Immobile Dislocations Research Articles

On the kinetic physical and mathematical metal creep theory controlled by thermally activated dislocation sliding

The rationale for the prospects of using the physical and mathematical theory of metal creep in creep computations is carried out by a comparative analysis of the classical phenomenological and physical and mathematical metal creep theories. On the example of the description by both theories specific results of non-stationary creep experiments and analysis of the theories equations it is shown that implementing the physical kinetic equation for the actual structural parameter of the material, namely the scalar density of immobile dislocations, makes the physical and mathematical theory universal for solving non-stationary metal creep problems with multiaxial loading, when change, including abruptly, temperature, forces and loading rates.

High-Strain-Rate Deformation Behavior of Co0.96Cr0.76Fe0.85Ni1.01Hf0.40 Eutectic High-Entropy Alloy at Room and Cryogenic Temperatures.

The deformation behaviors of Co0.96Cr0.76Fe0.85Ni1.01Hf0.40 eutectic high-entropy alloy (EHEA) under high strain rates have been investigated at both room temperature (RT, 298 K) and liquid nitrogen temperature (LNT, 77 K). The current Co0.96Cr0.76Fe0.85Ni1.01Hf0.40 EHEA exhibits a high yield strength of 740 MPa along with a high fracture strain of 35% under quasi-static loading. A remarkable positive strain rate effect can be observed, and its yield strength increased to 1060 MPa when the strain rate increased to 3000/s. Decreasing temperature will further enhance the yield strength significantly. The yield strength of this alloy at a strain rate of 3000/s increases to 1240 MPa under the LNT condition. Moreover, the current EHEA exhibits a notable increased strain-hardening ability with either an increasing strain rate or a decreasing temperature. Transmission electron microscopy (TEM) characterization uncovered that the dynamic plastic deformation of this EHEA at RT is dominated by dislocation slip. However, under severe conditions of high strain rate in conjunction with LNT, dislocation dissociation is promoted, resulting in a higher density of nanoscale deformation twins, stacking faults (SFs) as well as immobile Lomer-Cottrell (L-C) dislocation locks. These deformation twins, SFs and immobile dislocation locks function effectively as dislocation barriers, contributing notably to the elevated strain-hardening rate observed during dynamic deformation at LNT.

Effect of constrained conditions, crystallographic and geometric factors on deformation patterns in FCC single crystals. Molecular dynamics study

Predicting of the mechanical properties of a polycrystal requires knowledge of the behavior of its individual grains during deformation and their mutual influence on each other. The self-similarity of deformation processes at different scales in crystalline solids allows using of molecular dynamics simulations to analyze the deformation of individual grains of a polycrystal, treating them as single crystals. We have studied the patterns of slip and twinning deformation caused by differences in stacking fault energy, crystal morphology, crystallographic orientation and shear conditions towards the lateral surfaces. It was found that in addition to the stacking fault energy and the crystallographic direction of compression, the crystallographic orientation of the lateral faces and the boundary conditions on them must be taken into account. They affect the accumulation of dislocations, the types of formed dislocations, low-mobile and immobile dislocation complexes, and the shear propagation in the crystal. The changes in shear conditions towards the lateral faces explain the size effect of the grain size/thickness ratio on mechanical properties under uniaxial strain.

Atomistic perspective of anti-friction performance in graphene-coated multi-principle-element alloys

Multi-principal-component alloys (MPCAs) have received considerable attention due to their excellent strength, ductility, and the relatively low wear resistance, which limits their practical applications. One strategy for mitigating the detrimental effects of friction is to coat the alloy surfaces with graphene. Nevertheless, the deformation mechanism under wear at the atomic scale remains unclear. In this study, the wear behavior and hardening mechanism of the graphene-coated FeCrNi multi-principal-component alloy were investigated through molecular dynamics simulations. The results demonstrated that the graphene layer significantly improves the wear resistance of the FeCrNi MPCA substrate, with a reduction in the friction force and friction coefficient of 23.92 % and 68.36 %, respectively. In particular, the graphene coating acts as a powerful barrier, limiting the propagation of dislocations and promoting the generation of massive immobile dislocations, resulting in a significant hardening effect. Concurrently, the graphene coating effectively mitigates contact stress and surface thermal softening, which suppresses the accumulation of atoms and enhances the wear resistance. These findings provide theoretical insights into the friction behavior of graphene-coated MPCAs, paving the way for the achievement of superior surface properties in MPCAs.

Modeling hydrogen diffusion in precipitation hardened nickel-based alloy 718 by microstructural modeling

Abstract Environmentally assisted cracking can significantly affect the performance of high strength alloys and limit material selection to minimize the risk of subcritical crack growth in service. UNS N07718 is widely used in marine service applications and under a variety of conditions, such as: alternate immersion, different levels of cathodic protection, and freely corroding galvanic couples, because of its demonstrated corrosion and fracture resistance in these environments. In this work we developed a representative model of the material microstructure including the metal grains, the material texture, and the precipitates along the grain boundaries and within the grains. The microstructural model was subjected to the boundary conditions identified at the notch root of a fracture mechanics sample and the results are used as input for a simulation of hydrogen diffusion from the surface of the notch, assuming the material has been introduced to a hydrogen producing environment. The diffusion of hydrogen was modeled by Fick’s law and included both hydrostatic stress and mobile dislocation velocity as driving forces. The influence of immobile dislocations was also modeled to account for the irreversible trapping. The results show that hydrostatic stress and immobile dislocation trapping can significantly alter the highest concentration of hydrogen and its location within the microstructure towards the fracture process zone. Mobile dislocation velocity has a small influence in determining the hydrogen distribution near the fracture process zone.

Partition of plastic work into heat and stored cold work in CoCrNi-based chemically complex alloys

The Taylor–Quinney coefficient (TQC) stands as a critical parameter intricately linked to the thermomechanical coupling plastic deformation behavior, defined as the ratio of heat generation to plastic work. Combining experimental studies and atomistic simulations, the TQC is discussed in the context of three CoCrNi-based chemically complex medium/high-entropy alloys (CoCrNi, CoCrNiFe, and CoCrNiFeMn). Notably, the obtained TQC of these alloys hovers around 0.7, well below the generally assumed value of 0.9–1 in traditional metals associated with adiabatic shearing. The lower TQC implies that these alloys possess the much better capability of storing energy of cold-work. It is further found that immobile dislocations are the most effective carriers for storing the energy of cold-work. Among these three alloys, CoCrNiFeMn exhibits the highest TQC due to its relatively lower density of immobile dislocations and Lomer–Cottrell locks.

Toward all-dislocation-ceramics for high ionic conductivity produced by dry pressing at relatively low temperatures with and without ultrasound

Numerical simulations of the evolution of mobile and immobile dislocations in ceramics under applied pressure in dry pressing at a relatively low temperature are performed in order to study the possibility of production of all-dislocation-ceramics of solid electrolytes, which are expected to have extremely high ionic conductivity without dendrite formation because the diameter of a dislocation pipe is considerably larger than the distance between neighboring dislocations. The present numerical simulations are only for the densification process by plastic deformation of grains under high pressure under the assumption that the compaction of particles by their rearrangement is completed beforehand. By the plastic deformation, new dislocations are generated inside the grains. The required total dislocation density of about 1017 m−2 seems to be achievable under some conditions of dry pressing according to the present numerical simulations. Very short ultrasound irradiation at the beginning of the dry pressing sometimes considerably increases the dislocation density, while for other cases, it even considerably decreases the dislocation density due to enhanced annihilation of mobile dislocations by ultrasound.

In situ observation of electrical resistivity increase via creep-induced dislocations in n-type PbTe

A decrease in electrical conductivity is measured in situ in n-type PbTe during dislocation-climb creep deformation at 673 K. Transmission electron microscopy reveals the accumulation of high density of immobile dislocations that form stable subgrains which increase in density with increasing strain from 8 to 20%. At a constant applied stress, we conclude the increase in immobile dislocation density is primarily responsible for the continuous increase in the electrical resistivity with strain. With the assumption of constant dislocation velocity at a constant applied stress, the mobile dislocation density is a constant so the increase of immobile dislocation density with strain should dictate the total dislocation density increase during creep deformation. This effect of creep deformation on electrical conductivity, and thermoelectric properties in general, should help design materials and operational conditions to limit such adverse effects on device efficiency while engineering thermal conductivity reductions.

Microstructure Based Flow Stress Modelling of Superalloy 718

In order to get the insights about microstructural changes that occurs under the thermo-mechanical processing conditions, the physics based modelling approach is very useful. Therefore, the flow curves of alloy 718 are theoretical simulated using a dislocation density dependent constitutive model for different conditions. Presented model considers the microstructural ingredients that are immobile dislocation density, effective grain size and dislocation cell size as the variables to address the creep. The simulated flow curves show a good agreement with the experimental flow curves. The magnitude of immobile dislocation density and dislocation cell size in between 3.87× 1014 - 3.87× 1014­ m-2 and 8.29-8.45 μm, respectively, at the completion of the simulation. Furthermore, this approach also provides the possibility to quantify and depict the variation in each strengthening contributions.

Room temperature creep mechanisms of Ti–6Al–4V ELI alloy with equiaxed microstructure under different applied stresses

Titanium alloys are often used to make deep-sea pressure hulls and the creep strain produced during service is nonnegligible. The variation of dislocation structures with room temperature creep stresses in equiaxed α grains of Ti–6Al–4V ELI alloy was examined using transmission electron microscope. The plastic deformation mechanism varied with the applied stress, mainly manifested by the change of dislocation patterns and the sequential activation of slip systems. At the stress below the creep threshold, even though almost no macroscopic creep was generated, a small number of immobile dislocations and dislocation networks occurred in the sample. The networks were composed of dislocations with different Burgers vectors, and part of them would evolve into low angle grain boundaries (LAGBs). At the stresses above the threshold, the density of dislocations in α grains increased with the stress level, and the basal <a>, pyramidal <a> and <c+a> slips were activated successively which also contributed to creep and participated in the formation of LAGBs. Prismatic <a> slip was always the predominant creep deformation mechanism for the studied stress range. The activation of difficult slip systems was attributed to the stress concentration and stress redistribution between soft and hard phases/grains. In general, the amount of LAGBs increased with the applied creep stress, but the LAGBs formed by dislocation networks decreased.

Dissociation of edge and screw pyramidal I and II dislocations in magnesium

Pyramidal dislocations in magnesium (Mg) and other hexagonal close-packed metals play an important role in accommodating plastic strains along the c-axis. Bulk single crystal Mg only presents very limited plasticity in c-axis compression, and this behavior was attributed to out-of-plane dissociation of pyramidal dislocations onto the basal plane and resulted in an immobile dislocation configuration. In contrast, other simulations and experiments reported in-plane dissociation of pyramidal dislocations on their slip planes. Thus, the core structure and mode of dissociation of pyramidal dislocations are still not well understood. To better understand the dissociation behavior of pyramidal dislocations in Mg at room temperature, in this work, atomistic simulations were conducted to investigate four types of pyramidal dislocations at 300 K: edge and screw Py-I on {101¯1}, edge and screw Py-II on {112¯2} by using a modified embedded atom method (MEAM) potential for Mg and anisotropic elasticity dislocation model. The results show that when energy minimization was performed before relaxation, in-plane dissociation of edge dislocations on respective pyramidal plane could be obtained at room temperature for all four types of dislocation. Without energy minimization, the edge dislocations dissociated out-of-plane onto the basal plane. Calculations of potential energy and hydrostatic stress of individual atoms at the edge dislocation core show that the extraordinarily high energy and atomic stresses in the as-constructed dislocation structures caused the out-of-plane dissociation onto the basal plane. The core structures of all four types of pyramidal dislocation after in-plane dissociation were analyzed by computing the distribution of the Burgers vector.

Plastic deformation of Ag/MgO interface system during tensile fracture: A molecular dynamics study

Fracture experiments on layered metal-ceramic composites show that the plastic dissipation in the metal near the crack tip accounts for most of the macroscopic fracture toughness. In this work we studied the microscopic plastic deformation mechanisms of Ag/MgO interface systems using molecular dynamics (MD) method. As tensile strain increases, lattice dislocations nucleate at interface misfit dislocations and propagate in metal layer. The formation of immobile Hirth dislocations in Ag causes hardening. As the metal layer increases, the yield strength decreases and the hardening range is shortened. Large interface area increases the degree of inhomogeneity of dislocation motion and interface fracture behavior, leading to decreased interface yield strength.

Nonlinear unloading-reloading behavior and macro/micro models during multi-pass cyclic hot compression of aluminum alloys

Unloading-reloading behavior is of crucial importance in multi-pass forming of metal materials, the nonlinear of which creates challenges for the analysis of springback and residual stress of the precision manufacture components. Especially for the hot bulk-formed material at elevated temperature, the thermal-mechanical coupling effect makes the unloading-reloading process more complicated and thus more difficult to model and control, which remains to be solved. In this paper, the unloading-reloading behavior dependent on strain rate and deformation temperature and its model of hot compressive deformed aluminum alloys at elevated temperature were studied from the macroscopic and microscopic perspectives. The effect of deformation temperature, strain rate and strain on the unloading-reloading behavior of hot compressive deformed aluminum alloys were revealed, and corresponding micro-mechanism was elucidated and then discussed. Macroscopically, a strain-, strain rate- and temperature-dependent nonlinear macroscopic model describing unloading–reloading process was established, which can be used to describe the unloading stress relaxation and predict springback during multi-pass hot bulk forming. Microscopically, it is suggested that the relaxations of back stress and forest dislocation hardening stress collectively affect the unloading stress relaxation, due to the decrease of mobile and immobile (forest) dislocation density in unloading, while the dislocation-related behavior before yield, i.e. the dislocations’ bowing-out under pinning, affects the reloading behavior. Based on the micro-mechanism, a physically-based micro-model for describing unloading–reloading was constructed which further is used to clarify the physical mechanism of internal stress relaxation and inelastic strain recovery under multi-pass hot compression deformation. The comparison of the calculation results of the models with those of experiments indicated that the established unloading–reloading macroscopic and microscopic models are able to predict the stress–strain response upon the unloading–reloading loop of multi-pass cyclic hot compression deformation.

How can machine learning be used for accurate representations and predictions of fracture nucleation in zirconium alloys with hydride populations?

Zirconium alloys are critical material components of systems subjected to harsh environments such as high temperatures, irradiation, and corrosion. When exposed to water in high temperature environments, these alloys can thermo-mechanically degrade by forming hydrides that have a crystalline structure that is different from that of zirconium. Cracks can nucleate near these hydrides; hence, these hydrides are a direct link to fracture failure and overall large inelastic strain deformation modes. To fundamentally understand and predict these microstructural failure modes, we interrogated a finite-element database that was deterministically tailored and generated for large strain-dislocation-density crystalline plasticity and fracture modes. A database of 210 simulations was created to randomly sample from a group of microstructural fingerprints that encompass hydride volume fraction, hydride orientation, grain orientation, hydride length, and hydride spacing for a hydride that is physically representative of an aggregate of a hydride population. Machine learning approaches were then used to understand, identify, and characterize the dominant microstructural mechanisms and characteristics. We first used fat-tailed Cauchy distributions to determine the extreme events. A multilayer perceptron was used to learn the mechanistic characteristics of the material response to predefined strain levels and accurately determine the critical fracture stress response and the accumulated shear slips in critical regions. The predictions indicate that hydride volume fraction, a population-level parameter, had a significant effect on localized parameters, such as fracture stress distribution regions, and on the accumulated immobile dislocation densities both within the face centered cubic hydrides and the hexagonal cubic packed h.c.p. matrix.

High-entropy alloy nanocrystals with low-angle grain boundary for superb plastic deformability and recoverability

High entropy alloys (HEAs) have received widespread attention as structural and functional materials owing to their large atomic lattice distortion and vast compositional space. Recently, nanoscale HEAs have been proven to exhibit exceptional combinations of mechanical properties, thermal stability, and oxidation resistance. The structural and functional stabilities of nanoscale HEAs under practical loading conditions are vital to their applications. Here, based on a grain boundary (GB) design strategy, we introduced custom-designed low-angle GBs (LAGBs) into quinary face-centered cubic HEA nanocrystals, intending to improve the mechanical stability of nanoscale HEAs under external loading through molecular dynamics simulations. Using CuCoNiPdFe and FeNiCrCoCu HEAs as examples, we reveal two distinct LAGB-mediated deformation behaviors of nanoscale HEAs, which stem from the differences in lattice distortion and shear modulus of the materials. In the case of CuCoNiPdFe, the LAGB is composed of separate Shockley dislocations, endowing the material with extraordinary plastic deformability and structural stability. In the case of FeNiCrCoCu, the LAGB contains a series of parallel stacking faults cross-linked immobile dislocation segments, which severely damages the plastic deformability of the material. Based on the atomistic understanding of LAGB structure and migration behavior, we have screened out a range of material systems with small lattice distortion and shear modulus, realizing superb plastic deformability and structural recoverability in HEAs designed with LAGBs. These findings promote the understanding of GB-mediated deformation mechanisms in HEAs and provide insights into the structural and composition design of HEA nanomaterials.

Hierarchical toughening mechanisms in face centered cubic CoCrFeMnNi high-entropy alloy at room temperature and cryogenic temperatures

As a class of promising structural material, recently synthesized face centered cubic phased high-entropy alloys (HEAs) exhibit excellent room-temperature (RT) fracture toughness as well as an abnormally increasing one at cryogenic temperatures (CTs). The intrinsic toughening mechanisms are not yet well understood. Attention here is focused on the atomistic crack initiation and propagation in a model HEA CoCrFeMnNi under RT and CTs, by means of atomistic simulations integrated with theoretical analysis. Hierarchical deformation mechanisms of the incipient plasticity; the local amorphization; and the formation, growth, and coalescence of voids are found, based on which the strain energy stored in the material is continually dissipated, resulting in the outstanding fracture toughness of the HEA at both RT and CTs. The origin for low-temperature toughening may be attributed to fewer immobile dislocations at CTs, delaying the occurrence of amorphization and microvoids. The differences in mechanisms for low-temperature toughening of the HEA and low-temperature embrittlement of traditional metals are further comparatively revealed. This study provides mechanistic insights into the fundamental understanding of intrinsic toughening mechanisms in the HEA.

Formula omitted]-CP: Open source dislocation density based crystal plasticity framework for simulating temperature- and strain rate-dependent deformation

This work presents an open source, dislocation density based crystal plasticity modeling framework, ρ-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the deformation of polycrystalline bcc tantalum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model’s ability to predict large deformation and misorientation development during plastic deformation.

Untra-fine-grained equiatomic CoCrNi medium entropy alloys with high density stacking faults and strengthening mechanisms

This study introduces a powder metallurgy route (a combination of mechanical alloying (MA) and spark plasma sintering) to enhance the mechanical properties of equiatomic CoCrNi medium-entropy alloys (MEAs) using multiple strengthening mechanisms. The yield strength of MEA with an average grain size of 0.41 μm produced by MA is 777 ± 21 MPa, which is 121% higher than that of MEA with grains of 4.55 μm prepared from commercial powders. Additionally, the yield strength of the untra-fine-grained alloy is 231% higher than that of the one produced by casting. Such an enhancement of the strength is attributed to the coordination of the ultra-fine grains, twins, and high-density stacking faults. Moreover, the influence of twins and stacking faults was investigated using molecular dynamic simulations. The intersection of ultra-high density stacking faults generates many immobile dislocation locks and separates the grains into several small parts, leading to a dynamic grain-refinement effect. These findings indicate that MA is an effective way to produce MEAs with superior strength.

Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network

The reaction-diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction-diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (p2), and the average width of the walls (p3). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in p2 and p3 for test data having 10% deviation from the training data were within 7% of the average magnitude of p2 and p3. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.

Exploration of electrodeposited process of Ni-Co-Cr coating and investigation of Cr doping strengthening mechanism by indentation simulation

Ni-Co-Cr coating with excellent mechanical properties was successfully prepared by the electrodeposition process. Compared with the binary Ni-Co alloy coating, the hardness of the ternary coating is increased to 1247HV, an increase of 61%. The wear rate decreased by 40.7%. The exploration of the deposition process found that sodium formate and urea can effectively dissociate [Cr(H 2 O) 6 ] +3 complexes to realize the co-deposition of Cr 3+ . The strengthening mechanism of Cr doping was then investigated by molecular dynamics indentation simulation. It is found that grain refinement and solid solution strengthening contribute 20% (0.33 GPa) and 80% (1.33 GPa) to the hardness, respectively. The enhanced covalent character between Cr and solvent atoms improves the elastic modulus and promotes the dislocation nucleation, which originates from body-centered cubic-like (BCC-like) defect clusters. In the plastic deformation stage, Cr doping reduces the stacking fault energy of the alloy and makes the release of the plastic strain more uniform and stable. The denser 3D stacking fault network structures hinder the further propagation of dislocation loops and increase the dislocation reaction probability. More Lomer-Cottrell and Hirth Locks are generated and improve the strength of the coating. • An electrodeposited Ni-Co-Cr coating with excellent mechanical properties was developed. • The contribution of grain refinement and solid solution strengthening to hardness was quantitatively investigated. • The strengthening in the elastic stages comes from the enhanced covalent character between Cr and solvent atoms. • The strengthening in the plastic stages comes from the increase in the number of immobile dislocations.