A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by the Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of the Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [48] in which the long-range dislocation interaction is explicitly calculated.
Misfit-dislocation hierarchy governs sliding of asymmetric non-CSL grain boundaries
Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）；Institute of Microstructure and Property of Advanced Materials, Beijing Key Lab of Microstructure and Property of Advanced Materials, Beijing University of Technology（北京工业大学先进材料微结构及性能研究所）
Discrete dislocation plasticity (DDP) calculations are carried out to investigate the response of a single crystal contacted by a rigid sinusoidal asperity under sliding loading conditions to look for causes of microstructure change in the dislocation structure. The mechanistic driver is identified as the development of lattice rotations and stored energy in the subsurface, which can be quantitatively correlated to recent tribological experimental observations. Maps of surface slip initiation and substrate permanent deformation obtained from DDP calculations for varying contact size and normal…
Previous studies demonstrate that grain-boundary sliding could accelerate creep rate and give rise to large internal stresses that can lead to damage development, e.g. formation of wedge cracks. The present study provides more insight into the effects of grain-boundary sliding (GBS) on the deformation behaviour of realistic polycrystalline aggregates during creep, through the development of a computational framework which combines: i) the use of interface elements for sliding at grain boundaries, and ii) special triple point (in 2D) or triple line (in 3D) elements to prevent artificial dilatio…
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
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…
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.
Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional field. Since dislocation curvature represents a spatial derivative of the underlying discrete dislocation density tensor, the curvature field evolution equation of necessity contains numerically inconvenient higher-order derivatives of the density fields. We propose a simple approximation to express curvature in terms of density fields, and demonstrate its a…
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…
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…
Grain boundary complexions have been observed to affect the mechanical behavior of nanocrystalline metals, improving both strength and ductility. While an explanation for the improved ductility exists, the observed effect on strength remains unexplained. In this work, we use atomistic simulations to explore the influence of ordered and disordered complexions on two deformation mechanisms which are essential for nanocrystalline plasticity, namely dislocation emission and propagation. Both ordered and disordered grain boundary complexions in Cu-Zr are characterized by excess free volume and prom…
Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a coarse-graining length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow relative positions of dislocation pairs,…
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…
Effect of grain disorientation on early fatigue crack propagation in face-centred-cubic polycristals: A three-dimensional dislocation dynamics investigation
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…
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>…
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…
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 …
Multi-principal element alloys (MPEAs), commonly termed as medium- or high-entropy alloys containing three or more components in high concentrations, render a tunable chemical short-range order (SRO). Leveraging large-scale atomistic simulations, we probe the limit of Hall-Petch strengthening and deformation mechanisms in a model CrCoNi alloy and unravel chemical short-range ordering effects. It is found that, in the presence of SRO, the maximum strength is appreciably increased, and the strongest grain size drifts to a small value. Additionally, the propensity for faulting and deformation tra…
A generalized model to study dislocation loops growth in irradiated binary Zr-based alloys is presented. It takes into account temperature effects, efficiencies of loops to absorb point defects dependent on the loop size, an influence of locality of grain boundary sink strength, and concentration of the alloying element. This model is used to describe the dynamics of loop radii growth in zirconium-niobium alloys under neutron irradiation at reactor conditions. A growth of both loop radii and strains is studied at different grain sizes, location from grain boundaries, and concentration of niobi…
