross-slip to be effective macroscopically, however, small cross-slip nuclei (∼40b) must expand across the entire length of typical dislocation segments (102−103b). Here, a model is developed to compute the relevant activation energy distribution for cross-slip in a random FCC alloy over arbitrary lengths and under non-zero Escaig and Schmid stresses. The model considers cross-slip as a random walk of successive flips of adjacent 1b segments, with each flip having an energy consisting of a deterministic contribution due to constriction formation and stress effects, plus a stochastic contribution. The corresponding distribution is computed analytically from solute-dislocation and solute-solute binding energies. At zero stress, the probability of high activation energies increases with dislocation length. However, at stresses of just a few MPa, these barriers are eliminated and lower barriers are dominant. For increasing segment length, the effective energy barrier decreases according to a weak-link scaling relationship and good analytic predictions can be made using only known material properties. Overall, these results show that the effective cross-slip barrier in a random alloy is significantly lower than estimates based on average elastic and stacking fault properties of the alloy.

Numerical and approximate calculation of the generalized susceptibility matrix elements of dislocation segment in nondissipative crystal

Numerical calculation of the generalized susceptibility and the inverse generalized susceptibility matrix elements of the dislocation segment for edge and screw dislocations, different frequencies and different values of the dislocation segment length is performed. Certain regularities have been established. Based on the graphical results of numerical calculations, an approximate calculation of the generalized susceptibility matrix elements was carried out. Expressions for the diagonal and off-diagonal generalized susceptibility matrix elements of the dislocation segment are obtained.

Unravelling dislocation networks in metals

Understanding the intricate structure of dislocations in metals is a major issue in materials science. In this paper we present a comprehensive approach for the characterisation of dislocation networks, resulting in accurate quantification and significantly increasing the insight into the dislocation structure. Dislocation networks in metals consists of dislocation segments, pinned by microstructural obstacles. In the present paper a model is introduced that describes the behaviour of these dislocation segments in the pre-yield range of a tensile test on the basis of fundamental concepts of dislocation theory. The model enables experimental quantification of the dislocation density and segment length from the tensile curve. Quantitative results are shown and discussed on the development of the dislocation network as a function of increasing degree of plastic deformation, including validation and physical interpretation of the classical Taylor equation.

Zr alloying effect on the microstructure evolution and plastic deformation of nanostructured Cu thin films

The magnetron sputtering technique was employed to prepare Zr-alloyed Cu thin films with Zr addition ranging from 0 to 7.0 at.%. Microstructure evolution with Zr doping was characterized by using the transmission electron microscope and atom probe tomography. Plastic deformation characteristics (hardness, strain rate sensitivity and activation volume) of the Cu-Zr alloyed films were examined by using nanoindentation testing. Significant Zr doping effects on the microstructure were clearly uncovered that (i) the Zr segregated at grain boundaries and tuned the grain boundary structure. With increasing the Zr addition, CuZr amorphous particles at grain boundaries (3.0 at.% Zr) and even three dimensional CuZr amorphous grain boundary network (7.0 at.% Zr) were formed; (ii) the grains (size and morphology) and nanotwins were notably influenced by the Zr doping. In particular, the nanotwin thickness was reduced from ∼25 nm in the pure Cu film down to ∼5 nm in the Cu-Zr alloyed films. Accompanied with the microstructure evolution, the Cu-Zr thin films displayed hardness and strain rate sensitivity highly sensitive to the Zr doping, i.e., hardness increasing while strain rate sensitivity decreasing with raising the Zr addition. The strengthening and deformation mechanisms were discussed in terms of the microstructure-property relationship. Three regimes were divided within the studied Zr doping range: grain/nanotwin boundary-dominated strengthening mechanism in the regime I of pure Cu film, dislocation nucleation-controlled nanotwin softening mechanism in the regime II of Zr addition ≤3.0 at.%, and intergranular amorphous layer-mediated strengthening mechanism in the regime III of Zr addition up to 7.0 at.%. In addition, the reduction in strain rate sensitivity with Zr doping was quantitatively described by adopting a model that involves the thermally activated partials depinning mechanism based on the effective dislocation segment length.

Quantification of dislocation structures from anelastic deformation behaviour

The pre-yield deformation behaviour (i.e., at stresses below the yield stress) of two materials, pure iron and a low-alloy steel, and its anelastic nature are analysed at room temperature, before and after the dislocation structures are varied by plastic deformation. It is shown, based on tensile experiments, that this behaviour can be explained by limited reversible glide of dislocations without essential changes in the dislocation structure. Moreover, a physically-based model that characterises the dislocation structure by two variables, the dislocation density and the effective dislocation segment length, is used to quantitatively describe this deformation behaviour. The model validity is further evaluated by comparison with dislocation densities from X-Ray Diffraction measurements.

Constitutive Modeling of Primary Creep Behaviour of P9 Steel

A constitutive model developed for the description of primary creep behaviour in P9 steel has been presented. The concept of stress dependent activation volume and average dislocation segment length based on Friedel statistics has been incorporated into the kinetic creep law related to dislocation glide controlled by dispersed local obstacles. The kinetic creep law has been coupled with internal stress evolution relation in order to get better description of creep deformation behaviour. The model assumes that the internal stress evolves from the initial to saturation value during primary creep. The associated physical constants in the model have been determined by the minimization of errors between experimental and predicted creep strain–time data. The applicability of the constitutive model has been demonstrated by describing primary creep behaviour appropriately in P9 steel for wide stress range at 873 K.

A physically based yield criterion II. Incorporation of Hall Petch effect and resistance due to thermally activated dislocation glide

The anelastic model developed in part I of this paper [1] is extended to incorporate the Hall–Petch effect and the thermally activated pre yield phenomena that were revealed in the stress cycling experiments The yield criterion developed in [1] is tested by application to Hall–Petch experiments and measurements of the yield stress as a function of strain rate and temperature. The results of the strain rate/temperature experiments support the conclusion that reversible dislocation glide occurs before yield and massive dislocation multiplication. The model is substantiated by analysis of parameters pertaining to the initial dislocation structure viz. the average initial dislocation segment length and density computed from experimental data by application of the model equations.

Effect of a constant magnetic field on dislocation anharmonicity in silicon

The effect of constant magnetic fields on dislocation anharmonicity of p-type silicon single crystals with a conductivity of 6 Ω cm has been studied. It has been found that preliminary exposure of dislocation silicon (with a dislocation density of 104–106 cm−2) to a constant magnetic field (B = 0.7 T, t = 30 min) at room temperature causes a change in the nonlinear fourth-order elastic modulus βd. The observed changes are associated with the dynamics of magnetosensitive complexes of structural defects and, hence, with the changes in the length of the vibrating dislocation segment. Based on the dynamics of βd(t) after sample exposure to a magnetic field, the conclusion is made about an increase in the vibrating dislocation segment length Ld by 30%, and the characteristic relaxation times of observed effects are estimated.

Impulse Excitation Internal Friction Study of Dislocation and Point Defect Interactions in Ultra-Low Carbon Bake-Hardenable Steel

The simultaneous presence of interstitial solutes and dislocations in an ultra-low carbon bake-hardenable steel gives rise to two characteristic peaks in the internal friction (IF) spectrum: the dislocation-enhanced Snoek peak and the Snoek–Kê–Köster peak. These IF peaks were used to study the dislocation structure developed by the pre-straining and the static strain aging effect of C during the bake-hardening process. A Ti-stabilized interstitial-free steel was used to ascertain the absence of a γ-peak in the IF spectrum of the deformed ultra-low carbon steel. The analysis of the IF data shows clearly that the bake-hardening effect in ultra-low carbon steel is entirely due to atmosphere formation, with the dislocation segment length being the main parameter affecting the IF peak amplitude. Recovery annealing experiments showed that the rearrangement of the dislocation structure lead to the elimination of the C atmosphere.