Pearlitic steels achieve an exceptional balance of strength and ductility through the lamellar stacking of ferrite and cementite. While this synergy enhances mechanical performance, cementite also serves as a preferential site for crack initiation, making its thickness and the extent of deformation localization caused by dislocation pile-ups critical factors in the plasticity–fracture transition. In this study, molecular dynamics simulations were performed to clarify how cementite thickness and dislocation pile-ups govern deformation and fracture. The results reveal that thinner cementite or smaller pile-ups promote dislocation emission across the interface, whereas thicker cementite and larger pile-ups facilitate crack initiation within cementite. Comparison with a conventional continuum model showed qualitative agreement but also highlighted nanoscale effects—such as core relaxation of penetrated dislocations in cementite—that are beyond continuum descriptions. These findings provide atomistic insights into the mechanisms controlling the plasticity–fracture transition in pearlitic microstructures.

High-entropy alloys (HEAs) are multicomponent alloys composed of five or more than five elements with near equimolar concentrations. In this study, molecular dynamics (MD) simulations of grain boundary (GB) migration in HEAs were performed in order to systematically investigate the concentration dependence of the constituent elements on its migration behavior. We found that the driving force required for GB migration in the model HEAs reaches the maximum when the GB migration becomes intermittent or the velocity reduces. The maximum driving force is achieved at the maximum degree of GB segregation, showing that GB segregation, which can be controlled by the element composition in the HEAs, strongly affects the GB migration behavior such as the required force for the migration and the velocity. Our study indicates that the element composition in HEAs plays an important role in determining the GB migration behavior and the obtained results contribute to designing the HEAs with superior mechanical properties.

Molecular dynamics simulations were performed to investigate the dominant factors affecting the nucleation in deformation-induced martensitic transformation in grains and at grain boundaries in pure iron, and the effectiveness of microstructure designs incorporating the obtained dominant factors was verified. First, the local nucleation stress required for grain-boundary nucleation was lower than that for in-grain nucleation, indicating that the grain boundary is an effective nucleation site for martensitic transformation. Next, we investigated the dominant factors affecting the in-grain nucleation and the grain-boundary nucleation, and found that the dominant factor of the in-grain nucleation is the magnitude of the loading-direction component of the transformation strain induced by lattice deformation (Bain distortion), while the dominant factors of grain-boundary nucleation are the grain-boundary misorientation angle and grain-boundary free volume. Finally, the possibility of controlling the nucleation timing by designing the microstructures based on the obtained nucleation dominant factors was demonstrated by comparing two polycrystalline models with the same texture but different distributions of grain-boundary misorientation angles.

As one of the promising candidates for developing next-generation structural materials, high-entropy alloys (HEAs) have recently attracted significant interest because of their unique mechanical properties, including their coexisting of high strength and ductility properties. Here, through atomic simulations, we demonstrate that the segregation of elements to grain boundaries (GBs) due to atomic-size differences, which is one of the most important characteristics of HEAs, contributes to the coexistence of high strength and high ductility in HEAs. To focus on only the effect of the size difference on the GB segregation, ignoring the difference in the chemical bonding energies among all the constituent elements, we employ two-dimensional virtual quinary HEA models. The HEAs are subjected to tensile and compressive load tests, and the stress required for dislocation emission from the GBs is measured. We demonstrate that the GB segregation in the HEAs increases the stress required for dislocation emission from the GBs, thereby increasing the strength of the HEAs. This is because the GB segregation in the HEAs stabilizes the GB structure by decreasing the GB free volume. Notably, the GB segregation also decreases the heterogeneity of the mechanical field between the grain interiors and the GBs, which is an intrinsic attribute of ordinary materials, and the homogenization of the mechanical field can improve the ductility of HEAs, preventing intergranular fracture. Our results can serve as a guide for designing HEAs with both high strength and high ductility through the effective utilization of GB segregation.

In order to investigate the synergistic effect of different deformation modes (dislocations and local atomistic rearrangements) on the strength of mixed crystalline and amorphous materials, tensile and compressive deformation analyses of a two-dimensional binary system with various microstructures is performed through molecular dynamics simulations. The binary system is composed of atoms with two different atomic radii. By varying the mixing ratio and the interaction force between different atoms, 66 binary system models with various structures are represented, and each model is classified into three categories, crystalline, amorphous, and mixed crystalline/amorphous, through structural analysis. Deformation analysis shows that the strength of the mixed crystalline/amorphous models tends to be weaker than that of the crystal and amorphous models. The is because the edge of the force chain in the amorphous phase appears at the crystalline/amorphous interface, where dislocation release from the interface to the crystalline phase occurs easily.

Core–shell harmonic structure materials, in which coarse grains (core regions) are surrounded by many fine grains (shell region), have excellent mechanical properties, particularly, the coexistence of high strength and ductility. We use atomic and dislocation simulations to investigate the mechanism of the excellent mechanical properties. The harmonic structures are modeled simply while maintaining the three main characteristics of harmonic structure materials: heterogeneous distributed strength, interfaces between the core and shell regions, and shell region network. Based on the synergistic effect of the coexistence of core and shell regions, which is caused by the heterogeneous evolution of lattice defects near the core–shell interface as obtained in atomic and dislocation simulations, a possible mechanism providing high strength and ductility of the harmonic structure materials is discussed. Plastic deformation starts from the core regions with lower strength and progresses to the shell region with higher strength. The core–shell interfaces act as a strong barrier for the plastic deformation propagation from the core to shell regions because of the back stress caused by the transmitted dislocations in the shell regions, which increase the dislocation density of the core regions in contact with the interface, resulting in increased strength and work-hardening rate in the core regions. The former contributes to the high strength of the harmonic structure materials and the latter can suppress the plastic instability of the shell regions, resulting in high ductility of the harmonic structure materials.

The development of crystalline materials with both high strength and ductility has been a challenging task in the fields of materials science and engineering. In this study, we demonstrate that the transformation of specific types of grain boundaries (GBs) associated with dislocation emission can serve as a novel work-hardening mechanism to achieve multilayered nanopillars with high ductility. We performed atomic simulations of tensile deformation tests of bicrystal models and multilayered nanopillar models consisting of the GBs. The bicrystalsimulations showed that the critical stress for the dislocation emission from GBs progressively increased after the first emission of the dislocations owing to the transformation of the GB structure with a lower dislocation-source potential. Owing to this hardening of the dislocation sources, the plastic deformation propagated from grain to grain in the longitudinal direction of the multilayered nanopillar models, similar to the propagation of the Lüders band in discontinuous yielding, consequently attaining high ductility in the multilayered nanopillar models. This indicates that utilizing the untapped functions of GBs, that is, dislocation supplying and hardening capabilities, can facilitate high ductility in the multilayered nanopillars; hence, awakening the “dormant” functions of such lattice defects will facilitate the development of nanoscale materials with excellent mechanical properties, including high work-hardening capacity. The improved work-hardening capacity of nanoscale materials can promote the development of new strategies and approaches toward the advancement of nanoscale materials science research.

Molecular dynamics simulations were used to investigate cementite decomposition’s effect on ferrite/cementite interface-mediated plastic deformation. To model the cementite decomposition, an amorphous cementite phase is introduced between the ferrite and cementite layers with the Bagaryatski orientation relationship. The effects of the cementite decomposition on two plastic deformation phenomena are investigated by varying the thickness of the amorphous cementite layer: first, dislocation emission from the interface, and second, plastic deformation propagation from the ferrite phase to the cementite phase. The introduction of amorphous cementite into a ferrite/cementite interface containing interfacial dislocations causes the effective dislocation nucleation site originating from the interfacial dislocation to lose function, increasing the yield stress of the ferrite/cementite microstructure. The thicker the amorphous layer, the more difficult it is for the ferrite-phase plastic deformation to propagate to the cementite phase. These results suggest that cementite decomposition complicates plasticity phenomena at the interface. The effect of cementite decomposition on the work-hardening ability of the ferrite phase is discussed, as is the possibility of achieving both high strength and high ductility in drawn pearlite steel via appropriate interface structure design.

High-entropy alloys (HEAs) are solid solutions with five or more elements in near equiatomic fractions and exhibit excellent mechanical properties. However, the mechanism has not been fully understood yet. Because general grain boundaries (GBs) contain various sizes of atomic free volumes, a deviation of atomic composition at GBs may appear in HEAs by replacing atoms with ones having different atomic sizes to reduce atomic free volumes at GBs. Various equiatomic HEAs with five elements are modeled by a modified Morse (two-body interatomic) potential. Thermal equilibrium GBs at finite temperatures are obtained by hybrid Monte Carlo-molecular dynamics simulations. As results, GBs in HEAs mainly consist of two elements with the minimum and maximum atomic size and the critical stress to emit dislocations from the GBs increases as the deviation of atomic composition becomes large.

To investigate the reason why low-carbon steels with carbon-clusters shows the maximum strength during low-temperature aging, interactions between an edge dislocation and carbon clusters are performed through molecular dynamics (MD) simulations. Carbon clusters are modeled based on atom probe tomography (APT) observations. To express a transition process of carbon configurations from solid solution state to carbon cluster state to precipitation state during aging process, we reduce a carbon presence area with a fixed number of carbon atoms, i.e., the carbon concentration can be continuously increased. The MD simulations can represent the age hardening/softening tendency observed in the experiment and the carbon cluster state shows the maximum strength where the dislocation passes through the carbon cluster not by the Orowan but by the cutting mechanism. The MD analysis found that partial clusters in the carbon cluster act as the main resistance to dislocation passage; the biased distribution of carbon atoms is also confirmed in the actual observed carbon clusters by APT. A new interaction mechanism between dislocation and carbon clusters is developed based on the phenomena in the MD simulations and the availability is discussed.

The excellent combination of high strength and high ductility of drawn pearlitic steels is likely derived from the synergistic effects between the ferrite and cementite phases. However, the detailed mechanism, especially the mechanism responsible for the improvement in ductility, has not yet been fully elucidated. In this study, to achieve improved ductility of drawn pearlitic steels, interfacial-dislocation-controlled deformation and fracture in nanolayered composites of ferrite and cementite phases with the Bagaryatsky relationship are investigated via uniaxial tensile and compressive deformation tests using molecular dynamics simulations. Various modes of inelastic deformation are observed at the yield point according to the spacing of interfacial dislocations on the interface between the ferrite and cementite phases in the nanolayered-composite models. Spacing of the interfacial dislocations, which accommodates misfit strains between the ferrite and cementite phases, determines the phase stress and the interfacial dislocation structure in the nanolayered-composite models. This phase stress and interfacial dislocation structure influences the resolved shear/normal stress and the critical resolved shear/normal stress for each inelastic-deformation mode, respectively. Thus, interfacial dislocation spacings can control which inelastic deformation mode is activated at the yield point. We find specific interfacial dislocation structures on the ferrite–cementite interface that nucleate lattice dislocations with lower Schmid factors at the first plastic event. This interfacial dislocation structure can improve the ductility of drawn pearlitic steels because the high strain-hardening rate in the ferrite phases, resulting from the nucleation of dislocations with lower Schmid factors, is clearly expected to suppress the concentration of plastic deformation in the cementite phase [T. Ohashi et al., Mater. Sci. Eng. A 588 (2013) 214–220]. The possibility of the interfacial-dislocation-controlled deformation and fracture enabling higher ductility of drawn pearlitic steels is discussed.

Strain hardening of ferrite layers in pearlite microstructures plays a crucial role in the stability of elasto-plastic deformation of pearlite. The effects of layer thickness, crystal orientation relationship and loading direction on the strain-hardening characteristics of the ferrite layers were studied by crystal plasticity analysis. The results show that the strain-hardening rate increases in the ferrite layers with small thickness, whereas at the same thickness, the strain-hardening rate varies depending on the loading direction and crystal orientation relationship. When the Schmid factors and mean-free paths of the activated systems are small and short, the strain-hardening rate tends to be high. The ferrite layer exhibits a remarkably high strain-hardening rate when slip systems are sequentially activated with the increase of deformation.

To investigate the barrier effect of grain boundaries on the propagation of avalanchelike plasticity at the atomic scale, we perform three-dimensional molecular dynamics simulations by using simplified polycrystal models including symmetric-tilt grain boundaries. The cutoffs of the stress-drop distributions following power-law distributions decrease as the size of the crystal grains decreases. We show that some deformation avalanches are confined by grain boundaries; on the other hand, unignorable avalanches penetrate all the grain boundaries included in the models. The blocking probability that one grain boundary hinders this system-spanning avalanche is evaluated by using an elemental probabilistic model.

Severe plastic deformation (SPD) processes can produce the bulk ultrafine-grained metals with grain sizes of less than 1 μm. However, the mechanism of grain refinement during SPD is not completely understood. In this study, we perform molecular dynamics simulations of a SPD process like equal-channel angular pressing and demonstrate grain refinement phenomena during the SPD simulations. We propose a new mechanism of grain subdivision related to the mobility of partial disclinations formed in strain-gradient regions during SPD.

Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this paper, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is due to dislocation avalanche motions in Cu and Ni. A different mechanism of dislocation pinning is found in Al. These different stress relaxation mechanisms give different power-law exponents. We propose a probabilistic model to describe the novel dislocation motion in Al and analytically deduce the power-law behavior.

The intergranular fracture toughness of plastic deformable crystalline materials is strongly controlled by the plastic work ahead of the intergranular crack tip. Therefore, in studies of intergranular fracture toughness, the grain boundaries (GBs) should be regarded as both a cleavage plane and dislocation source. Combining continuum analyses and atomic simulations, this study investigates the atomic-scale mechanism of intergranular crack tip plasticity in aluminum 〈1 1 2〉 tilt GBs as an effective dislocation source. To quantitatively predict the first plastic deformation near the intergranular crack tip, we first model the dislocation emission from the GBs ahead of the intergranular crack tip and analytically derive the critical stress intensity factor. If the predicted first plastic phenomenon is dislocation emission from the GBs, the resulting wedge disclination can shield the stress field near the crack. Dislocation emissions from the crack tip are accompanied by dislocation emissions from the GBs, despite the predicted difficulty of the latter. The lattice defect evolution nucleates a nanograin with a disclination at the triple-junction ahead of the crack tip, which can weaken the mechanical field near the crack tip. Consequently, when improving the intergranular fracture toughness of materials, the role of GBs as dislocation sources cannot be ignored.

Dislocation multiplication from the Frank–Read source is investigated in aluminum by applying atomic models. To express the dislocation bow-out motion and dislocation loop formation, we introduce cylindrical holes as a strong pinning point to the dislocation-bowing segment. The critical configuration for dislocation bow-out in atomic models exhibits an oval shape, which agrees well with the results obtained by the line tension model. The critical shear stress for the dislocation bow-out in atomic models continuously increases with decreasing length L of the Frank–Read source (even at the nanometer scale). This is expressed by the function L−1 ln L, which is obtained by a continuum model based on elasticity theory. The critical shear stresses for the Frank–Read source are compared with those for grain boundary dislocation sources, as well as the ideal shear strength.

The role of the ferrite/cementite heterointerface on the mechanical properties of heavily-drawn-pearlitic steel is investigated via tensile deformation tests of multilayered composite models with brittle and ductile virtual materials in a two-dimensional triangle-lattice system by using molecular dynamics simulations. The interface strength is controlled by introducing a heterointerface potential. The dominant role of heterointerface on the mechanical properties of multilayered composite models is influenced by the interface strength. In case of weak interface strength, the heterointerface acts as a strong barrier to dislocation motion in the ductile phase; hence, the multilayered composite model shows high strength but extremely low ductility. This tendency corresponds well to that of as-drawn pearlitic steel with cementite decomposition. In case of strong interface strength, the heterointerface acts as a dislocation source of the brittle phase by dislocation transmission through the heterointerface from the ductile to brittle phase; hence, the multilayered composite model shows good ductility with a small decrease in strength. This tendency corresponds well to annealed pearlitic steel recovered from cementite decomposition. These results suggest that cementite decomposition decreases the plastic deformation potential of the heterointerface. The conditions necessary for the heterointerface to simultaneously exhibit high strength and ductility are discussed on the basis of the results of atomic simulations.

Elasto-plastic deformations in the microstructures of pearlite are studied by finite-element analyses. Various models for the lamellar structure are made and the material properties of cementite and ferrite are established. Deformation of a bare specimen of cementite is unstable immediately after the yield point, while cementite lamellae show some stability when they are layered with ferrite. When higher values of yield stress and strain hardening are used for ferrite phase, cementite deforms well beyond the elastic range and the distribution of plastic strain is not concentrated. These results show that not only the layered structure but also the improved mechanical property of fine lamellae of ferrite contribute largely to stable deformation in the pearlite microstructure.

Plastic deformation of fully pearlitic steels was investigated using a multiscale approach: experimentally, the finite element method and molecular dynamics. This paper is the first in a series of three papers demonstrating the strain distribution in uniaxial tensile deformationwith high-precision markers drawn by electron beam lithography. Strain was measured at loads of 1.98 kN, 2.21 kN and 2.28 kN in tensile deformation. Scanning electron microscopy (SEM) images and strain maps show the plastic deformation of cementite lamellae and homogenous plastic deformation under uniaxial tensile deformation in the area where the cementite lamellae are aligned in the tensile direction. The areas where strain was enhanced were both block/colony boundaries and the areas where the cementite lamellae are inclined approximately 45° to the tensile direction.

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.

In order to improve the fracture toughness in ultrafine-grained metals, we investigate the interactions among crack tips, dislocations, and grain boundaries in aluminum bicrystal models containing a crack and ⟨112⟩ tilt grain boundaries using molecular dynamics simulations. The results of previous computer simulations showed that grain refinement makes materials brittle if grain boundaries behave as obstacles to dislocation movement. However, it is actually well known that grain refinement increases fracture toughness of materials. Thus, the role of grain boundaries as dislocation sources should be essential to elucidate fracture phenomena in ultrafine-grained metals. A proposed mechanism to express the improved fracture toughness in ultrafine-grained metals is the disclination shielding effect on the crack tip mechanical field. Disclination shielding can be activated when two conditions are present. First, a transition of dislocation sources from crack tips to grain boundaries must occur. Second, the transformation of grain-boundary structure into a neighboring energetically stable boundary must occur as dislocations are emitted from the grain boundary. The disclination shielding effect becomes more pronounced as antishielding dislocations are continuously emitted from the grain boundary without dislocation emissions from crack tips, and then ultrafine-grained metals can sustain large plastic deformation without fracture with the drastic increase of the mobile dislocation density. Consequently, it can be expected that the disclination shielding effect can improve the fracture toughness in ultrafine-grained metals.

In order to investigate the effect of structural units on the ability of grain boundaries to generate dislocations, tensile and compressive loading tests were performed on aluminum bicrystals with ⟨112⟩ tilt grain boundaries using molecular-dynamics simulations. Five favored boundaries were found for ⟨112⟩ boundaries in an energy minimization analysis. Each structure could be identified using only its single structural unit period: 𝐴 unit for 𝛴⁢1 with 𝜃=0°, 𝐵 unit for 𝛴⁢11 with 𝜃=62.96°, 𝐶 unit for 𝛴⁢5 with 𝜃=90°, 𝐸 unit for 𝛴⁢7 with 𝜃=120°, and 𝐷 unit for 𝛴⁢3 with 𝜃=180°. The favored boundaries all show an energy cusp except for the 𝛴⁢7 boundary. Other boundaries could be represented by a combination of these five structural units. When 𝛴⁢11 with |𝐵| period showing a minimum energy cusp was used as a reference structure, the core of 2/11⁢[-3 1 -1] or 2/11⁢[3 -1 1] dislocations calculated for the displacement sift complete lattice of 𝛴⁢11 were introduced at interfaces having larger or smaller misorientation angles than 𝛴⁢11, respectively. Each grain-boundary dislocation corresponds to 𝐴 and 𝐶 units, respectively. For example, 𝛴⁢21 with 𝜃=44.42° and 𝛴⁢15 with 𝜃=78.46° consists of |𝐵⁢𝐵⁢𝐴| and |𝐵⁢𝐵⁢𝐶| periods, respectively. When the 𝛴⁢15 bicrystal was loaded in tension, lattice dislocations having the 1/2⁢[1 -1 0] core were emitted from 𝐶 units and then the 𝐶 units change their structure to the 𝐵 units. Therefore, the 𝛴⁢15 boundary can change its structure to the energetically stable 𝛴⁢11 structure by emitting dislocations from 𝐶 units. For 𝛴⁢21, the same structural change occurred when the 𝛴⁢21 bicrystal was deformed in compression. The simulation results show that there are tilt grain boundaries having the strong anisotropic strength and that the ability of grain boundaries to generate dislocations is closely related to their structural units.

Adaptivemesh refinement and local/non-local transition in our quasicontinuum method (Phys. Rev. B, Vol. 69, No. 21(2004), pp.214104(1-10)) are studied in this paper. Although deformation gradients have been used to determine the mechanical state of an element in the original quasicontinuum method, we adopt elastic stiffness coefficients, which govern stress-strain relationships at finite deformation. Because elastic stiffness coefficients are calculated using the interatomic potential function, we do not need to prepare reference node (atomic) positions. To confirm its applicability, we performed nano-indentation simulations in two dimensions, and found that the criterion values estimated using deformation gradients and elastic stiffness coefficients show a positive correlation.

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.

The interactions between edge dislocations and grain boundaries—dislocation pileup, dislocation absorption, and dislocation transmission—are studied by performing quasicontinuum simulations. The ⟨112⟩ asymmetrical tilt grain boundaries with different misorientation angles are used. The atomic configurations and stress fields of equilibrium and nonequilibrium asymmetrical grain boundaries are investigated in detail by comparison with analytical models. The influence of the grain boundary structure on the stress concentration due to dislocation pileup and the accommodation of extrinsic dislocations in the grain boundaries are also examined by using low- and high-angle grain boundaries. The critical forces on the dislocation in small-angle tilt grain boundaries for it to eject from the boundaries are evaluated by atomic simulations, and the results are compared with dislocation theory. It is also found that the rearrangement of the grain boundary dislocations with local grain boundary sliding in the local region, where the extrinsic dislocation is absorbed, is the characteristic accommodation mechanism of low-angle asymmetrical grain boundaries. The effects of the interaction between dislocations and grain boundaries on the mechanical properties of coarse-grained metals with dislocation sources in their grain and on those of nanocrystalline metals without sources in their grain are also discussed.

The collective grain movement of nanocrystalline metals and its temperature dependence are studied by using molecular dynamics simulations. First, a unit structure that consists of eight aluminium grains in the regular hexagonal shape with 5 nm grain size is prepared, and then an analysis model is made by arranging the same 144 unit structures in the two-dimensional periodicity. Thus the total number of grains is 1152. Various collective grain deformations occur at different temperatures under tensile loading. In the case of 100 K, shear bands formed by the collective grain deformation can be observed remarkably. On the other hand, in the case of 300 or 500 K, no remarkable inhomogeneous deformation such as shear bands occurs. This might be due to the different accommodation mechanism for geometrical misfits by local shear deformation at each different temperature. In order to investigate the effect of the collective grain deformation on the macro-scale mechanical properties, the stress–strain curve for the model with 144 unit structures and an averaged strain–stress curve for the 60 cases of a model with one unit structure are compared. Consequently, it is found that the inhomogeneous plastic deformation mode such as a shear band can influence the strength of nanocrystalline metals.

The influence of defects in nanograins, e.g. stacking faults and twinnings, on mechanical properties of nanocrystalline materials is studied by molecular dynamics simulations. Two types of many-body interatomic potential based on aluminium are adopted to investigate the influence of stacking fault energy on the deformation mechanism of nanocrystalline metals: one accurately reproduces the energy value of stacking faults for aluminium; the other underestimates the energy value for aluminium. Three different deformation processes are performed to nanocrystalline models with high or low stacking fault energy, and crystal slips occur in both models. In the case of the high stacking fault energy, crystal deformation occurs by perfect dislocations and no defects exist in the grains. Therefore, the strength almost recovers after relaxation. On the other hand, for low stacking fault energy, stacking faults remain through the grains after the crystal slips by partial dislocations. Consequently, these defects cause anisotropy in the mechanical properties of the simulated nanocrystalline metals.

The strength of nanocrystalline aluminum has been studied using molecular dynamics simulation. Nanocrystalline models consisting of hexagonal grains with grain size 𝑑 between 5 nm and 80 nm are deformed by the application of tension. A transition from grain-size hardening to grain-size softening can be observed in the region where 𝑑≈30nm, which is the optimum grain size for strength. In the grain-size hardening region, nanocrystalline models primarily deform by intragranular deformation. Consequently, a pile-up of dislocations can be observed. When the grain size becomes less than 30 nm, where the thickness of the grain boundaries cannot be neglected in comparison to the grain sizes, the dominant deformation mechanism of nanocrystalline metals is intergranular deformation by grain boundary sliding. Further, geometrical misfits by grain boundary sliding are accommodated by the grain rotation mechanism. Moreover, cooperative grain boundary sliding occurs in the 5 nm model. The optimum grain size is controlled by the relationship between resistance to intergranular deformation by grain boundary processes and intragranular deformation resisted by the grain boundary. Therefore, the primary role of the grain boundary changes in the region where the optimum grain size is observed.

The quasicontinuum method is a way of reducing the number of degrees of freedom in an atomistic simulation by removing the majority of the atoms in regions of slowly varying strain fields. Due to the different ways the energy of the atoms is calculated in the coarse-grained regions and the regions where all the atoms are present, unphysical forces called “ghost forces” arise at the interfaces. Corrections may be used to almost remove the ghost forces, but the correction forces are nonconservative, ruining energy conservation in dynamic simulations. We show that it is possible to formulate the quasicontinuum method without these problems by introducing a buffer layer between the two regions of space. The method is applicable to short-ranged potentials in the face-centered cubic, body-centered cubic, and hexagonal close-packed crystal structures.