Extrinsic Grain Boundary Dislocations Research Articles

The Effect of Deformation Temperature on the Yield Stress of Ultrafine-Grained Al-Cu-Zr Alloy Containing Grain Boundary Nanoprecipitates

A theoretical model is suggested that describes the effect of deformation temperature on the yield stress of an ultrafine-grained (UFG) Al-Cu-Zr alloy structured with severe plastic deformation. Within the model, nanoprecipitates (NPs) of Al2Cu act as sources of lattice dislocations in the presence of a number of extrinsic grain-boundary dislocations (EGBDs) near the NPs. It is shown that the number of EGBDs near the NPs decreases with a drop in the deformation temperature that increases the yield stress of the Al-Cu-Zr alloy. The proposed model is in good quantitative agreement with available experimental results.

Molecular dynamics simulation of the effect of cyclic stresses on nanocrystals with nonequilibrium grain boundaries: the role of the grain size

Grain boundaries (GBs) in bulk nanostructured materials processed by severe plastic deformation (SPD) have a nonequilibrium structure caused by extrinsic grain boundary dislocations (EGBDs) absorbed during deformation. Under external influences (annealing or cyclic straining) these GBs relax towards equilibrium resulting in a release of the excess energy of nanomaterials. Using our earlier developed method, atomic models of nanocrystals with nonequilibrium GBs having grain sizes of 10, 15, and 20 nm are constructed and relaxed by molecular dynamics. Then, the effect of oscillating tension-compression stresses with amplitudes of 2, 3 and 4 GPa on the systems thus obtained is simulated. Relaxation of nonequilibrium GBs by dislocation emission is found and the effect is shown to be independent of the grain size.

Molecular Dynamics Simulation of Nonequilibrium Grain Boundaries in Ultrafine-Grained Nickel and their Relaxation under Cyclic Loading

Atomistic simulations of the structure, energy and relaxation under the action of high frequency cyclic straining are carried out for columnar nickel nanocrystals with [112] column axis, the grain boundaries (GBs) of which are in a nonequilibrium state caused by the presence of extrinsic grain boundary dislocations (EGBDs). A special method of introducing EGBDs is used to create initial structures with nonequilibrium GBs. Energy of GBs as a function of the degree of nonequilibrium is evaluated and qualitatively compared to the results of dislocation and disclination modeling. It is shown that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

Nonequilibrium grain boundaries and their relaxation under oscillating stresses in columnar nickel nanocrystals studied by molecular dynamics

Atomic structure of columnar nickel nanocrystals with [1 1 2] column axis having nonequilibrium grain boundaries (GBs) containing extrinsic grain boundary dislocations (EGBDs) and its evolution under oscillating stresses are studied by molecular dynamics method. Energy of GBs as a function of the degree of nonequilibrium is evaluated. It is found that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

A method for the construction of initial structures for molecular dynamics simulations of nanocrystals with nonequilibrium grain boundaries containing extrinsic dislocations

A method for the construction of initial atomic models of nanocrystals with extrinsic grain boundary dislocations (EGBDs) in grain boundaries (GBs) for molecular dynamics (MD) simulations is developed. The method is realized for f.c.c. nanocrystals with columnar grains having common crystallographic axis [112] parallel to the column axis and thus divided only by [112] tilt GBs. This system is convenient for studies of interactions between GBs and lattice dislocations, since each grain can be deformed by edge dislocations of only one slip system, which have lines parallel to the [112] axis. In order to introduce extrinsic dislocations to the boundaries of a selected grain, its contour is assumed to be strained by a given shear strain  so that a contour of a freely sheared grain is formed. This contour is filled in by atoms of a f.c.c. lattice with [112] direction parallel to the column axis and then the grain thus formed is subjected to an elastic shear strain -. This results in a deformed grain having the original shape, on the boundaries of which precursors of EGBDs are formed. In order to prevent these precursors from spontaneous annihilation during MD relaxation, one can temporarily fix GB atoms, or apply a proper external stress, or do both. A case study is carried out using two different protocols of MD relaxation to determine atomic structures and energies of nonequilibrium GBs.

Grain Boundary Structure Dependence of Extrinsic Grain Boundary Dislocation Emission Phenomena: A Molecular Dynamics Study

Recently, it has been reported that extrinsic grain boundary dislocations (EGBDs) are often present in the grain boundaries of ultrafine-grained (UFG) metals produced by severe plastic deformation; therefore, the emission of EGBDs from the grain boundaries could afect the mechanical characteristics of UFG metals. In this paper, we use molecular dynamics to simulate the emission of EGBDs from grain boundaries, and we examine the grain boundary structure dependence of the emissions. Then we apply J-integral analysis to evaluate the Peach–Koehler force required for the grain boundaries to emit the EGBD. It can be confirmed that the Peach–Koehler force required to emit the EGBD is highly dependent on the relationship between the Burgers vector components of the EGBD and intrinsic grain boundary dislocations (IGBDs), which form the equilibrium grain boundaries. Comparing analyses of the linear elastic theory with atomic simulations, we confirm that nonlinear structural changes in the dislocation cores of the EGBD and IGBDs, which can only be expressed by atomic scale resolution, are responsible for such strong grain boundary structural dependence. We also verify that normal stress components perpendicular to the slip plane of EGBDs have a significant effect on the emission of EGBDs.

J-Integral Evaluation of Continuous Dislocation Emissions from the Crack Tip near Grain Boundaries in Atomic Simulations

Extrinsic grain boundary dislocations (EGBDs) are often observed in ultra fine-grained metals produced by severe plastic deformation processes. The mechanical properties of such metals are different from those of coarse-grained metals, so EGBDs could be important factor to elucidate the unique mechanical properties. In this paper, in order to clarify the influence of EGBDs on the emission of dislocations from the crack tip, we evaluate the mechanical field around the crack tip using J-integral in atomic simulations. It is found that quantitative evaluations of the crack-tip shielding effect due to EGBDs can be performed by J-integral taking grain boundary structures into account.

T0101-3-2 余分な粒界転位成分が及ぼすき裂先端に対する遮へい・反遮へい効果の分子動力学解析([T0101-3]マイクロ・ナノ材料システムの力学と強度・機能評価(3):先端材料システムの強度・機能解析(マクロ～マイクロ・ナノ))

Extrinsic grain boundary dislocations (EGBDs) are often observed in ultra fine-grained metals produced by severe plastic deformation (e.g. ECAP or ARB etc.). The mechanical properties of such metals are different from those of coarsegrained metals. That is, EGBDs could be important factor to elucidate the unique mechanical properties. In this study, introducing lattice dislocations into an equilibrium grain boundary by pre-deformation, we evaluate the influence of the EGBD component on the crack tip shielding effect using J-integral analyses.

Effect of Extrinsic Grain Boundary Dislocations on Mechanical Properties of Ultrafine-Grained Metals by Molecular Dynamics Simulations

The effect of extrinsic grain boundary dislocations (EGBDs) in nonequilibrium grain boundaries on the mechanical properties of ultrafine-grained metals is investigated by molecular dynamics simulations. Aluminum bicrystal models containing cracks and EGBDs impinged from the crack tips are prepared. First, the dependence of the local grain boundary structure on the accommodation mechanism of EGBDs, and on its stress field is studied. Then, the shielding effect of EGBDs on the emissions of dislocations from crack tips is investigated, and the effect of nonequilibrium grain boundaries on the intragranular deformation is discussed. Finally, to investigate the relationship between EGBDs and intergranular deformations, shear loading is applied to the bicrystal models. It is found that extrinsic grain boundaries function as the intergranular deformation source, and the Burgers vector components of the EGBDs lead to anisotropic grain boundary sliding.

On the Core Localization of Grain Boundary Extrinsic Dislocations in Nickel

Grain boundaries (GBs) have a significant influence on mechanical properties of single-phase materials. During deformation, matrix dislocations interact with GBs that constitute very strong barriers to dislocation glide processes. Some dislocations may enter the GB, giving rise to extrinsic grain-boundary dislocations (EGBDs) which disturb the ntrinsic GB structure. Stress relaxation associated to EGBDs must occur for the plastic deformation to go on and for the GB to return to equilibrium.

The effect of grain boundary character distribution on the high temperature deformation behavior of Ni–16Cr–9Fe alloys

The objective of this work was to test the Thaveeprungsriporn model for the dependence of creep rate on the coincident site lattice (CSL) fraction. The model attributed the large reduction in creep rate in alloys with a high population of CSL boundaries to the greater difficulty of extrinsic grain boundary dislocation (EGBD) absorption at coincident site lattice boundaries (CSLBs) vs. high angle boundaries (HABs). Ease of EGBD absorption was assessed by measuring the annihilation rates of EGBDs in both CSL-related and HABs following an anneal at 360 °C. Results showed that EGBDs are annihilated at HABs at a rate that is on average three times that at CSLBs, implying a grain boundary diffusion coefficient in CSLBs that is 12 times lower than that in HABs. The expectation that a reduction in EGBD absorption would lead to greater matrix hardening was investigated using nano-hardness measurements. Results showed that the hardness in the vicinity of CSLBs is greater than that near HABs, and the grain-averaged hardness increases with the fraction of contiguous CSLBs. Further, strain hardening is greater in CSL-enhanced samples than in reference, solution annealed samples. These results taken together substantiate the hypothesis that CSLBs impede dislocation absorption into the grain boundary, thereby increasing lattice hardening and internal stress in the sample, resulting in a reduced creep rate.

The effect of small deformation on abnormal grain growth in bulk Cu

The effect of small deformation below the level (about 8 pct) required for primary recrystallization on abnormal grain growth (secondary recrystallization) has been investigated in bulk polycrystalline Cu. The starting microstructure, without any texture and with a nearly uniform grain size of 168 µm, has been obtained by compressing a cylindrical Cu specimen and recrystallizing at 800 °C. The fully recrystallized specimen shows distinct abnormal grain growth (AGG) after heat treatment at 800 °C for 12 hours. Most of the grain boundaries are faceted when observed under transmission electron microscopy (TEM), and most of the faceted segments are expected to be singular. A singular grain boundary free of defects will migrate by two-dimensional nucleation of new layers, with its velocity varying nonlinearly with the driving force arising from the grain-size difference. Such a growth mechanism is analogous to the well known process for the growth of crystals with singular surfaces from liquid or vapor. The grains slightly larger than the average size will hardly grow, because the driving force for their growth is not sufficient for nucleation of new crystal layers at the boundaries. Those grains larger than a certain critical size will, however, grow at ever-increasing rates with their increasing size, because of the sufficient driving force for two-dimensional nucleation. Such a selective accelerated growth of large grains results in overall AGG behavior. The specimen deformed to 2 pct shows AGG after heat treatment for only 5 minutes at 800 °C, and after 1 hour, large impinged grains are obtained. The grain boundaries show many extrinsic dislocations even after the heat treatments. As proposed earlier by Gleiter, Balluffi, Smith, and their colleagues, the extrinsic grain-boundary dislocations increase the grain-boundary mobilities even at low driving forces, and, hence, even those grains slightly larger than the average size can rapidly grow at the early stages of the heat treatment, in agreement with the observation. In the specimens deformed to 4 to 8 pct, below the level for primary recrystallization, all grains grow steadily without producing distinct AGG. With high densities of extrinsic dislocations at the grain boundaries even after long heat treatments, all grains can readily grow, resulting in overall growth patterns resembling the normal growth. When deformed to 20 and 50 pct, primary recrystallization occurs, and the subsequent AGG behavior depends on the grain size obtained at the completion of the primary recrystallization. Similar small-deformation effects are observed with heat treatment at 600 °C.

The relation between grain-boundary structure and sliding resistance

Abstract During sliding, the grain-boundary (GB) energy depends on the atomic structures produced during relative translation of the two grains. The variation in the GB energy within the two-dimensional boundary unit cell (BUC) constitutes the GB-γ surface. Maxima in the slope of the γ surface determines the sliding resistance, that is the stress required to move the system over the lowest saddle points along a particular path within the BUC. In this paper we present the results of an atomistic study of the γ surfaces for two types of boundaries in a fcc metal. One of the boundaries is a Σg = 11, <110 > {131} which is a low-energy boundary and has a simple γ surface with a single stable configuration located at the corners and centre of the BUC. The resistance to sliding was determined by chain-of-states methods along four shear vectors connecting equivalent states within the BUC and is found to be very high in all cases. The asymmetric, Σ = 11, <110 > {252}-{414} GB, has a higher GB energy and its γ surface is much more complex, with distinctly different structures appearing at various locations in the BUC. At certain locations, more than one structure is found for the asymmetric GB. Although complex, a chain-of-states calculation along one path across the BUC suggests that the shear strength of this GB is also quite high. Extrinsic GB dislocations are found to lower the resistance to shear considerably and, therefore, to perform the same role in shear of GBs as do glide dislocations in slip of the lattice. The existence of multiple configurations has significant implications for the interaction of lattice dislocations with GBs, the core structure of GB dislocations, the temperature dependence of GB properties, and the GB sliding resistance, which we discuss.

The relation between grain-boundary structure and sliding resistance

Abstract During sliding, the grain-boundary (GB) energy depends on the atomic structures produced during relative translation of the two grains. The variation in the GB energy within the two-dimensional boundary unit cell (BUC) constitutes the GB-γ surface. Maxima in the slope of the γ surface determines the sliding resistance, that is the stress required to move the system over the lowest saddle points along a particular path within the BUC. In this paper we present the results of an atomistic study of the γ surfaces for two types of boundaries in a fcc metal. One of the boundaries is a Σg = 11, <110 > {131} which is a low-energy boundary and has a simple γ surface with a single stable configuration located at the corners and centre of the BUC. The resistance to sliding was determined by chain-of-states methods along four shear vectors connecting equivalent states within the BUC and is found to be very high in all cases. The asymmetric, Σ = 11, <110 > {252}-{414} GB, has a higher GB energy and its γ surface is much more complex, with distinctly different structures appearing at various locations in the BUC. At certain locations, more than one structure is found for the asymmetric GB. Although complex, a chain-of-states calculation along one path across the BUC suggests that the shear strength of this GB is also quite high. Extrinsic GB dislocations are found to lower the resistance to shear considerably and, therefore, to perform the same role in shear of GBs as do glide dislocations in slip of the lattice. The existence of multiple configurations has significant implications for the interaction of lattice dislocations with GBs, the core structure of GB dislocations, the temperature dependence of GB properties, and the GB sliding resistance, which we discuss.

A Revision of the Models for the Accommodation of Extrinsic Grain Boundary Dislocations

The kinetics of the spreading of electron diffraction contrast from extrinsic grain boundary dislocations (EGBDs) is studied in terms of the dissociation model. For the spreading time an equation similar to those given by Lojkowski-Grabski (W. Lojkowski and M.W. Grabski, in Deformation of Polycrystals: Mechanisms and Microstructures, edited by N. Hansen, A. Horswell, T. Leffers, and H. Lilholt (RisO Nat. Lab., Roskilde, Denmark, 1981), p. 329.) and Johannesson-Tholen (T. Johannesson and A. Tholen, Metal Sci. J. 6, 189 (1972).) formulae is obtained, but with a much less numeric coefficient which is approximately equal to the coefficient calculated in the incorporation model (A.A. Nazarov, A.E. Romanov, and R.Z. Valiev, Scripta Metall. Mater. 24, 1929 (1990).). A comparison with experimental data shows that the new equation describes the spreading kinetics better than the common formulae.

Kinetics of Grain Boundary Recovery in Deformed Polycrystals

Annealing kinetics are studied for nonequilibrium ensembles of dislocations occurring in grain boundaries during plastic deformation. Two types of dislocation ensembles are considered: 1) walls of sessile extrinsic grain boundary dislocations (EGBDs), which cause a change of the GB misorientation angle, and 2) arrays of glissile EGBDs having a Burgers vector tangential to the grain boundary plane. For both types similar exponential relationships are obtained for the relaxation of the average EGBD density, with approximately the same characteristic time proportional to the cube of grain size.

In-situtransmission electron microscopy study of the dislocation accommodation in [101] tilt grain boundaries in nickel bicrystals

The relaxation of stresses associated to extrinsic grain-boundary dislocations (EGBDs) in singular Σ = 3, {111}, in vicinal Σ = 11, {311} and in general Σ = 11, {332} grain boundaries (GBs) has been investigated by in-situ transmission electron microscopy (TEM) using weak-beam conditions. In a singular Σ = 3, {111} GB, reactions of combination and annihilation occur between extrinsic and intrinsic dislocations when they initially intersect each other. These reactions yield the parallelism of the two types of dislocation which is the preliminary configuration for any of the existing incorporation models to operate, but further evolution by decomposition of the EGBDs in glissile and sessile components, which can move away, as depicted by theory, was observed once only at a very high temperature. Furthermore, the rearrangement of all the sessile dislocations, extrinsic and intrinsic, in a periodic network was not observed, even after maintaining the thin foil at 930°C = 0.6T m (T m is the melting temperature) for a long time. In vicinal Σ = 11, {311} GBs, the continuous spreading of EGBD contrasts, previously observed by TEM in bright-field conditions, has been proved to be a decomposition process. Indeed, owing to the weak-beam technique, the wide image of a relaxed EGBD has been resolved in a set of small segments resulting from the interaction between the EGBD and the intrinsic dislocations. After annealing the thin foil at temperatures up to 0.4T m , all the GBDs had rearranged themselves in a quasiperiodic network, indicating that equilibration is almost achieved. In general Σ = 11, {332} GBs, the widening of the EGBD contrasts has never been associated with a decomposition phenomenon. No discrete product of EGBD decomposition has ever been observed by TEM, even in weak-beam conditions. The differences between the accommodation processes according to the GB type are discussed by referring to the GB atomic structure as described by the structural unit model.

Computer simulation of extrinsic grain-boundary defects in the ∑11, 〈101〉{131} symmetric tilt boundary

Abstract A computer simulation was performed to investigate the structure and properties of extrinsic grain-boundary (GB) defects in the {11, 〈101〉 {131} symmetric tilt boundary. An embedded-atom method potential was employed to represent aluminium. Standard molecular dynamics relaxation techniques were used to compute low-temperature (about 0 K) equilibrium structures. Extrinsic GB dislocations were introduced into the models by application of the exact anisotropic elastic displacement field for a bicrystal interface. Some dislocations were accompanied by geometrically necessary steps (in which case the pair form a disconnection) to avoid formation of GB faults. The structure and properties of the equilibrium GB were compared with GBs containing steps, dislocations and disconnections. A broad range of GB defects was studied in order to characterize their potential effect on GB sliding resistance.

Prediction of crack statistics in a random polycrystal damaged by the pile-ups of extrinsic grain-boundary dislocations

Crack nucleation due to the pile-ups of extrinsic grain-boundary dislocations around triple junctions is analysed. The analysis is based on a micromechanical model of interactions between the pile-ups and a triple-junction crack, and an approximate energy-based crack nucleation criterion. For a random microstructure of aluminium, the results show that the crack orientation, the crack length and the energy decrease due to crack formation have a rectangular, a skewed and a normal probability density distribution respectively. The effects of the remote loading state, the load magnitude and the mean grain size on the mean and standard deviation of the distributions are also quantified.

Prediction of crack statistics in a random polycrystal damaged by the pile-ups of extrinsic grain-boundary dislocations

Prediction of crack statistics in a random polycrystal damaged by the pile-ups of extrinsic grain-boundary dislocations