Inverse Hall-Petch Relation Research Articles

Structural, electrical, and mechanical characterization of Al 5086 alloy irradiated with 248 nm–20 ns KrF excimer laser

Williamson-Hall analysis of XRD patterns of Al 5086 alloy specimens (10 mm × 10 mm × 6 mm) irradiated with 100–500 KrF excimer laser pulses in air (1 bar) as well as in vacuum (10−3 mbar) was done to evaluate structural changes on laser irradiation. Both crystallite size (30 nm–99 nm) and lattice strain (0.00043–0.00241) were found, in general, to increase with the number of laser shots first rapidly up to 200 and later on rather slowly. Also, for a given number of laser shots, the crystallite size of the specimen laser-irradiated in vacuum was higher than that of the specimens laser-irradiated in air. Harris analysis of XRD patterns revealed that the most preferentially oriented plane was (200) with texture coefficient in the range 2.359–2.982. Electrical resistivity of the specimens was measured by four-point probe technique. It was found to increase with the number of laser shots up to 200, and later on decreases monotonically. However, for a given number of laser shots, its value was higher for the specimen laser-irradiated in air than that for the specimen laser-irradiated in vacuum. On plotting combined surface hardness data for un-irradiated and laser-irradiated specimens in air as well as in vacuum as a function of inverse square-root of crystallite size, a cross over from classical Hall-Petch relation (99 nm–55 nm) to inverse Hall-Petch relation (55 nm–30 nm) occurred at about 55 nm. This is true not only for the surface hardness but also for the hardness measured at 0.5 and 1.0 mm depth below the specimen surface. The intensity of laser-hardening effect gradually diminishes as one goes down from the uniformly laser-irradiated specimen surface to a depth of 3.0 mm below it. The relationship between electrical resistivity and surface hardness was linear.

Fourth-order strain-gradient phase mixture model for nanocrystalline fcc materials

The proposed modeling approach for nanocrystalline materials is an extension of the local phase mixture model introduced by Kim et al (2000 Acta Mater. 48 493–504). Local models cannot account for any non-uniformities or strain patterns, i.e. such models describe the behavior correctly only as long as it is homogeneous. In order to capture heterogeneities, the phase mixture model is augmented with gradient terms of higher order, namely second and fourth order. Different deformation mechanisms are assumed to operate in grain interior and grain boundaries concurrently. The deformation mechanism in grain boundaries is associated with diffusional mass transport along the boundaries, while in the grain interior dislocation glide as well as diffusion controlled mechanisms are considered. In particular, the mechanical response of nanostructured polycrystals is investigated. The model is capable of correctly predicting the transition of flow stress from Hall–Petch behavior in conventional grain size range to an inverse Hall–Petch relation in the nanocrystalline grain size range. The consideration of second- and fourth-order strain gradients allows non-uniformities within the strain field to represent strain patterns in combination with a regularization effect. Details of the numerical implementation are provided.

High-pressure torsion of aluminum with ultrahigh purity (99.9999%) and occurrence of inverse Hall-Petch relationship

Severe plastic deformation through the high-pressure torsion (HPT) method was applied to pure aluminum with a wide range of purity levels such as 99% (A1100), 99.5% (A1050), 99.99% (4NAl), 99.999% (5NAl) and 99.9999% (6NAl). The hardness of 6NAl decreased with straining and saturated to a level below the hardness level of the annealed sample. This softening behavior, which was similar to the behavior of metals with low melting temperatures such as indium, tin, lead and zinc, was not observed in 5NAl or less pure Al. It was found that the grain-size dependence of hardness became less significant with increasing the purity level, while the HPT-processed 6NAl followed an inverse Hall-Petch relationship. In 6NAl with large grain sizes, dislocations accumulated in the grains in the form of dislocation cells and enhanced the hardness, but when the grain size was small, the dislocations moved fast and disappeared in high-angle grain boundaries.

Impact of 1064 nm–10 ns pulsed laser on the surface morphology, structure, and hardness of Pd80Ni20 alloy

Specimens of Pd80Ni20 alloy were irradiated in air with 70, 80, 90, and 100 laser shots using a Q-switched Nd-YAG laser of 1064 nm wavelength with pulse duration 10 ns, energy 50 mJ, and repetition rate 10 Hz. Surface morphology of the laser-irradiated specimens was studied with the help of a scanning electron microscope. It includes wave-like structures or ripples, dips, ridges, microcones, flakes, and fissures, etc. The X-ray diffraction patterns of un-irradiated and irradiated specimens were analyzed using the Williamson–Hall method to evaluate crystallite size and microstrain. Texture coefficient was determined by Harris analysis. The peak intensity of (111), (200), (220), (311), and (222) planes increases linearly with laser shots, which shows that the concentration of point defects (i.e., vacancies) is progressively decreased on increasing the number of laser shots due to the annealing processes. Surface hardness was measured using a Vickers hardness tester. The average surface hardness of the specimens initially decreases on irradiation with 70 laser shots and later on increases linearly with increase in laser shots up to 100. An inverse Hall-Petch relationship is observed in the crystallite size range 19–27 nm. As crystallite size decreases from 27 to 19 nm, volume fraction of amorphous phase increases progressively. The amorphous phase being softer than crystalline phase due to increased atomic spacing leads to reduction in surface hardness of the material.

Impact of 532 nm 6 ns laser pulses on (104) oriented zinc single crystal: surface morphology, phase transformation, and structure hardness relationship

Specimens of (104) oriented Zn single crystal were irradiated in vacuum ∼10−3 Torr with pulsed Nd:YAG laser (λ = 532 nm, E = 50 mJ, τ = 6 ns) at a repetition rate 10 Hz. The number of laser shots was varied from 1 to 100. The laser fluence and laser intensity at the one laser shot irradiation spot on the target surface were 97.2 J cm−2 and 1.6 × 1010 W cm−2, respectively. Crater geometry of laser-irradiated specimens was examined by optical microscope. Crater area was found to increase with the increase in number of laser shots. The data points were encompassed by sigmoidal (Boltzmann) fit showing that crater area increases rapidly to begin with up to 50 laser shots and later on rather slowly till 100 laser shots. Surface morphology was examined by SEM and AFM, which revealed ripple patterns, cavities, trenches, ridges, nanohillocks, microcones, droplets, and solid flakes etc. Structural parameters, namely crystallite size and lattice strain were evaluated by Williamson–Hall analysis of x-ray diffraction patterns. Surface hardness was found to increase up to 50 laser shots and later on it decreased progressively till 100 laser shots. Correlation between surface hardness and crystallite size was also examined, and was found to obey inverse Hall–Petch relation.

Molecular dynamics simulation of micro-mechanical deformations in polycrystalline copper with bimodal structures

Molecular dynamics simulation (MD) was performed on the polycrystalline copper with bimodal structures. As our special grain size distribution based on the inverse Hall-Petch relation, the small grain region and large grain region play different roles in the uniaxial tensile tests. The large grain region imparts the bimodal Cu samples high strength for the lattice dislocations activation. The large grain size effect was studied in this paper. Through our MD simulations, an atomic scale view of the interactions between two regions is also presented with the deformation progress.

Effects of grain size and temperature on mechanical response of nanocrystalline copper

Molecular dynamics simulation is utilized to study the effects of grain size and temperature on the mechanical properties of quasi-two-dimensional (2D) nanocrystalline Cu with grain sizes of 3–8nm under uniaxial tensile tests. Our results show that the grain growth is caused by the grain rotation and leads to strain hardening at 300K for a grain size of <5nm and at 100K for a grain size of <4nm. For a grain size of ≤7nm, the inverse Hall–Petch relation was observed in the yield stress. The Young’s modulus for the quasi-2D system is higher than that for the three-dimensional (3D) system.

Effect of iron alloying in evolution of nanostructure and microstructural stability in nickel

Nanocrystalline materials show many interesting properties such as high strength and hardness due to nanosized grains and high density of interfaces. In this context, the present work reports the effect of Fe (iron) addition in Ni (nickel) on nanostructure retention during the annealing of Ni-Fe alloy (with 0, 18.5, 28.5 and 43 wt% Fe) at 450 °C for 16 h. Furthermore, effect of annealing on the deformation mechanism was investigated. The integral breadth method revealed the decrease in grain size with increase in wt% Fe in Ni. The strain rate sensitivity exponent which is a signature of operating deformation mechanism showed a higher value (0.10803) in case of Ni-18.5 wt% Fe during nanoindentation. However, Ni-0 wt% Fe, Ni-28.5 wt% Fe and Ni-43 wt% Fe were characterized by a relatively low strain rate sensitivity exponent (between 0.02069 and 0.10803). Results indicated the presence of Hall-Petch relationship up to 18.5 wt% Fe and inverse Hall-Petch relationship above 18.5 wt% Fe.

Theoretical interpretation of abnormal ultrafine-grained material deformation dynamics

Some recent experiments with ultrafine-grained metal samples reveal that it has an abnormal mechanical response on the intensive dynamical loading caused by its impact or electron beam irradiations. On the basis of the original plasticity model, which takes into account dislocation slip and grain boundary sliding, we show that this response is usual for such structure. Moreover, our calculations predict an inverse Hall–Petch relation for ultrafine grained metals at extremely high strain rates (above 107 s−1), while the classical low strain rate experiments and molecular dynamic simulations detects such inverse Hall–Petch relation only for nanocrystalline materials. The main outcomes of present work are the described plasticity model and the conclusions that the ultrafine-grained metals (with grains of about 100–200 nm in diameter) has to have maximal dynamic shear strength and it is the most persistent to dynamic spall fracture because of maximal energy dissipation in it.

The inverse hall–petch relation in nanocrystalline metals: A discrete dislocation dynamics analysis

When the grain size in polycrystalline materials is reduced to the nanometer length scale (nanocrystallinity), observations from experiments and atomistic simulations suggest that the yield strength decreases (softening) as the grain size is decreased. This is in contrast to the Hall–Petch relation observed in larger sized grains. We incorporated grain boundary (GB) sliding and dislocation emission from GB junctions into the classical DDD framework, and recovered the smaller is weaker relationship observed in nanocrystalline materials. This current model shows that the inverse Hall–Petch behavior can be obtained through a relief of stress buildup at GB junctions from GB sliding by emitting dislocations from the junctions. The yield stress is shown to vary with grain size, d, by a d1/2 relationship when grain sizes are very small. However, pure GB sliding alone without further plastic accomodation by dislocation emission is grain size independent.

MD simulation of nanoindentation on (001) and (111) surfaces of Ag–Ni multilayers

We perform MD simulations of the nanoindentation on (001) and (111) surfaces of Ag–Ni multilayers with different modulation periods, and find that both the hardness and maximum force increase with the increase of modulation period, in agreement with the inverse Hall–Petch relation. A prismatic partial dislocation loop is observed in the Ni(111)/Ag(111) sample when the modulation period is relatively large. We also find that misfit dislocation network shows a square shape for the Ni(111)/Ag(111) interface, while a triangle shape for the Ni(001)/Ag(001) interface. The pyramidal defect zones are also observed in Ni(001)/Ag(001) sample, while the intersecting stacking faults are observed in Ni(111)/Ag(111) sample after dislocation traversing interface. The results offer insights into the nanoindentation behaviors in metallic multilayers, which should be important for clarifying strengthening mechanism in many other multilayers.

Grain size effect on indentation of nanocrystalline copper

The nanoindentation process of single-crystal and nanocrystalline copper is studied with molecular dynamics simulations based on the many-body tight-binding potential. The grain size effect is evaluated in terms of slip vector, atomic stress, loading force, and hardness. The inverse Hall–Petch relation is found below 7nm. With grain size smaller than 5nm, the equivalent stress decreases quickly and stress-induced grain growth is observed in indentation process. Grain rotation is the main cause of grain coarsening for small grain sizes. For larger grain sizes, dislocations are found at the {111} close-packed plane and {100} plane.

The Inverse Hall-Petch Effect in Nd:YAG Laser Irradiated Nickel

Mechanically polished 4N pure nickel specimens were irradiated in air with Nd:YAG laser for laser shots ranging from 1000 to 5000 with an increment of 1000. The structural and mechanical characterization of the specimens was done using X-ray diffractometer (XRD) and Vickers hardness tester. The XRD patterns exhibit variation in the intensity of diffraction peaks pointing to significant structural changes on laser irradiation. Crystallite size, uniform deformation energy density, lattice deformation stress, and lattice strain were determined by Williamson-Hall analysis using uniform deformation energy density model. All the four structural parameters referred to were found to increase linearly with laser shots. On laser irradiation, surface hardness of nickel first increases up to 3000 laser shots, and later on it decreases up to 5000 laser shots. Crossover from classical Hall-Petch relation to inverse Hall-Petch relation occurs at about 69nm in the observed crystallite size range of 81 to 44nm.

Hardness–structure Relationship in Nd:YAG Laser Irradiated High-purity Zinc

Six specimens of 99.995% pure zinc were irradiated with a passive Q-switched pulsed Nd:YAG laser in a vacuum ̴ 10-3 Torr. The specimens were irradiated with 50 to 100 laser shots with an increment of 10 shots. Williamson-Hall analysis of XRD patterns of un-irradiated and irradiated specimens was carried out to evaluate the structural parameters, namely crystallite size and micro-strain. Surface hardness of the specimens was measured using Vickers hardness tester. An inverse Hall-Petch relation for the surface hardness was observed in the 28–35nm crystallite size range.

Effect of the structural factor on the inverse Hall-Petch dependence in nanocrystals

A gradated dislocation-disclination model of plastic shear in nanocrystals is generalized allowing for the structural factor (the distribution of the grain size in a polycrystalline ensemble) in the context of the three-dimensional problem when describing the mechanical behavior of nanocrystals in the region of the effect of the inverse Hall-Petch relation. The critical size of the crystal that corresponds to the change of the deformation mode, and the value of which for pure copper nanocrystals agrees with the experimental data without allowing for the structural factor is found using an analytical function calculated with the Mathematica 5.2 computer system. It is shown that the critical grain size increases rather than decreases as the standard deviation grows. The requirements for the form of the function describing the inverse Hall-Petch dependence are formulated.

Inverse pseudo Hall-Petch relation in polycrystalline graphene.

Understanding the grain size-dependent failure behavior of polycrystalline graphene is important for its applications both structurally and functionally. Here we perform molecular dynamics simulations to study the failure behavior of polycrystalline graphene by varying both grain size and distribution. We show that polycrystalline graphene fails in a brittle mode and grain boundary junctions serve as the crack nucleation sites. We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements. Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials. Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.

Structural characteristics and inverse Hall–Petch relation in high-purity nickel irradiated with nanosecond infrared laser pulses

Mechanically polished nickel specimens (99.99% purity) were irradiated in air with Nd:YAG laser for laser shots ranging from 1000 to 5000 with an increment of 1000. The structural and mechanical characterization of the specimens was done using an X-ray diffractometer (XRD) and a Vickers hardness tester. The XRD patterns exhibit variation in the intensity of diffraction peaks pointing to significant structural changes on laser irradiation. Stacking fault probability was found to increase on irradiation with laser shots up to 2000, and later on it remained constant. Crystallite size, uniform deformation energy density, lattice deformation stress, and lattice strain were determined by Williamson–Hall analysis using uniform deformation energy density model. All the four structural parameters referred to were found to increase linearly with laser shots. On laser irradiation, surface hardness of nickel first increases up to 3000 laser shots, and later on it decreases up to 5000 laser shots. Crossover from classical Hall–Petch relation to inverse Hall–Petch relation occurs at about 69nm in the observed crystallite size range of 81–44nm.

J1910203 宇宙環境における微細結晶粒からなるアルミニウムの材料特性の研究([J191-02]構造・材料の高度化に向けた宇宙工学と材料力学の展開(2))

Considering space utilization of the nanocrystalline metals, the influence of the nano-scale void is investigated via molecular dynamics (MD) method. As to nanocrystalline metals, grain boundary deformation is one of the important factors to explain the material characteristics. Considering the grain boundary deformation, we focus on the dislocation activity enhancement due to the nano-scale void. As the results, following three findings are acquired. 1) Inverse Hall-Petch relation is observed for aluminum nanocrystalline models with grain diameter less than 6 nm. 2) Grain boundary sliding is confirmed as deformation mechanism of aluminum nanocrystalline models. 3) There is no obvious size increase of nanocrystalline void or massive dislocation generation from the void if it exists in the grain surrounded by active grain boundaries with sliding deformation. From the third finding, we can conclude that it is crucial to investigate the relationship between the dislocation activities around nano-scale void and the sliding activities of surrounding grain boundaries to understand the effect of nano-scale void.

Nano-scale machining of polycrystalline coppers - effects of grain size and machining parameters

In this study, a comprehensive investigation on nano-scale machining of polycrystalline copper structures is carried out by molecular dynamics (MD) simulation. Simulation cases are constructed to study the impacts of grain size, as well as various machining parameters. Six polycrystalline copper structures are produced, which have the corresponding equivalent grain sizes of 5.32, 6.70, 8.44, 13.40, 14.75, and 16.88 nm, respectively. Three levels of depth of cut, machining speed, and tool rake angle are also considered. The results show that greater cutting forces are required in nano-scale polycrystalline machining with the increase of depth of cut, machining speed, and the use of the negative tool rake angles. The distributions of equivalent stress are consistent with the cutting force trends. Moreover, it is discovered that in the grain size range of 5.32 to 14.75 nm, the cutting forces and equivalent stress increase with the increase of grain size for the nano-structured copper, while the trends reserve after the grain size becomes even higher. This discovery confirms the existence of both the regular Hall–Petch relation and the inverse Hall–Petch relation in polycrystalline machining, and the existence of a threshold grain size allows one of the two relations to become dominant. The dislocation-grain boundary interaction shows that the resistance of the grain boundary to dislocation movement is the fundamental mechanism of the Hall–Petch relation, while grain boundary diffusion and movement is the reason of the inverse Hall–Petch relation.

Inverse Hall–Petch relationship in nanocrystalline tantalum

Tantalum polycrystals (grain sizes varying from 2.5 to 30nm) generated by Voronoi tessellation were subjected to tension and compression under uniaxial strain loading at strain rates on the order of 108–109s−1 using molecular dynamics (MD) simulations. In contrast with MD simulations of FCC metals, the response in tension is significantly different from that in compression. In tension, fracture is initiated at grain boundaries perpendicular to the loading direction. It propagates along grain boundaries with limited plastic deformation, at a stress in the range 10–14GPa. This brittle intergranular failure is a consequence of the high strain rate imposed by MD, leading to a stress that exceeds the grain-boundary cohesive strength. Thus, grain-boundary separation is the principal failure mechanism. In compression, on the other hand, there is considerable plastic deformation within the grains. This occurs at stresses higher than failure in tension. The difference between tensile and compressive response for tantalum is attributed to the difficulty in generating dislocations, in contrast with FCC metals, where tensile failure occurs by void nucleation at grain boundaries associated with partial and perfect dislocation emission. In BCC tantalum, both grain-boundary sliding and dislocation emission are much more difficult.The compressive yield stress is found to increase with grain size in the 2.5nm<d <30nm region. This inverse Hall–Petch relationship is analyzed in terms of the contributions of dislocation motion and grain-boundary shear to plastic deformation. As the grain size is increased the contribution of grain-boundary sliding is decreased and plastic strain is accommodated by dislocation and motion. In tensile deformation, on the other hand, this behavior is not observed.