Dislocation Kinetics Research Articles

A Dynamic Recrystallization (DRX) Constitutive Model for Elevated Temperature Flow Behavior of Cu-0.5Cr-0.1Zr Alloy

In order to obtain the high-temperature flow behavior of Cu-0.5Cr-0.1Zr alloy more accurately, the hot compression test of Cu-0.5Cr-0.1Zr alloy was performed at the strain rates from 0.001 to 1.0 s−1 and the deformation temperatures from 600 to 750 °C on a Gleeble-3800 thermo-simulation machine. The results show that the high-temperature flow stress and dynamic recrystallization behavior of Cu-0.5Cr-0.1Zr alloy are affected by strain rate and temperature. The peak stress is obvious under the condition of high temperature and low strain rate, and the flow stress curve shows a clear dynamic recrystallization phenomenon. On the contrary, there is no obvious peak stress at the low temperature and high strain rate, and dynamic softening behavior is mainly based on dynamic recovery. The high-temperature flow stress of Cu-0.5Cr-0.1Zr alloy is expressed as a result of multiple stress actions, such as work hardening, dynamic recovery softening, and dynamic recrystallization softening. The thermal deformation activation energy of this alloy can be calculated as 244.94 kJ/mol. The relationship between the critical stress and the critical strain of dynamic recrystallization and the Z parameter was established through the cubic linear fitting of the work hardening rate curve. Based on the stress–dislocation relation and kinetics of dynamic recrystallization, the constitutive equations before and after critical strain of Cu-0.5Cr-0.1Zr alloy were developed. The predicted stresses of the established DRX constitutive model agree well with the experimental stresses.

Dynamic Strength of Ni3Al Alloy Plates Under Shock Loads

The paper presents a theoretical research of the shock-induced deformation and fracture of Ni3Al alloy specimens depending on the type of its stress-strain curves. The modeling of deformation is based on a combination of the approaches of continuum mechanics and dislocation kinetics. The complex model is numerically implemented in a software system RANET-3.

A physics-based single crystal plasticity model for crystal orientation and length scale dependence of machining response

Abstract Crystal plasticity model with physics-based dislocation kinetics and hardening relations is presented in this work. The model is applied to simple shearing of machining to determine the shear angle by work minimization that is similar to the Merchant's principle. Model reveals crystal orientation dependence of cutting specific pressure during machining of single crystals in addition to the machining parameters such as friction coefficient, uncut chip thickness, rake angle, temperature, and cutting speed. The length scale dependence of machining forces is linked to the physical length of the shear plane which is treated as a limit for the mean-free-path. A unified approach is developed for the first time to account for a wide range of strain rates for machining process. Taylor-based rate insensitive model is also implemented and applied to the same problem. Taylor-based model captures the four-fold symmetry of the force patterns yet with incorrect prediction of force peak locations. The physics-based model predicts the values of cutting forces and its pattern more accurately than the Taylor-based rate-insensitive model. The significantly better results are obtained because of the treatment of stress on the shear plane in full tensor form, the strain hardening and its anisotropy, and the effect of temperature and strain-rate by the physics-based model.

The effect of phason defects on the radiation-induced swelling of quasicrystalline materials

ABSTRACTThe radiation-induced vacancy swelling of quasicrystals is considered. In quasicrystals, the dislocation kinetics involves the formation of phasons: vacancy- and interstitial-like localized topological defects. Phasons interact with radiation-induced point defects (PD; vacancies and interstitials) and influence the swelling behavior of quasicrystals. After absorption of vacancies, phasons of the interstitial type transform into phasons of the vacancy type and vice versa. In other words, phasons are the recombination centers of alternating polarity for PD. Assuming that (i) the production rate of phasons is proportional to the dislocation climbing rate and (ii) voids are the sinks for mobile phasons, the set of rate equations for PD and phasons is formulated and analyzed both analytically and numerically. It is shown that the swelling rate is lower in quasicrystals compared with crystals. Growth rates of loops and voids, as well as the swelling rate, strongly depend on the phason concentration which is controlled by phason diffusion to sinks.

A Three-Dimensional Multi-scale Plasticity Model for Metal-Intermetallic Laminate Composites Containing Phases of the L12 Structure

A three-dimensional plasticity model was developed and applied to metal-intermetallic laminate composites containing phases of the L12 structure. A multi-scale approach that combined the methods of continuum mechanics and dislocation kinetics was used. This model takes account of the different mechanisms of self-locking superdislocations, the dislocations and the dislocation walls’ density storage for each type of layer at the micro-scale. At the meso-scale, the solutions to the dislocation kinetics equations, in the form of stress–strain curves, were used to create the properties of a three-dimensional representative element. The numerical simulation study of the macroscopic deformation was carried out with the finite element method using the dynamic model of continuum mechanics, which included the classical conservation laws, constitutive equations and the equation of state. It was shown that the simulation results generated using this model were in good agreement with the mechanical tests conducted on the single crystals of the L12 structure. The model provides an excellent description of the high-temperature plastic strain superlocalization effect of single crystal intermetallics of the L12 structure. This paper describes the numerical results of the study of the tension and compression tests of metal-intermetallic laminate composites containing phases of the L12 structure. The model allows the description of the distribution of the accumulated plastic strain inhomogeneities and is capable of predicting the strengthening properties and plastic behaviour of the metal-intermetallic laminate composites containing phases of the L12 structure.

Direct prediction of the solute softening-to-hardening transition in W–Re alloys using stochastic simulations of screw dislocation motion

Interactions among dislocations and solute atoms are the basis of several important processes in metal plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive Peierls valleys. In alloys, dislocations and solutes affect each other’s kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to solute hardening is observed at a critical concentration. In this paper, we develop a kinetic Monte Carlo model of screw dislocation glide and solute diffusion in substitutional W–Re alloys. We find that dislocation kinetics is governed by two competing mechanisms. At low solute concentrations, nucleation is enhanced by the softening of the Peierls stress, which dominates over the elastic repulsion of Re atoms on kinks. This trend is reversed at higher concentrations, resulting in a minimum in the flow stress that is concentration and temperature dependent. This minimum marks the transition from solute softening to hardening, which is found to be in reasonable agreement with experiments.

The size effects upon shock plastic compression of nanocrystals

For the first time a theoretical analysis of scale effects upon the shock plastic compression of nanocrystals is implemented in the context of a dislocation kinetic approach based on the equations and relationships of dislocation kinetics. The yield point of crystals τy is established as a quantitative function of their cross-section size D and the rate of shock deformation as τy ~ e2/3 D. This dependence is valid in the case of elastic stress relaxation on account of emission of dislocations from single-pole Frank–Read sources near the crystal surface.

A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals

A framework for dislocation-based viscoplasticity and dynamic ductile failure has been developed to model high strain rate deformation and damage in single crystals. The rate-dependence of the crystal plasticity formulation is based on the physics of relativistic dislocation kinetics suited for extremely high strain rates. The damage evolution is based on the dynamics of void growth, which are governed by both micro-inertia as well as dislocation kinetics and dislocation substructure evolution. An averaging scheme is proposed in order to approximate the evolution of the dislocation substructure in both the macroscale as well as its spatial distribution at the microscale. Additionally, a concept of a single equivalent dislocation density that effectively captures the collective influence of dislocation density on all active slip systems is proposed here. Together, these concepts and approximations enable the use of semi-analytic solutions for void growth dynamics developed in (Wilkerson and Ramesh, 2014), which greatly reduce the computational overhead that would otherwise be required. The resulting homogenized framework has been implemented into a commercially available finite element package, and a validation study against a suite of direct numerical simulations was carried out.

Modeling of High-Temperature Plastic Deformation of Layered Composites Based on Alloys with L12 Superstructure

Method of mathematical modeling is used to investigate macrolocalization of plastic deformation and, in particular, the possibility of forming superlocalization bands in layered composites exposed to hightemperature uniaxial deformation. Modeling is based on a combination of continuum mechanics methods and dislocation kinetics of alloys with L12 superstructure. Numerical modeling is performed by the finite elements method.

Dislocation kinetics in nonmagnetic crystals: a look through a magnetic window

We discuss new kinematic magnetoplasticity features established experimentally and by simulations. We examine the motion of a dislocation through randomly distributed point defects under the influence of a magnetic field that reduces the impurity pinning forces. In addition to the measurable characteristics of motion, hidden motion parameters amenable only to simulation studies are investigated for the first time. It is shown that the distribution of stoppers on a dislocation is independent of the impurity concentration C, whereas the average number of stoppers and the critical force for the dislocation breakaway are proportional to . A model is proposed that for the first time explains the observed concentration dependence of the average dislocation speed in a magnetic field, . The model suggests that there is hidden room for an orders-of-magnitude increase in v, something which was already realized in NaCl crystals additionally subjected to a weak electric field.

On the micromechanics of void dynamics at extreme rates

In an earlier work, we derived evolution equations governing the dynamic growth of voids considering the combined retarding effects of micro-inertia and dislocation kinetics. Here we derive closed-form approximate solutions to these governing equations that accurately capture the transient evolution of void size history. In addition to being invaluable to the development of computationally-efficient dynamic ductile failure frameworks, these closed-form models help reveal deeper insights into the underlying physics governing complex dynamic void growth. In particular, we show that the transient effects of inertia are important for families of voids that nucleate from coarse, micron-sized second phase particles. For nano-sized voids the finite kinetics of dislocation substructure evolution towards a saturated state play a vital role. In spite of the significant complexity associated with capturing an evolving substructure, an elegant closed-form approximation presents itself. These closed-form models are further bolstered by good agreement with molecular dynamics calculations. Lastly, we derive closed-form models of void size distribution evolution to confirm an experimentally observed transition in fracture surface characteristics above a critical loading rate.

Specimen size and shape dependent yield strength in micropillar compression deformation of Mo single crystals

The deformation behavior of [1¯25]-oriented Mo micropillars with rectangular cross-sections having the [111] primary slip direction parallel to one of the two orthogonal side-surfaces has been investigated as a function of specimen size and shape (with varying ratios for two side-edge lengths of the cross-section). Micropillars with square-shaped cross-sections exhibit a size dependence of the critical resolved shear stress τCRSS approximated by τCRSS∝L−m with a power-law exponent of m ∼0.5 (L: cross-section side length). For a series of micropillars with a fixed length for the side-edge perpendicular to [111] (CE series), the CRSS also exhibit a power-law relationship with a relatively small exponent of m = 0.3. In contrast, an unexpected size-dependence is observed with two strength plateaus being connected by a strongly size dependent region (m ∼ 1) for a series of micropillars having a fixed length for the other cross-section side (CS series). The observed specimen size and shape dependence of CRSS of Mo micropillars is discussed based on the stochastic dislocation source length model and the dislocation kinetics model.

脉冲电流作用下电子风应力模型与计算示例

电致塑性是利用电场和脉冲电流改善材料塑性的方法。为了揭示脉冲电流作用下的电子风影响塑性的机理，在Conrad电子风力模型的基础上，提出电子风应力模型。在复杂体系的LAZ922 (Mg-Li-Al-Zn)合金中给出电子风应力计算实例。计算发现，基于位错动力学的电子风应力与实际应力十分吻合，而基于量子力学的电子风应力与实际应力相差很大，造成量子力学方法计算值偏低的原因是没有考虑合金中存在的第二相阻碍电子运动的情况。 Electro-plasticity (EP) is an approach to improve the plasticity using electric field and electric pulse current. To disclose the mechanism of EP under the pulse current, a new electron wind stress model was proposed based on Conrad’s electron wind force model. Calculation examples were given in a complex system LAZ922 (Mg-9Li-2Al-2Zn) alloy. It is found through calculation that the electron wind stress based on dislocation kinetics is in good agreement with the practical pulse current stress. However, the electron wind stress based on quantum mechanics is too low and differs greatly from the practical pulse current stress. This is because that the influence of the second phases on the movement of electrons is not considered.

Dislocation kinematics: a molecular dynamics study in Cu

The kinematics and kinetics of edge and screw dislocations in FCC materials were studied by molecular dynamics, with Cu as a case study. It was found that with increasing stress screw dislocations enter into the transonic regime continuously and that they remain stable up to a velocity of about 2.2 km s−1. Edge dislocations are limited by the transverse sound velocity at low stresses and discontinuously cross into the transonic regime at higher stresses. For sufficiently long edge dislocations, the subsonic–transonic transition is initiated by an athermal nucleation process. Finally, an expression for the velocity dependence of the dislocation mobility was derived.

Observation of anisotropic distribution of microstructure in GaP/GaAs epitaxial layers

Anisotropic distribution of microstructure in GaP/GaAs epitaxial layers is investigated by performing high resolution x-ray diffraction (HRXRD) experiments for symmetric reflections at different azimuths. The observed anisotropy leads to the different values of lattice relaxation along the [011¯] and [01¯1¯] directions as revealed by the reciprocal space maps recorded at 0° and 90° azimuths for (42¯2¯) and (422¯) reflections. The anisotropic relaxation process causes large differences in the full width at half maximum of (400) diffraction peaks of omega scans along the [011¯] and [01¯1¯] directions. It therefore provides large differences in the values of microstructural parameters of the GaP epitaxial layer along the two in-plane orthogonal directions. A systematic Williamson-Hall analysis of HRXRD data confirms the presence of large anisotropy of lattice relaxation process along the [011¯] and [01¯1¯] directions. Due to the large lattice mismatch, the GaP/GaAs epilayer presented here possesses grain boundaries and the broadening of the HRXRD pattern is strongly affected by the anisotropy of microstructure and dislocations. The kinetics of dislocations is discussed where it is observed that the misfit strain is primarily relieved by 90° partial dislocations up to a certain thickness of epilayer and thereafter the nucleation of 60° perfect dislocations dominates the strain relaxation process. The effect of the anisotropic distribution of relaxation process is also seen in the surface topography of GaP epilayer as revealed by atomic force microscopy images. The origin of the anisotropic distribution of dislocations is explained by considering the Burgers vector network, and its consequences are also observed in the cross sectional transmission electron microscopy images.

Физическая кинетика движения дислокаций в немагнитных кристаллах: взгляд через магнитное окно

Физическая кинетика движения дислокаций в немагнитных кристаллах: взгляд через магнитное окно

Controlling strength and ductility: Dislocation-based model of necking instability and its verification for ultrafine grain 316L steel

A phenomenological dislocation-based approach is proposed to account for the necking phenomenon during tensile deformation of metals and alloys. The critical strain corresponding to the onset of tensile instability is predicted in a simple explicit form based on the Kocks-Mecking dislocation kinetics approach. The model strongly suggests that uniform elongation is controlled primarily by the rate of dislocation recovery. The role of the stain rate sensitivity in stabilizing uniform plastic flow is also elucidated. Model predictions are found to be in excellent agreement with experimental data obtained for ultrafine grained 316L steel produced by severe plastic deformation. The approach presented provides general ques for designing materials with enhanced ductility, including ultrafine grained and bulk nanostructured metals and alloys. The proposed recipe is based on microstructural control of the rate of dynamic recovery of dislocation.

Materials genomics of thin film strain relaxation by misfit dislocations

We summarize the development and implementation of a “process simulator” for modeling thin film strain relaxation by injection of misfit dislocations. The process simulator, initially developed for GexSi1−x/Si(100) lattice-mismatched epitaxy, integrates elasticity and dislocation theory with experimental measurements of kinetic parameters describing dislocation nucleation, propagation, and interactions. This enables predictive simulation of the development of misfit dislocation arrays during growth and thermal annealing sequences. Further, in the spirit of the materials genome initiative, we show how once a relatively complete description is built for one materials system, extension to a related system may be implemented using a greatly reduced data set. We illustrate this concept by translation of the simulator for GexSi1−x/Si(100) epitaxy into predictive simulation for the GexSi1−x/Si(110) system (which has quite different dislocation microstructure and kinetics) using greatly reduced data sets for the latter system and incorporating data refinement methods to extract unknown kinetic parameters. This sets the platform for extension of these methods to a broader set of strained layer systems.

Microscopic Mechanism and Experiment Research of Electromagnetically Induced Acoustic Emission

Based on the electrical activated plastic concept and mobile dislocation model, the mechanism of electromagnetically induced acoustic emission (EMAE) will be studied at a microscopic level. From the perspective of driving effect between electrons and dislocation, a new formulation and numerical calculation for the determination of AE radiation energy in electromagnetic loading will be derived to address the acoustic effect on the crack tip of metals. The EMAE experiments under different exciting conditions are carried out. According to dislocation kinetics theory and plastic AE theory, the mechanism and characteristics of the EMAE have a deeper analysis with experimental AE signals, validating the feasibility of the theoretical prediction of the foundation and demonstrating its superior features and value.

A physically-based constitutive model for high temperature deformation of Cu-0.36Cr-0.03Zr alloy

Hot deformation behavior of Cu-0.36Cr-0.03Zr alloy is investigated by hot compression tests in a wide range of temperatures (800, 900, 950 °C) and strain rates (0.001, 0.01, 0.1, 1, 10, 20 s−1). For eliminating friction effects during tests and adiabatic effects at high strain rates, true stress–strain curves are friction corrected and then temperature corrected to elucidate real hot deformation behavior. True stress–strain curves after correction exhibit typical characteristics of dynamic recovery and dynamic recrystallization. The deformation activation energy of this alloy under this test condition is calculated as 432.6 KJ/Mol. Based on the stress–dislocation relation and kinetics of dynamic recrystallization, a physically-based constitutive model is developed. The predicted stresses agree well with experimental ones with the correlation coefficient (R) of 0.9982 and the average absolute relative error (AARE) of 3.47%.