Strength weakening by nanocrystals in ceramic materials

A key question in nanomechanics concerns the grain size effects on materials' strength. Correct solution to this question is critical to design and tailor the properties of materials for particular applications. The full map of grain sizes-hardness/yield stress relationship in metals has been built. However, for ceramic materials, the similar studies and understandings are really lacking. Here we employed a novel technique to comparatively study the mechanical features of titanium dioxide (TiO(2)) with different crystallite sizes. On the basis of peak profile analysis of the X-ray diffraction data, we determined yield strength for nanocrystalline and bulk TiO(2). Our results reveal a remarkable reduction in yield strength as the grain size decreases from 30-40 microm to approximately 10 nm, providing the only evidence of a strength weakening by nanocrystals relative to their bulk counterparts. This finding infers an inverse Hall-Petch effect, the first of its kind for ceramic materials, and a dramatic strength weakening after the breakdown of classic Hall-Petch relation below a characteristic grain size.     

The combined influence of grain size distribution and dislocation density on hardness of interstitial free steel

Understanding the relationship between microstructure features and mechanical properties is of great significance for the improvement and specific adjustment of steel properties. The relationship between mean grain size and yield strength is established by the well-known Hall-Petch equation. But due to the complexity of the grain configuration within materials, considering only the mean value is unlikely to give a complete representation of the mechanical behavior. The classical Taylor equation is often used to account for the effect of dislocation density, but not thoroughly tested in combination with grain size influence. In the present study, systematic heat treatment routes and cold rolling followed by annealing are designed for interstitial free(IF) steel to achieve ferritic microstructures that not only vary in mean grain size, but also in grain size distribution and in dislocation density, a combination that is rarely studied in the literature. Optical microscopy is applied to determine the grain size distribution. The dislocation density is determined through XRD measurements. The hardness is analyzed on its relation with the mean grain size, as well as with the grain size distribution and the dislocation density. With the help of the variable selection tool LASSO, it is shown that dislocation density, mean grain size and kurtosis of grain size distribution are the three features which most strongly affect hardness of IF steel.     

Enhanced Hall-Petch strengthening in graphene/Cu nanocomposites

Grain size dependent strength,known as Hall-Petch relation,has been approved to be valid in crystalline metals and alloys.However,softening would eventually occur as grain size reduced into nanoscale that below a critical value.Hence,it is essential to find a way to break the strength limitation by avoiding the deformation mechanism transition from dislocation-mediated to grain-boundary-mediated processes.By replacing grain boundary (GB) of nanocrystalline Cu with graphene,in the present study,molecular dynamics simulations show that graphene-boundary (GrB) embedded GrB/Cu nanocomposites exhibit enhanced enlarged Hall-Petch slope with decreasing grain size.The absence ofinverse-Hall-Petch relation and the extremely high strength derived at the GrB/Cu nanocomposites were interpreted by the high back stress and abundant dislocation activity that attributed from the high-degree of heterogeneous structure of the nanocomposites.     

Mechanics of a nanocrystalline coating and grain-size dependence of its plastic strength

From the mechanics perspective the most critical properties of a coating material are likely its yield strength, hardness, and wear resistance. These properties are intimately related to each other as a material with high yield strength usually also possesses superior hardness and strong wear resistance. Our objective in this study is to seek for the strongest material state in terms of its plastic strength, and the critical grain size at which this strength can be attained. Based on the cross-sectional morphology of a nanocrystalline coating we first conceive a composite plate model consisting of the columnar grains and the grain boundary affiliated region (broadly called the GB zone), and present a plane-stress theory to investigate its in-plane behavior. We then make use of a linear comparison composite and a field fluctuation approach to explore the competition between the grain interior and the plastically softer GB zone as the grain size decreases from the coarse grain to the nanometer range. Based on the developed model the anisotropic stress-strain relations of a ZrN coating are illustrated as a function of grain size in both in-plane and out-of-plane directions. It is demonstrated that, as the grain size decreases, the variation of plastic strength in the Hall-Petch plot undergoes a transition from a positive to a negative slope, exhibiting the Hall-Petch and the inverse Hall-Petch effects. The strength-differential effect between tension and compression is also observed. The critical grain sizes at which the maximum strength develops are found to be lower along the out-of-plane direction than along the in-plane ones, and also lower under compression than under tension. Based on Tabor’s law, our calculated critical grain size for the hardness was about 16 nm, while a recent indentation test indicated a range of 14.2-19 nm. The existence of Hall-Petch, inverse Hall-Petch, and strength-differential effects, and of an optimal grain size, is thus theoretically proven for the first time for nanocrystalline coatings.     

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.     

Dynamic Failure Behavior of Nanocrystalline Cu at Atomic Scales

Large-scale molecular dynamics (MD) simulations are used to investigate the effects of microstructure and loading conditions on the dynamic failure behavior of nanocrystalline Cu. The nucleation, growth, and coalescence of voids is investigated for the nanocrystalline metal with average grain sizes ranging from 6 nm to 12 nm (inverse Hall-Petch regime) for conditions of uniaxial expansion at constant strain rates ranging from 4x107 s - 1 to 1010 s - 1. MD simulations suggest that the evolution of voids can be described in two stages: The first stage corresponds to the nucleation of voids and the fast linear initial growth of all the individual voids. The second stage of void growth corresponds to the steady (slower) growth and coalescence of the void aggregates/clusters. The evolution of void fraction is found to be strongly dependent on the loading strain rates, but is less dependent on the grain size of the nanocrystalline metal. Higher strain rates require larger plastic strains to nucleate voids, whereas the larger grain sizes require lower plastic strains to nucleate voids in the inverse Hall-Petch regime. The spall strength of the nanocrystalline metal is less affected by the grain size, but is strongly affected by the loading strain rates.     

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。     

纳米晶体材料的Hall—Petch关系

本文综述了纳米晶体材料力学性能如屈服应力，显微硬度的研究，尤其是偏离正常Ｈａｌｌ－Ｐｅｔｃｈ关系的现象及几种解释这种反常效应的模型，分析表明：纳米晶体材料的强度或硬度取决于材料的界面缺陷结构，界面过剩能与过剩体积。     

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.     

Influence of grain size on the mechanical behaviour of some high strength materials

Combining in an additive or synergetic manner the most potent strengthening mechanisms available in an alloy is the art of the metallurgist. The various models proposed in the literature in order to interpret the Hall-Petch relation are critically reviewed by comparison with experimental data. The pile-up models and the work hardening theories must include the inner structure of the grain in the case of alloys hardened by a second phase. Similarly, the properties and structure of the grain boundaries are influenced by impurities or the presence of particles. Ultra-fine grain sizes can provide ductility to high strength materials when surface preparation eliminates microcracks.In steady-state creep equations, introducing the influence of grain size in complex alloys by incorporating the Hall-Petch stress as one component of the internal stress helps in rationalizing the existence of an optimal grain size where creep resistance is maximized. Slower crack growth rates can be obtained by controlling the grain boundary structure as well as grain size. Fatigue tests at room temperature clearly point out the interest of small grain sizes for reducing crack initiation, usually associated, however, with lower propagation threshold and somewhat faster growth rates.     

Dislocation-disclination transformations and the reverse Hall-Petch effect in nanocrystalline materials

A relay-race dislocation-disclination model of plastic shear development in nanocrystalline materials is proposed, which is based on the mechanism of switching between translational and rotational deformation modes. The dependence of the external deforming stress on the grain size is calculated. It is shown that the switching from the translational to rotational deformation mode and back explains the reverse Hall-Petch effect in nanocrystalline materials.     

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.     

Structure and properties of nanocrystalline materials

The present article reviews the current status of research and development on the structure and properties of nanocrystalline materials. Nanocrystalline materials are polycrystalline materials with grain sizes of up to about 100 nm. Because of the extremely small dimensions, a large fraction of the atoms in these materials is located at the grain boundaries, and this confers special attributes. Nanocrystalline materials can be prepared by inert gas-condensation, mechanical alloying, plasma deposition, spray conversion processing, and many other methods. These have been briefly reviewed. A clear picture of the structure of nanocrystalline materials is emerging only now. Whereas the earlier studies reasoned out that the structure of grain boundaries in nanocrystalline materials was quite different from that in coarse-grained materials, recent studies using spectroscopy, high-resolution electron microscopy, and computer simulation techniques showed unambiguously that the structure of the grain boundaries is the same in both nanocrystalline and coarse-grained materials. A critical analysis of this aspect and grain growth is presented. The properties of nanocrystalline materials are very often superior to those of conventional polycrystalline coarse-grained materials. Nanocrystalline materials exhibit increased strength/hardness, enhanced diffusivity, improved ductility/toughness, reduced density, reduced elastic modulus, higher electrical resistivity, increased specific heat, higher thermal expansion coefficient, lower thermal conductivity, and superior soft magnetic properties in comparison to conventional coarse-grained materials. Recent results on these properties, with special emphasis on mechanical properties, have been discussed. New concepts of nanocomposites and nanoglasses are also being investigated with special emphasis on ceramic composites to increase their strength and toughness. Even though no components made of nanocrystalline materials are in use in any application now, there appears to be a great potential for applications in the near future. The extensive investigations in recent years on structure-property correlations in nanocrystalline materials have begun to unravel the complexities of these materials, and paved the way for successful exploitation of the alloy design principles to synthesize better materials than hitherto available.     

Localized plastic flow autowaves and the Hall-Petch relation in aluminum

Characteristics of the plastic strain macrolocalization are compared to parameters of the Hall-Petch relation for the flow stress in polycrystalline aluminum samples with grain sizes ranging from 0.008 to 5 mm. It is established that, in the range of brain sizes studied, there are two possible types of the dependence of the length of localized strain autowave on the grain size and two variants of the Hall-Petch relation. It is shown that the boundary between the two variants in both cases corresponds to d ≈ 0.1 mm. Interconnection of the patterns of plastic flow localization and the Hall-Petch relation is traced.     

The combined effects of grain and sample sizes on the mechanical properties and fracture modes of gold microwires

Hall-Petch relation was widely applied to evaluate the grain size effect on mechanical properties of metallic material. However, the sample size effect on the Hall-Petch relation was always ignored. In the present study, the mechanical test and microstructure observation were performed to investigate the combined effects of grain and sample sizes on the deformation behaviors of gold microwires. The polycrystalline gold microwires with diameter of 16 ?m were annealed at temperatures from 100°C to 600°C, leading to different ratios(t/d) of wire diameter(t) to grain size(d) from 0.9 to 16.7. When the t/d was lower than 10, the yield stress dropped fast and deviated from the Hall-Petch relation. The free-surface grains played key role in the yield stress softening, and the volume fraction of free-surface grains increased with the t/d decreasing. Furthermore, the effects of t/d on work-hardening behaviors and fracture modes were also studied. With t/d value decreasing from 17 to 3.4, the samples exhibited necking fracture and the dislocation pile-ups induced work-hardening stage was gradually activated.With the t/d value further decreasing(t/d 3.4), the fracture mode turned into shear failure, and the work-hardening capability lost. As the gold microwire for wire bonding is commonly applied in the packaging of integrated circuit chips, and the fabrication of microwire suffers multi-pass cold-drawing and annealing treatments to control the grain size. The present study could provide instructive suggestion for gold microwire fabrication and bonding processes.     

Grain size dependence of strength of nanocrystalline materials as exemplified by copper: an elastic-viscoplastic modelling approach

The purpose of this work is to model the mechanical behavior of nanocrystalline materials. Based on previous rigid viscoplastic models proposed by Kim et al. (Acta Mater, 48: 493, 2000) and Kim and Estrin (Acta Mater, 53: 765, 2005), the nanocrystalline material is described as a two phase composite material. Using the Taylor–Lin homogenisation scheme in order to account for elasticity, the yield stress of nanocrystalline materials can be evaluated. The transition from a Hall–Petch relation to an inverse Hall–Petch relation is defined and is related to a change in plastic deformation mode in the crystallite phase from a dislocation glide driven mechanism to a diffusion-controlled process.     

Improvement of NiTi Shape Memory Actuator Performance Through Ultra‐Fine Grained and Nanocrystalline Microstructures

Ultra‐fine grain sizes have been shown to enhance some key mechanical and functional properties of engineering materials, including shape memory alloys. While the effect of ultra‐fine and nanocrystalline grain sizes on pseudoelastic shape memory materials is well‐appreciated in medical device engineering, the effect of such microstructures on actuators has not been sufficiently characterized. In the present work, it is demonstrated that NiTi spring actuators with ultra‐fine grained microstructures can be obtained by conventional wire drawing in combination with heat treatments and that the final grain size can be controlled by varying the final annealing temperature. Annealing at 400 °C for 600 s allows for the evolution of microstructures with median grain sizes of about 34 nm, while annealing at 600 °C for the same length of time results in median grain sizes of about 5 µm. It is observed that the grain size strongly affects the elementary processes of the martensitic phase transformation. Small austenite grain sizes inhibit twinning accommodation of transformation strains, such that a higher driving force is required to nucleate martensite. This increase in the martensite nucleation barrier decreases the martensite transformation temperatures such that only partial transformation to martensite is possible upon cooling to room temperature. The incomplete martensitic transformation reduces the exploitable actuator stroke; however, a reduction in grain size is shown to improve the functional stability of the material during thermal and thermomechanical cycling by reducing the irreversible effects of dislocation plasticity.     

Finite-element modeling of rate dependent mechanical properties in nanocrystalline materials

A generalized self-consistent polycrystal model is used to study the mechanical properties of polycrystalline metals as the grain size decreases from the ultra-fine size to the nanometer scale. The model takes each oriented grain and its immediate grain boundary to form a pair. Then by making use of a composite model, the nonlinear behavior of the nanocrystalline polycrystal is determined. The finite-element method is employed in conjunction with the unit cell of the composite to investigate the rate-dependent tensile behavior of the system. A dislocation density based constitutive equation is used to describe the plastic flow behavior of the grain interior. The boundary phase is assumed to have the mechanical properties of quasi-amorphous material. The constitutive equations for both grain interior and boundary phase are implemented into a finite-element program and the results of the calculations are compared with previously published experimental data. For some cases, an optimization procedure was used to tune some parameters of the model in order to decrease the distance between the calculated and experimental stress–strain curves. The agreement between results indicates the suitability of the updated model for nanocrystalline materials.     

Nonlinear microstructural constitutive equation of nanocrystalline metals

Summary. Based on experimental observations, nanocrystalline materials are modeled as composite systems in which the amorphous interfacial phase is treated as the matrix, whereas the nano-scale single crystals are modeled as inclusions. Generally speaking, the elastic moduli of nanoscale crystals are higher than those of the amorphous matrix phase, and the deformation mechanism of nanocrystalline materials depends heavily on the size of the crystals. For conventional macro size crystal materials, such as coarse-grained polycrystalline materials, the deformation mechanism due to dislocation movement is dominant. When the crystal size is reduced to a certain critical value, plastic deformation is caused by shear banding in the amorphous matrix. In order to model such a deformation mechanism in nanocrystalline materials, constitutive equations are established based on internal variable theory. The proposed model reveals the relation between the yield strength and the grain size of the material.     

Dislocation motion-induced strain in nanocrystalline materials: Overlooked considerations

The amount of plastic strain caused by the motion of a single dislocation across an individual nanosize grain is drastically higher than the amount recorded for larger grain sizes. As a result, in nanocrystalline materials, only a small number of dislocations would need to move within each individual grain in order to accommodate the plastic strain on the entire sample. This observation leads to a quantitative criterion for determining if observed dislocation activity is sufficient to accommodate realistic applied plastic strains. This new criterion is directly applicable to the interpretation of in situ TEM experiments and computational molecular dynamics simulations.