Reverse Hall-Petch Effect Research Articles

Reverse Hall–Petch Effect of Nano-Bainite in a High-Carbon Silicon-Containing Steel

High-strength steels are widely used in various mechanical production and construction industries for their low cost, high strength and high toughness. Among these, bainitic steels have better comprehensive performance relative to martensite and ferrite. In this paper, from the point of view of its microscopic fine structure and mechanical properties, the high-carbon silicon-containing steel Fe-0.99C-1.37Si-0.44Mn-1.04Cr-0.03Ni was austenitized at high temperature after a brief isothermal treatment at 280 °C and is briefly reviewed. We have used EBSD, TEM and 3D-APT to observe a unique transformation in which high-carbon silicon-containing steels form nanostructured bainite with nanometer widths. Intriguingly, as the isothermal duration decreases, the beam bainite width becomes increasingly finer. When the beam bainite width falls below 50 nm, there is a sudden shift in defect type from the conventional edge-type dislocations to a defect characterized by the insertion of a semi-atomic surface in the opposite direction, which leads to different degrees of reduction in the micro- and macro-mechanical properties of high-carbon silicon-containing steels from 1754 MPa to 1667 MPa. This sudden change in the sub-structural properties is typical of the reverse Hall–Petch effect.

Hierarchical crystalline–amorphous nanocomposites with high strength and large deformability enabled by elemental diffusion

Amorphous/nanocrystalline dual-phase structures have recently emerged as an effective way for overcoming the strength–ductility trade-off and breaking the limitation of the reverse Hall–Petch effect. Here, we proposed a new strategy to develop a hierarchical and interconnected amorphous–crystalline nanocomposite arising from the nanoscale elemental interdiffusion and oxygen adsorption behavior during thermal treatment processes. The nanocomposite consisted of a three-dimensional (3D) hierarchical network structure where the crystalline phase (Cr–Co–Ni–Al) was embedded into the Al–O-based amorphous phase network with critical feature sizes encompassing three orders of magnitude (from micrometer to nanometer scale). It can achieve ultrahigh compression yield strength of ∼3.6 GPa with large homogeneous deformation of over 50% strain. The massive interstitial atoms induced lattice distortion and hierarchical amorphous phase boundary contributed to the strength improvement. in situ Uniaxial compression inside a transmission electron microscope (TEM) revealed that the exceptional deformability of the nanocomposites resulted from the homogenous plastic flow of nano-sized amorphous phase and the plastic co-deformation behavior restricted by the nano-architected dual-phase interface. The proposed dual-phase synthesis approach can outperform conventional nanolaminates design strategies in terms of the mechanical properties achievable while providing a pathway to easily tune the microstructure of these nanolaminates.

Size dependence for mechanical properties of Ti/Cu multilayered nanowire with a semi-coherent interface

Metallic multilayered nanowires have a wide application prospect in micro-nano devices because of their superior physical and chemical properties and microstructure designability. Size effects on the tensile behaviors of Ti/Cu multilayered nanowires are investigated by molecular dynamic simulations. Aspect ratios of 1:4, 1:3, 1:2, 1:1, 1:0.75, and 1:0.67 and sectional dimensions of 3, 4, 5, 6, and 7 nm are adopted to construct nanowires with different sizes. Simulation results indicate that the strength of Ti/Cu nanowires decreases with the decrease of aspect ratio in the large aspect ratio range (>1:2) and all simulated sectional dimension ranges, showing a reverse Hall-Petch effect. The Hall-Petch law can only be satisfied in a small aspect ratio range (<1:2). Deformation mechanism transition is found in the critical aspect ratio of 1:2. When the aspect ratio is larger than 1:2, crystalline phases of Ti and Cu layers dominate the plastic deformation of Ti/Cu nanowires. Crystal phases and interface both bear plastic deformation when the aspect ratio is smaller than 1:2. Interface is an important factor in the strength and deformation of Ti/Cu nanowires. The variation of interface fraction and interaction between interface and dislocation motion determine the tendency of strength variation for Ti/Cu nanowires.

Investigation on the Mechanical Properties of Polycrystalline Mg Using Molecular Dynamics Simulation

Magnesium (Mg) and its composites have been widely used in different fields, but the mechanical properties and deformation mechanisms of polycrystalline Mg (polyMg) at the atomic scale are poorly understood. In this paper, the effects of grain size, temperature, and strain rate on the tensile properties of polyMg are explored and discussed by the Molecular dynamics (MD) simulation method. The calculated results showed that there exists a critical grain size of 10 nm for the mechanical properties of polyMg. The flow stress decreases with the increase of grain size if the average grain size is larger than 10 nm, which shows the Hall-Petch effect, and the deformation mechanism of large grain-sized polyMg is mainly dominated by the movement of dislocations. When the average grain size is less than 10 nm, it shows the reverse Hall-Petch effect that the flow stress decreases with the decrease of grain size, and the deformation mode of polyMg with small grain-size is the movement and deformation of atoms at the grain boundary. Due to the more active motion of atoms as the system temperature increases, the material can easily reach the plastic stage under tensile loading, and the mechanical properties of polyMg decrease at high temperatures. The strain rate has a hardening effect on the properties of composite. Based on our calculated results, it can provide theoretical guidance for the applications of Mg metal and Mg matrix composites.

Fracture of void-embedded high-entropy-alloy films: A comprehensive atomistic study

Comprehensive molecular dynamics (MD) simulations are performed to study the stress response and deformation mechanism in void-embedded, single-crystal and polycrystalline, high-entropy-alloy (HEA) films under uniaxial tensile loading. Our results reveal that certain void-embedded HEA films can be, by far, superior to pure Ni in terms of tensile ductility and the resistance to crack propagation. The fracture strain of the 10%Co CoCrFeMnNi and the equiatomic CoFeMnNi, respectively, doubles or triples that of the equiatomic CoCrFeMnNi, which still doubles that of pure Ni. Regarding the deformation mechanism, high tensile ductility of HEAs can be attributed to the formation of partial dislocations, nanotwinning and the impediment of the otherwise glissile dislocations due to the lattice distortion effect. The ultimate tensile strength of HEA film shows better resistance against stress deterioration due to elliptical voids. The stress response of the void-embedded, polycrystalline Ni films obeys the reverse Hall–Petch effect, while the void-embedded, polycrystalline HEA films do not.

Fracture of Void-Embedded High-Entropy-Alloy Films: A Comprehensive Atomistic Study

Comprehensive molecular dynamics (MD) simulations are performed to study the stress response and deformation mechanism in void-embedded, single-crystal and nanocrystalline, high-entropy-alloy (HEA) films under uniaxial tensile loading. Our results reveal that certain void-embedded HEA films can be, by far, superior to pure Ni in terms of tensile ductility and the resistance to crack propagation. The fracture strains of 10%Co CoCrFeMnNi and the equiatomic CoFeMnNi, respectively, double or triple that of the equiatomic CoCrFeMnNi, which still doubles that of pure Ni. Regarding the deformation mechanism, high tensile ductility of HEAs can be attributed to the formation of partial dislocations, nanotwinning and the impediment of the otherwise glissile dislocations due to the weak pinning effect. The ultimate tensile strength of HEA film shows better resistance against stress deterioration due to elliptical voids. The stress response of the void-embedded, nanocrystalline Ni films obeys the reverse Hall-Petch effect, while the void-embedded, equiatomic HEA film does not. The maximum stresses of nanocrystalline HEA films of different grain size are virtually the same. The void-embedded, finer-grain HEA film exhibits a better tensile ductility than the void-embedded, coarser-grain HEA film.

Self-assembly of nanocrystalline@amorphous core-shell nanostructure in the TA19 alloy film to achieve high strength

Improving the strength of alloy materials and simultaneously retaining high toughness are strongly desirable by various engineering applications. Nanocrystalline@amorphous dual-phase nanostructure consisting of nanocrystalline-cores encapsulated with amorphous-shells has been regarded as one of the most effective routes to achieve high strength yet high toughness, which may overcome the limitation of either single-phase nanocrystalline alloys or single-phase metallic glasses because of reverse Hall-Petch effect or shear-band deformation. Herein, nanocrystalline@amorphous core-shell nanostructure has been successfully assembled in the sputtered TA19 alloy film only by regulating bias voltages (Vb), and then Vb induced evolution of microstructure and mechanical property was further investigated by combined experiments of X-ray diffraction (XRD), atomic force microscope (AFM), scanning electron microscope (SEM), select area electron diffraction (SAED), transmission electron diffraction (TEM) and nanoindentation. The results show that the bombardment of energy ions can promote formation of amorphous zones in TA19 alloy film, successfully achieving ordered core-shell nanostructure at −120 V of Vb, while single-phase nanocrystalline occurs at Vb = −40 V and amorphous dominated structure appears at Vb = −200 V. Maximum hardness value of 11.2 GPa achieves at Vb = −120 V when the ordered core-shell nanostructure is formed with invisible shear bands around indenter, but more amorphous result in disappearance of core-shell nanostructure at Vb = −200 V, which worsens hardness, accompanying with presence of obvious shear bands around indenter. This novel core-shell-like structure succeeded in achieving high strength or hardness yet high toughness by providing strong resistance to hinder movements of both grains and shear bands due to large amount of nanocrystalline@amorphous interfaces. It is suggested that the Vb as a key factor controlling the core-shell-like structure of TA19 films, which may provide a new strategy to improve mechanical properties of alloy films.

Effect of thickness for nanotwins on the mechanical properties of a Hastelloy

The processes of nanoindentation on Hastelloy alloy with nanoscale twin boundary (TB) are calculated by molecular dynamics (MD). The effect of nanoscale TB’s thickness on the mechanical properties are investigated. The results show that the thickness of nanoscale TBs has obvious influence on the properties of Hastelloy alloy. The TBs obviously play the role of obstacle when the crystal lattice was destroyed by the force of indenter. Although the nanoscale twin boundaries can resist the movement to a certain extent, it does not mean that the thicker nanoscale TBs make the properties better. In these simulations, the Hall–Petch effect and the reverse Hall–Petch effect are observed, and the critical value of thickness is 25.493 A.

Effects of Grain Size Distribution on the Mechanical Properties of Polycrystalline Graphene

One of the characteristics of polycrystalline graphene that determines its material properties is grain size. Mechanical properties such as Young’s modulus, yield strain and tensile strength depend on the grain size and show a reverse Hall-Petch effect at small grain size limit for some properties under certain conditions. While there is agreement on the grain size effect for Young’s modulus and yield strain, certain MD simulations have led to disagreement for tensile strength. Song et al. showed a decreasing behavior for tensile strength, that is, a pseudo Hall-Petch effect for the small grain size domain up to 5 nm. On the other hand, Sha et al. showed an increasing behavior, a reverse Hall-Petch effect, for grain size domain up to 10 nm. Mortazavi et al. also showed results similar to those of Sha et al. We suspect that the main difference of these two inconsistent results is due to the different modeling. The modeling of polycrystalline graphene with regular size and (hexagonal) shape shows the pseudo Hall-Petch effect, while the modeling with random size and shape shows the reverse Hall-Petch effect. Therefore, this study is conducted to confirm that different modeling is the main reason for the different behavior of tensile strength of the polycrystalline structures. We conducted MD simulations with models derived from the Voronoi tessellation for two types of grain size distributions. One type is grains of relatively similar sizes; the other is grains of random sizes. We found that the pseudo Hall-Petch effect and the reverse Hall-Petch effect of tensile strength were consistently shown for the two different models. We suspect that this result comes from the different crack paths, which are related to the grain patterns in the models. Key words: Polycrystalline graphene, Molecular dynamics, Mechanical properties, Hall-Petch effect

Dual-phase nanostructuring as a route to high-strength magnesium alloys.

It is not easy to fabricate materials that exhibit their theoretical 'ideal' strength. Most methods of producing stronger materials are based on controlling defects to impede the motion of dislocations, but such methods have their limitations. For example, industrial single-phase nanocrystalline alloys and single-phase metallic glasses can be very strong, but they typically soften at relatively low strains (less than two per cent) because of, respectively, the reverse Hall-Petch effect and shear-band formation. Here we describe an approach that combines the strengthening benefits of nanocrystallinity with those of amorphization to produce a dual-phase material that exhibits near-ideal strength at room temperature and without sample size effects. Our magnesium-alloy system consists of nanocrystalline cores embedded in amorphous glassy shells, and the strength of the resulting dual-phase material is a near-ideal 3.3 gigapascals-making this the strongest magnesium-alloy thin film yet achieved. We propose a mechanism, supported by constitutive modelling, in which the crystalline phase (consisting of almost-dislocation-free grains of around six nanometres in diameter) blocks the propagation of localized shear bands when under strain; moreover, within any shear bands that do appear, embedded crystalline grains divide and rotate, contributing to hardening and countering the softening effect of the shear band.

Grain Size Effect on Mechanical Properties of Polycrystalline Graphene

Characteristics of nanocrystalline materials are known substantially dependent on the microstructure such as grain size, crystal orientation, and grain boundary. Thus it is desired to have systematic characterization methods on the various nanomaterials with complex geometries, especially in low dimensional nature. One of the interested nanomaterials would be a pure two-dimensional material, graphene, with superior mechanical, thermal, and electrical properties. In this study, mechanical properties of “polycrystalline” graphene were numerically investigated by molecular dynamics simulations. Subdomains with various sizes would be generated in the polycrystalline graphene during the fabrication such as chemical vapor deposition process. The atomic models of polycrystalline graphene were generated using Voronoi tessellation method. Stress strain curves for tensile deformation were obtained for various grain sizes (5~40 nm) and their mechanical properties were determined. It was found that, as the grain size increases, Young`s modulus increases showing the reverse Hall-Petch effect. However, the fracture strain decreases in the same region, while the ultimate tensile strength (UTS) rather shows slight increasing behavior. We found that the polycrystalline graphene shows the reverse Hall-Petch effect over the simulated domain of grain size (< 40 nm).

Large indentation strain-stiffening in nanotwinned cubic boron nitride.

Recent experiments reported a substantial strengthening of cubic boron nitride by nanotwinning. This discovery raises fundamental questions about new atomistic mechanisms governing incipient plasticity in nanostructured strong covalent solids. Here we reveal an unusual twin-boundary dominated indentation strain-stiffening mechanism that produces a large strength enhancement at nanometer-scale twinning size where a strength reduction is normally expected due to the reverse Hall-Petch effect. First-principles calculations unveil significantly enhanced indentation shear strength in nanotwinned cubic boron nitride by bond rearrangement at the twin boundary under indentation compression and shear strains that produces especially strong stress response. This remarkable strain-stiffening mechanism offers fundamental insights for understanding the stress response of nanotwinned covalent solids under indentation.

Variation In Mechanical Properties With Substrate Temperature Of SbTi Thin Film Deposited By RF Sputtering Technique

Nanoindentation technique has been used to determine the mechanical properties of bismuth layered structure ferroelectric thin films, which have been shown to be promising for MEMS based devices used in sensing, actuation and energy harvesting, especially at elevated temperatures. SBTi (SrBi4Ti4O15) is a promising layered ferroelectric material and thin films of this composition are deposited on amorphous fused silica substrates by rf sputtering technique varying the substrate temperature from 600–725 o C. The crystal structure and surface morphology of SBTi thin films are characterized by X-ray diffraction and atomic force microscopy. Depth- sensing nanoindentation system is used to measure the mechanical characteristics of SBTi thin films. Nanoindentation measurements reveal that the Young’s modulus and hardness of SBTi thin films are related with grain size and crystal orientation which in turn depend on substrate temperature. The increase in mechanical properties with grain size is observed, indicating the reverse Hall-Petch effect. Furthermore, hardness and Young’s modulus of the (119) oriented films were higher than those of (0010) oriented films. The tribological properties of these films are confirmed by performing the scratch tests on the same films.

Controversy about ultrahard nanotwinned cBN

Arising from Y. Tian et al. , 385–388 (2013)10.1038/nature11728 Tian et al.1 report synthesis of “nanotwinned” cubic boron nitride (“nt-cBN”). These authors claim that its unprecedented Vickers hardness of 108 GPa is due to nanotwinning, and that hardening of cBN is continuous with decreasing twin thickness down to the smallest size investigated, in contrast to the expected reverse Hall–Petch effect. We demonstrate here that it has been known for tens of years that “nt-cBN” (refs 2–4) hardens owing to a complex of phenomena associated with its microstructure and defects; we also consider that Tian et al.1 provide no proof that the hardness of “nt-cBN” is larger than 85 GPa, which is the previously reported maximum for nanostructured boron nitride2,4. Thus the claim of continuous hardening down to a few nanometres twin thickness is, in our opinion, unjustified. There is a Reply to this Brief Communication Arising by Tian, Y. et al. Nature 502, http://dx.doi.org/10.1038/nature12621 (2013).

A maximum in the hardness of nanotwinned cadmium telluride

By varying the twin thickness from 4 to 23 nm, a maximum of hardness is achieved by molecular dynamics simulations at a twin thickness of 16 nm. When the twin thickness is >16 nm, the hardness is consistent with the Hall–Petch effect, whereas the hardness of a twin ⩽16 nm thick is in a good agreement with the reverse Hall–Petch effect. This is attributed to a transformation of the synergistic effect between both twin boundaries from monotonically increasing to decreasing with increasing twin thickness.

Structure and mechanical properties of ultra-nanocrystalline diamond and nanocrystalline Cu from atomistic simulations

Several nanocrystalline metals demonstrate the so-called “reverse Hall–Petch effect” and become softer as their average grain size, d, decreases. Using atomistic simulations, we found that ultra- nanocrystalline diamond (UNCD) shows the same behaviour. We also examined a typical metal (Cu) and found that softening at small grain sizes is not limited to hardness or yield stress, but is also evident in the cohesive energy and elastic constants of the material. The effect is attributed to the larger concentration of grain boundary atoms at smaller d. Our model, which separately considers contributions to the cohesive energy, and consequently to elastic constants, from atoms in the grains and from atoms at the grain boundaries, fits simulation results extremely well for both materials. We calculate structural properties, elastic constants and estimate the hardness to find that the two materials have several qualitative similarities, such as linear scaling of the fraction of non-crystalline atoms with respect to 1/d and similar scaling laws for cohesive energy and elastic constants. At the same time, several quantitative differences, such as broader peaks in the pair correlation function for UNCD, lead to different magnitude for the scaling coefficients. Our results compare well with experimental observations. Moreover, our theoretical analysis yields universal scaling relations for properties of nanocrystalline materials as a function of the average grain size.

Ultrahard nanotwinned cubic boron nitride

Cubic boron nitride (cBN) is a well known superhard material that has a wide range of industrial applications. Nanostructuring of cBN is an effective way to improve its hardness by virtue of the Hall-Petch effect--the tendency for hardness to increase with decreasing grain size. Polycrystalline cBN materials are often synthesized by using the martensitic transformation of a graphite-like BN precursor, in which high pressures and temperatures lead to puckering of the BN layers. Such approaches have led to synthetic polycrystalline cBN having grain sizes as small as ∼14 nm (refs 1, 2, 4, 5). Here we report the formation of cBN with a nanostructure dominated by fine twin domains of average thickness ∼3.8 nm. This nanotwinned cBN was synthesized from specially prepared BN precursor nanoparticles possessing onion-like nested structures with intrinsically puckered BN layers and numerous stacking faults. The resulting nanotwinned cBN bulk samples are optically transparent with a striking combination of physical properties: an extremely high Vickers hardness (exceeding 100 GPa, the optimal hardness of synthetic diamond), a high oxidization temperature (∼1,294 °C) and a large fracture toughness (>12 MPa m(1/2), well beyond the toughness of commercial cemented tungsten carbide, ∼10 MPa m(1/2)). We show that hardening of cBN is continuous with decreasing twin thickness down to the smallest sizes investigated, contrasting with the expected reverse Hall-Petch effect below a critical grain size or the twin thickness of ∼10-15 nm found in metals and alloys.

Phase field crystal simulation of microscopic deformation mechanism of reverse Hall-Petch effect in nanocrystalline materials

The nanocrystalline (NC) materials of several average grain sizes ranging from 11.61 to 31.32 nm were obtained by using the phase field crystal model (PFC), and the microscopic deformation mechanism of strengthening law for the uniaxial tensile deformation was discussed. Simulated results show that grain rotation and grain boundary (GB) migration are mainly responsible for the microscopic deformation. Since small grain size is favorable for grain rotation so that it can make the yield strength reduced; and the NC materials would show a reverse Hall-Petch effect. When the grain size is so small and the strain exceeds the yield point to about 4%, dislocation activities begin to occur. Mainly by the change of GB structure (disorganizing triple grain boundary junction and then promoting grain migration), the GB can play a finite contribution to deformation. With increasing grain size, grain rotation becomes difficult, and the grain serration and emission of dislocations are observed.

Continuum modeling of the reverse Hall–Petch effect in nanocrystalline metals under uniaxial tension: how many grains in a finite element model?

Owing to their very high strength, nanocrystalline metals have been extensively studied over the recent years. The direct Hall–Petch law, empirically proportioning the material strength to the inverse square root of its grain size has been shown to break down below a grain size of the order of tenths of nanometers. This phenomenon has been widely rationalized as a gradual switch from intragrain mediated deformation mechanisms to grain boundary mediated deformation mechanisms. This transition has been observed in many finite element simulations, despite the intrinsic restriction of necessarily limiting the nanocrystalline representative assembly to only a few grains. Such a limitation is generally overlooked, and its influence on an uniaxial tension test – when compared to a complete sample of millions of grains – ignored. We propose here to quantify the approximation done by considering a finite number of grains by means of a simple analytical model based on the early work of Stevens [R.N. Stevens, Philos. Mag. 23 (1971) p. 265]. The finite element approximation is demonstrated to be relatively good, even down to only three grains in width, and a method to “correct” the stress-strain curves of small representative volumes is proposed.

Mechanical properties of sol–gel derived lead zirconate titanate thin films by nanoindentation

Lead zirconate titanate (PZT) thin films are deposited on platinized silicon substrate by sol–gel process. The crystal structure and surface morphology of PZT thin films are characterized by X-ray diffraction and atomic force microscopy. Depth-sensing nanoindentation system is used to measure mechanical characteristics of PZT thin films. X-ray diffraction analyses confirm the single-phase perovskite structures of all PZT thin films. Nanoindentation measurements reveal that the indentation modulus and hardness of PZT thin films are related with the grain size and crystalline orientation. The increases of the indentation modulus and hardness with grain size are observed, indicating the reverse Hall–Petch effect. Furthermore, the indentation modulus of (1 1 1)-oriented PZT thin film is higher than those of (1 0 0)- and random-oriented films. The consistency between experimental data and numerical results of the effective indentation moduli for fiber-textured PZT thin films using Voigt–Reuss–Hill model is obtained.