The dynamics of dislocation assemblies in deforming crystals indicate the emergence of collective phenomena, intermittent fluctuations and strain avalanches. In polycrystalline materials, the understanding of plastic deformation mechanisms depends on grasping the role of grain boundaries on dislocation motion. Here the interaction of dislocations and elastic, low angle grain boundaries is studied in the framework of a discrete dislocation representation. We allow grain boundaries to deform under the effect of dislocation stress fields and compare the effect of such a perturbation to the case of rigid grain boudaries. We are able to determine, both analytically and numerically, corrections to dislocation stress fields acting on neighboring grains, as mediated by grain boundary deformation. Finally, we discuss conclusions and consequences for the avalanche statistics, as observed in polycrystalline samples.
The theory of dislocation mediated plastic flow proposed by Langer, Bouchbinder, and Lookman is applied to compute the stress-strain curve of aluminum and aluminum alloys over a wide range of temperatures and strain rates. The comparison with experiment shows excellent agreement.
Scanning tunneling microscopy combined with molecular dynamics simulations reveal a dislocation-mediated island diffusion mechanism for Cu on Ag(111), a highly mismatched system. Cluster motion is tracked with atomic precision at multiple temperatures and diffusion barriers and prefactors are determined from direct measurements of hop rates. The non-monotonic size dependence of the diffusion barrier is in good agreement with simulations and can lead to enhanced mass transport upon coarsening, in surprising contrast to the traditional island diffusion models where diffusivity reduces with clust…
Dislocation-solute interaction plays fundamental roles in mechanical properties of alloys. Here, we disclose the essential features of dislocation-carbon interaction in austenitic Fe at the atomistic scale. We show that passage of a Shockley partial dislocation in face-centered cubic iron is able to move carbon atoms on the slip plane forward by one Burgers vector, revealing a novel dissociated dislocation-mediated transport mechanism. This mechanism is induced by shear, which is distinct from the normal thermally activated diffusion process. Furthermore, we show that there exists a fast diffu…
Edge Dislocation Mediated Anomalous Charge Transfer in Face Centered Cubic High Entropy Alloys
School of Materials Science and Technology, IIT-BHU（印度理工联合学院瓦拉纳西分校材料科学与技术学院）；National Centre for Computational Sciences, Oak Ridge National Laboratory（橡树岭国家实验室国家计算科学中心）；Department of Metallurgy and Materials Engineering, IIEST Shibpur（IIEST Shibpur冶金与材料工程系）
We propose an explanation of anomalies observed in the behavior of deformation hardening of Invars. An extremely strong volume magnetostriction, typical of Invars, results in an enhancement of the exchange contribution to the energy of the dislocation system by about three orders of magnitude with respect to its value in conventional ferromagnetics. Both the self energy of individual dislocations and the interaction between them, determined usually only by the elastic deformation, in Invars is strongly diminished by the contribution of the exchange energy. This fact explains a strong suppressi…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case study is carried out on the boundary conditions affecting work hardening of a bicrystal subjected to plane constrained shear for three types of grain boundaries: (i) impermeable hard grain boundary, (ii) grain boundary that allows dislocation transfer without absorption, (iii) grain boundary that absorbs dislocations and allows them to pass later.
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated with the constituent dislocations subject to the constraint of Frank's formula. The orientation-dependent continuous distributions of dislocation lines on grain boundaries are described conveniently using the dislocation density potential functions, whose contour lines on the grain boundaries represent the dislocations. The energy of a grain boundary is the t…
In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion of grain boundaries (i.e., motion of the constituent dislocations in the grain boundary normal direction) and equations for the dislocation structure evolution on the grain boundaries. This model is derived from the discrete dislocation dynamics model. The long-range elastic interaction between dislocations is included in the continuum model, which ensures …
Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary-dislocation interactions
Nanoscale Thermal Imaging of Dislocation-Mediated Heat Transport
International Center for Quantum Materials and Electron Microscopy Laboratory, School of Physics, Peking University（北京大学物理学院量子材料国际中心与电子显微镜实验室）；Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院）；Tsientang Institute for Advanced Study, Zhejiang（浙江谦塘高等研究院）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料跨学科研究所与轻元素先进材料研究中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
A continuum dislocation model of formation of grains whose boundaries have a non-vanishing thickness is proposed. For a single crystal deforming in simple shear the lamellar structure of grains with thin layers containing dislocations as the geometrically necessary boundaries turns out to be energetically preferable. The thickness and the energy of this type of grain boundary are computed as functions of the misorientation angle.
Addition of solutes is commonly used to stabilize nanocrystalline materials against grain growth. However, segregating at grain boundaries, these solutes also affect the process of dislocation nucleation from grain boundaries under applied stress. Using atomistic simulations we demonstrate that the effect of solutes on the dislocation nucleation strongly depends on the distribution of solutes at the grain boundary, which can vary dramatically depending on the solute type. In particular, our results indicate that the solutes with a smaller size mismatch can be more effective in suppressing disl…
Dislocation and grain boundary melting are studied in three dimensions using the Phase Field Crystal method. Isolated dislocations are found to melt radially outward from their core, as the localized excess elastic energy drives a power law divergence in the melt radius. Dislocations within low-to-mid angle grain boundaries melt similarly until an angle-dependent first order wetting transition occurs when neighboring melted regions coalesce. High angle boundaries are treated within a screening approximation, and issues related to ensembles, metastability, and grain size are discussed.
Coarse-grained, metallic materials undergo microstructure refinement during tribological loading. This in turn results in changing tribological properties, so understanding deformation under tribological load is mandatory when designing tribological systems. Single-trace experiments were conducted to understand the initiation of deformation mechanisms acting in various tribological systems. The main scope of this work was to investigate the influence of normal and friction forces as well as crystal orientations on the dominating deformation mechanism in a face-centred cubic concentrated solid …
Results of recent large-scale molecular dynamics simulations of dislocation-mediated solid plasticity are campared with predictions of the statistical thermodynamic theory of these phenomena. These computational and theoretical analyses are in substantial agreement with each other in both their descriptions of strain-rate dependent steady plastic flow and of a transient stress peak associated with initially small densities of dislocations. The comparisons between the numerical simulations and basic theory reveal inconsistencies in some conventional phenomenological descriptions of solid plasti…
In this paper, we present a continuum model to compute the energy of low angle grain boundaries for any given degrees of freedom (arbitrary rotation axis, rotation angle and boundary plane orientation) based on a continuum dislocation structure. In our continuum model, we minimize the grain boundary energy associated with the dislocation structure subject to the constraint of Frank's formula for dislocations with all possible Burgers vectors. This constrained minimization problem is solved by the penalty method by which it is turned into an unconstrained minimization problem. The grain boundar…
The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of yielding transitions and grain-size effects in polycrystalline solids. Calculations are based on the 1995 experimental results of Meyers et al. for polycrystalline copper under strain-hardening conditions. The main assertion is that the well known Hall-Petch effects are caused by enhanced strengths of dislocation sources at the edges of grains instead of the commonly assumed resistance to dislocation flow across grain boundaries. The theory describes rapid transitions between elastic an…
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved dislocations on the grain boundary. Illposedness due to nonconvexity of the total energy is fixed by a numerical treatment based on a projection method that maintains the connectivity of the constituent dislocations. An efficient simulation method is developed, in which the critical but computationally expensive long-range interaction of dislocations is repl…
We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterization tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbor grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we…
Dislocation dynamics simulation is used to investigate the effect of grain size and grain shape on the flow stress in model copper grains. We consider grains of 1.25-10 $μ$m size, three orientations (<135>, <100> and <111>) and three shapes (cube, plate and needles). Two types of periodic aggregates with one or four grains are simulated to investigate different dislocation flux at grain boundaries. It is shown that in all cases the flow stress varies linearly with the inverse of the square root of the grain size, with a proportionality factor varying strongly with the grain orientation and sha…
Thermodynamic dislocation theory incorporating dislocation impediment by the grain boundaries is developed to analyze the shear test of polycrystals. With a small set of physics based material parameters, we are able to simulate the stress-strain curves for the load and its reversal, which are consistent with the experimental curves of Thuillier and Manach [2009]. Representative distributions of plastic slip under load and its reversal are presented, and their evolution explains the extended length of the transition stage during load reversal.
The deformation behaviour of the intermetallic Al$_{2}$Cu-phase was investigated using atomistic simulations and micropillar compression, where slip on the unexpected {211} and {022} slip planes was revealed. Additionally, all possible slip systems for the intermetallic phases were further evaluated and a preference for the activation of slip systems based on their effective interplanar distances as well as the effective Burgers vector is proposed. The effective interplanar distance corresponds to the manually determined interplanar distance, whereas the effective Burgers vector takes a potent…
It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effo…
Enabling plastic co-deformation of disparate phases in a laser rapid solidified Sr-modified Al-Si eutectic through partial-dislocation-mediated-plasticity in Si
We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional …
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducin…
The nonequilibrium dynamics of diffusion-mediated plasticity and creep in materials subjected to constant load at high homologous temperatures is studied atomistically using Phase Field Crystal (PFC) methods. Creep stress and grain size exponents obtained for nanopolycrystalline systems, $m \simeq 1.02$ and $p \simeq 1.98$, respectively, closely match those expected for idealized diffusional Nabarro-Herring creep. These exponents are observed in the presence of significant stress-assisted diffusive grain boundary migration, indicating that Nabarro-Herring creep and stress-assisted boundary mig…
Matallic alloys, such as Al or Cu, or mild steel, display plastic instabilities in a well defined range of temperatures and deformation rates, a phenomenon known as the Portevin-Le Chatelelier (PLC) effect. The stick-slip behavior, or serration, typical of this effect is due to the discontinuous motion of dislocations as they interact with solute atoms. Here we study a simple model of interacting dislocations and show how the classical Einstein fluctuation-dissipation relation can be used to define the temperature in a range of model parameters and to construct a phase diagram of serration tha…
We report a first-principles density functional theory study on the role of grain boundary and dislocation loop in H blistering in W. At low temperature, the {\Sugma}3(111) tilt grain boundary, when combined with a vacancy of vanishing formation energy, can trap up to nine H atoms per (1x1) unit in (111) plane. This amount of H weakens the cohesion across the boundary to an extent that a cleavage along the GB is already exothermic. At high temperature, this effect can be still significant. For an infinitely large dislocation loop in (100) plane, four H can be trapped per (1x1) unit even above …
Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory mainly stems from the discrete nature of the core region, which induces a drag force on the dislocation core during glide. Depending on external conditions, different drag mechanisms are activated that govern the dynamics of dislocations in their own way. This is revealed by the resultant speed of the dislocation. In this work, we develop a theoretical frame…
Nanoindentation is a convenient method to investigate the mechanical properties of materials on small scales by utilizing low loads and small indentation depths. However, the effect of grain boundaries (GB) on the nanoindentation response remains unclear and needs to be studied by investigating in detail the interactions between dislocations and GBs during nanoindentation. In the present work, we employ a three-dimensional multiscale modeling framework, which couples three-dimensional discrete dislocation dynamics (DDD) with the Finite Element method (FEM) to investigate GB effects on the nano…
Many systems where a liquid metal is in contact with a polycrystalline solid exhibit deep liquid grooves where the grain boundary meets the solid-liquid interface. For example, liquid Ga quickly penetrates deep into grain boundaries in Al, leading to intergranular fracture under very small stresses. We report on a series of molecular dynamics simulations of liquid Ga in contact with an Al bicrystal. We identify the mechanism for liquid metal embrittlement, develop a new model for it, and show that is in excellent agreement with both simulation and experimental data.
Three-dimensional dislocation dynamics simulations are used to study micro-crack interaction with the first micro-structural barrier in face-centred cubic bi-crystals loaded in high cycle fatigue conditions. In the examined configuration, we assumed that micro-crack transmission occurs due to surface relief growth in the secondary grain ahead of the primary crack. This indirect transmission mechanism is shown to strongly depend on grain-1/grain-2 disorientation. For instance, small grain disorientation induces plastic strain localisation ahead of the crack and faster transmission through the f…
Ionic conductivity blocking at grain boundaries in polycrystalline electrolytes is one of the main obstacles that need to be overcome in order to improve the performance of solid state fuel cells and batteries. To this aim, harnessing the physical properties of grain boundaries in ionic conducting materials such as yttria stabilized zirconia (YSZ) down to the atomic scale arises as a greatly important task. Here we present a structural and compositional analysis of a single grain boundary in a 9 mol% yttria content YSZ bicrystal by means of aberration corrected scanning transmission electron m…
A Mesoscale Model for Interface-Mediated Plasticity: Investigation of Ductile and Brittle Fracture
City University of Hong Kong（香港城市大学）；University of California, Los Angeles（加州大学洛杉矶分校）；The University of Hong Kong（香港大学）；University of Birmingham（伯明翰大学）
We reformulate the theory of polycrystalline plasticity, in externally driven, nonequilibrium situations, by writing equations of motion for the flow of energy and entropy associated with dislocations. Within this general framework, and using a minimal model of thermally assisted depinning with essentially only one adjustable parameter, we find that our theory fits the strain-hardening data for Cu over a wide range of temperatures and six decades of strain rate. We predict the transition between stage II and stage III hardening, including the observation that this transition occurs at smaller …
Through the combination of transmission electron microscopy analysis of the deformed microstructure and molecular dynamics computer simulations of the deformation processes, the mechanisms of plastic strain recovery in bulk AgCu eutectic with either incoherent twin or cube-on-cube interfaces between the Ag and Cu layers and a bilayer thickness of 500 nm have been revealed. The character of the incoherent twin interfaces changed uniquely after dynamic compressive loading for samples that exhibited plastic strain recovery and was found to drive the recovery, which is due to dislocation retractio…
The effect of grain size on the flow stress of FCC polycrystals is analyzed by means of a multiscale strategy based on computational homogenization of the polycrystal aggregate. The mechanical behavior of each crystal is given by a dislocation-based crystal plasticity model in which the critical resolved shear stress follows the Taylor model. The generation and annihilation of dislocations in each slip system during deformation is given by the Kocks-Mecking model, which was modified to account for the dislocation storage at the grain boundaries. Polycrystalline Cu is selected to validate the s…
The dislocation structures appearing in highly mis-oriented soft/hard grain pairs in near-alpha titanium alloy Ti6242Si were examined with and without the application of load holds (dwell) during fatigue. Dislocation pile-up in a soft grain resulted in internal stresses in an adjacent hard grain which could be relaxed by dislocation multiplication at localized Frank-Read sources, a process assisted by the provision of a relaxation time during a load hold. The rate of this process is suggested to be controlled by <c+a> pyramidal cross-slip and <a> basal junction formation. A high density of <a>…
Dislocations can climb out of their glide plane by absorbing (or emitting) point defects (vacancies and self-interstitial atoms (SIAs)). In contrast with conservative glide motion, climb relies on the point defects' thermal diffusion and hence operates on much longer timescales, leading to some forms of creep. Whilst equilibrium point defect concentrations allow dislocations to climb to relieve non-glide stresses, point defect supersaturations also lead to osmotic forces, driving dislocation motion even in the absence of external stresses. Self-interstitial atoms typically have significantly h…
Hydrogen atoms absorbed by metals in the hydrogen-containing environments can lead to the premature fracture of the metal components used in load-bearing conditions. Since metals used in practice are mostly polycrystalline, grain boundaries (GBs) can play an important role in hydrogen embrittlement of metals. Here we show that the reaction of GB with lattice dislocations is a key component in hydrogen embrittlement mechanism for polycrystalline metals. We use atomistic modeling methods to investigate the mechanical response of GBs in alpha-iron with various hydrogen concentrations. Analysis in…
The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictate…
In this paper we present a simple and effective numerical method which allows a fast Fourier transformation-based evaluation of stress generated by dislocations with arbitrary directions and Burgers vectors if the (site-dependent) dislocation density is known. Our method allows the evaluation of the dislocation stress using a rectangular grid with shape-anisotropic discretization cells without employing higher multipole moments of the dislocation interaction coefficients. Using the proposed method, we first simulate the stress created by relatively simple nonhomogeneous distributions of vertic…
Damage nucleation from repeated dislocation absorption at a grain boundary is simulated with molecular dynamics. At the grain boundary-dislocation intersection site, atomic shuffling events determine how the free volume brought by the incoming dislocation is accommodated. This process in turn determines the crack nucleation mechanism, as well as the critical strain and number of dislocations that can be absorbed before cracking. Slower strain rates promote earlier crack nucleation and a damage nucleation mode where cracking is preceded by dislocation emission. The simulation methodology presen…
Interfacial nucleation is the dominant process of dislocation generation during the plastic deformation of nano-crystalline materials. Solute additions intended to stabilize nano-crystalline metals against grain growth, may segregate to the grain boundaries and triple junctions where they can affect the process of the dislocation emission. In this Letter we demonstrate that the effect of solute addition in a nano-crystalline material containing competing solute segregation sites and dislocation sources can be very complex due to different rates of segregation at different interfaces. Moreover,…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disorder…
Dislocation interactions at the crack nucleation site were investigated in near-alpha titanium alloy Ti-6242Si subjected to low cycle fatigue. Cyclic plastic strain in the alloy resulted in dislocation pile-ups in the primary alpha grains, nucleated at the boundaries between the primary alpha and the two-phase regions. These two phase regions provided a barrier to slip transfer between primary alpha grains. We suggest that crack nucleation occurred near the basal plane of primary alpha grains by the subsurface double-ended pile-up mechanism first conceived by Tanaka and Mura. Superjogs on the …
