Disclination mechanism for plastic deformation of nanocrystalline materials

A model is developed for the plastic deformation of nanocrystalline materials in terms of the evolution of a spatial grid of disclinations located at the triple junctions of grains. Plastic deformation takes place as the result of plastic rotation of grains, the mismatch of whose rotations causes the nucleation of partial disclinations at the junctions of intergrain boundaries. It is shown that the distinctive feature of the mechanical behavior of nanocrystals is a deviation from the Hall-Petch law up to a critical grain size D _cr⩽25 nm. Fiz. Tverd. Tela (St. Petersburg) 39, 2023–2028 (November 1997)     

多晶银纳米线拉伸变形的分子动力学模拟研究

纳米尺度金属Ag以其独特的导电和导热性,广泛应用于微电子、光电子学、催化等领域,特别是在纳米微电极和纳米器件方面的应用.本文采用分子动力学方法模拟了不同晶粒尺寸下多晶银纳米线的拉伸变形行为,详细分析了晶粒尺寸对多晶银纳米线弹性模量、屈服强度、塑性变形机理的影响.发现当晶粒尺寸小于13.49 nm时,多晶Ag纳米线呈现软化现象,出现反Hall-Petch关系,此时的塑性变形机理主要以晶界滑移、晶粒转动为主,变形后期形成五重孪晶;当晶粒尺寸大于13.49 nm时,塑性变形以位错滑移为主,变形后期产生大量的孪晶组织.     

Molecular dynamics simulation of mechanical properties of nanocrystalline platinum: Grain-size and temperature effects

A series of molecular dynamics simulations has been carried out to study the mechanical properties of nanocrystalline platinum. The effects of average grain size and temperature on mechanical behaviors are discussed. The simulated uniaxial tensile results indicate the presence of a critical average grain size about 14.1 nm, for which there is an inversion of the conventional Hall-Petch relation at temperature of 300 K. The transition can be explained by a change of dominant deformation mechanism from dislocation motion for average grain size above 14.1 nm to grain boundary sliding for smaller grain size. The Young's modulus shows a linear relationship with the reciprocal of grain size, and the modulus of the grain boundary is about 42% of that of the grain core at 300 K. The parameters of mechanical properties, including Young's modulus, ultimate strength, yield stress and flow stress, decrease with the increase of temperature. It is noteworthy that the critical average grain size for the inversion of the Hall-Petch relation is sensitive to temperature and the Young's modulus has an approximate linear relation with the temperature. The results will accelerate its functional applications of nanocrystalline materials.     

Reconstruction of the autowave structure upon deformation of polycrystalline aluminum

The evolution of zones of localized plastic deformation in polycrystalline aluminum was investigated. At the stage of the linear strain hardening, such zones were established to move synchronously, whereas at the stage of parabolic strengthening they are stationary. The quantitative characteristics (wavelength, propagation velocity) of deformation waves that are formed at the stage of linear strengthening were determined. A relation between the quantitative characteristics of the process of deformation localization and the grain size was found. The distribution of local deformations upon transition from one stage of plastic flow to another was investigated. A model that explains the generation of coarse-scale structures of localized plastic deformation is suggested.     

Physical mesomechanics of grain boundary sliding in a deformable polycrystal

The temperature-rate dependences of strain resistance and the mechanisms of grain boundary sliding in Pb polycrystals and Pb-based alloys under active tension were investigated. The activation energy of plastic deformation and grain boundary sliding was determined. The structural mechanisms of grain boundary sliding were studied in a wide temperature range. The conclusion was made that self-consistency of grain boundary sliding and intragranular plastic flow has its origin in rotational deformation modes, with the grain boundary sliding being a primary process. Theoretical analysis of rotational deformation modes involved in grain boundary sliding was performed. It is shown that the dependence of deforming stress on the polycrystal grain size is impossible to describe by one universal Hall-Petch equation.     

Influence of the transverse size of samples with micro- and nano-grained structures on the yield and flow stresses

The effects of reduction in the strength and deviation from the Hall-Petch relationship under plastic deformation of specimens with micro- and nano-grained structures with decreasing size of their cross section have been considered theoretically. The analysis is based on the kinetic equation for the dislocation density, which takes into account that the surface of the specimen serves as both the source and the sink for dislocations, whereas the grain boundaries are barriers limiting the mean free path of dislocations. It has been found that, when the ratio of the transverse size of the specimen D to the grain size d becomes less than 3, in the dependence of the yield stress on the size of the specimen there appears a minimum as a result of the increase in the number of near-surface grains that exhibit a weak resistance to plastic deformation due to the withdrawal of dislocations through the external surface of the fine-dimensional specimen. The minimum of the strength in the range d < D < 3d is a consequence of the competition and nonlinear interaction of the size factors D and d.     

Phenomenology of wave processes in a localized plastic flow

The motion of localized deformation sites in mono-and polycrystallites of metals and alloys is investigated experimentally at the stages of easy slip and linear strain hardening. The wave nature of localization of deformation at these stages of plastic flow is established, and the velocity of waves and their dispersion relation are determined. The scale effect and the dependence of the localized deformation wavelength on the grain size are investigated. A qualitative interpretation of the results obtained is proposed.     

纳米多层膜“软"相结构参量对硬度的Hall-Petch表征

采用直流磁控溅射方法制备了不同调制比的Ni/Al纳米多层膜,利用X射线衍射技术和纳米压入连续刚度法分析了薄膜微结构及塑性变形的尺度依赖性.实验结果表明,尽管调制比有所不同,多层膜的硬度与“软"相的微结构特征参量随调制波长减小具有相似变化规律,说明多层膜的变形机制对“软"相的微结构约束存在敏感性.随着薄膜特征尺度的减小,为统一多层膜中晶界和膜界两种强化机制,提出一个与“软”相相关的表征参量r(r＝L_sub/d,L关键词： 纳米多层膜 塑性变形 调制波长 Hall-Petch关系     

Nanocrystalline gold with small size: inverse Hall–Petch between mixed regime and super-soft regime

ABSTRACT

Molecular dynamics simulations were used to study the atomic mechanisms of deformation of nanocrystalline gold with 2.65–18?nm in grain size to explore the inverse Hall–Petch effect. Based on the mechanical responses, particularly the flow stress and the elastic-to-plastic transition, one can delineate three regimes: mixed (10–18?nm, dislocation activities and grain boundary sliding), inverse Hall-Petch (5–10?nm, grain boundary sliding), and super-soft (below 5?nm). As the grain size decreases, more grain boundaries present in the nanocrystalline solids, which block dislocation activities and facilitate grain boundary sliding. The transition from dislocation activities to grain boundary sliding leads to strengthening-then-softening due to grain size reduction, shown by the flow stress. It was further found that, samples with large grain exhibit pronounced yield, with the stress overshoot decrease as the grain size decreases. Samples with grain sizes smaller than 5?nm exhibit elastic-perfect plastic deformation without any stress overshoot, leading to the super-soft regime. Our simulations show that, during deformation, smaller grains rotate more and grow in size, while larger grains rotate less and shrink in size.     

Kinetics of structural relaxation and regularities of plastic flow of metallic glasses

On the basis of a calculation of the structural relaxation rate and an experimental acoustical-emission determination of the temperature of the transition from localized to uniform flow it is argued that the type of plastic deformation of metallic glasses is uniquely determined by the kinetic structure of the relaxation. In the case of a kinetically hindered structural relaxation, which is characteristic for tests of initial samples at temperatures T<380–420 K, a localized dislocational deformation is realized. At higher temperatures, “memory” of the thermal prehistory of the samples is lost (aging at room temperature), the structural relaxation rate grows abruptly and plastic flow becomes uniform viscoplastic flow. Fiz. Tverd. Tela (St. Petersburg) 41, 2167–2173 (December 1999)     

THE INFLUENCE OF GRAIN SIZE AND TEMPERATURE ON THE MECHANICAL DEFORMATION OF NANOCRYSTALLINE MATERIALS: MOLECULAR DYNAMICS SIMULATION

Nanocrystalline (nc) materials are characterized by a typical grain size of 1-100nm. The uniaxial tensile deformation of computer-generated nc samples, with several average grain sizes ranging from 5.38 to 1.79nm, is simulated by using molecular dynamics with the Finnis-Sinclair potential. The influence of grain size and temperature on the mechanical deformation is studied in this paper. The simulated nc samples show a reverse Hall-Petch effect. Grain boundary sliding and motion, as well as grain rotation are mainly responsible for the plastic deformation. At low temperatures, partial dislocation activities play a minor role during the deformation. This role begins to occur at the strain of 5%, and is progressively remarkable with increasing average grain size. However, at elevated temperatures no dislocation activity is detected, and the diffusion of grain boundaries may come into play.     

Elastic,micro- and macroplastic properties of polycrystalline beryllium

The Young’s modulus and the internal friction of beryllium polycrystals (size grain from 6 to 60 μm) prepared by the powder metallurgy method have been studied as functions of the amplitude and temperature in the range from 100 to 873 K. The measurements have been performed using the composite piezoelectric vibrator method for longitudinal vibrations at frequencies about 100 kHz. Based on the acoustic measurements, the data have been obtained on the elastic and inelastic (microplastic) properties as functions of vibration stress amplitudes within the limits from 0.2 to 30–60 MPa. The microplastic deformation diagram is shown to become nonlinear at the amplitudes higher than 5 MPa. The beryllium mechanical characteristics (the yield strength σ _0.2, the ultimate strength σ _u , and the conventional microscopic yield strength σ _y ) obtained with various grain sizes are compared. At room temperature, all the parameters satisfactorily obey the Hall-Petch relationship, although there is no complete similarity. The temperature dependences are quite different, namely: σ _0.2(T) and σ _u (T) decrease monotonically during heating from room temperature to higher temperatures; however, σ _y (T) behaves unusually, and it has a minimum near 400 K. The different levels of stresses and the absence of similarity indicate that the scattering of the ultrasound energy and the formation of a level of the macroscopic flow stresses in beryllium occur on dislocation motion obstacles of different origins.     

晶体相场法模拟纳米晶材料反霍尔-佩奇效应的微观变形机理

采用晶体相场模型模拟获得了平均晶粒尺寸从11.61–31.32 nm的纳米晶组织, 研究了单向拉伸过程纳米晶组织的强化规律的微观变形机理. 模拟结果表明: 晶粒转动、晶界迁移等晶间变形行为是纳米晶材料的主要微观变形方式, 纳米晶尺寸减小, 有利于晶粒转动, 使屈服强度降低, 显示出反霍尔-佩奇效应.当纳米晶较小时, 变形量超过屈服点达到4%, 位错运动开启, 其对变形的直接贡献有限, 主要通过改变晶界结构而影响变形行为, 位错运动破坏三叉晶界, 引发晶界弯曲, 促进晶界迁移. 随纳米晶增大, 晶粒转动困难, 出现晶界锯齿化并发射位错的现象. 关键词： 晶体相场 纳米晶 反霍尔-佩奇效应 微观变形     

Superplasticity in A Zn-1·1 wt.% Al alloy III. The influence of grain size

The paper represents the third instalment of the series dealing with the superplastic deformation in a Zn-1·1 wt. % Al alloy and is devoted to the influence of grain size on the deformation behaviour of this alloy. Deformation characteristics were measured at two temperatures — 293 and 500 K. The grain size dependence of the flow stress observed was found opposite to that predicted by the Hall-Petch relation. Such a behaviour was explained under the assumption that grain boundaries might act as sites of rapid recovery of lattice dislocations. The results obtained at temperature 293 K proved that the transition between the regions of abnormal behaviour (with the flow stress increasing with increasing grain size) and normal behaviour (with the flow stress decreasing with increasing grain size) was not directly connected with the transition from the superplastic to the nonsuperplastic state. The results obtained at 500 K revealed dynamic recrystallization and a grain refinement in samples with initially coarser structures. Such a change in grain structure was accompanied with a development of superplastic characteristics.     

Disclination Mechanism of Plastic Deformation of Nanocrystalline Materials

A model describing mechanical behaviour of nanocrystalline materials (NC) obtained by crystallization from amorphous precursor is presented. In the framework of this model a structure of such NCs is represented as a composite consisting of amorphous matrix and absolutely rigid inclusions corresponding to crystalline phase. Dependencies of stress concentration coefficient and yield stress of NCs on the average grain size are obtained. It is shown that the dependence of the yield stress has a point of inflection at the critical grain size in the range of 20–25 nm and is inverse to the Hall-Petch relationship at grain sizes smaller than the critical one. The model predicts a formation of a superlattice from disclinations located in triple junctions of grains on the stage of NC plastic flow. A process of the plastic flow of NC's amorphous matrix and amorphous metallic alloys is described as a go-ahead mechanism of dislocation movement, which includes emission, absorption and reemission of dislocations by disclinations.     

Dispersion of autowaves in a localized plastic flow

The dispersion relation for localized plastic deformation autowaves emerging at the easy glide and strain-hardening stages in metals and alloys is established experimentally and analyzed. The quadratic form of this relation and the form of the wavenumber dependence of the phase and group velocities of autowaves are explained, as well as the quantitative interrelation between the characteristics of autowave processes of plastic flow localization and crystal lattice parameters of strained solids.     

Mechanism of the formation of shear microbands under plastic deformation of nanocrystalline materials

The mechanism of deformation localization and formation of shear microbands under plastic deformation of submicrocrystalline and nanocrystalline materials is theoretically discussed in the framework of the dislocation-kinetic approach. An equation of evolution of the density and self-organization of dislocations in these materials is formulated taking into account that the grain boundaries are the main sources, sinks, and barriers to moving dislocations. By solving this equation, it is found that the width of microbands and the distance between them depend on the nanograin size and the degree of plastic deformation. It is also demonstrated that there exists a critical grain size (350 nm in the case of α-Fe) above which no microbands are formed in the nanomaterial. The theoretical results are compared with the data available in the literature.     

Origin of Elastic–Plastic Deformation Invariant

We consider the autowave mechanism of evolution of a localized plastic deformation of crystalline solids of different origins. It is found that localization of the plastic flow is determined by the relation between elastic and plastic phenomena in deforming materials. It is shown that the main parameter of deformation processes is the elastic–plastic deformation invariant, viz., a dimensionless quantity connecting quantitatively the parameters of elastic waves and self-sustained waves (autowaves) of localized plastic deformation. The correctness of this statement is verified for metals, alkali-halide crystals, and rocks. The physical origin of the invariant is explained on the basis of thermodynamic considerations.     

Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals

The relationship between deformation and dislocation properties has been studied for pure polycrystalline nickel and austenitic stainless steel AISI 316L in stage III. Special care was taken to study statistically the effects of the grain size and grain orientation on dislocation densities and distribution. It is shown that the nature of dislocation cells depends on grain size and crystallographic orientation. The dimensional parameters, which depend on grain size, i.e. the inter-boundary spacing (λ) and boundary thickness (e), define three domains of crystallographic orientation and depend on the grain size. Scaling hypotheses reveal two physical mechanisms which, at this level of plastic strain, are correlated to a specific value of the noise, associated with distribution functions. Similarities between structural parameters and dislocation densities in each phase (walls and inter-walls spacing) are identified and discussed in terms of kinetic equations describing dislocation density evolution and fluctuations of certain physical parameters. This similarity provides physical signification of the scaling distribution obtained on λ and e in terms of a stochastic approach to dislocation distribution. The origin of Hall–Petch behaviour observed at large strain is interpreted in terms of an interaction between inter- and intra-granular long-range internal stresses, which depends on grain size. We conclude that, at high strain, the Hall–Petch phenomenological relationship is a consequence of plastic strain history and strain gradient in grains. From this last point, a length scale arises naturally, which depends on stacking fault energy.     

Plasticity and strength of FCC metals with a nanotwinned submicrograined structure

The plasticizing and hardening effects associated with the existence of nanotwins with a density 1/λ (where λ is the average size (thickness) of nanotwin lamellae) in a submicrograined structure of fcc metals have been theoretically discussed in the framework of the dislocation-kinetics approach. The strength of the nanotwinned submicrocrystalline structure, which is increased as compared to the initial submicron structure, is determined, as in the case of nanograin boundaries, by the action of nanotwin boundaries as sources and barriers for moving dislocations that provide the normal Hall-Petch effect for the flow stress σ ∼ γ^−1/2. The inverse Hall-Petch effect σ ∼ γ ^p (where p > 0), as in the case of nanograin boundaries, is associated with the dislocation absorption by the twin boundaries. The related increased strain-rate sensitivity of the flow stresses is responsible for the significant increase in the uniform strain (from 2–3 to 8–9% in the case of nanotwinned copper) during tension of the specimens with nanotwinned submicrograined structures with retaining a high strength of the material.