Hall-Petch Behavior Research Articles

Bifurcation in deformation behavior of Cu and Ta by accumulative roll-bonding at high temperature

Cu and Ta are co-deformed at 673K by the accumulative roll-bonding technique up to 8 passes. At an equivalent von Mises strain (ɛvm) of ~2 the deformation is bifurcated into shear accommodated by the ‘soft’ Cu, and plane-strain by the ‘hard-but-ductile’ Ta. This is attributed to transitions occurring collectively at ɛvm ~2 in crystallographic texture, partitioning of recovery and recrystallization, and the nature of interfaces as elucidated by orientation relations, Hall-Petch behavior and manifestation of instabilities at higher strain.

Rapid solidification mechanism of Fe-Al-Nb alloy droplet and its influence on microhardness under microgravity condition

High temperature Fe-Al-Nb alloys will be prospectively applied to the industrial field, i.e., aviation, gas turbine, etc. In this paper, rapid solidification of Fe67.5Al22.8Nb9.7 ternary alloy under microgravity condition is realized by using drop tube containerless processing technique. Our purpose is to investigate the microstructural transition pattern and relevant micromechanical properties, and then to reveal the influence of rapid eutectic growth on application performance. The sample of 2 g is placed in a quartz tube with an orifice at the bottom, and the quartz tube is then placed at the top of 3 m drop tube. The sample is inductively melted and further superheated to a certain temperature with the protecting mixture gas composed of argon and helium. The alloy melt is ejected through the orifice by an argon gas flow and dispersed into fine droplets. The droplets are undercooled and finally rapidly solidified during their free fall in the drop tube. The alloy droplets with the diameter sizes ranging from 40 to 1000 m are achieved. The liquidus temperature of the alloy is 1663 K. The microstructure of the alloy consists of Nb(Fe, Al)2 and (Fe) phases. In the master alloy prepared by arc melting, the segregation along the gravity direction takes place because of the difference in cooling rate inside the master alloy. By comparison, the microstructures of the alloy droplets are homogeneous. The variations of thermodynamical parameters with droplet size are analyzed. As droplet diameter decreases, its Nusselt and Reynolds numbers rise from 3 to 8 and from 5 to 137, respectively, its undercooling and cooling rate increase from 50 to 216 K and from 1.23103 to 5.53105 K s-1 respectively. This causes the corresponding microstructural transition. A small amount of primary Nb(Fe, Al)2 phase transforms from dendrite to equiaxed grain, the lamellar eutectic is replaced by the fragmented eutectic. The relationship between eutectic interlamellar spacing and undercooling satisfies an exponential equation, indicating that the eutectic is refined by three times. Consequently, mainly owing to the eutectic refinement, the microhardness of the alloy increases by 10% with the increase of undercooling according to the Hall-Petch behavior in terms of both eutectic grain size and interlamellar spacing. Compared with the microstructure of the alloy undercooled to the same level under electromagnetic levitation in our recent work, the microstructure in drop tube is more refined due to the larger cooling rate, contributing to the microhardness of the alloy increasing by 2%-6%.

An investigation of microstructural evolution in 304L austenitic stainless steel warm deformed by cyclic channel die compression

Microstructural evolution during warm severe plastic deformation of 304L austenitic stainless steel is investigated in the present work by employing Electron backscattered diffraction (EBSD) analysis. A total effective plastic strain of 4.8 is imparted through cyclic channel die compression technique at 500 °C. Macrostructural studies revealed distinct flow lines characterized by heterogeneous deformation bands indicative of deformation inhomogeneity. EBSD based microstructural analysis indicated substantial grain refinement wherein the grain size is decreased from ∼15 μm in the initial condition to ∼0.27 μm in warm deformed condition. Continuous dynamic recrystallization (CDRX) is identified as the dominant grain refinement mechanism evidenced by strain induced boundaries, subgrains bounded by low angle grain boundaries and thin deformation microbands. The role of deformation bands in facilitating grain refinement is evidenced. CDRX driven grain subdivision/fragmentation through the evolution of spatially distributed misoriented subgrains is corroborated to the significant increase in low angle grain boundaries in deformed condition. Considerable improvement in strength is evidenced from the evolution of microhardness and tensile behaviour. Two-fold increase in microhardness and three-fold increase in yield strength is observed. Towards the end, the grain size dependence on yield strength and microhardness is suitably described by Hall-Petch behaviour.

Effect of initial alpha lamellar thickness on deformation behavior of a near-α high-temperature alloy during thermomechanical processing

The hot deformation behavior of a near-α high-temperature Ti-5.4Al-3.7Sn-3.3Zr-0.5Mo-0.4Si alloy with initial alpha lamellar thicknesses from 1µm to 10µm was investigated by conducting a series of isothermal hot compression tests. The effect of initial alpha lamellar thickness on the flow behavior, apparent activation energy, strain-rate sensitivity and microstructure evolution under different hot deformation conditions were analyzed based on the experimental data. The results show that the flow stress of the alloy display an overall decreasing trend with the increasing of initial alpha lamellar thickness for a given temperature and strain rate. The peak stress and the apparent activity energy during thermomechanical processing were quantitatively described as a function of alpha platelet thickness based on the Hall-Petch behavior. According to various deformation mechanisms, the variations of apparent activity energy and strain rate sensitivity associated with different initial alpha lamellar thicknesses were calculated and analyzed for the alloy, which indicate that the thin initial alpha lamellar microstructure with higher apparent activation energy and strain rate sensitivity shows easier occurrence of dynamic globularization than thick initial alpha lamellar microstructure. Furthermore, the characterization of microstructure evolution for the alpha lamellae with different thicknesses were observed and the thin lamellae was more easily fragmented into fine α phase while most of the thick lamellae were elongated or buckled at same processing conditions.

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.

Synthesis of Al2O3/SiO2 nano‐nano composite ceramics under high pressure and its inverse Hall–Petch behavior

AbstractWe report the synthesis of alumina/stishovite nano‐nano composite ceramics through a pressure‐induced dissociation in Al2SiO5 at a pressure of 15.6 GPa and temperatures of 1300°C‐1900°C. Stishovite is a high‐pressure polymorph of silica and the hardest known oxide at ambient conditions. The grain size of the composites increases with synthesis temperature from ~15 to ~750 nm. The composite is harder than alumina and the hardness increases with reducing grain size down to ~80 nm following a Hall–Petch relation. The maximum hardness with grain size of 81 nm is 23 ± 1 GPa. A softening with reducing grain size was observed below this grain size down to ~15 nm, which is known as inverse Hall–Petch behavior. The grain size dependence of the hardness might be explained by a composite model with a softer grain‐boundary phase.

Inverse Hall–Petch like behaviour in a mechanically milled nanocrystalline Al5Fe2 intermetallic phase

In the present investigation, the indentation study on the high-energy ball-milled nanocrystalline Al5Fe2 intermetallic compound has established the inverse Hall–Petch (IHP) behaviour. The structural characterisation of the milled powder particles by X-ray diffraction (XRD) and transmission electron microscopy has shown the evolution of nanocrystalline phase. Micro-indentation measurements have revealed the increase in hardness with decreasing grain size, reaching to a maximum of 9.0 ± 0.3 GPa up to a grain size of 32 ± 4 nm, followed by a decrease. The decrease in hardness with further refinement, an indication of grain size softening, demonstrates the IHP-like behaviour. The deviation from the Hall–Petch behaviour has been discussed using various models based on the dislocations and grain boundary-mediated processes. From the analysis, it appears that the model based on mesocopic grain boundary sliding phenomena is more appropriate to account for the observed grain size softening.

A Multiple-Mechanism-Based Model for Prediction of Yield Strength in Bicrystals

Different mechanisms such as glide of lattice dislocation and grain boundary mediated processes may be active during the plastic deformation of polycrystals with small grain size. A continuum model for polycrystal plasticity has been developed to capture such a feature. Specifically, the strain gradient effect due to dislocation pile-up, dislocation emission/absorption at surface and grain boundary sliding have been taken into account from the perspective of energy storage. As an application of the model, a bicrystal under plane constrained shear has been considered. The dependence of yield strength on the thickness of the bicrystal has been investigated. It has been demonstrated the present model predicts the yield strength of the bicrystal first increases and then decrease with decrease in the thickness, which is similar to the inverse Hall–Petch behavior but with a different scaling. Such behavior is attributed to the transition in different dominant deformation mechanisms at different values of the thickness.

Influence of hot-press sintering parameters on microstructures and mechanical properties of h-BN ceramics

Pure h-BN ceramics were processed at different sintering temperatures and hold times using ball milled nanocrystalline or amorphous h-BN powders. Increases in sintering temperature induced greater grain growth but reduced relative densities and mechanical properties. Changes in sintering hold times caused further increases in grain sizes and relative density, but had little impact on mechanical properties. The grain sizes play an important aspect of strength in h-BN ceramics. The relationship of flexural strength and grain sizes in h-BN ceramics conforms to Hall-Petch behavior. When the grain size of h-BN ceramics increased from 0.3 μm to 8 μm, the flexural strength declined from 163 ± 6 to 84 ± 4 MPa. The mechanical properties of h-BN ceramics depend both on relative densities and grain sizes.

A study of densification and phase transformations of nanocomposite Cu-Fe prepared by mechanical alloying and consolidation process

The purpose of this study is an attempt to obtain nanocrystalline bulk Cu-40 at.% Fe alloy by mechanical alloying followed by consolidation process under 7 GPa and annealing. The transformations occurring in the material were studied by the use of X-ray diffraction. The structural investigations revealed that consolidation enabled supersaturated Cu(Fe) to precipitate out Cu4Fe and CuFe4 intermetallics. A limited grain growth was noticed after annealing. The results of microhardness have shown that the hardening increases similarly up to 40 h milling. The variation of microhardness as a function of the reciprocal square root of the grain size demonstrates that the rate of hardening is similar to that predicted by the Hall-Petch behavior.

Microstructure, phase composition and hardness evolution in 316L stainless steel processed by high-pressure torsion

A 316L stainless steel was processed by high-pressure torsion (HPT) to evaluate the grain refinement and phase transformation. The initial material was essentially a single phase γ-austenite with a coarse-grained microstructure of ∼42µm but the grain size was reduced to ∼45nm after 10 turns of HPT. In addition, there was a phase transformation and the initial γ-austenite transformed initially to ε-martensite and finally to α′-martensite with increasing strain. The dislocation density increased to an exceptionally high value, of the order of ∼1016m−2, in the main α′-martensite phase after 10 HPT revolutions. The formation of the multiphase nanocrystalline microstructure yielded a four-fold increase in hardness to reach an ultimate value of ∼6000MPa. The Hall–Petch behaviour of the HPT-processed alloy is compared directly with coarse-grained materials.

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.

Role of Different Fractions of Nano-size SiC and Milling Time on the Microstructure and Mechanical Properties of Al–SiC Nanocomposites

High energy ball milling was implemented to produce Al-matrix composites reinforced with 2.5, 5, 10, 15 and 20 wt% silicon carbide (SiC) nano-particles. In this regard, Scanning electron microscopy, X-ray diffraction and microhardness tests were applied to clarify the role of milling time and the percentage of nanometric SiC on structural evolutions and mechanical properties of the composites. An increase in the SiC proportion resulted in accelerating the milling process, leading to faster work hardening rate and fracture of the aluminum matrix. Thus, the crystallite size of Al in Al–20wt.%SiC composite reached a low of 20 nm after milling for 25 h and the microstrain trend experienced higher increasing rate in composites with higher amounts of SiC. Similarly, as a result of the rise in SiC percentage, there was a growth in the microhardness of composites. This phenomenon was mainly attributed to grain refinement, explained by Hall–Petch equation. On the other hand, inverse Hall–Petch behavior was observed for a ultra fine-grain sample, Al–20wt.%SiC milled for 25 h.

Strong Hall-Petch Type Behavior in the Elastic Strain Limit of Nanotwinned Gold Nanowires.

Pushing the limits of elastic deformation in nanowires subjected to stress is important for the design and performance of nanoscale devices from elastic strain engineering. Particularly, introducing nanoscale twins has proved effective in rising the tensile strength of metals. However, attaining ideal elastic strains in nanotwinned materials remains challenging, because nonuniform twin sizes locally affect the yielding behavior. Here, using in situ high-resolution transmission electron microscopy tensile testing of nanotwinned [111]-oriented gold nanowires, we report direct lattice-strain measurements that demonstrate a strong Hall-Petch type relationship in the elastic strain limit up to 5.3%, or near the ideal theoretical limit, as the twin size is decreased below 3 nm. It is found that the largest twin in nanowires with irregular twin sizes controls the slip nucleation and yielding processes in pure tension, which is in agreement with earlier atomistic simulations. Continuous hardening behavior without loss of strength or softening is observed in nanotwinned single-crystalline gold nanowires, which differs from the behaviors of bulk nanocrystalline and nanotwinned-nanocrystalline metals. These findings are of practical value for the use of nanotwinned metallic and semiconductor nanowires in strain-engineered functional microdevices.

Modeling the Hall-Petch Relation of Ni-Base Polycrystalline Superalloys Using Strain-Gradient Crystal Plasticity Finite Element Method

Abstract A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior ofa Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessarydislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interactioncoefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate thegeometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was alsoused to represent the shear rate of an individual slip system. The constitutive model was implemented in a user materialsubroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that thepresent constitutive model fairly reasonably predicts 0.2 %-offset yield stresses in a limited range of the grain size.Key wordscrystal plasticity, strain gradient plasticity, finite element method, hall-petch relation, polycrystal.

Grain Size Effect on the Thermal-induced Martensitic Transformation in Polycrystalline Cu-based Shape Memory Alloys

In Cu-based SMA alloys, the grain size (d) effect on the martensitic transformation temperature was investigated for a wide range of d. Specimens were prepared by different heat treatments in order to create a range of grain sizes, from about 500nm (ribbons and tapes obtained by rapid solidification techniques) up to 6mm diameter single-crystals (grown by the Bridgman method). Information obtained from the literature was also included in the set of analyzed experimental data. The reduction of grain size shifts the forward transformation temperature downwards. These grain-size effects are observed in specimens with d below ∼ 100μm, and become more pronounced for d below ∼ 20μm. An empirical expression was obtained that describes the grain-size effect over the whole temperature range. The obtained curve differs considerably from the Hall-Petch behaviour reported in the literature by some other investigators.

Microstructural thermal stability of CNT-reinforced composites processed by severe plastic deformation

The microstructural thermal stability and mechanical properties of carbon nanotube (CNT)-reinforced Ni matrix composites processed by high pressure torsion (HPT) are investigated. A structural assessment of the CNTs at the different processing steps was performed by means of Raman spectroscopy, not detecting any significant modification of the CNT structure throughout the whole procedure. After deformation, the composites showed a maximum fivefold increase in hardness, related to their microstructure and resembling a Hall–Petch behavior. In order to study the thermal stability, an annealing was made at a homologous temperature of 0.33, which exceeds the grain growth onset temperature for this type of composites. The presence of CNTs helped stabilize the microstructure by pinning the grain boundaries during HPT. This stabilization translated into a significant increase in hardness and remained, to a certain degree, after the thermal treatment. Our results highlight the feasibility of obtaining CNT-reinforced composites by this means, improving the properties without compromising the structural features of the reinforcement and increasing their distribution within the matrix.

Grain Growth Behavior and Hall–Petch Strengthening in Friction Stir Processed Al 5059

Friction stir processing (FSP) of Al 5059 is studied in which subsequent heat treatment is conducted to investigate its effects on grain size and hardness. It was found that mainly elongated and rhomboidal morphologies of Al6(Mn,Fe) particles are present in the alloy both before and after FSP, where the rhomboidal particles are more effective in pinning grain boundaries during heat treatment. The stir zone reached a temperature of 705 K (432 °C), and ThermoCalc modeling confirmed that the Al6(Mn,Fe) particles will remain stable at this temperature. Negligible grain growth was observed during FSP of the Al 5059 due to low grain boundary mobility resulting from slow diffusion associated with a high Mg content in the alloy. During heat treatment at 448 K (175 °C) grain growth could be correlated with time using a particle-controlled grain growth model. Microhardness values indicate that Hall–Petch behavior occurs in the processed alloy, while dislocation density and particle dispersion play a minor role in strengthening.

Inverse Hall-Petch Like Mechanical Behaviour in Nanophase Al-Cu-Fe Quasicrystals: A New Phenomenon

The structural and mechanical stability of quasicrystals are important issues due to their potential for possible applications at high temperatures and stresses. The aim of the present work is, therefore, to review the earlier works on conventional crystalline and quasicrystalline materials and also to report the results and the analysis on the Hall Petch and inverse Hall Petch like behavior of nanoquasicrystalline Al62.5Cu25Fe12.5 alloys. It was observed that, at large grain sizes, the hardness increases with decreasing grain size, exhibiting the conventional Hall Petch relationship, whereas for smaller grains, inverse Hall Petch behavior was identified. The inverse Hall Fetch behavior in the nanoquasicrystalline phase could be attributed to thermally activated shearing of the grain boundaries, leading to grain boundary sliding in nanostructures of quasicrystalline grains. These results were analyzed based on the dislocation pile-up model as well as the grain boundary shearing models applicable to nanomaterials.

Grain-Size Dependency of Low-Temperature Creep in Ultrafine-Grained Aluminum

The grain size dependence of creep behavior from coarse grain to ultrafine grain regions was examined using fully-annealed specimens fabricated from a single process route. For coarse-grained sample, in tensile deformation, stress-strain curves show slow work hardening, and the proof stress shows typical Hall-Petch behavior. On the other hand, creep behavior is observed under the stress above the proof stress, and the creep rate has no grain size dependence. For ultrafine-grained sample, in the tensile deformation, stress-strain curves show yielding behavior, and the yield stress shows Hall-Petch behavior also. On the other hand, creep behavior was observed below the proof stress, but the creep rate decreases with a decrease in grain size.