Structural mechanisms of fracture of nanocrystalline materials

Structural mechanisms and features of brittle and quasi-brittle fracture of nanocrystalline materials are theoretically analyzed. The role of size effects and internal stresses caused by a nonequilibrium structure during brittle trans-and intercrystallite fracture is studied. The dependence of the nanocrystalline material durability on the working stress and grain size is calculated. The conditions for certain mechanisms of plastic deformation to be operative in nanocrystalline materials are analyzed. The influence of the grain-boundary and dislocation mechanisms of plastic deformation on the conditions of nanocrack formation is studied. The dependence of the fracture toughness of nanomaterials on structure parameters is calculated.     

Roughness of boundary interfaces in polycrystals and its influence on the yield strength of nanocrystalline materials

The distribution in roughness of grain-boundary interfaces in polycrystals is measured metallographically. The result shows that there are high populations of localized interface areas with roughness much lower than the average in polycrystals. Effects of the roughness on the boundary sliding in nanocrystalline materials are discussed, suggesting that the sliding in the localized interface areas produces stress concentrations to cause a reduction in the yield strength of nanocrystalline materials.     

Structural states and specific features of the deformation behavior of metals and alloys with mixed nano-and micrograin structure

A classification of the structural states of materials with a mixed nano-and microcrystalline structure is proposed. Theoretical analysis of the structural mechanisms and peculiarities of plastic flow of singlephase and two-phase nanostructured metals and alloys with a bimodal size distribution of grains and phases is performed. The effect of grain-boundary and dislocation mechanisms of plastic flow on the specific features of the deformation behavior and plasticity of nanocrystalline materials is analyzed. A microstructural model of strain hardening of a material with two-scale nano-and micrograin structure is proposed and the condition for the loss of plastic flow stability of such a material is investigated. The dependence of the yield strength and uniform strain of nanocrystalline materials with a two-scale structure on the grain size and the ratio of the volume fractions of the nano-and microstructural components is calculated.     

Flow stress/strain rate/grain size coupling for fcc nanopolycrystals

A Hall–Petch (H–P)-type dependence is demonstrated for reciprocal activation volume measurements for nanocrystalline and conventional grain size, strengthened Ni and Cu materials, consistent with predictions derived from the dislocation pile-up model. The observed H–P dependence indicates that the shear stress for cross-slip must be involved in the full grain size regime for transmission of plastic flow at the grain boundaries of fcc metals.     

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.     

Mechanism of deformation-twin formation in nanocrystalline metals

A theoretical model is proposed to describe the nucleation of deformation twins at grain boundaries in nanocrystalline materials under the action of an applied stress and the stress field of a dipole of junction or grain-boundary wedge disclinations. The model is used to consider pure nanocrystalline aluminum and copper with an average grain size of about 30 nm. The conditions of barrier-free twinning-dislocation nucleation are studied. These conditions are shown to be realistic for the metals under study. As the twin-plate thickness increases, one observes two stages of local hardening and an intermediate stage of local flow of a nanocrystalline metal on the scale of one nanograin. In all stages, the critical stress increases with decreasing disclination-dipole strength. The equilibrium thickness and shape of the twin plate are analyzed and found to agree well with the well-known results of experimental observations.     

Mechanical properties of nanocrystalline copper under thermal load

The material properties of nanocrystallines are known to generally have a strong dependence on their nanoscale morphology, such as the grain size. The Hall-Petch effect states that the mechanical strength of nanocrystalline materials can vary substantially for a wide range of grain sizes; this is attributed to the competition between intergranular and intragranular deformations. We employed classical molecular dynamics simulations to investigate the morphology-dependent mechanical properties of nanocrystalline copper. The degradation of material properties under thermal load was investigated during fast strain rate deformation, particularly for the grain size. Our simulation results showed that the thermal load on the nanocrystalline materials alters the grain-size behavior of the mechanical properties.     

纳米多晶铜的超塑性变形机理的分子动力学探讨

在聚能装药爆炸压缩形成射流的过程中, 伴随着金属药型罩的晶粒细化, 从原始晶粒30-80 μm细化到亚微米甚至纳米量级, 从微观层面研究其细化机理和动态超塑性变形机理具有很重要的科学意义. 采用分子动力学方法模拟了不同晶粒尺寸下纳米多晶铜的单轴拉伸变形行为, 得到了不同晶粒尺寸下的应力-应变曲线, 同时计算了各应力-应变曲线所对应的平均流变应力. 研究发现平均流变应力最大值出现在晶粒尺寸为14.85 nm时. 通过原子构型显示, 给出了典型的位错运动过程和晶界运动过程, 并分析了在不同晶粒尺寸下纳米多晶铜的塑性变形机理. 研究表明: 当晶粒尺寸大于14.85 nm时, 纳米多晶铜的变形机理以位错运动为主; 当晶粒尺寸小于14.85 nm时, 变形机理以晶界运动为主, 变形机理的改变是纳米多晶铜出现软化现象即反常Hall-Petch关系的根本原因. 通过计算结果分析, 建立了晶粒合并和晶界转动相结合的理想变形机理模型, 为研究射流大变形现象提供微观变形机理参考.     

Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

Determining characteristic plastic-relaxation times using micro- and nanocrystalline nickel as an example

Based on the concept of the incubation time of plastic deformation, an integral yield criterion is introduced and time effects of irreversible deformation are considered. The efficiency of the approach is demonstrated using micro?and nanocrystalline nickel as an example. The parameters of the phenomenological model are treated physically from the viewpoint of the behavior of the defect structure of the material, which is controlled by the dislocation sliding and grain-boundary slip mechanisms in a wide range of the rate of deformation.     

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.     

Constrained grain-boundary sliding and inelasticity of polycrystals

A model of inelastic behavior of polycrystals that is based on the idea of constrained grain-boundary sliding is developed. This model assumes that grain-boundary sliding is accommodated only through grain elastic deformation, which is valid under low stresses. By way of examples, the dynamic inelastic behavior and a decrease in the elastic moduli of polycrystals subjected to a small-amplitude ultrasonic field are investigated. It is shown that some of the available experimental data obtained on ultra-fine-grained materials can be explained in terms of the model. The theory predicts that the decrease in the elastic moduli is a size effect that is bound to be observed when the grain size is small. These predictions are supported experimentally.     

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.     

Emission of partial dislocations by grain boundaries in nanocrystalline metals

A theoretical model is proposed to describe the emission of partial dislocations by grain boundaries in nanocrystalline materials during plastic deformation. Partial dislocations are assumed to be emitted during the motion of grain-boundary disclinations, which are carriers of rotational plastic deformation. The ranges of the parameters of a defect structure in which the emission of partial dislocations by grain boundaries in nanocrystalline metals are energetically favorable are calculated. It is shown that, as the size of a grain decreases, the emission of partial dislocations by its boundary becomes more favorable as compared to the emission of perfect lattice dislocations.     

Effect of grain size dispersion on the strength and plasticity of nanocrystalline metals

The effect of the dispersion of the grain size distribution on the yield stress, ultimate stress, and uniform strain of nanocrystalline metals is analyzed theoretically. It is shown that, as the grain size dispersion increases, the degree of grain boundary hardening (Hall-Petch effect) of nanocrystalline materials decreases, the onset of the grain boundary softening (inverse Hall-Petch effect) shifts to smaller nanograin sizes, and the uniform strain at which necking occurs increases.     

Interface stress in polycrystalline materials: the case of nanocrystalline Pd

Based on a generalization of a capillary equation for solids, we develop a method for measuring the absolute value of grain-boundary stress in polycrystalline samples having a large interface-to-volume ratio. The grain-boundary stress in nanocrystalline Pd is calculated from x-ray diffraction measurements of the average grain size and the residual-strain-free lattice spacings, yielding a value of 1.2+/-0.1 N/m. The random distribution of crystallite orientations in the sample suggests that this value is characteristic of high-angle grain boundaries in Pd.     

Rate of creep due to grain-boundary diffusion in polycrystalline solids with grain-size distribution

For steady-state deformation caused by grain-boundary diffusion, the macroscopic creep rate is analysed for a three-dimensional polycrystal consisting of space-filling grains, by taking into account the effects of diffusional interaction between grains, viscous grain-boundary sliding and grain-size distributions. For regular polyhedral grains, the grain–grain interactions increase the degree of symmetry of diffusional field, resulting in a decrease of the effective diffusion distance. Meanwhile, both the viscous grain-boundary sliding and the grain-size distribution are found to decrease the creep rate. At decreasing grain sizes, the influence of the viscous grain-boundary sliding becomes increasingly important, which explains the recent experimental observations that the creep rates of nanosized grains are much lower than those predicted by grain-boundary diffusion. On the effect of the grain-size distribution, the upper-bound and lower-bound creep rates are estimated.     

Cooperative grain boundary sliding in nanocrystalline materials

Superplastic behaviour of microcrystalline materials is now believed to be controlled by cooperative grain boundary sliding (CGBS). An increasing role of grain boundary mediated plasticity with decreasing grain size down to the nanoscale was predicted leading to the prospect of enhanced superplasticity in nanocrystalline materials. Nevertheless, materials with nanosized grains have revealed a significant decrease in plasticity contrary to theoretical prediction. Direct evidence of CGBS in nanocrystalline Ni₃Al alloy from SEM surface analysis and in-situ TEM tensile testing was detected, confirming one similarity in the rheology of deformation processes between micro- and nanomaterials. Thus, differences in deformation behaviour of materials at these two length scales are related to the probability of sliding surface formation, sliding distance and related accommodation mechanisms.