Dislocation Velocity Research Articles

Glide and mixed climb dislocation velocity in γ-TiAl investigated by in-situ transmission electron microscopy

Dislocation velocities at high temperatures in metallic systems are believed in literature to be different for glide and climb, the values being bigger in case of glide. However, this has not been experimentally established. Therefore, in this study, dislocation velocities were measured with simultaneous determination of the corresponding mechanism (glide or mixed climb). For this purpose, coupled experiments of measurements of dislocation velocities by in-situ TEM investigations and of determination of movement planes by stereographic analyses have been carried out at 770–790 °C in the γ phase of an intermetallic Ti-48.4Al-0.1B (at.%) alloy. Mixed climb and pure glide mechanisms have thus been identified, both leading to dislocation velocities in the same order of magnitude (in the 0.5–5 nm/s range), showing that within a transition temperature domain, mixed climb can reach the velocity of glide.

Mobility of carbon-decorated screw dislocations in bcc iron

We investigate the mobility of screw dislocations decorated by carbon solutes in body-centred cubic iron based on density functional theory (DFT) calculations and transmission electron microscopy (TEM) observations of in-situ straining experiments. We focus on the high-temperature domain, between 500 and 800 K, where plasticity is controlled by the slow glide of decorated screw dislocations with a mobility similar to the Peierls mechanism existing below 300 K, at variance with the athermal regime observed at intermediate temperatures. We propose that due to the strong pinning of reconstructed dislocation lines by carbon solutes, dislocation glide occurs by the formation and migration of kinks, both controlled by the jumps of carbon atoms. We calculate the associated kink-pair nucleation and formation energies as well as the migration energies of isolated kinks and use these DFT values to predict the dislocation velocity as a function of temperature, applied stress and dislocation length. The validity of the mobility law is assessed by the comparison with dislocation velocities measured in TEM observations at different temperatures and local shear stresses. The quantitative agreement between the experimental measurements and the analytical model supports the proposed glide mechanism and the DFT values obtained for kink energies.

Unified crystal plasticity model for fcc metals: From quasistatic to shock loading

Mechanical response of metals is strongly dependent on the strain rate and exhibits drastic change as the strain rate varies across >10 orders of magnitude from quasistatic to shock loading. In this paper, we developed a unified crystal plasticity model for face-centered cubic (fcc) metals to describe the mechanical response in a wide range of strain rate from ${10}^{\ensuremath{-}5}$ to ${10}^{7}/\mathrm{s}$. The plasticity framework adopts the dislocation-based Orowan equation. Specifically, the mobility law for dislocation velocity incorporates both the thermal activation mechanism dominating at low strain rates and drag mechanism dominating at high strain rates, through a repeating waiting-running model. The rate dependence of total dislocation density (${\ensuremath{\rho}}_{t}$) evolution in the Orowan equation (implicitly) is captured by coupling the rate-dependent annihilation and the stress-dependent nucleation. More importantly, to capture the huge variation in mobile/total dislocation ratio ($f={\ensuremath{\rho}}_{m}/{\ensuremath{\rho}}_{t}$) at different strain rates, we propose a physics-based law for mobile dislocation fraction $f$ based on the exponential distribution of dislocation link lengths through a critical link length determined by the local stress. In addition, a thermohyperelastic model is supplemented to account for the nonlinear elastic behavior and thermoelastic coupling at shock loading. This unified model is validated against the mechanical response of single-crystal aluminum from quasistatic $(10{}^{\ensuremath{-}}5/\mathrm{s})$ to shock loading (${10}^{7}/\mathrm{s}$), where the features of thermal softening in static loading, thermal hardening in shock loading, and the strain-rate hardening in the medium strain-rate range are all quantitatively evaluated by a single set of parameters with a high average ${R}^{2}$ value of 0.93.

Hydrogen-induced degradation behavior of nickel alloy studied using acoustic emission technique

Hydrogen embrittlement susceptibility of nickel alloy (Inconel 625) is examined by a conventional strain rate tensile test (10−3 s−1) equipped with an acoustic emission (AE) setup. From the spectral analysis of AE signals coupled with the clustering procedure followed by the electron microscopic characterization, we have demonstrated the capability of the AE technique in identifying the hydrogen-dislocation interactions, crack initiation and propagation in various hydrogen-charged samples. The enhanced hardening behavior of hydrogen-charged samples is investigated from the viewpoint on the elementary dislocation theory, using a phenomenological relationship between the acoustic emission power and the experimentally measurable strain hardening parameters derived from the monotonic tensile test. In this way, we have shown that the mobile dislocation density increases with hydrogen content. In addition, the average velocity of dislocations is assessed from the AE data, and it is found to be reduced with the hydrogen concentration. The statistical crack analysis reveals the crack transition from the transgranular to intergranular mode in the samples failed under the hydrogen environment. The competition between these two fracture modes is explained by relating the hydrogen concentration profile with loading conditions.

MODEL OF FORMATION AND PROPAGATION OF SLIP BANDS IN METALS

A theoretical study of the processes of localization of plastic deformation in metals has been carried out. Within the framework of the system of evolutionary equations for dislocation density, taking into account the multiplication and annihilation of dislocations, the possibility of a running solution for the slip strip is established. It is shown that the initial system has two equilibrium states. For the total dislocation density and dislocation charge normalized to a stationary homogeneous solution for dislocation density, these are the states (0,0) and (1,0) on the phase plane of the above variables in dimensionless form. From the analysis of singular points, it follows that the point (0,0) is a stable node, and the equilibrium state (1,0) is a saddle. In this case, the desired solution of the initial system of evolutionary equations is a separatrix going from point (0,0) to point (1,0), which corresponds to solutions in the form of a drop wave for the dislocation density forming the slip band and a momentum for the dislocation charge. It is shown that the dislocation charge propagates in the front of the slip band, which moves at a velocity u = kV (V is the drift velocity of dislocations due to external load, the proportionality coefficient k satisfies the condition 0 < k < 1). After analyzing the existence of self-similar solutions, it follows that non-homogeneous wave solutions occur only at A = t1/t2 > 1, where t1 and t2 are, respectively, relaxation times of the total dislocation density and dislocation charge to a homogeneous state. Estimates show that for a given dislocation kinetics (dislocation generation and annihilation processes) A > 1, i.e. satisfy the conditions for the formation of a slip strip of a given type. The stability of the obtained wave stationary self-similar solutions is considered. Assuming that deviations from stationary solutions for the dislocation density and dislocation charge are limited to a given domain, and considering the deviations small, we obtain the Sturm – Liouville problem for own functions and eigenvalues with zero boundary conditions at the boundary of this domain. The appropriate transformation reduces the problem to an equation of the Schrodinger equation type. It is shown that under certain conditions the spectrum of the Schrodinger operator is in the left half-plane, i.e. deviations of dislocation density and dislocation charge decay exponentially over time and the desired stationary solutions are asymptotically stable. The issue related to the determination of the steady-state velocity of wave propagation is considered. Linearization of the initial system of equations for dislocation density and dislocation charge allowed us to obtain a linear sine-Gordon equation, from the solution of which the steady-state wave velocity is determined. It is shown that for the initial system of the system of equations for A > 1, arbitrary initial distributions of the desired variables acquire the form of self-similar solutions over time and move at the lowest possible speed u = 2VA1/2/(1 + A).

Energy and velocity of sliding of edge and screw dislocations in austenite and Hadfield steel: Molecular dynamics simulation

The sliding of edge and screw dislocations in Hadfield steel and in pure HCC iron (austenite) depending on temperature and deformation rate was studied by the method of molecular dynamics. The complete dislocation appears in the present model immediately in the form of a split into a pair of partial Shockley dislocations separated by a packing defect. The distance between partial dislocations is several nanometres. As the shear rate increases, this distance decreases. According to the data obtained, the energies of edge and screw dislocations in steel are higher than in pure austenite. The energy of the total edge dislocation in γ-iron and Hadfield steel averages 2.0 and 2.3 eV/Å, helical – 1.3 and 1.5 eV/Å respectively. Dependences of the sliding velocity of the edge and screw dislocations on the shear rate and temperature were obtained. The sliding velocity of the edge dislocation is in all cases higher than the screw one, which is explained by the difference in the propagation velocity of longitudinal and transverse waves in the material. With an increase in the shear rate, the sliding speed increases to a certain limit, depending on the propagation velocity of the corresponding elastic waves. At low and normal temperatures, the sliding velocity of dislocations in Hadfield steel is significantly (about one and a half times) lower compared to pure HCC iron. In pure iron, the sliding velocity of dislocations decreases with increasing temperature. However, for Hadfield steel, this dependence is nonmonotonic: as the temperature increases to about 500 K, the dislocation rate increases. That is probably due to the intensification of diffusion of impurity carbon atoms; then, as in iron, it decreases.

Tensile Behavior, Constitutive Model, and Deformation Mechanisms of MarBN Steel at Various Temperatures and Strain Rates.

To reduce harmful gas emission and improve the operational efficiency, advanced ultra-supercritical power plants put forward higher requirements on the high temperature mechanical properties of applied materials. In this paper, the tensile behavior and deformation mechanisms of MarBN steel are discussed at different strain rates (5 × 10-3 s-1, 5 × 10-4 s-1, and 5 × 10-5 s-1) under room temperature and 630 °C. The results show that the tensile behavior of the alloy is dependent on temperature and strain rate, which derived from the balance between the average dislocation velocity and dislocation density. Furthermore, observed dynamic recrystallized grains under severe deformation reveal the existence of dynamic recovery at 630 °C, which increases the elongation compared to room temperature. Finally, three typical constitutive equations are used to quantitatively describe the tensile deformation behavior of MarBN steel under different strain rates and temperatures. Meanwhile, the constitutive model of flow stress for MarBN steel is developed based on the hyperbolic sine law.

Atomic-scale modeling of [formula omitted] edge dislocations in UO[formula omitted]: Core properties and mobility

The dislocation properties of UO2, the main nuclear fuel material, are important ingredients to model the mechanical properties and predict nominal and accidental operations of nuclear plant reactors. However, the plastic behaviour of UO2 is complex with little known about dislocations and other extended defects. In this study, we use a combination of interatomic potential-based atomistic simulations and ab initio calculations to investigate the core structure and mobility of the 12〈110〉{001} edge dislocation, which controls the plasticity of UO2 single crystals. Various dislocation cores are obtained and compared, including the classical asymmetric Ashbee core and a so-far unreported core made of an alternation of both variants of the Ashbee core along the dislocation line. This new core, called here zigzag, is ubiquitous in molecular dynamics simulations at high temperature in the nominal-to-accidental transient regime (1600 to 2200 K). Molecular dynamics is also used to determine the velocity of the edge dislocation as a function of temperature and stress. A dislocation mobility law is adjusted from the simulations and provides an up-scaling ingredient central to the multi-scale modeling of UO2 nuclear fuel mechanical properties.

Plastic deformation of superionic water ices

Due to their potential role in the peculiar geophysical properties of the ice giants Neptune and Uranus, there has been a growing interest in superionic (SI) phases of water ice. So far, however, little attention has been given to their mechanical properties, even though plastic deformation processes in the interiors of planets are known to affect long-term processes, such as plate tectonics and mantle convection. Here, using density functional theory calculations and machine learning techniques, we assess the mechanical response of high-pressure/temperature solid phases of water in terms of their ideal shear strength (ISS) and dislocation behavior. The ISS results are well described by the renormalized Frenkel model of ideal strength and indicate that the SI ices are expected to be highly ductile. This is further supported by deep neural network molecular dynamics simulations for the behavior of lattice dislocations for the SI face-centered cubic (fcc) phase. Dislocation velocity data indicate effective shear viscosities that are orders of magnitude smaller than that of Earth's lower mantle, suggesting that the plastic flow of the internal icy layers in Neptune and Uranus may be significantly faster than previously foreseen.

Limiting velocities and transonic dislocations in Mg

To accurately predict the mechanical response of materials, especially at high strain rates, it is important to account for dislocation velocities in these regimes. Under these extreme conditions, it has been hypothesized that dislocations can move faster than the speed of sound. However, the presence of such dislocations remains elusive due to challenges associated with measuring these experimentally. In this work, molecular dynamics simulations were used to investigate the dislocation velocities for the basal edge, basal screw, prismatic edge, and prismatic screw dislocations in Mg in the sub-, trans-, and supersonic regimes. Our results show that only prismatic edge dislocations achieve supersonic velocities. Furthermore, this work demonstrates that the discrepancy between the theoretical limiting velocity and the MD results for Mg is due to its sensitivity to large hydrostatic stress around the dislocation core, which was not the case for fcc metals such as Cu.

Correlating dislocation mobility with local lattice distortion in refractory multi-principal element alloys

Multi-principal element alloys (MPEAs) exhibit different degrees of intrinsic lattice distortion, which varies with constituent species. Using atomistic simulations, here we found the mobilities of both edge and screw dislocations are dependent on lattice distortion in body-centered-cubic (BCC) MPEAs. Lattice distortion influences not only the activation of kink nucleation and propagation governing screw dislocation motion, but also the strength of local pinning for edge dislocations. As a consequence, the disparity between the velocities of screw and edge dislocations decreases with increasing lattice distortion. We further demonstrate that lattice distortion can be taken as an indicator to correlate with the reported brittleness of BCC MPEAs. This implies that maximizing lattice distortion could be a plausible strategy to improve the ductility for brittle BCC MPEAs.

An advanced mean field dislocation density reliant physical model to predict the creep deformation of 304HCu austenitic stainless steel

Physical based creep modelling enables to understand the life-limiting factors that are required for a safe and economic operation of power plant components. Thus, herein an improved physical approach to address the creep behavior of 304HCu austenitic stainless steel is presented. This approach combines a dislocation density reliant physical model with a continuum damage mechanics (CDM) model. Two different dislocation densities: mobile and forest, and dislocation mean free path are used to describe the substructure in order to model the creep strain. The original Orowan’s equation for estimating creep strain rate is modified employing CDM based softening parameters to take account of damage causing tertiary creep. The model is advantageous in the sense that with the ongoing creep, the evolution of different variables that are dislocation densities, dislocation mobility, dislocation velocity, internal stress, effective stress and damage evolution is tracked and discussed thoroughly. Furthermore, the model output is corroborated with experimental creep data of 304HCu steel. The predicted values of forest dislocation density, mobile dislocation density, mean free path, internal stress, effective stress, dislocation mobility and dislocation velocity are in the range of 7.91 × 1011 – 1.01 × 1013 m−2, 8.16 × 1010 – 4.56 × 1011 m−2, 9.35 – 9.80 µm, 11.70 – 35.50 MPa, 86.0 – 165.0 MPa, 1.68 × 10−9 – 2.11 × 10−7 Pa−1s−1 and 6.48 × 10−11 – 7.45 × 10−9 m/s, respectively, at the end of simulation.

Creep curve modelling of Austenitic Steel 316LN

Physical based creep models that elucidate the creep deformation behaviour with ongoing microstructural evolution can be a useful tool for the components life assessment as well as the design of improved materials, deployed at high temperature and pressure. In this research work, a creep model that is a combination of physical based model and CDM approach is employed to predict the creep curves of steel 316LN. The microstructure based variables those are different dislocation densities (mobile and forest) are the input parameters. The model provides a provision for the assessment of each microstructural variable, in each time step of the creep deformation. Consequently, other than creep curves, the model also demonstrates the evolution of dislocation density (mobile and forest), dislocation velocity, dislocation mobility and mean free path. Initial values of input parameters (various dislocation densities and mean free path) are obtained from the literature for initializing the model. It can be observed that the predicted creep curves are in reasonable agreement with experimental ones and the evolution of other involved parameters is discussed thoroughly.

Dynamic strain aging and the role of the Cottrell atmosphere

We have developed an atomistic kinetic Monte Carlo (kMC) model describing carbon diffusion, trapping and detrapping in the stress field generated by a 1/2[111] screw dislocation in bcc iron. By performing long time scale carbon diffusion simulations we study the formation of carbon Cottrell atmospheres around screw dislocations at different temperatures and background carbon concentrations. The kMC simulations allow us to predict the rate of formation and strength of carbon atmospheres which control the dislocation's behavior resulting in dynamic strain aging in steel. From the kMC simulations of carbon diffusivity in a block of iron crystal containing a screw dislocation we extract the effective diffusion constants. Our results show that except at low carbon concentrations the diffusivity resulting from carbon transport inside the dislocation core dominates the effective diffusivity, which indicates that pipe diffusion in a screw dislocation is likely. The kMC approach, which explicitly accounts for the behavior of individual carbon atoms, offers an atomistic view of the carbon drag mechanism by which mobile dislocations can collect and transport carbon within their cores. We simulate the carbon drag mechanism at different temperatures, background carbon concentrations, and dislocation velocities and estimate the maximal dislocation velocity at which the atmosphere of carbon atoms can follow a moving screw dislocation.

Nanoscale defect evaluation framework combining real-time transmission electron microscopy and integrated machine learning-particle filter estimation

Observation of dynamic processes by transmission electron microscopy (TEM) is an attractive technique to experimentally analyze materials’ nanoscale phenomena and understand the microstructure-properties relationships in nanoscale. Even if spatial and temporal resolutions of real-time TEM increase significantly, it is still difficult to say that the researchers quantitatively evaluate the dynamic behavior of defects. Images in TEM video are a two-dimensional projection of three-dimensional space phenomena, thus missing information must be existed that makes image’s uniquely accurate interpretation challenging. Therefore, even though they are still a clustering high-dimensional data and can be compressed to two-dimensional, conventional statistical methods for analyzing images may not be powerful enough to track nanoscale behavior by removing various artifacts associated with experiment; and automated and unbiased processing tools for such big-data are becoming mission-critical to discover knowledge about unforeseen behavior. We have developed a method to quantitative image analysis framework to resolve these problems, in which machine learning and particle filter estimation are uniquely combined. The quantitative and automated measurement of the dislocation velocity in an Fe-31Mn-3Al-3Si autunitic steel subjected to the tensile deformation was performed to validate the framework, and an intermittent motion of the dislocations was quantitatively analyzed. The framework is successfully classifying, identifying and tracking nanoscale objects; these are not able to be accurately implemented by the conventional mean-path based analysis.

Quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations

This is the first report of a quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations. The multiplication was studied as a function of dislocation density and effective shear stress in periodic boundary conditions close to melting point of Ge, utilizing a specifically developed diamond cubic dislocation mobility module in agreement with experiments in literature. We report an average dislocation velocity law of a dislocation ensemble linearly proportional to the resolved shear stress – analogous to the single dislocation velocity law – with a reduced average dislocation mobility. Exponential dislocation multiplication was observed with a multiplication parameter δ linear proportional to the effective shear stress for various stress states and simulation volumes. The coefficient of the dislocation multiplication law was determined to be 4.0 ⋅10−3 [mN−1].

Atomistic investigation of elementary dislocation properties influencing mechanical behaviour of Cr15Fe46Mn17Ni22 alloy and Cr20Fe70Ni10 alloy

In this work, molecular dynamics (MD) simulations were used to investigate elementary dislocation properties in a Co-free high entropy (HEA) model alloy (Cr15Fe46Mn17Ni22 at. %) in comparison with a model alloy representative of Austenitic Stainless Steel (ASS) (Cr20Fe70Ni10 at. %). Recently developed embedded-atom method (EAM) potentials were used to describe the atomic interactions in the alloys. Molecular Statics (MS) calculations were used to study the dislocation properties in terms of local stacking fault energy (SFE), dissociation distance while MD was used to investigate the dissociation distance under applied shear stress as a function of temperature and strain rate. It was shown that higher critical stress is required to move dislocations in the HEA alloy compared with the ASS model alloy. The theoretical investigation of simulation results of the dislocation mobility shows that a simple constitutive mobility law allows to predict dislocation velocity in both alloys over three orders of magnitude, covering the phonon drag regime and the thermally activated regime induced by dislocation unpinning from local hard configurations.

Kink Migration along 30° Si‐Core Partial Dislocations in 4H‐SiC

Single‐layer Shockley‐type stacking fault (SSF) expansion in 4H‐SiC due to irradiation by a focused e‐beam in the scan mode with a different rate and at fixed points has been studied. It is shown that the focused e‐beam enhances the 30° Si‐core partial dislocation glide at room and liquid nitrogen temperatures only at distances smaller than about 10 μm. The dislocations are found to glide as straight lines with a velocity independent of their length even when this length essentially exceeds the size of excitation volume and the diffusion length. The results obtained show that the dislocation velocity under irradiation is mainly determined by the double kink generation rate and allow to conclude that kink migration can occur without any excitation. The kink velocity in 4H‐SiC is estimated for the first time and the lower limit for the kink velocity is of 2 × 10−4 cm s−1 at room temperature and about 2 times smaller at liquid nitrogen temperature that confirming the small activation energy for the kink migration in 4H‐SiC.

Unveiling the Mechanisms of High-Temperature 1/2[111] Screw Dislocation Glide in Iron–Carbon Alloys

We have developed a self-consistent model for predicting the velocity of 1/2[111] screw dislocation in binary iron–carbon alloys gliding by a high-temperature Peierls mechanism. The methodology of modelling includes: (i) Kinetic Monte-Carlo (kMC) simulation of carbon segregation in the dislocation core and determination the total carbon occupancy of the core binding sites; (ii) Determination of kink-pair formation enthalpy of a screw dislocation in iron—carbon alloy; (iii) KMC simulation of carbon drag and determination of maximal dislocation velocity at which the atmosphere of carbon atoms can follow a moving screw dislocation; (iv) Self consistent calculation of the average velocity of screw dislocation in binary iron–carbon alloys gliding by a high-temperature kink-pair mechanism under a constant strain rate. We conduct a quantitative analysis of the conditions of stress and temperature at which screw dislocation glide in iron–carbon alloy is accomplished by a high-temperature kink-pair mechanism. We estimate the dislocation velocity at which the screw dislocation breaks away from the carbon cloud and thermally-activated smooth dislocation propagation is interrupted by sporadic bursts of dislocation activity.

Dislocation Dynamics in Monocrystalline Si near the Melting Point Studied in Situ by X‐Ray Bragg Diffraction Imaging

To study dislocation dynamics in a model sample, an intrinsic float zone (FZ) Si wafer is chosen as seed to initiate directional solidification. During the temperature ramp, a Von Laue diffraction spot is recorded by a camera. It provides time‐resolved information on the evolution of silicon crystalline quality and on the defect nucleation locations and dynamics. With increasing temperature, dislocations are observed to propagate through the seed starting mainly from the sample edges. The effective thermomechanical local stress is estimated as low as (1.2 ± 0.4) × 105 Pa in a thermal gradient of (1.8 ± 0.2) × 102 K m−1. The latter is sufficient to allow dislocation nucleation and motion at temperatures beyond (1523 ± 9) K. Dislocation velocity increases with temperature and reaches a maximum velocity of (3.0 ± 0.5) × 10−4 m s−1 close to the silicon melting point. From the dislocation velocity measurements as a function of temperature, an activation energy of (3.1 ± 0.6) eV is estimated and this value is discussed, along with dynamical interactions between defects and dislocations.