Hall-Petch Behavior Research Articles

Assessing the fracture toughness in Tungsten-based nanocomposites: A micro-mechanical approach

Nanocrystalline tungsten-copper composites can favorably combine the outstanding material properties of both elements. This work investigates tungsten-copper composites fabricated from elemental powders with 80 wt.% tungsten and either copper or α-brass containing 20 wt.% zinc, respectively. Moreover, high-pressure torsion is used to compact the powders, strengthen the resulting composite by grain refinement, and tailor the grain-size in the nanocrystalline regime by varying the deformation temperature between RT, 400°C and 550°C, resulting in grain-sizes of 9 nm 14 nm and 28nm, respectively. Hardness measurements revealed a transition from normal to inverse Hall-Petch behavior for grain-sizes below 11 nm. To examine the fracture properties, micro-cantilever bending beams with a cross-section of 10x10µm2 were fabricated. Evaluation of these experiments indicated a fracture toughness of 3 MPam. The slight decrease of fracture toughness between a grain-size of 9 nm to 14 nm indicates a reduction of the grain boundary cohesion strength. The grain-size increase to 28nm reversed the trend in fracture toughness and raised it to 3.4MPam, which points to activating additional deformation mechanisms, such as dislocation-accumulation and twinning. Additionally, alloying with zinc raised the composites strength and retained the composites fracture toughness, benefiting the damage tolerance.

Atomic insight into nanoindentation response of nanotwinned FeCoCrNiCu high entropy alloys

FeCoCrNiCu high-entropy alloys (HEAs) exhibit extraordinary mechanical properties and have the capability to withstand extreme temperatures and pressures. Their exceptional attributes make them suitable for diverse applications, from aerospace to chemical industry. We employ atomic-scale simulations to explore the effects of twinning boundary and twinning thickness on the mechanical behavior of nanotwinned FeCoCrNiCu during nanoindentation. The findings suggest that as the twinning thickness decreases within the range of 19.3–28.9 Å, both twinning partial slips (TPSs) and horizontal TPSs gradually become dominant in governing the plastic behaviors of the nanotwinned FeCoCrNiCu, thereby resulting in an inverse Hall–Petch effect. Remarkably, when the twinning thickness is compressed below 19.3 Å, a shift in the plastic deformation mechanism emerges, triggering the conventional Hall–Petch relation. The observed Hall–Petch behavior in nanotwinned FeCoCrNiCu is attributed to the strengthening effect imparted by the twinning boundaries. Consequently, the twinning boundary play an instrumental role in steering the plastic deformation mechanism of the nanotwinned FeCoCrNiCu when the twinning thickness descends beneath 19.3 Å. This study contributes significant insights towards the design of next-generation high-performance HEAs, underpinning their potential industrial utilization.

Tensile deformation of fine-grained Mg at 4K, 78K and 298K

The impact of grain size, ranging from 0.9 μm to 9 μm, on the mechanical properties of commercially pure Mg is investigated at temperatures of 4K, 78K, and 298K. The mechanisms governing plastic flow are influenced by both grain size and temperature. At 4K and 78K, dominant deformation modes in Mg involve dislocation glide and extension twinning, regardless of grain size. The interactions between basal and non-basal dislocations and dislocations with grain boundaries promote an unusually high rate of work hardening in the plastic regime, leading to premature failure. The yield stress follows the Hall-Petch relationship σy∼k/d, with the slope k increasing with decreasing temperature. At 298K, in addition to dislocation glide and twinning, grain boundary sliding (GBS) becomes significant in samples with grain sizes below 3 μm, considerably enhancing the material’s deformability. GBS activation provides an additional recovery mechanism for dislocations accumulating at grain boundaries, facilitating their absorption during sliding and rotation. Analysis of σΘ relationship suggests that the basal slip is the dominant dislocation mode in Mg at 298K. Decreasing grain size suppresses dislocation activity and twinning and increases GBS, resulting in lower Θ and σΘ values. Suppressing conventional deformation modes coupled with enhanced GBS yields stress softening, breaking down the Hall-Petch relationship in Mg below 3 μm grain size, leading to an inverse Hall-Petch behaviour. The work reports new data on the strength, ductility, work hardening and fracture behaviour, and their variations with Mg grain size across different temperature regimes.

Hardness and fracture toughness enhancement in transition metal diboride multilayer films with structural variations

The simultaneous enhancement of hardness (H) and fracture toughness (KIC) through the formation of superlattice structures challenges the conventional belief that these quantities are mutually exclusive. Here, this approach has been applied to the transition metal diborides, whose inherent brittleness severely restricts their application potential. The mechanical properties of TiB2/TaB2 systems as a function of bi-layer period Λ are investigated, combining theoretical and experimental approaches. Density Functional Theory is used to investigate the structural stability and mechanical properties of stoichiometric hexagonal TiB2/TaB2 superlattices for Λ = 3.9 – 11.9 nm. The calculations predict the highest H = 38 GPa and KIC (100) of 3.3 MPa.m1/2 at the value of Λ = 5.2 nm. Motivated by the theoretical results, multilayer films with Λ = 4–40 nm were prepared by direct current magnetron sputtering. Due to the sputtering effects, the deposited diboride films differ significantly from the view of stoichiometry and structure. A detailed structure investigation reveals TiB2/TaB2 in form of superlattices exhibiting coherent interfaces for Λ = 4 nm. For higher Λ, parts of TaB2 layers transform from the crystalline to the disordered phase. These transformations are reflected in the mechanical properties as measured by nanoindentation and micromechanical bending tests. The evolution of hardness follows Hall-Petch behavior, reaching a maximum of 42 GPa at Λ = 6 nm. Enhancing fracture toughness involves more complex mechanisms resulting in two KIC maxima: 3.8 MPa.m1/2 at Λ = 6 nm and 3.7 MPa.m1/2 at Λ = 40 nm.

Reversing inverse Hall-Petch and direct computation of Hall-Petch coefficients

A 2D bicrystal atomistic model of dislocation transmission through a Σ11<101>{131} symmetric-tilt grain boundary reveals details of Hall-Petch breakdown in the single dislocation regime in Al, Ni, and Cu. Partly based on a previous study [1], this research determines the stress required for a single dislocation to be transmitted through the Σ11 boundary and finds that single dislocation transmission typically deviates from Hall-Petch behavior because the leading partial dislocation becomes trapped in the boundary and emits glissile grain boundary disconnections that cause boundary sliding deformation at stresses well below boundary transmission stresses. Thus, mechanisms of inverse Hall-Petch, namely grain boundary shear and sliding, are shown to operate in lieu of grain boundary transmission in the single dislocation regime. However, by controlling the applied stresses, inverse Hall-Petch can be reversed and typical Hall-Petch grain boundary transmission regained. This, in turn, allows the direct computation of Hall-Petch coefficients. A second dislocation on the same slip plane preserves typical Hall-Petch behavior for Al and Ni and does not lead to boundary sliding events, thus implying a critical grain size for Hall-Petch breakdown based on the pileup model.

Breaks in Hall-Petch Relationship in Magnesium

Magnesium and its alloys display a non-usual relationship between flow stress and grain size at room temperature. Breaks in the Hall-Petch relationship have been reported in the literature. Inverse Hall-Petch behavior in which flow stress reduces with grain size decreasing has also been reported in pure magnesium and magnesium alloys with ultrafine and nanocrystalline structures. The present overview discusses these effects in terms of controlling deformation mechanisms. The distinct strength observed in pure magnesium and magnesium alloys with ultrafine grained structure is also discussed. It is shown that experimental data for fine and ultrafine grained magnesium alloys agree with a model suggested recently based on the mechanism of grain boundary sliding. It is also exhibited that the stability of the grain structure might control the strength of ultrafine grained samples.

Mobile dislocation mediated Hall-Petch and inverse Hall-Petch behaviors in nanocrystalline Al-doped boron carbide

The Hall-Petch and inverse Hall-Petch behaviors in nanocrystalline ceramics are not well understood because dislocation activities, which are important in metals, are usually limited in these materials. In this study, we use molecular dynamics simulations with a machine-learning force field to investigate the shear deformation behaviors of nanocrystalline Al-doped boron carbide (n-B12-CAlC) as the grain size varies. We find a transition from the Hall-Petch to inverse Hall-Petch behavior in n-B12-CAlC when the grain size reaches its critical value of 6.09 nm, with a maximum shear strength of 14.93 GPa. Interestingly, mobile dislocation nucleated from grain boundaries (GBs) is activated in n-B12-CAlC due to the breakage of weakened C-Al chain bonds, which plays a significant role in its Hall-Petch behaviors. As the grain size decreases, the increasing GB regions homogenize the shear stress, which suppresses dislocation nucleation from GBs and strengthens the material, as observed in the conventional Hall-Petch relationship. However, with a further decrease in the grain size (< ∼ 6 nm), the increasing GB regions provide more favorable sites and a higher possibility for dislocation nucleation, reducing the shear strength and triggering a transition into the inverse Hall-Petch behavior. These findings shed light on deformation behaviors and mechanisms of nanocrystalline ceramics and provide an explanation for the transition from Hall-Petch to inverse Hall-Petch behaviors.

Effect of constrained inter-granular regions on the inverse Hall-petch phenomena

The paper makes an effort to lay out a critical assessment of grain size and its role in limiting strength gains in stable nanocrystalline (NC) metals. In particular, this study uses copper-tantalum binary alloys, in which the predominate mechanisms of grain boundary sliding and rotation are shut down, to decipher the breakdown of classical Hall-Petch behavior and its underlining mechanisms. Through varying grain sizes and tantalum concentrations, the results show Cu–Ta's strength exceeds the traditional strength limits anticipated when strictly applying smaller grain size translates to greater strength than that from the Hall-Petch relationship for NC Cu. Within this work, we also highlight the consistent linear behavior holding up to the point of losing full crystallinity given this alloy's ability to constrain failures occurring within other non-stabilized NC systems.

Twin thickness-dependent tensile deformation mechanism on strengthening-softening of Si nanowires

Twin thickness-dependent deformation and the transition from strengthening to softening in twinned silicon nanowires are investigated using molecular dynamics simulations with cylindrical and hexagonal cross sections. The results show that the transition from strengthening to softening occurs at critical twin thicknesses of 8.1 nm (11.0 TB s) with cylindrical cross section and 11.0 nm (8 TBs) with hexagonal cross section with decreasing twin thickness, and that the strongest twin thickness originates from a transition in the initial plasticity mechanism from full dislocation nucleation and interaction with the TBs to partial dislocation nucleation and gliding parallel to the TBs. Moreover, it is found that the relationship between peak stress and twin thickness can be divided into two regions. Several full and partial dislocations are formed in the regions with strengthening twin thickness range. The accumulation and pile-up of these dislocations and their interaction with the TBs at high density cause the Hall-Petch strengthening behavior. In contrast, few full and partial dislocations are formed with softening twin thickness range. These dislocations are nucleated and propagate parallel to the TBs, resulting in TB migration that causes inverse Hall-Petch softening behavior. Our simulation results provide sufficient insight into the mechanical behavior of twinned silicon nanowires with cylindrical and hexagonal cross sections. The study will be helpful to the further understanding of CTB-related mechanical behaviors of non-metallic materials and non-metallic system.

A regime beyond the Hall–Petch and inverse-Hall–Petch regimes in ultrafine-grained solids

The strength of polycrystal increases as the grain diameter l decreases, i.e. the Hall–Petch behaviour. This trend reverses at about 3 < l < 15 nm, i.e. the inverse-Hall–Petch behaviour. How the grain size affects material’s strength at l < 3 nm (~12 particles) remains unclear. Here our simulations use mixtures of soft and hard particles so that compression can continuously reduce l to merely a few particles, resulting in ultrafine-grained solids termed as glass-crystal composites. Beyond the conventional Hall–Petch strengthening and inverse-Hall–Petch softening, we observe a power-law strengthening at l < 14 particles as a result of the blockage of shear-banding by crystalline grains. Amorphous and crystalline regions accommodate shear strains via bond-breaking and collective rotation, respectively. Moreover, a polycrystal–glass transition occurs at l = 14 particles featured with peaks of various quantities, which deepens the understanding on softening–strengthening transition.

An inverse Hall-Petch behavior and improving toughness in translucent nanocrystalline high-entropy zirconate ceramic

Short-range order is a new strengthening effect that can significantly affect the mechanical properties of high-entropy materials. Furthermore, simulation results show that this strengthening effect at a quasi-atomic scale can suppress the grain size softening, leading to the disappearance of inverse Hall-Petch behavior in nanocrystalline high-entropy materials. In this work, the evident inverse Hall-Petch behavior is confirmed in the translucent nanocrystalline high-entropy ceramic (HEC) with an average grain size below 10 nm, fabricated by a high-pressure low-temperature sintering technique. Besides, the as-obtained nanocrystalline HEC also shows an improving fracture toughness compared with the corresponding coarse-crystalline HEC.

Inhibiting the inverse Hall-Petch behavior in CoCuFeNiPd high-entropy alloys with short-range ordering and grain boundary segregation

The mechanical implications of short-range ordering (SRO) and grain boundary (GB) segregation in the inverse Hall-Petch behavior of nanocrystalline CoCuFeNiPd high-entropy alloys (HEAs) were studied using hybrid Monte Carlo (MC)/Molecular Dynamics (MD) simulations. Results show that the presences of SRO and GB segregation inhibit the grain size softening (inverse Hall-Petch relation), leading to grain-size independence of the high flow stress. We find that the dislocation nucleation at triple junctions is suppressed by the SRO due to the increased stacking fault energy, which attenuates the dislocation activities. Furthermore, the strain localization at GBs is intensified by the GB segregation due to the increased GB energy, which facilitates the GB activities and glass-like deformation. The GB-governed plasticity associated with glass-like deformation leads to suppression of the inverse Hall-Petch effect. These findings may provide useful strategies for the design of high-performance HEAs by tuning the GB composition and SRO structure.

Temperature dependent anisotropic mechanical behavior of TiAl based alloys

γ-based titanium aluminides exhibit remarkable mechanical properties at high temperatures and are deployed in jet engines. The microstructure of these alloys, consisting of alternating plates of the γ (TiAl) and α2 (Ti3Al) phases, exhibits highly anisotropic mechanical behavior. However, deep understanding of the associated micromechanics is lacking. The effect of differential strength of the slip/twin systems, structural length scales and temperature in determining the homogeneity of deformation at the intercolony and intracolony level has not been well understood. Hence, we establish structure–property relationships, under uniaxial compression and uniaxial tension, by crystal plasticity finite element techniques. The deviation from Hall–Petch behavior and the temperature-dependent yield stress anomaly are rationalized and included in the model. Our results reveal a complex interplay between lamellar orientation, structural length scale, temperature, and stress state. Key findings include: (1) Basal slip in the α2 phase can be activated by differential strengthening of slip systems at lamellar interfaces. Basal slip increases the propensity for crack nucleation due to coarse slip bands. (2) There is preferential activation of twinning in the γ phase under tension. These twins can improve ductility by increasing strain hardening. However, they can also promote crack nucleation. (3) Smaller lamellar widths at higher temperatures can improve strain homogeneity between the γ and α2 phases. (4) Yield stress anisotropy exhibited a non-monotonic variation with lamellar size and temperature. (5) Increasing the strength of slip/twin systems through solid solution or precipitation strengthening can improve intracolony deformation homogeneity, reducing crack nucleation. We suggest strategies for alloy and microstructure design to improve damage tolerance in these alloys.

Inhibiting the Inverse Hall-Petch Behavior in CoCuFeNiPd High-Entropy Alloys with Short-Range Ordering and Grain Boundary Segregation

Inhibiting the Inverse Hall-Petch Behavior in CoCuFeNiPd High-Entropy Alloys with Short-Range Ordering and Grain Boundary Segregation

Nanograin size effects on deformation mechanisms and mechanical properties of nickel: A molecular dynamics study

The grain size refinement of metallic materials to the nanometer scale produces interesting properties compared to the coarse-grained counterparts. Their mechanical behavior, however, cannot be explained by the classical deformation mechanisms. Using molecular dynamics simulations, the present work examines the influence of grain size on the deformation mechanisms and mechanical properties of nanocrystalline nickel. Samples with grain sizes from 3.2 to 24.1 nm were created using the Voronoi tessellation method and simulated in tensile and relaxation tests. The yield and ultimate tensile stresses follow an inverse Hall-Petch relationship for grain sizes below ca. 20 nm. For samples within the conventional Hall-Petch regime, no perfect dislocations were observed. Nonetheless, a few extended dislocations were nucleated from triple junctions, suggesting that the suppression of conventional slip mechanism is not uniquely responsible for the inverse Hall-Petch behavior. For samples respecting the inverse Hall-Petch regime, the high number of triple junctions and grain boundaries allowed grain rotation, grain boundary sliding, and diffusion-like behavior that act as competitive deformation mechanisms. For all samples, the atomic configuration analysis showed that Shockley partial dislocations are nucleated at grain boundaries, crossing the grain before being absorbed in opposite grain boundaries, leaving behind stacking faults. Interestingly, the stress relaxation tests showed that the strain rate sensitivity decreases with grain size for a specific grain size range, whereas for grains below approximately 10 nm, the strain rate sensitivity increases as observed experimentally. Repeated stress relaxation tests were also performed to obtain the effective activation volume parameter. However, the expected linear trend in pertinent plots required to obtain this parameter was not found.

Deformation mechanisms in ultrafine-grained metals with an emphasis on the Hall–Petch relationship and strain rate sensitivity

Ultrafine-grained materials display almost no strain hardening, an enhanced strain rate sensitivity and grain boundary offsets during plastic deformation. It is expected that dislocation climb is active in order to enable prompt recovery. The present analysis proposes a deformation mechanism that includes these effects and follows from the mechanism for high temperature grain boundary sliding. This mechanism predicts the relationship between strain rate, flow stress, grain size, temperature and basic material properties such as the Burgers vector modulus, the shear modulus and the grain boundary diffusion coefficient. The model may be used to estimate the final grain size achieved by severe plastic deformation and the strain rate sensitivity. An analysis shows that the predicted behavior agrees with the data from multiple experimental investigations and provides a good estimate of the Hall–Petch slope for different materials which includes breakdown and inverse Hall–Petch behavior under some conditions. The incorporation of a threshold stress provides an opportunity to predict the relationship between flow stress and grain size for a broad range of grain sizes, strain rates and temperatures. An excellent agreement is observed between the predictions of the model and experimental data for Al, Cu, Fe (α), Fe(γ), Mg, Ni, Ti and Zn.

Crystal Plasticity with Micromorphic Regularization in Assessing Scale Dependent Deformation of Polycrystalline Doped Copper Alloys

It is planned that doped copper overpacks will be utilized in the spent nuclear fuel repositories in Finland and in Sweden. The assessment of long-term integrity of the material is a matter of importance. Grain structure variations, segregation and any possible manufacturing defects in microstructure are relevant in terms of susceptibility to creep and damage from the loading evolution imposed by its operating environment. This work focuses on studying the microstructure level length-scale dependent deformation behavior of the material, of particular significance with respect to accumulation of plasticity over the extensive operational period of the overpacks. The reduced micromorphic crystal plasticity model, which is similar to strain gradient models, is used in this investigation. Firstly, the model’s size dependent plasticity effects are evaluated. Secondly, different microstructural aggregates presenting overpack sections are analyzed. Grain size dependent hardening responses, i.e., Hall-Petch like behavior, can be achieved with the enhanced hardening associated with the micromorphic model at polycrystalline level. It was found that the nominally large grain size in the base material of the overpack shows lower strain hardening potential than the fine grained region of the welded microstructure with stronger strain gradient related hardening effects. Size dependent regularization of strain localization networks is indicated as a desired characteristic of the model. The findings can be utilized to provide an improved basis for modeling the viscoplastic deformation behavior of the studied copper alloy and to assess the microstructural origins of any integrity concerns explicitly by way of full field modeling.

Transition between Hall-Petch and inverse Hall-Petch behavior in nanocrystalline silicon carbide

Despite much experimental and simulation effort, the existence of a Hall-Petch to inverse Hall-Petch transition in nanocrystalline ceramics remains elusive. By employing molecular dynamics simulations, we unambiguously reveal a transition from strengthening to softening in the shear deformation of nanocrystalline silicon carbide ceramics as a function of grain size. Results show a well-defined maximum in the shear strength for grain sizes in the range 6.2 to 7.7 nm. Further decrease in grain size leads to diminishing strength, consistent with an inverse Hall-Petch behavior. As grain size is reduced the increasing grain boundary (GB) regions lead to homogenization of shear stresses across the microstructure, allowing for lower local shear stress levels at higher macroscopically applied stresses. This delays shear localization within GB regions, preventing cavitation, nanocracking, and premature failure, and is responsible for the observed Hall-Petch behavior. In contrast, at grain sizes 6.2 nm, the rather compliant nature of the structurally disordered GB regions dominates the mechanical response, reducing the shear strength and triggering a transition into the inverse Hall-Petch behavior. A composite model delineating the transition between Hall-Petch and inverse Hall-Petch behavior is successful at describing the mechanical behavior of nanocrystalline silicon carbide as a function of grain size.

Breakdown of the Hall-Petch relationship in extremely fine nanograined body-centered cubic Mo alloys

Mechanical properties and deformation behavior have been studied in face-centered cubic (fcc) metals with extremely fine grain sizes, even below about 20 nm, but this range is rarely studied in the body-centered cubic (bcc) metals. Here, we study the hardness and deformation behavior of bcc Mo(O) alloys with grain sizes from 120 to 4 nm, covering the range of classical Hall-Petch behavior as well as the regime where that scaling law breaks down, between about 11 and 4 nm. A hardness as high as 17.3 GPa was achieved at the strongest grain size of 11 nm, and the breakdown at smaller grain sizes is associated with a number of changes in behavior: an inflection in activation volume (associated with a change in rate dependence of deformation) and increasing shear localization. At coarser grain sizes this is associated with shear offsets at grain boundaries, pointing to an increasing prevalence of intergranular deformation (by sliding or grain rotation). At finer grain sizes localization is associated with the formation of large shear bands at scales far greater than the grain size. These behaviors are suggestive of a crossover from crystal-like to glass-like deformation behaviors at the finest grain sizes, consistent with the increasing fraction of disordered regions in the structure.

An energy based modeling for the acoustic softening effect on the Hall-Petch behavior of pure titanium in ultrasonic vibration assisted micro-tension

The acoustic softening effect in metals during plastic deformation has been widely investigated in the past decades. However, the mechanism of such an acoustic plasticity remains controversial. As a result, several models were proposed to understand the acoustic softening effect in terms of stress superposition, thermal activation theory, crystal plastic theory and other mechanisms associated with dislocation evolution. In this study, we proposed a mechanism that the athermal dislocation dynamics may heterogeneously change at microstructure level during ultrasonic vibration assisted (UVA) deformation. Specifically, the work required to eject dislocations from grain boundaries may be altered by the acoustic energy absorption difference of a dislocation in the grain interior and one in the grain boundary. As a result, the acoustic softening effect on the Hall-Petch behavior was modeled by incorporating a power function of acoustic energy density into the dislocation ejection work. To validate the developed model, UVA micro-tension tests were conducted on pure titanium specimens. Results showed that the Hall-Petch slope decreased due to ultrasonic vibration, and the ultrasound-induced decrease of the Hall-Petch slope increased with plastic deformation. Note that our model predictions matched well with the experimental results at the lower strains, providing an alternative insight into the acoustic softening effect on the Hall-Petch behavior. Microstructure examinations showed that the superimposed ultrasonic vibration in micro-tension could lead to the retardation of texture evolution, the decreases in kernel average misorientation (KAM) value, low-angle grain boundary (LAGB) fraction and dislocation density in titanium foils, which somewhat supported our model assumptions in terms of the acoustic energy dependent reduction in dislocation density and the enhanced dislocation ejection causing the improvement of plastic compatibility.