Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation

The mechanical behaviour of nanocrystalline materials (that is, polycrystals with a grain size of less than 100 nm) remains controversial. Although it is commonly accepted that the intrinsic deformation behaviour of these materials arises from the interplay between dislocation and grain-boundary processes, little is known about the specific deformation mechanisms. Here we use large-scale molecular-dynamics simulations to elucidate this intricate interplay during room-temperature plastic deformation of model nanocrystalline Al microstructures. We demonstrate that, in contrast to coarse-grained Al, mechanical twinning may play an important role in the deformation behaviour of nanocrystalline Al. Our results illustrate that this type of simulation has now advanced to a level where it provides a powerful new tool for elucidating and quantifying--in a degree of detail not possible experimentally--the atomic-level mechanisms controlling the complex dislocation and grain-boundary processes in heavily deformed materials with a submicrometre grain size.     

Electrical properties of the grain boundaries of oxygen ion conductors: Acceptor-doped zirconia and ceria

This article reviews the current understanding of the electrical properties of the grain boundaries of acceptor-doped zirconia and ceria, however, with an emphasis on the grain-boundary defect structure. From an electrical point of view, a grain boundary consists of a grain-boundary core and two adjacent space-charge layers. The grain-boundary cores of acceptor-doped zirconia and ceria are positively charged, probably owing to the oxygen vacancy enrichment there. Oxygen vacancies are therefore depleted in the space-charge layer. The grain-boundary conductivities of acceptor-doped zirconia and ceria are at least two orders of magnitude lower than the corresponding bulk values, depending on temperature and dopant level. Such a phenomenon is due to the facts: (1) that oxygen vacancies are severely depleted in the space-charge layer, and (2) that the grain-boundary impurity phase blocks the ionic transport across the grain boundaries by decreasing the conduction path width and constricting current lines. In materials of high purity, the effect of the space-charge depletion layer is dominant; however, in materials of normal purity, the effect of the grain-boundary impurity phase is dominant. A Schottky barrier model satisfactorily explains all the phenomenological observations of the grain-boundary electrical properties of materials of high purity, and experimental evidence soundly supports the model. Various factors (alumina addition and grain size) influencing the grain-boundary electrical properties are discussed, and some special aspects of nanocrystalline materials are highlighted.     

A micro-continuum model for the creep behavior of complex nanocrystalline materials

A nanocrystalline material which has an average grain size of less than 100 nm is characterized with a significant portion of atoms residing in the grain boundaries or in the grain-boundary affected zone (GBAZ), while nanocrystalline materials with a more complex structure may contain additional strengthening nanoparticles or nano pores. In this article we develop a micro-continuum model to capture the creep response of such a complex nanocrystalline system. We make use of the concept of a three-phase composite with the GBAZ serving as the matrix, and grain interiors and dispresed particles (or voids) as two distinct types of inclusions. Both the grain interior and the GB zone are capable of undergoing the rate-dependent plastic deformation, but the strengthening nanoparticles or pores are taken to deform only elastically. During deformation the porosity will continue to evolve; its evolution is also addressed. In addition, the effect of temperature on the overall creep response is also accounted for. Several important features of creep characteristics in light of grain size, and nanoparticle and nanopore concentrations, are illustrated, and it is also demonstrated that the calculated results are in reasonable agreement with available experimental data.     

Nanomechanics of Hall-Petch relationship in nanocrystalline materials

Classical Hall-Petch relation for large grained polycrystals is usually derived using the model of dislocation pile-up first investigated mathematically by Nabarro and coworkers. In this paper the mechanical properties of nanocrystalline materials are reviewed, with emphasis on the fundamental physical mechanisms involved in determining yield stress. Special attention is paid to the abnormal or ‘inverse’ Hall-Petch relationship, which manifests itself as the softening of nanocrystalline materials of very small (less than 12 nm) mean grain sizes. It is emphasized that modeling the strength of nanocrystalline materials needs consideration of both dislocation interactions and grain-boundary sliding (presumably due to Coble creep) acting simultaneously. Such a model appears to be successful in explaining experimental results provided a realistic grain size distribution is incorporated into the analysis. Masumura et al. [Masumura RA, Hazzledine PM, Pande CS. Acta Mater 1998;46:4527] were the first to show that the Hall-Petch plot for a wide range of materials and mean grain sizes could be divided into three distinct regimes and also the first to provide a detailed mathematical model of Hall-Petch relation of plastic deformation processes for any material including fine-grained nanocrystalline materials. Later developments of this and related models are briefly reviewed.Prof. Frank Nabarro was a physicist by training, a metallurgist by profession and a genius by nature, blessed with a unique ability to treat everyone as his equal. During his later years he was very much interested in the mechanical properties of nanocrystalline materials. This review on that topic is our contribution to the special issue of Progress in Materials Science honoring him.     

Mechanical properties of nanocrystalline materials

The mechanical properties of nanocrystalline materials are reviewed, with emphasis on their constitutive response and on the fundamental physical mechanisms. In a brief introduction, the most important synthesis methods are presented. A number of aspects of mechanical behavior are discussed, including the deviation from the Hall-Petch slope and possible negative slope, the effect of porosity, the difference between tensile and compressive strength, the limited ductility, the tendency for shear localization, the fatigue and creep responses. The strain-rate sensitivity of FCC metals is increased due to the decrease in activation volume in the nanocrystalline regime; for BCC metals this trend is not observed, since the activation volume is already low in the conventional polycrystalline regime. In fatigue, it seems that the S-N curves show improvement due to the increase in strength, whereas the da/dN curve shows increased growth velocity (possibly due to the smoother fracture requiring less energy to propagate). The creep results are conflicting: while some results indicate a decreased creep resistance consistent with the small grain size, other experimental results show that the creep resistance is not negatively affected. Several mechanisms that quantitatively predict the strength of nanocrystalline metals in terms of basic defects (dislocations, stacking faults, etc.) are discussed: break-up of dislocation pile-ups, core-and-mantle, grain-boundary sliding, grain-boundary dislocation emission and annihilation, grain coalescence, and gradient approach. Although this classification is broad, it incorporates the major mechanisms proposed to this date. The increased tendency for twinning, a direct consequence of the increased separation between partial dislocations, is discussed. The fracture of nanocrystalline metals consists of a mixture of ductile dimples and shear regions; the dimple size, while much smaller than that of conventional polycrystalline metals, is several times larger than the grain size. The shear regions are a direct consequence of the increased tendency of the nanocrystalline metals to undergo shear localization.The major computational approaches to the modeling of the mechanical processes in nanocrystalline metals are reviewed with emphasis on molecular dynamics simulations, which are revealing the emission of partial dislocations at grain boundaries and their annihilation after crossing them.     

Mechanical spectroscopy of nanocrystalline aluminum films: effects of frequency and grain size on internal friction

Energy dissipation by internal friction is a property of fundamental interest for probing the effects of scale on mechanical behavior in nanocrystalline metallic films and for guiding the use of these materials in the design of high-Q micro/nanomechanical resonators. This paper describes an experimental study to measure the effects of frequency, annealing and grain size on internal friction at room temperature in sputter-deposited nanocrystalline aluminum films with thicknesses ranging from 60 to 120 nm. Internal friction was measured using a single-crystal silicon microcantilever platform that calibrates dissipation against the fundamental limits of thermoelastic damping. Internal friction was a weak function of frequency, reducing only by a factor of two over three decades of frequency (70 Hz to 44 kHz). Annealing led to significant grain growth and the average grain size of 100 nm thick films increased from 90 to 390 nm after annealing for 1 h at 450?(°)C. This increase in grain size was accompanied by a decrease in internal friction from 0.05 to 0.02. Taken together, these results suggest that grain-boundary sliding, characterized by a spectrum of relaxation times, contributes to internal friction in these films.     

A micromechanical approach to the stress–strain relations, strain-rate sensitivity and activation volume of nanocrystalline materials

This review highlights a secant viscosity approach that has wide applicability for the determination of mechanical properties of nanocrystalline materials. Along the way we also add some new elements and provide fresh perspectives. This approach was originally proposed for the nonlinear, time-dependent, work-hardening creep of dual-phase composites (Li and Weng, J Mech Phys Solids 45:1069–1083, 1997a), but by conceiving a nanocrystalline material as a composite of the stronger grain interior and the softer grain-boundary (GB, or grain-boundary affected zone GBAZ), it becomes possible to extend it to calculate the grain-size dependence of their flow stress, strain-rate sensitivity, and activation volume. We also use it to explain how the flow stress first increases and then decreases as the grain size decreases from the coarse grain to the nanometer range, leading to the Hall–Petch and the inverse Hall–Petch relations. The critical state at which the slope of the strength variation with respect to the grain size becomes zero also yields the strongest material state. In this way the two most important parameters for material design—the maximum strength and the critical grain at which it occurs—can be obtained. The strain-rate sensitivity parameters are also shown to follow a similar pattern as the flow stress, but the activation volume varies in an exactly reverse way.     

Influence of interface energy and grain boundary on the elastic modulus of nanocrystalline materials

With reducing the grain size into nanometer scale for polycrystalline materials, the influence of nonlocal interactions in grain boundaries on the mechanical properties of the material is reinforced as well as the interface energy stemming from the surfaces of grains is increased, resulting in that the mechanical properties of the polycrystalline represent size-dependence significantly. In this work, the influence of the interface energy and grain boundaries on the elastic properties of nanocrystalline materials is investigated in the framework of continuum mechanics. An analytical expression of the elastic modulus is addressed to describe the grain size effects on the Young’s modulus of nanocrystalline materials. The numerical results illustrate that the elastic modulus of nanocrystalline materials decreases with the reduction of the grain size to nanometer scale. The grain size effects become remarkable when the grain size lowers down to several tens nanometers, and the influence of the interface energy and grain boundary must be taken into account. The contribution of the density on the mechanical properties in nanocrystalline materials is analyzed by discussing the influence of the grain boundary thickness on the elastic modulus. The comparison between the proposed theoretical results and the present measurement shows that the proposed model can predict the experiments quite well.     

Combined atomistic and mesoscale simulation of grain growth in nanocrystalline thin films

We have combined molecular-dynamics (MD) simulations with mesoscale simulations to elucidate the mechanism and kinetics of grain growth in nanocrystalline palladium with a columnar grain structure. The conventional picture of grain growth assumes that the process is governed by curvature-driven grain-boundary (GB) migration. Our MD simulations demonstrate that, at least in a nanocrystalline material, grain growth can also be triggered by the coordinated rotations of neighboring grains so as to eliminate the common GB between them. Such rotation–coalescence events result in the formation of highly elongated, unstable grains which then grow via the GB migration mechanism. These insights can be incorporated into mesoscale simulations in which, instead of the atoms, the objects that evolve in space and time are discretized GBs, grain junctions and the grain orientations, with a time scale controlled by that associated with grain rotation and GB migration and with a length scale given by the grain size. These mesoscale simulations, with physical insight and input materials parameters obtained by MD simulation, enable the investigation of the topology and long-time grain-growth behavior in a physically more realistic manner than via mesoscale simulations alone.     

Mechanics of creep resistance in nanocrystalline solids

Summary In a nanocrystalline solid a significant portion of atoms resides in the grain boundary and the nearby outer grain. This combined region, known as the grain-boundary affected zone (GBAZ), is plastically softer than the grain interior, and it are the combined contributions of the grain interior and GBAZ that give rise to the overall response. In this spirit a two-phase composite model is developed to study the high-temperature creep resistance of nanocrystalline materials. Here the rate equation of each phase is represented by a power law and the Arrhenius function, but that of the grain interior is further taken to scale with the Hall–Petch relation whereas that of the GBAZ remains independent of grain size. This unified constitutive equation in turn leads to the concept of secant viscosity. Then a homogenization theory is developed by means of a transition from linear viscoelasticity to nonlinear viscoplasticity with the Maxwell viscosity constantly replaced by the secant viscosity. Subsequently a field-fluctuation method is called upon to determine the effective stress of both phases. The developed theory is applied to model the creep behavior of nanocrystalline Cu, NiP alloy, and Ni at various levels of stress, temperature, and grain size, with results that reflect good agreement with available experiments. We then applied the theory to examine the nature of creep resistance as the grain size decreases in the nanometer range in some detail, and it was discovered that creep resistance in the Hall–Petch like plot undergoes a transition from a positive slope to leveled off, and then to a negative slope. The leveled-off value in effect represents the maximum creep resistance that a material can attain, and it is found that this occurs at a critical grain size, d _crit, that exists in the nanometer range. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

The effects of strain rate and grain size on nanocrystalline materials: A theoretical prediction

The article describes a dislocation-based model for the coupling effects of strain rate and grain size on the mechanical behavior of nanocrystalline materials. Two important experimental findings about nanocrystalline materials are explained by the model: 1. the difference of the dependencies of strain rate sensitivity (SRS) on grain size between FCC and BCC nanocrystalline materials and 2. the abnormal dependency of activation volume on thermally activated stress. Our analysis shows that the strain rate-dependent behavior of nanocrystalline materials is mainly determined by the ratio between the activation volumes in grain and grain boundary regions.     

Structure and thermal stability of nanocrystalline materials

Nanocrystalline materials, which are expected to play a key role in the next generation of human civilization, are assembled with nanometre-sized “building blocks” consisting of the crystalline and large volume fractions of intercrystalline components. In order to predict the unique properties of nanocrystalline materials, which are a combination of the properties of the crystalline and intercrystalline regions, it is essential to understand precisely how the structures of crystalline and intercrystalline regions vary with decrease in crystallite size. In addition, study of the thermal stability of nanocrystalline materials against significant grain growth is both scientific and technological interest. A sharp increase in grain size (to micron levels) during consolidation of nanocrystalline powders to obtain fully dense materials may consequently result in the loss of some unique properties of nanocrystalline materials. Therefore, extensive interest has been generated in exploring the size effects on the structure of crystalline and intercrystalline region of nanocrystalline materials, and the thermal stability of nanocrystalline materials against significant grain growth. The present article is aimed at understanding the structure and stability of nanocrystalline materials.     

纳米晶Ba_（1－x）Pb_xTiO_3的合成与表征

以醋酸铅、硬脂酸钡和钛酸丁酯为原料，用硬脂酸凝胶法（ＳＡＧ）合成了粒度均匀、粒径１０－２０ｎｍ的Ｂａ（１－ｘ）ＰｂｘＴｉＯ３纳米晶粉末．利用红外光谱（ＩＲ）、热重（ＴＧ）和差热分析（ＤＴＡ）研究了纳米晶粉末的合成过程．用ＴＥＭ、ＸＲＤ观察和研究纳米晶的形貌及晶体结构，并用发射光谱测定样品的纯度．     

Consolidation of nanocrystalline Fe-1.6 wt%C via low temperature hot isostatic pressing

Ball-milled Fe-1.6 wt% C powder with a nanocrystalline substructure was consolidated to full density via hot isostatic pressing at 500 °C and 414 MPa. The HIPped microstructure remained largely nanocrystalline (~39 nm in diameter). Although the grain size increased, the grain size distribution was not significantly altered. The results of this study suggest that other nanocrystalline materials in powder form may be consolidated via HIPping at temperatures low enough to prevent extensive grain growth.     

Approach to the Theoretical Strength of Ti—Ni—Cu Alloy Nanocrystals by Grain Boundary Design

The grain boundary design was used to introduce boride Ti_2B and TiB_2 nanoparticles of 5 nm in size into grain boundaries of nanocrystalline Ti_(50)Ni_(25)Cu_(25) alloy.As a result,the maximum normalized microhardness was increased by 20%and the theoretical limit of hardness is substantially approached.It is proposed that boride nanoparticles suppressed low-temperature grain-boundary sliding and,therefore,shifted the range of the anomalous behavior of Hall-Petch relation toward smaller sizes of the Ti-Ni-Cu nanocrystals.     

纳米材料微阵列超塑微成形机理与尺度效应

微成形技术是未来批量制造高精密微小零件的关键技术,但是,微小尺度下材料的塑性变形行为不仅表现出明显的尺度效应,而且零件尺度已经接近常规材料的晶粒尺寸,每个晶粒的形状、取向、变形特征对整体变形产生复杂的影响,难以保证微成形的工艺稳定性。本项目采用纳米材料进行微成形,制造微阵列,零件内部包含大量的晶粒,可以排除晶粒复杂性的影响,而且纳米材料具有超塑性,在超塑状态下,变形抗力和摩擦力都明显降低,从而显著降低微成形工艺对模具性能的苛刻要求,提高工艺稳定性和成形精度。目前,纳米材料超塑性微成形技术方面的研究极少,变形时纳米材料的力学行为、变形机理、尺度效应、位错演化、力学模型等关键问题还有待研究。采用电沉积技术制备晶粒尺寸可控的纳米材料,将工艺实验研究、性能测试、组织分析、力学性能表征、数值模拟相结合,深入探究了纳米材料微阵列超塑性微成形机理和成形规律,以促进该技术的广泛应用。     

Effects of grain refinement and strength on friction and damage evolution under repeated sliding contact in nanostructured metals

The early stage sliding contact fatigue behavior of nanocrystalline materials, with average and total range of grain sizes well below 100 nm, was studied. The evolution of friction and damage during repeated sliding contact in the nanocrystalline metals and alloys was systematically compared and contrasted with that in ultrafine-crystalline and microcrystalline materials so as to develop a broad perspective on the effects of grain size on sliding contact fatigue. Some critical experiments were performed to separate the effects of material strength and grain size on friction and damage evolution. Over the range of materials examined, strength rather than grain size appeared to dominate the steady-state friction coefficient and damage accumulation, each diminishing with substantial increases in material strength.     

Phase transformations and phase stability in nanocrystalline materials

The current state of the researches on diffusionless phase transformations, including allotropic, polymorphous and martensitic transformations, and phase stability are reviewed. The behaviors of phase transformation and phase stability in nanocrystalline materials are markedly affected by the non-equilibrium conditions involved in their preparation, as a result, in this review an ideal demonstrating method of critical size for the stability of a high-temperature phase at low-temperatures is suggested, and the intrinsic conditions of the phase stability are clarified. Our recent experiments exhibit that the reversal transformation temperatures of low-temperature phases in nanocrystalline Co bulk metal and Fe–30Ni wt% alloy are significantly raised up over 800 °C when their grain sizes are smaller than about 15 nm, while in the reported experiments of nanocrystalline particles or films the reversal transformation temperature lowers with decreasing grain size or is independent of grain size. Therefore, the author suggests that more experiments and theories for phase stability in reversal transformation should be performed. The study of grain growth kinetics of nanocrystalline materials, as a basic of investigating phase stability, is another attention aspect.