Hall-Petch Effect Research Articles

Model for the hardness-depth relationships of ion-irradiated nanocrystalline metals

In this work, a mechanistic model is proposed for ion-irradiated nanocrystalline (NC) metals to characterize the evolution of hardness as a function of the indentation depth at room temperature and under quasi-static loading condition. At the grain level, grain interiors (GIs) and grain boundaries (GBs)-dominated hardening are addressed simultaneously in the developed model, which is able to effectively characterize the contribution of geometrically necessary dislocations (GNDs), statistically stored dislocations (SSDs), irradiation-induced defects, Hall-Petch effect and the intrinsic strength of GBs. Thereinto, the GIs-dominated hardening mechanisms are systematically analyzed by considering the evolution of microstructures, which include the average density of dislocations and irradiation-induced defects within the plastic zone, and are noticed to be affected by the high ratio of GBs. Main attentions are focused on the description of GBs influence that covers dislocation hardening and defect hardening. The rationality and accuracy of the proposed model are validated by comparing the theoretical results with corresponding experimental data under different irradiation conditions. The proposed model offers a promising way to analyze the irradiation hardening mechanisms of NC metals.

An atomistic study on grain-size and temperature effects on mechanical properties of polycrystal CoCrFeNi high-entropy alloys

The origin of the outstanding mechanical properties of high-entropy alloys (HEAs) is still elusive. In this paper, we have investigated the influence of grain size and temperature on the mechanical properties of polycrystalline CoCrFeNi HEAs via molecular dynamics simulations. The critical grain size for the inverse Hall-Petch effect in CoCrFeNi HEAs is approximately 11.65 nm. During the stage of the positive Hall-Petch effect (where smaller grain sizes lead to higher tensile strength), there is a positive correlation between the tensile strength and dislocation density in CoCrFeNi HEAs. The higher tensile strength at low temperatures in CoCrFeNi HEAs is also attributed to an increase in dislocation density. At low temperatures, the reduced thermal vibrations of atoms slow down the motion of dislocations, leading to an increased storage time of dislocations within the crystal. In the stage of the inverse Hall-Petch effect, due to a significant reduction in grain size, the storage capacity of dislocations within grains decreases. This leads to the accumulation of more dislocations at grain boundaries, forming defects, and consequently causing a decrease in the tensile strength of CoCrFeNi HEAs as the grain size decreases. Our results might be helpful in material design of polycrystal HEAs.

Effect of strain inhomogeneity on flow behavior, dynamic recrystallization and substructure evolution of a 904 L super austenitic stainless steel

In this work, two typical deformation processes were conducted on a 904 L super austenitic stainless steel to investigate its hot deformation behavior. Two regions with distinct effective strains were selected on identical cross section to examine the microstructural features, including substructures in the deformed matrix and dynamically recrystallized grains. The flow stress curves generally reflect the physical events that occurred at low strain range. When inhomogeneous microstructure and external factors such as friction become more remarkable at high strain level, some metallurgical events (e.g., partial dynamic recrystallization) are hard to be deduced from the flow curves. Meanwhile, strain dependent friction correction on the flow curves does not completely eliminate an obvious abnormal increase in flow stress, especially for the process with the deformation condition of 900 ℃ - 1 s−1. Based on the crystallographic analysis on the barreling zone of the deformed samples, it can be concluded that the strain-induced sub-boundaries that formed in the deformed matrix play a vital role in restricting the material flow behavior because these dense boundaries have a Hall-Petch strengthening effect. This is an intrinsic microstructure mechanism to explain the reason that the flow stress increases abnormally at large strains in the absence of dynamic recrystallization. In addition, the formation of twin boundaries at different deformation conditions are also discussed.

Probing the Respective Strengthening Mechanism of High-entropy (CoCrFeNi/CoCrFeNiMn) and Single-principle-element (Cu-4Al) Alloys

The strengthening mechanism of high-entropy alloys (CoCrFeNi/CoCrFeNiMn) is investigated and compared with a single-principle-element alloy (Cu-4Al) with similar stacking fault energy. Hall-Petch effect dominates the strain hardening of both alloys during progressive grain refinement to the ultrafine regime. Moreover, the high density of Lomer-Cottrell locks offers unique and extra hardening to ultrafine-grained high-entropy alloys.

Atomistic insights into the synergistic effect of nanotwins and nano-precipitates on the mechanical behavior of superalloys

As one of the typical nanostructures, nanotwins (NTs) have been utilized to evade the trade-off between strength and ductility, which is also applicable to improve the mechanical properties of superalloys. However, the optimization capability of mechanical properties by tailoring NTs has encountered bottleneck for the reasons such as inverse Hall-Petch effect and anisotropic effect. Based on the experimental observation of a special distribution pattern of NTs and nano-precipitates (NPs) in superalloys, that is, NPs are located at the twin boundaries (TBs), our work aims to study the distinctive synergistic deformation mechanism between NTs and NPs, which could become a new microstructure design strategy to optimize the mechanical properties of superalloys. Specifically, molecular dynamic (MD) method was employed to unveil the synergistic deformation mechanism of NTs and NPs in a model Ni-based superalloy. As expected, the introduction of NPs onto TBs can inhibit dislocation motion along or parallel to TBs, despite the softening deformation mode of NTs is activated. Moreover, the existence of NPs onto TBs can greatly improve the strengthening efficiency of NTs by impeding twin thickening/thinning. On the other hand, both phase boundaries and NPs interior have obstructive effect on dislocation motion, which could also be beneficial for material strengthening. More interestingly, anti-phase boundary (APB) structure will form along with the dislocations cutting through NPs. Subsequently, the APB structure can act as channels for dislocation slip and dislocation nucleation site induced by a kind of TB confinement effect, which may effectively accommodate plastic deformation. Our research outcomes could be utilized to facilitate the development of high-performance superalloys via rational collaborative design of NTs and NPs.

Developing a steady state wear equation for AA7050 hybrid composites/steel interface at elevated temperature

ABSTRACT In this research work, an attempt was made to reinforce AA7050/5Gr composites with multi-walled carbon nanotube (MWCNT) of varying weight percentages processed through stir casting route. SEM with EDS mapping revealed that the particles were uniformly distributed over the composites. Hardness reduces with increasing MWCNT weight percentage owing to the inverse hall petch effect and increment in void content. A third-body abrasion, which happens when the CNT in the aluminium matrix material detaches from the surface and erodes material from the composites pin as well as the counter face, causes the wear resistance to rise with the addition of CNT particles. A mechanically mixed layer, which avoids direct metal-to-metal contact and thus increases wear resistance, was created at the abraded surface and at high temperature, where the reduction of wear rate was due to the development of oxide protective layer. A steady-state wear equation for the contacting surface at high temperature (R = 1/Y √(ln W/2X)) for AA7050 hybrid composites–steel interface was developed. The enhancement in wear resistance was directly proportional to the proportion of ferrous content present on the surface, which was confirmed on the elemental analysis. Pock marks, micropits, craters and cracks were the features observed on the worn surface morphology, whereas delamination and plasticisation were the observed modes of wear mechanism.

Effect of machining processes on the quenching and tempering surface layer of ultra-high strength steel

The initial characteristics of the surface layer following the quenching and tempering treatment of ultra-high-strength steel play a significant role in determining the subsequent precision machining. This study focus on investigating the influence of machining processes on the quenching and tempering surface layer. The machining processes affect both the oxidation of the quenching and tempering treatment and the development of a distinct preferred grain orientation. Gradual diminishment of surface abrasions leads to the transformation of the needle-like oxidation pattern into a layered oxidation structure. The preferred orientation of the grains prevents the grains from shear sliding, thereby enhancing the Taylor effect. Formation mechanisms of the microhardness and residual stress of the quenching and tempering surface layer induced by machining processes were also discussed and completely revealed. The microhardness is mainly attributed to the dynamic Hall-Petch effect, while plastic strain, dislocation energy storage, and phase transformation contribute to the residual stress changes.

Mechanical behaviors and microstructure evolution of Ni[sbnd]W medium heavy alloy at various strain rates under uniaxial tension

In this study, a novel medium-heavy alloy (MHA) of 56Ni-38 W-5Co-1Ta was prepared using conventional casting and forging methods. This novel NiW alloy exhibits a unique combination of medium density, high strength and ductility under quasi-static loading conditions. In this study, the dynamic mechanical behaviors and deformation mechanisms of this novel NiW alloy were systematically investigated. The NiW alloy exhibited that yield strength increase form ∼1.6 GPa (1 × 10−3 s−1) to ∼2.0 GPa (3 × 103 s−1) owing to the formation and accumulation of nano-sized deformation twinning at dynamic loading condition. Although twin boundaries are attributed to their higher strength owing to the Hall-Petch effect, nano-sized cracks also prefer to nucleate at twin boundaries because of the strong interaction between dislocations and twins. This strong interaction introduces local stress concentration and crack nucleation at deformed zone and finally lead to the decreasing of uniform elongation form ∼0.31 (1 × 10−3 s−1) to ∼0.18 (1–3 × 103 s−1). The major deformation mechanism exhibited a clear transition from dislocation slip to deformation twinning in the NiW alloys under dynamic loading. Our results provide a comprehensive picture of how the deformation modes govern the mechanical behavior and failure of NiW MHA at high strain rates.

Influence of deformation substructure on the strain compatibility of ferrite and bainite in a commercial pipeline steel

The strain instability due to hardening of the soft phase is a key factor in premature failure of pipeline steels after work hardening. In this work, we reveal the hardening mechanism of ferrite is actually the strengthening effect of deformation substructures on the flow stress, where the strengthening contribution by the low angle grain boundaries (LAGBs) is the main stress enhancement way. It is able to subdivide the ferrite into many sub-grain structures through dynamic evolution between geometrically necessary dislocations (GNDs), LAGBs and high angle grain boundaries (HAGBs) during work hardening. These subgrains have independent orientations and can be further subdivided, thus causing the Hall-Petch strengthening effect. Based on the hardening mechanism of ferrite, the representative volume element model with different levels of work hardening is developed. As the level of work hardening increases, the strain compatibility is gradually reduced between ferrite and bainite. The strain localization factor is increased from 0.023 to 0.061, the plastic deformation difference between the two phases is increased from 6.71% to 10.93%, and strain partitioning coefficient is reduced from 7.11 to 3.07. This work will contribute to better understand the substructure strengthening of dual-phase materials and provide a new idea for the protection of work-hardened metals.

Superior tensile properties and unique damage-fracture characteristics of Ti-2.5Cu α-titanium alloy at liquid-nitrogen temperature

α-titanium alloys are extensively applied under cryogenic environment and thereby their cryogenic mechanical properties and service failures deserve to be deeply studied. Here, tensile behaviors and damage-fracture characteristics of Ti-2.5Cu α-titanium alloy were systematically investigated at liquid-nitrogen temperature (LT) plus room temperature (RT) for comparison. It is found that the LT samples possess superior strength and ductility concurrently. Both yield strength (σy) and ultimate tensile strength (σb) improve more than 70%, whilst total elongation at fracture (A) adds more than 33% in comparison with the RT counterparts. Meanwhile, the LT samples are stretched mainly by uniform strain without noticeable necking. Fracture analysis indicates that being different from typical cup-and-cone fracture surface in the RT samples, the ‘radial’ fracture surface appears in the LT samples. Such specific fracture surface is constructed by two characteristic morphologies of crack-initiation zone at sample surface and the ensuing crack-propagation zone. Furthermore, it is seen that a large number of micro-voids are dispersed underneath fracture surface in the RT samples, whereas the number of micro-voids is sharply reduced at LT. Nevertheless, Vickers hardness at the position is always much higher in the LT samples. These novel mechanical properties and damage-fracture characteristics in the LT samples are closely associated with the prevalent deformation twinning in microstructure. Deformation twinning itself and plentiful twins-induced dynamic Hall-Petch effect steadily accommodate plastic deformation, contributing to the simultaneous enhancement of strength and ductility. This process also results in high stress state in samples, increasing the sensitivity of surface cracking. Hence, the ‘radial’ fracture morphology is finally formed. These findings enrich our fundamental understanding on deformation-damage-fracture process of α-titanium alloys, and also provide implicit guidance for the design of titanium alloys with high performance.

Molecular dynamics simulation of the effect of supersonic fine particle bombardment on the mechanical behaviour of γ-TiAl alloy: The effect of grain size

Due to the nanoscale inverse Hall-Petch (H-P) effect, the grain size exerts a significant influence on the mechanical behaviour of the material. The impact of supersonic fine particle bombardment (SFPB) on the mechanical response of γ-TiAl alloy with varying grain sizes was investigated using molecular dynamics simulations. The dislocation density and stress state of the material surface were analyzed before and after SFPB treatment. The results indicate that the degree of grain refinement in the matrix varies depending on the grain size following SFPB treatment. In contrast, the critical average grain size for observing the H-P effect is determined to be 9.96 nm. The hardness of the material increases as the average grain size decreases, but it decreases below the critical average grain size. Moreover, monocrystalline samples exhibit the highest hardness and demonstrate greater sensitivity to elastic recovery in both depth and width directions compared to polycrystalline samples. The variation in grain size following SFPB impact influences the distribution of von Mises stress and hydrostatic stress. The present study investigates the grain refinement and mechanical behaviour of polycrystalline γ-TiAl alloys at the atomic scale, thereby offering valuable insights into the SFPB process.

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.

Introducing local chemical ordering to trigger a planar-slip-initiated strain-hardening mechanism in high entropy alloys

This study demonstrates that we can break the strength-ductility paradox in face-centered cubic (FCC) high-entropy alloys (HEAs) by introducing local chemical ordering. Employing high-resolution transmission electron microscopy, atom probe tomography, and electron-chanelling contrast imaging in CoFeNi and CoCrFeNi HEAs with (Al/Ti) additions, we report a planar-slip-induced strain-hardening mechanism that operates at significantly higher stresses compared to the well-known transformation induced plasticity (TRIP) and twinning induced plasticity (TWIP) mechanisms. Our results provide clear evidence that the introduction of chemical ordering in HEAs promotes localized slip along multiple {111} planes. Importantly, the interactions between planar slip activities on non-parallel {111} planes triggers a dynamic Hall-Petch like effect that continually refines the slip length. This is in contrast to hexagonal closed packed (HCP) alloys, where such glide plane softening typically causes catastrophic failure. Consequently, this newly identified mechanism increases the yield-strength while maintaining a better combination of strength and ductility in our FCC-based HEAs. These findings, together with our previous results [33,34], establish a compelling alloy design paradigm for the discovery of FCC-based HEAs that can circumvent the strength-ductility paradox.

Analytical flow equation for irradiated low-alloy steels established by multiscale modeling

In this paper, we show how results of multiscale modeling can be condensed to establish a simple analytical flow equation for irradiated low-alloy steels. The flow equation accounts for temperature, strain rate, the initial and irradiation microstructure. Starting from a complete set of constitutive equations describing crystal plasticity of irradiated ferritique steels, simple assumptions and approximations are used to integrate the equations over the homogenized polycrystal. The final flow equation incorporates the lattice friction resistance, the Hall-Petch effect, the forest strengthening and irradiation hardening. Every component is established by multiscale modeling at lower scales. Irradiation hardening is attributed to solute clusters. Their size and density are determined in experiment, their shear resistance computed by atomistic simulations and their contribution to the flow stress assessed using dislocation dynamics simulations. The formation of solute clusters is found to increase the flow stress and the strain hardening modulus. Irradiation hardening decreases with temperature and with the yield stress of the unirradiated material. Predictions of the tensile curves and irradiation hardening are compared with many experimental results. A special section is dedicated to the interpretation of irradiation hardening measured in a surveillance program.

Local measurement of geometrically necessary dislocation densities and their strengthening effect in ultra-high deformed pearlite

The strength of pearlitic wires can be increased by cold-drawing to a world record level for bulk ductile materials of 7 GPa. The underlying strengthening mechanisms are not fully understood, as the application of usual characterization is challenging because of the small grain sizes and the high degree of deformation. Here we demonstrate that the microstructure of the wires can be directly probed by nano-beam diffraction (NBD) orientation mapping in a transmission electron microscope even after a drawing strain of 6.52. We observe a highly fragmented microstructure with a high density of low-angle grain boundaries (LAGBs) within the ferrite lamella. That makes it difficult to define grain sizes in the ordinary way. We thus calculate an equivalent grain size based on the density of high-angle grain boundaries (HAGBs) per measurement area and an average density of geometrically necessary dislocations (GNDs) calculated from all local misorientation gradients below 15° misorientation. Total strengths calculated from a summed Hall-Petch and Taylor effect of the latter values as well as carbon solid solution hardening are in good agreement with the strengths as measured by tensile tests. Our results show that the GNDs are similarly important as HAGBs in terms of their contributions to the total strength. On this basis, the experimental evidence of the strengthening mechanism with emphasis on GNDs, particularly in ultra-high deformed materials is highlighted. The present results also validate the application of NBD to assessing mechanical properties of other ultra-high deformed materials where mechanical tests often are not feasible.

Enhanced strength in Co-free Ni47.5-xFe25Cr25AlxTi2.5 high entropy alloys via introducing dual precipitates

Synergistic strengthening mechanisms (e.g. solid solution strengthening, grain/twin boundary strengthening, dislocation strengthening, and precipitation strengthening) have been shown to effectively achieve a balance between strength and ductility of mechanical properties of metal materials. In this study, Co-free AlxNi47.5-xFe25Cr25Ti2.5 high entropy alloys (HEAs) mainly strengthened by grain boundary/twin-precipitation were successfully prepared by combining rolling and annealing. The phase-field method was used to demonstrate that twins enhance the Hall-Petch effect by introducing additional twin boundaries. Only a small amount of lamellar L12 phase is precipitated in the aged Al2.5 HEA. The tensile strength is 1086 MPa and the elongation is 30.8%. With the increase of Al content, the volume fraction of L12 phase in the alloy increases, and the bulk B2 phase is precipitated. When the Al content increases to 7.5 at. %, the strength of the alloy increases to 1757 MPa, but the plasticity is catastrophically reduced to only 3.4%. The excellent strength of aged Al7.5 HEA is mainly due to the good combination of grain/twin boundary strengthening and precipitation strengthening.

The evolution of dual-phase core–shell structure and mechanical properties induced by Co addition in as-cast high-entropy intermetallic

In this work, three as-cast L12-type HEIs with different content of Co element were carefully examined combined with TEM, SEM and XRD technologies. The main matrix of three alloys was L12 ordered phase, and Si,Ti-rich grain-boundary precipitate phase generated with the addition of Co. In Co1 alloy, distinct dual-phase core–shell structure was found within grain due to the precipitation of extra FCC disordered secondary phase, which leads to a better strength-plasticity combination (compressive strength of 3441 ± 50 MPa, and fracture strain of 46.0 ± 1.5%) than Co0 and Co0.5 alloy at room temperature. With the increase of temperature, particular anomalous yield effect was discovered in Co1 alloy. It is clear that SFs became main deformation substructure in Co1 alloy at elevated temperature, and the interaction between non-coplanar SFs motivated the generation of L-C Locks, which assists the K-W Locks to pin dislocations movement and enhance the yield strength from room temperature to about 650 ℃. In addition, the interaction between SFs resulted in the formation of nano-spaced SF network, which contributes to the dynamic Hall-Petch effect. Finally, excellent high-temperature yield strength was achieved in as-cast Co1 alloy, which is higher than room-temperature yield strength until 950 ℃.

Dynamic and Postdynamic Recrystallization Behavior of GWZ Magnesium Alloy Under Double‐Hit Hot Compression

Herein, dynamic and postdynamic recrystallization behaviors of GWZ magnesium are investigated. Toward this end, the single‐hit and double‐hit hot compression tests are conducted under strain rate of 0.001 s−1 at 400 °C. The prestrains of 0.1 and 0.5 are considered to investigate the effect of interpass time (5–300 s) on the compressive strength level. At the low strain level of 0.1, the contribution of Hall–Petch effect is considerable due to the occurrence of static recrystallization. In addition, the rare earth texture component is eliminated during interpass annealing. This causes increasing the strength of the material during second pass of hot compression. In contrast, at higher imposed strain, the strength level decreases with increasing the interpass time of annealing. The high amount of strain is completely consumed and the remaining stored energy is not high enough to trigger the occurrence of static recrystallization. The occurrence of metadynamic recrystallization and subsequent growth are characterized. In addition, the texture does not change in respect of the intensity or numbers/types of components. Accordingly, the observed decreasing trend of the strength is justified relying on the occurrence grain growth.

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.

Strengthening mechanism of NiCoAl alloy induced by nanotwin under Hall-Petch effect

Grain boundary plasticity dominates the mechanical behavior of materials, and the introduction of intragranular nanotwins can achieve coordination between strength and ductility in metals and alloys. In this effort, nanotwins with different volume contents are introduced in NiCoAl alloys to explore the strengthening mechanism under the Hall-Petch effect from perspectives such as grain boundary energy, grain rotation angle, and grain coarsening. The results indicate that the introduction of nanotwins with critical volume fraction effectively inhibits grain boundary migration and grain combination, and improves the strength of the alloy by reducing grain boundary energy and hindering grain rotation. Meanwhile, it leads to a change in the strengthening mechanism from the combined effects of dislocation movement, grain boundary migration and deformation twinning to the dual strengthening of local movement of dislocations within the grain and Lomer-Cottrell locks. The latter hinders the slip of local dislocations within the grain and improves the mechanical property. In addition, based on the average grain size and atomic mean square displacement after high-temperature annealing, the stability mechanism of nanotwins in the alloy can obtain an insight from the aspect of atomic motion. This article explains the Hall-Petch strengthening mechanism from a more detailed and interesting point and provides insights into the strengthening mechanism of nanotwins under the Hall-Petch effect.