Splitting Of Dislocations Research Articles

Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

It is known that the meso- and microstructures of metals determine the physical, mechanical and operational properties of their final products. Scientific and technological progress of recent decades has given impetus to the elaboration and use of models capable of describing the evolving structure of materials. The most promising are multilevel models that include internal variables and are based on physical theories of elastoplasticity (elastoviscoplasticity). This paper presents the structure and basic relationships of a three-level (macro-, meso-1 and meso-2 levels) elastoviscoplastic model. The developed model operates on such internal variables as dislocation densities on slip systems, barriers on split dislocations and sources of edge dislocations. The model describes the mechanisms of production, annihilation, formation of barriers and sources of dislocations. The law of hardening directly takes into account the densities of dislocations and barriers. The mechanism of inelastic deformation is the gliding of edge dislocations along slip systems. Special emphasis is placed on the influence of split dislocations (prone to forming hard Lomer–Cottrell and Hirth barriers) on the deformation of the material. The model is used to describe the behavior of an elastoviscoplastic polycrystalline aggregate with an FCC lattice. Geometric nonlinearity is taken into account by utilizing decomposition of the crystallite motion into quasi-rigid and deformation components. For this purpose, a rigid moving coordinate system for the crystal lattice is introduced. Examples of the application of the model for analyzing the simple and complex deformation mechanisms of materials with different stacking fault energies and, consequently, with different tendencies toward the decomposition of dislocations and barrier formation are given.

Transport Properties of Low-Angle Grain Boundaries in High-Temperature Superconductors under the Model of Split Dislocations of the Boundary

Transport Properties of Low-Angle Grain Boundaries in High-Temperature Superconductors under the Model of Split Dislocations of the Boundary

The Three-Level Elastoviscoplastic Model and Its Application to Describing Complex Cyclic Loading of Materials with Different Stacking Fault Energies.

The development of new technologies for thethermomechanical processing of metals and the improvement of the existing ones would be unattainable without the use of mathematical models. The physical and mechanical properties of alloys and the performance characteristics of the products made of these alloys are generally determined by the microstructure of materials. In real manufacturing processes, the deformation of metals and alloys occurs when they undergo complex (non-proportional) loading. Under these conditions, the formation of defect substructures, which do not happen at simple (proportional) loading, can take place. This is due to the occurrence of a great number of slip systems activated under loading along complex strain paths, which leads, for instance, to the more intense formation of barriers of different types, including barriers on split dislocations. In these processes, the formation and annihilation of dislocations proceed actively. In this paper, we present a three-level mathematical model that is based on an explicit description of the evolution dislocations density and the formation of dislocations barriers. The model is intended for the description of arbitrary complex loads with an emphasis on complex cyclic deformation.The model is composed of macrolevel (a representative macrovolume of the material that can be considered as an integration point in the finite-element modeling of real constructions), and mesolevel-1 (description of the mechanical response of a crystallite) and mesolevel-2 (description of the defect structure evolution in a crystallite) submodels. Using the model, we have performed a series of numerical experiments on simple and complex, monotonic and cyclic deformations of materials with different stacking fault energies, analyzed the evolution of defect densities, and analyzed the challenges of a relationship between the complexity of loading processes at a macrolevel and the activation of slip systems at low scale levels.

Three-level model based on physical theories of plasticity: Formulation, implementation algorithms, results of application to the study of cyclic loading

The physical and mechanical properties of metals and alloys, as well as, the operational characteristics of products made of them, are known to be significantly determined by the meso- and microstructure of materials. Therefore, physically oriented models that can be used to analyze the material structure evolution have been intensively developed and widely applied in recent decades for the study of thermomechanical processing of metals and alloys. These models are based on the introduction of internal variables, theories of crystal plasticity (elastoviscous plasticity), and a multilevel approach. In this paper, we consider the structure, mathematical formulation and algorithm for implementing a three-level (macro-, meso-1, and meso-2 levels) dislocation-oriented model designed to study the behavior of a representative macrovolume (macrosample) of mono- and polycrystalline alloys under cyclic deformation paths. The loading is given, and the Voigt (Taylor) hypothesis is used to connect the macro- and mesolevel-1. The mesolevel-2 submodel operates with the densities and velocities of full and split edge dislocations on slip systems. Interactions of dislocations of various systems, such as annihilation, hardening due to forest dislocations, formation of barriers of a dislocation nature (Lomer–Cottrell, Hirt) are taken into account. At mesolevel-1, the description is carried out in terms of shear stresses and shear rates along slip systems, determined by the Orowan equation using the mesolevel-2 data. A rigid moving coordinate system associated with a crystal lattice is introduced to evaluate the rotation of crystallites. The response of the material at the macro level is determined by averaging the stresses in crystallites. The results of applying the model to the study of deformation of alloy macrosamples with different values of stacking fault energy along simple and complex deformation trajectories are presented. It is shown that the materials with low stacking fault energy demonstrate the effect of additional cyclic hardening when loaded along complex deformation trajectories.

Structure and chemical composition of grain boundaries in the magnetic semiconductor GaSb<Mn>

The structure and chemical composition of grain boundaries in GaSb<Mn> magnetic semiconductors have been investigated. We determined that quenching of the GaSb melt with 2% Mn results in the formation of a textured polycrystal (111). The grain boundaries of the texture are formed by split 60 degree dislocations with <110> dislocation lines. Microinclusions based on the ferromagnetic compound MnSb are located on the stacking faults of split dislocations. The chemical compositions of microinclusions differ, but their average composition is close to Mn1.1Sb. The synthesized GaSb<Mn> is a soft ferromagnet with a coercive force of 10 Oe and a magnetic state approaching superparamagnetic

Orientation-related twinning and dislocation glide in a cantor high entropy alloy at room and cryogenic temperature studied by in situ TEM straining

In situ straining experiments were performed in a TEM on an equimolar CoCrFeMnNi (Cantor) high entropy alloy at room and cryogenic temperature. Perfect and partial dislocation activity were recorded in both cases. Twinning directly follows the development of partial dislocation shearing that has various origins (perfect dislocation splitting, anchoring). It is shown that, although twinning is more frequently observed at liquid nitrogen temperature, its prevalence depends mainly on crystal orientation. As a result, twinning and perfect dislocation plasticity are likely to occur jointly in random oriented polycrystals, even at early stages of deformation.

Stacking fault energy in concentrated alloys

We revisit the meaning of stacking fault energy (SFE) and the assumptions of equilibrium dissociation of lattice dislocations in concentrated alloys. SFE is a unique value in pure metals. However, in alloys beyond the dilute limit, SFE has a distribution of values depending on the local atomic environment. Conventionally, the equilibrium distance between partial dislocations is determined by a balance between the repulsive elastic interaction between the partial dislocations and a unique value for SFE. This assumption is used to determine SFE from experimental measurements of dislocation splitting distances in metals and alloys, often contradicting computational predictions. We use atomistic simulations in a model NiCo alloy to study the dislocation dissociation process in a range of compositions with positive, zero, and negative average SFE and surprisingly observe a stable, finite splitting distance in all cases at low temperatures. We then compute the decorrelation stress and examine the balance of forces on the partial dislocations, considering the local effects on SFE, and observe that even the upper bound of SFE distribution alone cannot satisfy the force balance in some cases. Furthermore, we show that in concentrated solid solutions, the resisting force caused by interaction of dislocations with the local solute environment becomes a major force acting on partial dislocations. Here, we show that the presence of a high solute/dislocation interaction, which is not easy to measure and neglected in experimental measurements of SFE, renders the experimental values of SFE unreliable.

The Tree-Level Viscoelastic Model: Analysis of the Influence of the Packing Defect Energy to the Response of Materials under Complex Loading

The development of new and improvement of existing modes of thermomechanical treatment of metals and alloys in present conditions is impossible without development of appropriate mathematical models, that allow determining material characteristics during technological processes. Constitutive equations are the core, the main components that determine the quality of such models. Macrophenomenological theories of plasticity relying on processing the results of experiments on macrosamples, have become widespread as such in solving applied problems of solid mechanics. Taking into account the need to describe the memory of processes, the equations of this class have a complicated mathematical structure, require expensive tests (generally speaking, for complex loading) for each material, due to which they are not universal. In the past 15-20 years, constitutive models based on the introduction of internal state variables, of a multilevel approach, and physical theories of inelasticity (plasticity, viscoplasticity) became very popular. Models of this class are focused on describing the evolving structure (including microstructure), which ultimately determines the physical and mechanical properties of materials and constructions. As the physical mechanisms and their carriers are identical for wide classes of materials, the models of this class have significant versatility, including the prediction of behavior of new, not yet existing materials, to study the physical mechanisms of the occurrence of various effects, observed in macro experiments. Hardening is one of interesting effects observed in experiments on complex (including cyclic) loading (as compared to directional loading) of samples, made of various metals and alloys, arising from a significant evolution of the microstructure. Empirical data analysis made it possible to establish that the tendency to manifest this effect is usually experienced by metals and alloys with a low stacking fault energy (SFE). The paper provides a brief analysis of the experimental work and mathematical models describing the response of a material to complex deformation. It is noted that macrophenomenological theories do not allow one to describe in an explicit form the evolution of the microstructure and the carriers of plastic deformation and hardening mechanisms, thus they do not provide an opportunity to explain the physical reasons for the above effects. The purpose of this work is to develop, study and implement a multilevel elasto-visco-plastic model that allows describing the evolution of crystal lattice defects in materials with different SFE under different thermomechanical processing, different strengthening mechanisms at different structural-scale levels. In the framework of constructing a constitutive model, special attention is paid to the development of a submodel, focused on description of the evolution dislocations and barrier densities on slip systems. Kinetic equations for dislocation densities on slip systems make it possible to analyze the nucleation of dislocations due to the activation of Frank - Read sources, annihilation of dislocations of different signs on one slip system, interaction of split dislocations of intersecting slip systems with the formation of barriers. Relations for the description of hardening are given, taking into account the current density of dislocations and barriers. The general structure of the model and the relationship between the parameters of submodels of different levels are considered. An algorithm and a program of implementing the model were developed, the evolution of dislocation densities on slip systems was analyzed, and the intensity of hardening and the formation of barriers on split dislocations were obtained depending on the type of loading.

Molecular static simulation of edge dislocation core in bcc iron

We simulate the dislocation core structure in bcc iron using the modified Molecular Static method. A feature of this method is the application of an iterative procedure in which the atomic structure in the vicinity of the defect and the constants that determine the displacements of atoms immersed in the elastic continuum are calculated in a self-consistent manner. Following the mentioned approach, we develop a model for calculating the atomic structure of edge dislocations, taking into account the anisotropy of the elastic medium surrounding the main calculation cell. Anisotropy is taken into account by introducing an explicit angular dependence for the parameters of the elastic field created by the dislocation: magnitude of Burgers vector and Poisson’s ratio. Simulation is carried out for a split dislocation with Burgers vector along [100]. The convergence of the iterative algorithm is shown and the influence of the computational cell size on the results is considered. Calculated results are: atomic structure of dislocation in bcc iron, angular dependence of the parameters describing the elastic dislocation field at large distances from the dislocation line, and the strain tensor components in the entire simulation area.

Mechanism of Implementation of High Ductility in Ultrafine-Grained Aluminum after Annealing and Subsequent Deformation

A theoretical model that describes the implementation of high ductility in high-pressure torsion (HPT) processed ultrafine-grained aluminum subjected to annealing and additional HPT deformation, is suggested. In the framework of the model, the plastic deformation is realized through the successive emission of lattice dislocations from triple junctions of grain boundaries due to splitting of head dislocations in pile-ups of grain boundary dislocations, which are pressed by an external shear stress against these triple junctions, and their subsequent glide in grain interior and climb along surrounding grain boundaries. The energy characteristics and the critical stresses of dislocation emission have been determined for ultrafine-grained aluminum subjected to annealing with small additional HPT deformation. The theoretical stress–strain curves demonstrate good agreement with experimental data available in the literature.

Application of Fundamental Models for Creep Rupture Prediction of Sanicro 25 (23Cr25NiWCoCu)

Creep rupture prediction is always a critical matter for materials serving at high temperatures and stresses for a long time. Empirical models are frequently used to describe creep rupture, but the parameters of the empirical models do not have any physical meanings, and the model cannot reveal the controlling mechanisms during creep rupture. Fundamental models have been proposed where no fitting parameters are involved. Both for ductile and brittle creep rupture, fundamental creep models have been used for the austenitic stainless steel Sanicro 25 (23Cr25NiWCoCu). For ductile creep rupture, the dislocation contribution, solid solution hardening, precipitation hardening, and splitting of dislocations were considered. For brittle creep rupture, creep cavitation models were used taking grain boundary sliding, formation, and growth of creep cavities into account. All parameters in the models have been well defined and no fitting is involved. MatCalc was used for the calculation of the evolution of precipitates. Some physical parameters were obtained with first-principles methods. By combining the ductile and brittle creep rupture models, the final creep rupture prediction was made for Sanicro 25. The modeling results can predict the experiments at long-term creep exposure times in a reasonable way.

Ultrasonic-assisted laser welding on AISI 321 stainless steel

Ultrasonic-assisted laser welding on 321 stainless steel has been carried out to find out the effect of ultrasonic energy input on the microstructure and strength of the weld metal. Ultrasonic energy was transmitted from a transducer, via two waveguides and hard alloy indenter fixed perpendicularly on the workpiece surface. Real-time ultrasonic oscillation amplitude distributions over the workpiece surface and in the bulk of the workpiece have been obtained using the laser Doppler vibrometry and finite element simulation which allowed estimating the close to reality ultrasonic energy input values. The real energy input was at least two orders of magnitude less than that calculated from the nominal ultrasonic source power. The welded joints have been characterized for microstructure, microhardness, and tensile strength. It was shown using TEM that higher microhardness of the sonicated welded joint is due to high concentration of split dislocations induced by ultrasonics. The tensile strength of the ultrasonic-assisted-welded joint depended on the ultrasonic energy input and was higher than that of the base metal in case of sonication by 600 W output power.

Molecular Dynamics Simulation of the Migration of Tilt Grain Boundaries in Ni and Ni3Al

The migration of the 〈100〉 and 〈111〉 tilt boundaries in Ni and the Ni3Al intermetallic compound is studied by molecular dynamics simulation. The low-angle 〈100〉 boundaries in Ni and Ni3Al are shown to migrate much more slowly (by approximately two times at a temperature of 1700 K) that the 〈111〉 boundaries, which is related to different migration mechanisms of the 〈100〉 and 〈111〉 boundaries. The migration of the 〈100〉 boundaries is found to occur by the splitting of paired grain-boundary dislocations followed by a change of partner dislocations, which proceeds via the slip of split dislocations. The 〈111〉 tilt boundaries move according to a combined action of the following two mechanisms: the mechanism described above and the mechanism consisting in joint slip of paired grain-boundary dislocations, which have common slip planes in contrast to the grain-boundary dislocations in 〈100〉 boundaries. Since the joint slip of paired dislocations has a relatively low activation energy, the mobility of the 〈111〉 tilt boundaries is higher than that of the 〈100〉 boundaries. Our molecular dynamics studies demonstrate that the migration rate of analogous boundaries in Ni3Al is significantly lower than in Ni (by approximately three times at a temperature of 1700 K), which is partly caused by the additional energy consumed for the formation of a disordered region behind a migrating boundary in Ni3Al. Because of a relatively low boundary mobility in Ni3Al, the contribution of diffusion atomic displacements during boundary migration is higher as compared to Ni.

Bandlike and localized states of extended defects in n-type In0.53Ga0.47As

In0.53Ga0.47As p + n diodes with different densities of extended defects have been analyzed by detailed structural and electrical characterization. The defects have been introduced during Metal-Organic Vapor Phase Epitaxy (MOVPE) growth by using a lattice-mismatched layer on a semi-insulating InP or GaAs substrate. The residual strain and indium content in the n-type In0.53Ga0.47As layer have been determined by high-resolution X-ray diffraction, showing nearly zero strain and a fixed indium ratio of 0.53. The deep levels in the layer have been characterized by Deep Level Transient Spectroscopy. The mean value of electron traps at 0.17 ± 0.03 eV below the conduction band minimum EC is assigned to the “localized” states of α 60° misfit dislocations; another broad electron trap with mean activation energies between EC− 0.17 ± 0.01 and 0.39 ± 0.04 eV, is identified as threading dislocation segments with “band-like” states. A high variation of the pre-exponential factor KT by 7 orders of magnitude is found for the latter when changing the filling pulse time, which can be explained by the coexistence of acceptor-like and donor-like states in the core of split dislocations in III-V materials. Furthermore, two hole traps at EV+ 0.42 ± 0.01 and EV+ 0.26 ± 0.13 eV are related to the double acceptor of the Ga(In) vacancy (VGa/In3-/2-) and 60° β misfit dislocations, respectively. Finally, the dislocation climbing mechanism and the evolution of the antisite defects AsGa/In are discussed for n-type In0.53Ga0.47As.

Nucleation of deformation twins on gliding grain-boundary dislocations in nanomaterials

A new micromechanism of nucleating deformation twins in nanocrystalline and ultrafine-grained materials under action of severe mechanical stresses has been proposed and theoretically described. The mechanism is a subsequent splitting of grain-boundary dislocations into lattice partial and sessile grain-boundary dislocations. Ensembles of gliding partial dislocation forms deformation twins. The energy characteristics of this process are calculated. The nucleation of the twins is shown to be energetically profitable and can be athermic (without an energy barrier) under conditions of severe mechanical stress. The dependence of a critical stress at which the barrier-less nucleation of twins took place on the widths of these twins is calculated.

Atomistic simulation of stacking faults in cementite: Planes containing vector [100

The method of molecular dynamics (MD) has been used to study γ surfaces in crystallographic planes of cementite containing Burgers vector [100]. Displacement vectors that correspond to stable stacking faults (SFs) and the energies of these SFs have been determined. The energies of unstable SFs, which characterize the tendency of the material toward plastic relaxation, have been estimated. It has been established that, in all these planes except for (013), the dislocations with the Burgers vector [100] are not split. Planes have been found that are most suitable for the slip of these dislocations. The opportunity of the propagation of stacking faults in these planes is discussed; reactions of the splitting of perfect dislocations with the Burgers vector [100] in the plane (013) have been suggested.

Simulations of dislocation mobility in magnesium from first principles

The strength and ductility of metals are governed by the motion of dislocations, which is quantified by the Peierls stress (σp). We use orbital-free density functional theory (OFDFT) to characterize the motion of 13〈112¯0〉 dislocations on the basal {0001} and prismatic {11¯00} planes in hexagonal-close-packed magnesium (Mg) in order to understand its deformation mechanisms. We predict σp values of edge dislocations on the basal and prismatic planes to be 0.6 and 35.4MPa, respectively. The presence of stable stacking faults only on the basal plane produces partial dislocation splitting, which significantly lowers σp for basal dislocations. Our atomic scale simulations reveal that dislocation mobility is strongly correlated with the number of core atoms moving collectively. OFDFT σp results are in excellent agreement with experiments (∼0.5 and 39.2MPa), further validating OFDFT as an independent and predictive tool for simulating plastic behavior in main group metals at the mesoscale with first principles’ accuracy.

Multilevel models of polycrystals using crystal plasticity: investigation of hardening laws influence on the macro effects of cyclic loading

The problem of constructing a physically based hardening laws of mono- and polycrystalline samples in multi-level theories using crystal plasticity is considered, these hardening laws should allow describing the process of the defect structure evolution of the material due to the intensive inelastic deformations. It is also should be applicable to the description of simple and cyclic loading. An approach to the construction of a general and a particular form of hardening law is proposed, which takes into account the interaction of full and split dislocations with each other, forming and destruction of dislocation barriers, annihilation of dislocations during reverse loading. Using the obtained hardening law, the known experimental effects of simple and cyclic loading are described.

Atomistic simulation of stacking faults in (001), (010), and (100) planes of cementite

Molecular-dynamics method was used to study γ surfaces for the (001), (010), and (100) planes of cementite. Displacement vectors corresponding to stable stacking faults have been determined. The energy of these stacking faults has been calculated by the molecular-dynamics and ab initio methods. The energy of unstable stacking faults, which characterizes the tendency of a material to plastic relaxation, has been estimated. The reactions of the splitting of perfect dislocations have been suggested; the possibility of the propagation of stacking faults in the planes under consideration is discussed.

Dislocation structure of cementite in granular pearlite after cold plastic deformation

Cementite microstructure of the U8 steel with a granular pearlite structure has been investigated by the method of electron microscopy. It has been established that, at the early stages of deformation, carbide particles are deformed through the movement of stacking faults, which are characterized by an α[010] partial shift in the (001) planes of cementite. The Burgers vector, the slip plane [010](001) of the split dislocations forming pileups, and deformation bands have been determined using gb analysis. The stacking fault energy has been estimated in a (001) cementite plane: γsf ∼ 12.8 mJ/m2. With increasing degree of deformation, an additional slip has been shown to occur in cementite by the system [100](011).