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With the development of structural architectures, the demand for metamaterials with multiphysical characteristics has increased. The relationships between different properties, such as mechanical and mass-transport properties for bone scaffolds, are often mutually conflicting. Consequently, the optimization of these properties for metamaterials structured on the micro- to macroscale is challenging. In this study, inspired by the Hall–Petch relation, which indicates how one can independently tailor the strength and mass, we use a diamond configuration to construct microlattice metamaterials with decoupled mechanical and mass-transport properties to cater to artificial bone scaffolds. The elasticity and permeability are synchronously optimized using simple scaling laws. The results of compression experiments and transportation calculations demonstrate the promising performance of microlattices with an aspect ratio of 1 and at least 4 unit cells in the array direction. Furthermore, hierarchical microlattice metamaterials partitioned into spongy and compact zones are designed for bone scaffold applications. The proposed approach provides an innovative framework for developing multi-physics metamaterials for widespread engineering applications. [Display omitted] [ABSTRACT FROM AUTHOR]

Matrix-body PDC bits endure the reactive shear force and impact damage during the rotary cutting of rock formations under downhole, making the bit blades vulnerable to premature breakage. To avoid the blade breakage, the key is to improve the fracture strength (also known as transverse rupture strength, TRS) of the matrix body of PDC bits. This work investigated the effects of size, shape, and type of tungsten carbides on fracture strength. Weibull distribution was adopted to describe the variations in the repeated TRS test results, which proved to be more appropriate than the normal distribution and could be used as an indirect indicator of the quality and performance of the matrix body. The results of this study showed that the median particle size is the predominant factor determining the TRS performance of the matrix body. Small-sized carbide particles deliver higher TRS, indicating that the fracture strength of the matrix body follows the Hall-Petch relation. Based on this finding, the fracture strength can be significantly reinforced to extend the service life of matrix-body PDC bits under harsh downhole conditions, leading to the reduction of trips and dramatic savings. However, the small-sized carbide particles are inherent lack of erosion resistance and accordingly limit their applications. • Fracture strength of the matrix body of PDC drill bits follows the Hall-Petch relation. • Small-sized tungsten carbide particles deliver higher fracture strength. • However, small carbide particles are inherent lack of erosion resistance and accordingly limit their applications. • Weibull distribution is more appropriate than normal distribution to represent strength variations in repeated tests. • The calculated Weibull modulus is a valuable indirect measurement of the infiltration quality and matrix performance. [ABSTRACT FROM AUTHOR]

A new physical model to explain the Hall–Petch relation is proposed. The main assumption is that the Hall-Petch slope (ky), is proportional to the work required to eject dislocations from grain boundaries. The model predicts a traditional Hall–Petch relation down to a grain size of about 5 μm, below which a deviation from linearity is observed. The strengthening peaks in the vicinity of 30 nm, and further grain refinement leads to softening. A semi-empirical equation is developed, which takes into account the effects of grain boundary strain energy. The model is applicable to both equiaxed and non-equiaxed grain structures. [Copyright &y& Elsevier]

It has been shown experimentally that the Hall-Petch relation of nanocrystalline (NC) metal will be broken down when the average grain size (d) is below a critical value, but the mechanism behind this remains to be quantitatively analyzed. In order to capture the subtle evolution of grain boundaries (GBs), we recently developed a novel algorithm by using moving least-squares (MLS) interpolant. Moreover, the phase field model is used to build NC copper with more natural and physical GBs for molecular dynamics (MD) tensile simulation. The results show that the variation of stress at GBs (σ GB) and at grain interiors (σ GI) in the elastic stage are in good agreement with previous study. The σ GB exhibits periodic vibration, while σ GI shows a linear behavior. From the stress distribution, we find that the increased σ GB in one cycle can make the σ GI increase. The microplasticity of GBs occurs when σ GB increases to a peak value, which attenuates the stress concentration and then leads to the decrease of the σ GB. Therefore, the σ GI can be affected by the frequency of vibrated σ GB. The fast Fourier transform (FFT) results show that the dominant frequency for the model with d of 13.8 nm is larger than that for other models, which causes a larger Young's modulus in the model. The GBs and GIs supplement each other during deformation: GBs providing an extra stress to GIs, GIs supplying the space for microplasticity of GBs. Besides, the fraction of deformed GBs and rotated GBs in the model are also large. GB activities are the results of overall microplasticity before σ GB = σ GI and deformation during the plastic stage. The rotated GBs results in the emission of many Shockley partial dislocation (partials) from GBs since they create larger paths for dislocation movement. Thus, many twinning boundaries (TBs) are generated in the model with d of 13.8 nm by partials gliding on the successive plane of adjacent stacking faults (SFs) structures, which plays an important role in work hardening of NC Cu. Image 1 • A novel algorithm is compiled to quantitatively analyze GB activities. • NC Cu with more natural GBs is created by phase field for MD simulation. • GBs providing extra stress to GIs, GIs supplying space for microplasticity of GBs. • Young's modulus can be affected by dominant frequency of the vibrated σ GB. • Reverse Hall-Petch relation of flow-stress strongly depends on GBs activities. [ABSTRACT FROM AUTHOR]

Highlights: [•] Dislocation based continuum plasticity model incorporating Frank–Read sources. [•] Simple representation of densities of curved dislocations with their local geometry. [•] Derived from and validated by discrete dislocation model. [•] Grain aspect ratio dependent Hall–Petch relations in 2-dimensions are derived. [•] Predictions of our formulas agree excellently with discrete dislocation simulations. [ABSTRACT FROM AUTHOR]

Abstract: We have used a high-energy ball mill to prepare single-phased nanocrystalline Fe, Fe90Ni10, Fe85Al4Si11, Ni99Fe1 and Ni90Fe10 powders. We then increased their grain sizes by annealing. We found that a low-temperature anneal (T <0.4 T m) softens the elemental nanocrystalline Fe but hardens both the body-centered cubic iron- and face-centered cubic nickel-based solid solutions, leading in these alloys to an inverse Hall–Petch relationship. We explain this abnormal Hall–Petch effect in terms of solute segregation to the grain boundaries of the nanocrystalline alloys. Our analysis can also explain the inverse Hall–Petch relationship found in previous studies during the thermal anneal of ball-milled nanocrystalline Fe (containing ∼1.5at.% impurities) and electrodeposited nanocrystalline Ni (containing ∼1.0at.% impurities). [Copyright &y& Elsevier]

Understanding the effect of temperature variation on the microstructural evolution is particularly important to refractory high-entropy alloys (RHEAs), given their potential high-temperature applications. Here, we experimentally investigated the grain-growth behavior of the HfNbTaZrTi RHEAs during recrystallization at temperatures from 1,000 to 1,200 °C for varied durations, following cold rolling with a 70% thickness reduction. Following the classical grain-growth kinetics analysis, two activation energies are obtained: 205 kJ/mol between 1,000 and 1,100 °C, and 401 kJ/mol between 1,100 and 1,200 °C, which suggests two mechanisms of grain growth. Moreover, the yield strength – grain size relation was found to be well described by the Hall-Petch relation in the form of σ y = 942 + 270 D − 0.5 . It was revealed that the friction stress, 942 MPa, in the HfNbTaZrTi HEA is higher than that of tungsten alloys, which indicates the high intrinsic stress in the BCC-RHEA. The coefficient, 270 MPa/μm −1/2, is much lower than that in the 316 stainless steel and Al 0.3 CoCrFeNi HEAs, which indicates low grain-boundary strengthening. • HfNbTaTiZr HEA with a 70% cold-rolled reduction was annealed from 1000 from 1200 °C. • Grain-growth exponent and activation energy were obtained by grain-growth kinetic. • Yield strength – grain size relation was described by the Hall-Petch relation. • A high friction stress is found in the HfNbTaZrTi HEA. [ABSTRACT FROM AUTHOR]

Abstract Zirconium carbide (ZrC x) is an important structural material. Its high strength and hardness makes it suitable for application in hard materials and non-oxide type new ceramics. Hence, several researches have been carried out with the aim of understanding its mechanical properties. In this paper, the mechanical properties of ZrC x (0.45 ≤ x ≤ 0.72) were investigated considering the grain size effect. The bending strength as a function of grain size obeyed the Hall–Petch relation. The composition dependence of the strength linearly decreased with decreasing carbon content, followed by saturation at x = 0.6, corresponding to the lowest x value of the ZrC x single phase region. The Young's modulus and hardness monotonically decreased with decreasing carbon content, independently of grain size. The annealing of ZrC 0.45 at 1273 K for 18 ks led to the formation of Zr precipitates, which showed an orientation relationship with the ZrC matrix of (0001) Zr //(111) ZrC. These precipitations formed compressive residual stress in the ZrC phase, resulting in an 80% increase in the bending strength after annealing. Graphical abstract fx1 Highlights • Effect of composition and grain size on mechanical properties of ZrC x investigated. • Bending strength obeyed the Hall–Petch relation. • Young's modulus and hardness were independent of grain size. • Young's modulus and hardness monotonically decreased with decreasing carbon content. • Annealing of ZrC 0.45 formed coherent Zr precipitates, improving bending strength. [ABSTRACT FROM AUTHOR]

This study focuses on the role of pyramidal 〈 c + a 〉 dislocations in the grain refinement mechanism in the Ti-6Al-4V alloy with an initial { 11 2 ¯ 0 } < 10 1 ¯ 0 > rolling texture. A large number of pyramidal 〈 c + a 〉 dislocations were activated in the sample subjected to the severe shot peening process. Two important roles of pyramidal 〈 c + a 〉 dislocations were discovered. First, pyramidal 〈 c + a 〉 slip coordinates the large c -axis strain, thereby achieving generalized plastic flow, especially in nanograins. Second, the unique low-angle grain boundaries (LAGBs) with basal-pyramidal dislocation locks (prismatic 〈 c 〉 and prismatic 〈 c + a 〉 dislocations) were produced for the first time by pyramidal 〈 c + a 〉 interacting with basal 〈 a 〉 dislocations. This unique low-energy boundary greatly enhances the stability of the strain-induced grain boundary and dislocation density (~6.6 × 1015 m −2 in nanograins). The grain refinement process contains three types of subdivision modes: (I) dislocation walls with pyramidal 〈 c + a 〉 dislocations in coarse grains; (II) basal 〈 a 〉 intersecting with prismatic 〈 a 〉 dislocations in coarse grains; and (III) basal 〈 a 〉 intersecting with pyramidal 〈 c + a 〉 dislocations in coarse grains, ultrafine-grains and nanograins. The occurrence of slip modes depends on the initial texture and texture evolution during dynamic recrystallization. Besides, Hall-Petch breakdown at the nanoscale was found and is attributed to the decreasing critical resolved shear stress of pyramidal 〈 c + a 〉 slip at the nanoscale. This study provides a new approach for the design of stable nanostructured hexagonal close-packed metals by the unique LAGBs with basal-pyramidal dislocation locks. Image, graphical abstract [ABSTRACT FROM AUTHOR]

The high texture dependence of a Hall–Petch slope (k) for Mg alloys has been frequently reported. Several important equations used to calculate k have been previously developed, and although they seem to work well for fc c and bcc materials, they often fail to predict the highly texture-dependent k in Mg alloys. A new equation based on the dislocation pile-up model was developed in this study. The validity of this new equation was tested through a comparison of the predicted k values with the experimental values as well as the calculations from older equations. The results indicate that the new equation can achieve an accurate prediction for several previously reported texture effects on k , whereas the k values predicted by the older equations often exhibit a clear deviation. The reasons for this were analyzed and discussed. The strong deformation anisotropy for Mg alloys leads to a complex texture effect on k , including the effects from both external and internal stresses. Both effects are well expressed in the new equation. In contrast, the old equations consider the external stress effect, but do not express well the internal stress effect. In addition, the old equations consider only the predominant deformation mode. However, our results indicate that the activation of a portion of another deformation mode other than the predominant one plays an important role in the k value. In the new equation, all possible deformation modes and their fractions are considered in the calculation. Using the important parameters of the new equation, the mechanisms for several texture effects on k as previously reported were discussed and new understandings were obtained. Image 1 [ABSTRACT FROM AUTHOR]

[Display omitted] • MD is used to study the tensile, and fracture mechanics of NC 2D SiC. • Effects of grain size on the stress–strain profile of the NC-SiC have been investigated. • The NC-SiC encounters a substantial degradation in mechanical properties relative to its single-crystal counterpart. • Fracture strength as a function of grain size can be characterized by the inverse pseudo Hall-Petch relation. • Increasing grain size brings about more elasticity in the structure, albeit at the price of fracture strain. Two-dimensional Silicon Carbide (SiC) has opened the route to a cornucopia of advanced functionalities in the realm of quantum condensed matter. It holds great promise for highly efficient nanoelectronic, optoelectronic, renewable energy, and spintronic applications thanks to the confluence of a wide spectrum of mesmerizing physical properties like a wide direct bandgap with high exciton binding energy, robust spin–orbit-coupling, excellent photoluminescence, suitable mechanical strength, and thermodynamic stability. Nonetheless, it is still a daunting challenge to incorporate SiC in functional systems since extensive analyses of the mechanical properties, and fracture mechanism of nanocrystalline (NC)-SiC is still obscure. In this light, this work is an attempt to report detailed information concerning the room-temperature tensile mechanical properties and fracture phenomena of NC-SiC executing Molecular Dynamics (MD) simulations. In particular, effects of grain size on the stress–strain profile, fracture strength, fracture strain, and Young's modulus of the NC-SiC have been thoroughly investigated. It has been found that the strength as a function of grain size can be characterized by the inverse pseudo Hall-Petch relation. Increasing grain size brings about more elasticity in the structure, albeit at the price of fracture strain. The NC-SiC encounters a substantial degradation in mechanical properties relative to its single-crystal counterpart. Afterward, we performed an exhaustive fracture analysis on two NC-SiC samples of different grain sizes. The single-crystal SiC can endure more tensile strain before rupture compared to that of the NC-SiC. At last, the nanosheet exhibits more immunity to fracture with decreasing grain size. This study would lay the groundwork for NC-SiC to be successfully realized in functional systems as well as serving as a solid roadmap for engineering the mechanical properties of nanocrystalline materials. [ABSTRACT FROM AUTHOR]

• Grain refining increased yield stress by 100 % in the Cr 40 Co 40 Ni 20 alloy. • TRIP effect follows the Hall-Petch relation: σ TRIP = σ TRIP, 0 + k TRIP.d-0.5. • Hall-Petch slope is similar for both yield stress and TRIP effect (k y ≈ k TRIP). • Model correlating applied stress, transformed phase fraction, and FCC grain/crystallite size. A Cr 40 Co 40 Ni 20 (at.%) alloy with different grain/crystallite sizes was analyzed through in-situ synchrotron X-ray diffraction during tensile testing. The FCC starting structure underwent a partial strain-induced transformation to HCP (TRIP effect) and the percent transformed was measured throughout the deformation. The critical stress required to form a certain HCP fraction was shown to follow a Hall-Petch relation (σ TRIP = σ TRIP, 0 + k TRIP d-0.5), with the Hall-Petch slope being approximately the same for yield stress and TRIP effect (k y ≈ k TRIP). Furthermore, this work developed a Hall-Petch-based model that correlates the applied stress, the transformed phase fraction, and the initial FCC grain/crystallite size. It predicts the stress required to form a certain HCP fraction, or the fraction formed when a certain stress is applied, for different grain/crystallite sizes. We also proposed a mechanism to explain the grain/crystallite size dependence of the TRIP effect and discuss how the TRIP effect and its early activation in the Cr 40 Co 40 Ni 20 alloy provide high work-hardening capacity, which improves ductility and toughness. Here, a refined FCC grain size (d = 1.3; c = 0.7 μm) was shown to increase the yield stress by at least 100 % (417 → 834 MPa), compared to a coarser grain material (17; 6.8 μm), while maintaining a high ductility of 41 %. This work contributes to a better understanding of the deformation mechanisms, mainly the strain-induced phase transformation (TRIP), highlighting their impact and importance on mechanical properties. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The present work investigates Ni–nanodiamond and Ni–graphite composites produced by mechanical synthesis and subsequent heat treatments. Processing of nickel–carbon nanocomposites by this powder metallurgy route poses specific challenges, as carbon phases are prone to carbide conversion and amorphization. The processing window for carbide prevention has been established through X-ray diffraction by a systematic variation of the milling parameters. Transmission electron microscopy confirmed the absence of carbide and showed homogeneous particle distributions, as well as intimate bonding between the metallic matrix and the carbon phases. Ring diffraction patterns of chemically extracted carbon phases demonstrated that milled nanodiamond preserved crystallinity, while an essentially amorphous nature could be inferred for milled graphite. Raman spectra confirmed that nanodiamond particles remained largely unaffected by mechanical synthesis, whereas the bands of milled graphite were significantly changed into the typical amorphous carbon fingerprint. The results on the annealed nanocomposites showed that milling with Ni accelerated graphitization of the carbon phases during heat treatments at 973 and 1073K in both composites. At the finer scales, the nanocomposites exhibited a remarkable microhardness enhancement (∼70%) compared with pure nanostructured nickel. The Hall–Petch relation and the Orowan–Ashby equation are used to discuss strengthening mechanisms and the load transfer ability to the reinforcing particles. [Copyright &y& Elsevier]

Abstract: Strengthening by refinement of lamellar thickness was studied at room temperature on dual phase Ti–39.4mol%Al alloy over a wide range of average lamellar thickness λ from 850 to 20 nm. The relation between yield stress σy and λ was examined, paying special attention to the change in lamellar boundary structure. The γ/α2 lamellar boundaries in the alloy are found to be perfectly coherent in thin lamellar structure formed at low aging temperatures. In thick lamellar structure formed at high aging temperatures, misfit dislocations were introduced to relieve the lattice misfit and are found on the lamellar boundaries. Both thin lamellae with coherent boundaries and thick lamellae with dislocated ones are present in a lamellar structure formed at an intermediate aging temperature. The critical thickness of γ lamella for the introduction of misfit dislocations is about 50 nm. The dislocated boundaries render a high resistance to dislocation motion across the boundaries. A Hall–Petch relation holds in the range of λ>170 nm, and the Hall–Petch slope takes a large value corresponding to the high boundary resistance. The coherent boundaries provide a relatively low resistance. Another σy–λ correlation typical of the coherent boundary appears in the range of λ<100 nm. The yield stress saturates to an upper limit of 1 GPa at λ=70 nm. The transition from the property of dislocated boundary to that of coherent boundary proceeds with an increase in the density of the coherent boundaries within the range of λ=170–100 nm. [Copyright &y& Elsevier]

• A novel Peridynamic model is proposed for large-area polycrystalline graphene. • Coupling effect of pre-crack length and grain size on the inverse pesudo Hall-Petch relation is revealed. • Classical Griffith theory is applicable to brittle fracture analysis of graphene. • Fracture analysis of graphene provides guidance on its fragmentation for practical use. Although graphene is believed to be the strongest material, many properties of this material are still worth exploring and discovering, especially the influence of inevitable defects in its preparation on the mechanical and fracture properties which are of high significance. This work provides a new feasible way to study the mechanical and fracture properties of graphene. The novelties of this study are threefold: (1) A novel peridynamic (PD) model is proposed for polycrystalline graphene in which grains of large size exist; (2) The coupling effect of the pre-crack length and the grain size on the inverse pseudo Hall-Petch relation is revealed; (3) The results confirm the applicability of classical Griffith theory in brittle fracture analysis of graphene. Based on the proposed PD model, dependence of the mechanical and fracture properties on the grain size which changes from a few to hundreds of nanometers is investigated in this study. The fracture forms of graphene are consistent with the experimental observations. Based on the Griffith theory, the obtained fracture toughness such as K c (i.e. 3.8 MPa m - 6.3 MPa m) or G c (i.e. 14.0 J/m2 – 40.9 J/m2) is comparable with previously reported theoretical and experimental values, which proves the validity of the proposed PD model. Besides, the fracture toughness can be greatly enhanced by the blunt pre-crack tip. This work presents insights into mechanical failure of graphene and guidance on fragmentation of graphene for its practical use. [Display omitted] [ABSTRACT FROM AUTHOR]

To develop transparent materials with superior mechanical properties, nanocrystalline magnesium aluminate (MgAl 2 O 4) spinel with grain sizes ranging from 3.7 to 80 nm has been synthesized by environmentally controlled pressure assisted sintering. In this study, we investigated the microstructure and grain size dependence of the mechanical properties of nanocrystalline MgAl 2 O 4 by performing transmission electron microscopy, nanoindentation, uniaxial micropillar compression, and micro-cantilever bending. Electron microscopy confirmed that the environmentally controlled pressure assisted sintering technique produces a nearly fully dense grain structure with a porosity of less than 1% in larger grain-sized ceramics and observably pore-free grain structures in the smaller grain-sized ceramics. Mechanical characterization revealed that nanoindentation hardness, compressive fracture strength, and fracture toughness each exhibit distinct grain size dependence. Our experimental results and numerical analyses point to a change in dominant strain accommodating mechanisms from dislocation-based plasticity to shear banding as the grain size is reduced, as previously suggested by the literature. Practical implications of the change in strain accommodation mechanisms manifest as the emergence of indentation size effect, weak grain size dependence of hardness and strength, and a ∼2-fold increase in apparent fracture toughness for the smaller grain-sized ceramics. [Display omitted] [ABSTRACT FROM AUTHOR]

• Presents a fully resolved, three-dimensional computational characterization of the interaction effects between grain size and initial texture strength on the orientation-dependent macroscopic mechanical responses of magnesium alloy. • Offers insights into microstructure-property linkages. • Makes projections of the grain size and texture dependent net plastic anisotropy on the possible ductile failure by porosity evolution. This work systematically investigates the microstructure-property relationship in Mg alloys. Emphasis is placed on understanding, through high resolution crystal plasticity modeling, how grain size and texture collectively impact material strengthening and hardening, net plastic anisotropy, and tension-compression asymmetry. To achieve this, 528 fully three-dimensional finite element calculations are performed, which comprise eleven textures, four grain sizes, six loading orientations, and two uniaxial loading states (tension and compression). The grain size effect follows Hall-Petch relation that depends on both, loading orientation and initial texture. The reduction in extension twinning with grain size refinement is influenced by texture as well. Below a threshold textural strength, grain size refinement leads to an appreciable reduction in the net plastic anisotropy at yield, quantified using Hill anisotropy, and reduced tension-compression asymmetry. Using a micromechanical basis, the effect of grain size and texture on material ductility is predicted to be non-monotonic. The computational predictions serve as synthetic data sets for experimental validation and reduced-order modeling. [ABSTRACT FROM AUTHOR]

The influence of changes in crystallographic texture on the Hall–Petch (H–P) relationship for an Mg alloy was investigated. First, the texture variations were facilitated by changing the uniaxial tensile loading orientation with respect to the normal direction of the rolled Mg plate. With a strong plane texture of the as-received material, the initial dominant deformation mechanisms were systematically varied from the basal slip and prismatic slip to extension twinning, as well as combinations thereof. Second, different grain sizes were produced for each loading orientation through isochronal annealing at various temperatures up to 773 K while closely monitoring grain size and texture distributions. The experimental results are presented for the grain growth kinetics during annealing, changes in yielding behavior as a function of grain size and initial texture, and H–P relationship as a function of the texture. Moreover, the effects of changes in texture and dominant deformation mechanism on H–P parameters – namely, friction stress, σ o , and strength coefficient, k σ – are discussed. Finally, H–P relationships for each individual deformation mode including basal, prismatic and pyramidal slips as well as extension twin are identified. [ABSTRACT FROM AUTHOR]

Abstract: Bulk ultrafine-grained nickel specimens having grain sizes in the range of 0.25–5μm were consolidated by hot isostatic pressing technique. The resulting microstructures were characterized by transmission electron microscopy and X-ray diffraction analysis. Compression tests were carried out at room temperature and at strain rate of 1.6×10−4 s−1. It was found that the measured yield strength does not follow the Hall–Petch law as a consequence of the presence of oxide phase. Therefore, the use of micromechanics based model, which takes into account only the Hall–Petch relationship at grain level for predicting the grain sized effects on mechanical behavior of this kind of materials, is not accurate yet. In this study, a modification made to the generalized self-consistent model was proposed for studying both grain size and oxide phase dependence of ultrafine-grained materials behavior. Because of the novel modification, an optimization procedure with two steps was required to identify the parameters of micromechanical model. An acceptable agreement between experimental and numerical results was achieved. Moreover, the influence of texture on the yield strength and the application of the proposed model to the spark plasma sintering processed materials were also discussed. [Copyright &y& Elsevier]

Three magnesium alloys, AE21, AE42 and LAE442, were prepared by ECAP employing 1–12 passes. The microstructure evolution during ECAP was systematically analyzed by EBSD. The AE21 and AE42 alloys show typical texture after ECAP with grains predominantly oriented with basal planes inclined by ∼55° from processing direction. This texture results from activation of basal slip during ECAP following the route B C . The LAE442 alloy showed different texture formation, which is fully explained by different c / a ratio and activation of non-basal slip. The differences in the microstructure evolution resulted in different performance in mechanical loading. In the present study a complex investigation of mechanical properties is performed using uni-axial tensile and compression deformation tests and also by Vickers indentation that simulates multi-axial deformation. Resulting microhardness evolution was therefore correlated to grain size according to Hall–Petch relation and to the evolution of dislocation density measured by positron annihilation spectroscopy. On the other hand, the yield stress in the tensile and compression uni-axial deformation tests was determined mainly by the texture. It was shown that by tailoring the c / a ratio the typical texture development could be effectively suppressed in magnesium alloys processed by ECAP and in such way the negative effect of texture on strength can be avoided. [ABSTRACT FROM AUTHOR]

Inelastic deformation of a high-strength martensitic steel (P91) is investigated using a strain gradient crystal plasticity model implemented using the finite element method. Voronoi tessellation is used to model the hierarchical structure, prior austenite grain (PAG)/packet/block, of the martensitic steel and the effect of PAG/packet/block size on the macro- and micro-scale mechanical response is analysed numerically. The role of lath interaction and the influence of dislocation type (statistically stored and geometrically necessary dislocations) are investigated. It is found that block size determines the overall mechanical response, consistent with the Hall-Petch relation, while packet and block diameters influence the microplastic strain distribution. A modified Hall-Petch relation is examined which provides a relationship between material flow strength and block diameter (size) which holds for a wide range of initial dislocation densities and block diameters. • Block diameter controls size dependent behaviour of flow stress in martensitic steel. • A new modified Hall-Petch relation is introduced which holds for a wide range of initial dislocation density and block size. • The effect of lath misorientation on the predicted tensile response is negligible. [ABSTRACT FROM AUTHOR]

Abstract The effect of the volume fraction (0.6–8.4%) of the icosahedral phase (I -phase) on the microstructure, texture and mechanical properties of extruded Mg-Zn-Y alloys was examined. During extrusion, the eutectic and divorced eutectic I- phase in the cast microstructures was broken into small particles, and the particles were dispersed along the extrusion direction, forming parallel particle bands. The broken I -phase particles promoted grain refinement via a particle-stimulated nucleation mechanism and led to basal texture weakening through dynamic recrystallization. The work hardening rate increased with an increase in the volume fraction of I -phase. However, the strength decreased with an increase in the volume fraction of I -phase due to the texture softening effect. To incorporate the texture softening effect into the Hall-Petch relation, a modified Hall-Petch equation, which simultaneously considers the effects of grain size and texture on strength, was developed using the Schmid factors for basal slip. The proposed equation predicts smaller Hall-Petch slope, friction stress and yield strength with easier activation of basal slip, agreeing with the experimental observations. Highlights • The volume fraction effect of I -phase on the extruded Mg-Zn-Y alloys was examined. • The work hardening rate increased with increasing the volume fraction of I -phase. • The strength decreased with increasing volume fraction of I -phase. • Texture effect on strength was incorporated into the Hall-Petch relation. • Smaller Hall-Petch slope and friction stress with easier activation of basal slip. [ABSTRACT FROM AUTHOR]

A hot-rolled Ti–6Al–4V (Ti-64) sheet was surface-treated by pulsed laser at two different powers (100 and 200 W), with microstructural features and hardness before and after the laser surface treatment (LST) systematically investigated. Results show that after the LST at both powers there are two modification zones with distinct microstructural characteristics: melted zone (MZ) near the laser beam center, completely composed of fine martensitic plates with dense {10–11} nanotwins inside them; heat-affected zone (HAZ) far away from the laser beam center, comprised of mixed structures of short-rod β particles, martensitic plates and untransformed bulk α grains. Hardness measurements reveal that the hardness of the Ti-64 sheet can be markedly increased (especially in the MZ) after the LST. In-depth analyses suggest that the hardness increase in the MZ can be ascribed to combined contributions from grain refinement, presence of nanotwins and solid solution of alloying elements, while only the structural refinement by fine plate structures contributes to hardening in the HAZ. Comparisons between both the LSTed specimens reveal that increasing the laser power from 100 W to 200 W can effectively enlarge the laser-modified zones (both the MZ and the HAZ) and simultaneously refine plate structures, leading to further hardness increase. Image 1 • Two modification zones (MZ and HAZ) are identified in Ti–6Al–4V LSTed at 100 and 200 W. • MZ is composed of fine martensitic plates with dense {10–11} nanotwins inside them. • HAZ is comprised of β particles, martensitic plates and untransformed bulk α grains. • Hardness increase in MZ results from grain refinement, nanotwins and solid solution. • Increasing power can enlarge laser-modified zones and simultaneously refine plate structures. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Defect evolution process of polycrystal copper is studied by MD simulations. • Nanoindentation induces the gradient internal stress and potential energy fields in the surface and subsurface of copper. • All samples follow the inverse Hall-Petch relation. • Plastic deformation mechanism of polycrystal copper relies on grain size. • Microstructural component effect is related to the nanoindentation process. Abstract Using molecular dynamics (MD) simulations, the defect evolution and plastic deformation mechanism of single-crystalline and polycrystalline copper under spherical nanoindentation are investigated and compared with previous nanoindentation simulations and experiments. To reveal the grain size effects on the indentation-induced internal stress and deformation behavior, the polycrystalline copper with different grain size are adopted in nanoindentation simulations, whose grain size are follow the inverse Hall-Petch relation. To study the grain boundary network effect, the grain boundary interface is further divided into three microstructural components with different dimensions. The results show that the indentation force of single-crystalline copper is larger than that of polycrystalline copper, and that of polycrystalline copper continuously decreases with the decrease of grain size due to softening phenomenon. The defect nucleation and propagation region in both single-crystalline and polycrystalline copper appear below the tool tip, due to the high internal stress and atomic potential energy induced by nanoindentation. The horizontal propagation of defects is faster and larger than the vertical propagation of that, and such defects are limited in the grains around the tool tip due to grain boundary network. An obvious stresses and potential energy gradient exist under tool tip in single-crystalline copper, and such gradients are possibly distributed along multiply direction in the polycrystalline copper. The internal stresses and atomic potential energy in the region of VP are highest, followed by that in TJ, GB and VP, resulting in the defect nucleation and propagation are more possible occur in VP than other microstructural components. [ABSTRACT FROM AUTHOR]

• The proposed CPFEM accurately predicts the grain size strengthening and anisotropic deformation behavior of LDED Inconel 718 alloy during the tensile process. • The slip systems with maximum and secondary Schmid factors being more easily activated during deformation. • When the tensile load is applied to the dominant direction of the long axis of the grain, the rotation angle of the grain is larger, resulting in easier deformation of the material. • The plastic anisotropy is negatively correlated with the ratio of grain length and short axis. During laser directed energy deposition (LDED), the complex microstructure created by multiple rapid heating and cooling cycles results in the uneven performance of the parts. This work investigates the microstructure evolution and mechanical properties of LDED Inconel 718 samples with different deposit shapes of single-track and thin-wall. The crystal plasticity constitutive and statistical microstructure modeling combined with experiments were performed to explore the influence of microstructure on tensile property. Compared to the thin-wall samples, the single-track sample has smaller sub-grains because of the higher cooling rate, resulting in higher hardness. Furthermore, the anisotropy of the mechanical properties is not changed by the scanning strategy, although the grain size and the yield strength with the Hall-Petch relation are affected by the scanning strategy. The slip system with maximum and secondary Schmid factors is more easily activated during deformation. The rotational behavior of the grains suggests that the anisotropy of mechanical properties is closely linked to the dominant texture of the 〈0 0 1〉 orientation crystals, including the dominant direction of the grain long axis and the ratio of the long and short axis. The results can provide guidance for understanding the deformation mechanism of LDED parts and optimizing the strength design. [ABSTRACT FROM AUTHOR]

A nanocrystalline metal's strength increases significantly as its grain size decreases, a phenomenon known as the Hall-Petch relation. Such relation, however, breaks down when the grains become too small. Experimental studies have circumvented this problem in a set of Ni-Mo alloys by stabilizing the grain boundaries (GB). Here, using atomistic simulations with a machine learning-based interatomic potential (ML-IAP), we demonstrate that the inverse Hall-Petch relation can be correctly reproduced due to a change in the dominant deformation mechanism as the grain becomes small in the Ni-Mo polycrystals. It is found that the atomic von Mises strain can be significantly reduced by either solute doping and/or annealing for small-grain-size polycrystals, leading to the increased strength of the polycrystals. On the other hand, for large-grain-size polycrystals, annealing weakens the material due to the large atomic movements in GB. Over a broad range of grain size, the superposition of the solute and annealing effects on polycrystals enhances the strength of those with small grain size more than those with large ones, giving rise to the continuous strengthening at extremely small grain sizes. Overall, this study not only demonstrates the reliability of the ML-IAP, but also provides a comprehensive atomistic view of complex strengthening mechanisms in nanocrystals, opening up a new avenue to tailor their mechanical properties. • Hall-Petch and inverse Hall-Petch relations can be correctly reproduced by machine learning interatomic potentials. • The atomic strain can be significantly reduced by either solute doping and/or annealing for small-grain-size polycrystals. • For large-grain-size polycrystals, annealing weakens the material due to the large atomic movements in GB. • The different effects on small- and large- grain alloys can lead to continuous strengthening down to extremely small sizes. [ABSTRACT FROM AUTHOR]

Abstract: Hardness of WC–Ni cemented carbides with tiny addition of TiC is studied. The addition of TiC changes the shape of WC crystals to a flatter triangular prism with lower value of the shape equiaxiality P WC. The hardness increases 8–15% on the alloys with lower value of P WC. It is shown that none of the existing models for hardness can explain the effect of the shape. A modification to Hall–Petch relation and Lee & Gurland model for hardness is suggested to accommodate the anisotropy and the shape of WC crystals. The mean linear intersections of the carbide and binder phases are multiplied by the normalized shape equiaxiality . The modified Lee & Gurland model for anisotropic WC crystals gives a satisfactory fit to the experimental data. In addition, the relationships between fracture toughness and strength vs. hardness for these cemented carbides are presented and discussed. [Copyright &y& Elsevier]

The microstructure, texture and mechanical property evolution of the extruded Mg- x Y (x = 1, 5 wt.%) alloys during equal channel angular pressing (ECAP) were systematically investigated using an optical microscope, electron backscatter diffraction (EBSD) and uniaxial tensile test. The Mg-Y alloys exhibited a weakened basal texture before the ECAP, and the texture was further weakened with the max basal poles dispersed along ∼45° between the extrusion direction and the transverse direction after the ECAP. The Mg-5Y alloys always exhibited a finer grain size comparing to that of Mg-1Y for the same ECAP process. With a proper ECAP process, both the strength and elongation of Mg-5Y alloy could be improved simultaneously after the ECAP, i.e., the yield strength (273.9 ± 1.2 MPa), ultimate strength (306.4 ± 3.0 MPa), and elongation (23.9 ± 1.0%) were increased by 10%, 6%, and 72%, respectively, comparing to that before the ECAP. This was considered to be arose from the combined effects of grain refinement, significant improved microstructure homogeneity and solid solution hardening. In addition, it was found that Mg-Y alloy with better comprehensive properties could be obtained by the decreasing-temperature ECAP processes. The yield strength-grain size relationship could be well described by the Hall-Petch relation for all the ECAPed Mg-Y alloys, which was consistent with that the texture changes did not significantly affect the average Schmid factors of basal, prismatic and pyramidal slips for both Mg-Y alloys. [ABSTRACT FROM AUTHOR]

Traditionally, modeling the effect of grain size on the mechanical behavior of crystalline materials is based on assuming an equivalent homogenous microstructure with strength being dependent on the average grain size, for example the well-known Hall-Petch relation. However, assuming an equivalent homogenized microstructure for a highly heterogeneous microstructure can lead to inaccurate prediction of strength and ductility, especially when the gradients in the spatial heterogeneity are severe. In this work, we employ a multiscale dislocation-based model combined with a strain/stress-gradient theory to investigate the effect of spatial heterogeneity of the microstructure on strength and ductility. We concentrate on understanding the effect of various grain size spatial distributions on the mechanical properties of interstitial free (IF)-steel. The results show that by controlling some parameters in the spatial distribution of the microstructure with regions composed of micro-grains and nano-grains one can achieve improved strength and ductility. Based on these results, it is suggested that the mechanical properties of gradient materials can be described by phenomenological relations that include two structural parameters, grain size and grain-size gradient, in contrast to Hall-Petch relation for homogenous materials where only grains size appears in the equation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work reports on the formation of anti-site defects in mechanically alloyed PbTe samples and their anomalous effects on the optical and electrical properties of the sample. PbTe nanoparticles have been synthesised by mechanical alloying of the elemental Pb and Te powders mixed in stoichiometric ratio under an inert (Ar) atmosphere for different time durations. The structural and microstructural characterisations have been carried out by analysing X-ray diffraction (XRD) patterns, field-emission scanning electron microscope (FESEM), and high-resolution transmission electron microscope (HRTEM) images. The elemental composition has been revealed from the energy-dispersive X-Ray (EDX) spectrum. The phase pure cubic PbTe is formed within just 30 min of milling. The Rietveld analysis of XRD patterns, FESEM, and HRTEM images revealed the crystallite size reduction and the increase in r.m.s. lattice strain with the increase in milling durations. Inclusions of more and more anti-site defects of type [Pb Te ] with increasing milling time are reflected in the expansion of the cubic lattice parameter with milling durations. Fourier-transform infrared (FTIR) spectrum reveals that PbTe is a narrow bandgap semiconductor, and the bandgap shows a redshift with increased milling time and reduced crystallite size. This anomalous behaviour of the optical bandgap with reduced particle size is well explained by Urbach tailing due to increased defects in the more extended milled sample. The positions of the conduction and valence bands in the milled PbTe samples are determined for different milling times. The DC conductivity study also shows anomalous behaviour; electrical conductivity increases with particle size reduction in more extended milling time samples. It is resolved by considering that the carrier concentration increases with a longer milling time due to induced anti-site defects while milling. It results in bandgap reduction with milling durations and shows the predominant effect of electronic conductivity over ionic conductivity. The conduction mechanism is explained as per the Pertritz model, and the dependence of activation energies on particle size and temperature has been explained in detail. The Vickers hardness of the milled samples is determined, and its variation with grain size is explained with the Hall-Petch relation. The improved electrical conductivity with increased milling is also manifested in the measured hardness values. Conduction band and valence band potentials along with bandgap energy of PbTe nanostructures (Left) and correlation of microhardness, optical bandgap and electrical conductivity using load of 50gf (Right). [Display omitted] • PbTe of different sizes have been synthesized by facile mechanical alloying. • Redshift observed in bandgap with reducing size is explained by Urbach tailing. • Anomalous behaviour of conductivity with grain size is explained by anti-site defects. • The conduction mechanism is explained as per the Pertritz model. • Grain size variation of micro-hardness is explained with the Hall-Petch relation. • Empirical equations relating optical, electric and mechanical properties are derived. [ABSTRACT FROM AUTHOR]

The chemical short-range order (CSRO) and grain size affect the strength and ductility of high-entropy alloys (HEAs). However, their superposition effect has not yet been studied, limiting further improvement in performance. In this work, we examined the synergistic effect of the CSRO and grain size on the tensile properties of CoCrFeMnNi at room temperature by conducting atomic simulations, because performing an experimental investigation on the formation and movement of dislocations is difficult. The results showed that the preferable locations of the various elements were different. Cr and Mn were preferentially distributed on the grain boundary, Co and Fe were enriched inside the grain, and Ni accumulated in the transition zone from the grain boundary to the intragranular region. In addition, increasing the CSRO appropriately can optimize the density and distribution of dislocations, simultaneously enhancing the strength and ductility of HEAs. Furthermore, an inverse Hall-Petch relation was observed in the system without the CSRO. The simulation computation revealed that the critical grain size that induces the inverse Hall-Petch relation is approximately 13.1 nm. However, the presence of the CSRO eliminates the inverse Hall-Petch relation. • The density and distribution of dislocations can be optimized by increasing the CSRO. • Increasing the CSRO appropriately can enhance the strength and ductility of HEAs simultaneously. • The presence of the CSRO eliminates the inverse Hall-Petch relation. [ABSTRACT FROM AUTHOR]

Classical molecular dynamics (MD) simulation method is employed to study the uniaxial tensile deformation of nanocrystalline magnesium (Mg) of varying grain size levels. The mean grain size of the sample is varied from 6.4 nm to 45 nm, with each sample containing about 43 million atoms in the modeling system. The deformation nanomechanics reveals two distinct deformation mechanisms. For larger grain-sized samples, dislocation dominated deformation is observed while, in smaller grain-sized samples, grain boundary-based mechanisms such as grain boundary sliding, grain boundary rotation are observed. The transition of normal and inverse Hall–Petch relation occurs at around 10 nm. Dislocation density quantification shows that the dislocation density in the sample drastically reduces with decreasing grain size. Elastic modulus of nanocrystalline Mg with mean grain size above 20 nm remains comparable to that of the coarse-grained polycrystalline bulk, followed by a rapid reduction below that grain size. The present work reveals the nanomechanics of nanocrystalline Mg, facilitating the design and development of Mg-based nanostructured alloys with superior mechanical properties. [ABSTRACT FROM AUTHOR]

Contrary to the characteristic strengthening of polycrystalline ceramics with a decrease in grain size, extremely fine nanocrystalline ceramics exhibit softening, increased plasticity and an inverse Hall-Petch relation. Despite experimental evidence, questions remain regarding the underlying deformation mechanisms governing this abnormal mechanical behavior. In the present study, an in-depth microstructural examination was performed on nanostructured transparent magnesium aluminate spinel (MgAl 2 O 4) subjected to microhardness tests. Microstructural observations revealed regions strained to various degrees below the point of indentation, containing varying amounts of dislocations and nano-cavities. Furthermore, the residual strain in different areas was estimated by local electron diffraction. These observations and analysis provided evidence for grain boundary (GB) mediated mechanisms (e.g. , GB sliding and rotation). Moreover, shear bands formed and were found to be associated with micro-cracking. By combining the microstructural analysis with suitable models, it was concluded that these mechanisms govern plastic deformation. By elucidating how strain is accommodated within nanocrystalline ceramics, a deeper understanding of their unique mechanical behavior is gained. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Tantalum thin films may be deposited in two phases. The stable bulk alpha phase is well known, but the metastable tetragonal beta phase is relatively poorly understood. We reported previously on a series of 100% β -Ta films deposited under varying sputter pressures in a low-oxygen environment, and discussed texture, stresses, and phase selection. Here, we discuss microstructure, morphology, and properties of these same β -Ta films. Grain size increases with sputter pressure, which can be explained by the energies of incident species at the growing film. Mechanical properties were measured by nanoindentation. Hardness decreases with grain size in accordance with the Hall-Petch relation while comparison of indentation modulus with biaxial modulus measurements indicates that the β phase is elastically anisotropic, and much stiffer in the [001] direction than in others. Finally, a canonical resistivity value for virtually oxygen-free, 100% β -Ta films of 169 ± 5 µΩcm is reported for the first time. Image, graphical abstract [ABSTRACT FROM AUTHOR]

A new small strain multi-directional forging (MDF) with gradient cooling was proposed to tailor the microstructure and improve the mechanical properties of Mg alloys. Using MDF with a cumulative strain of 2.7, a uniform fine-grained microstructure with an uncommon bimodal basal texture was achieved. Influenced by the Schmid factor, the twins in the< 10–10 > type grains rotated the basal poles toward the last forging direction (LFD), whereas the twins in the< 11–20 > type grains refined the microstructure. The dominant refinement mechanisms at high temperatures were twinning segmentation (TS) and discontinuous dynamic recrystallization (DDRX). It gradually became continuous dynamic recrystallization (CDRX) as the temperature was lowered. Twinning-induced recrystallization (TDRX) also occurred at 200 ℃. The plastic deformation and DRX mechanism affected the texture evolution of the grains. With a cumulative strain of less than 0.3, {10–12} twinning was dominant and responsible for the formation of the< 0001 > //LFD texture. As the cumulative strain increased to 0.9, multiple slips began to dominate the deformation, and a relatively stable< 10–12 > –< 11–24 > //LFD bimodal basal texture was formed. In contrast, the DRXs had little effect on texture types. The yield strengths were affected by the grain sizes and textures during MDF. The fluctuations of strength in the initial stage were mainly attributed to the texture change. When the texture was stabilized, the increases in strength were owing to grain refinement. The yield strengths can be accurately estimated by an improved Hall-Petch relation that includes the texture effect. • A newly small strain multi-directional forging with gradual cooling was proposed. • Fine-grained microstructure achieved undergoing sequential TS, DDRX, CDRX and TDRX. • Uncommon bimodal basal texture attributed to multiple slips activated by the MDF path. • Yield strengths and the anisotropy well estimated by an improved Hall-Petch relation. [ABSTRACT FROM AUTHOR]

• There is a strong orientation dependence of Hall-Petch relation for pure Ti. • Previous model and its parameters predict a reverse trend to the experimental observations. • Orientation mediated activation of additional deformation modes mainly accounts for the orientation dependence of Hall-Petch slope. • A new method combining the use of CPFEM and Eshelby's model for stress concentration at grain boundary is proposed to analyze orientation dependence of Hall-Petch relation. The Hall-Petch slope k represents the magnitude of grain boundary strengthening. For the first time, a strong orientation dependence of the k for pure titanium (Ti) is reported in the present study, namely, a much lower k for the TD-tension of a Ti plate (188 MPa μm1/2) than the k values for the RD-tension of the Ti plate (358 MPa μm1/2), SD-tension (369 MPa μm1/2) and SD-compression (397 MPa μm1/2) of a Ti rod. Here, the RD and TD are respectively the rolling direction and transverse direction of the plate, and SD is the axial direction of the rod, while tension and compression stand for uniaxial tension and compression, respectively. It is found that the mechanisms reported previously cannot explain the orientation dependence of k experimentally observed in the present study. A new mechanism is proposed by combining crystal plasticity finite element modeling and the Eshelby model for the stress concentration at grain boundaries. The results indicate that an orientation-mediated deformation-transfer is the main contributor to this orientation effect on k. More specifically, for the RD-tension, SD-tension and SD-compression, a single slip system is predominant in most grains when plastic deformation-transfer occurs. In contrast, multiple slip systems are activated in the majority of grains in the TD-tension. The activation of additional slip systems remarkably reduces the stress concentration at grain boundaries, leading to a lower k. Afterward, the reasons for the orientation-mediated deformation transfer behavior are discussed. [ABSTRACT FROM AUTHOR]

Severely deformed cold-rolled tungsten is a promising structural material for future fusion reactor applications due to high melting temperature and excellent mechanical properties. However, the fine-grained microstructure after deformation is not stable at temperatures above 800 °C, leading to brittle material behaviour. In this study, we utilize potassium-doping to inhibit recrystallization of tungsten sheets, a mechanism well known from incandescent lamp wires. We produced K-doped tungsten sheets by warm-rolling and subsequent cold-rolling with five different logarithmic strains up to 4.6, and equivalently rolled pure tungsten sheets. Both sets of materials are compared using EBSD and microhardness testing. In both materials, the hardness increases and the grain size along normal direction decreases with strain; the densities of low and high angle boundaries increase in particular during cold-rolling. The K-doped W sheet reaches the highest hardness with 772 ± 8 HV0.1, compared to the pure W sheet with 711 ± 14 HV0.1. All boundaries taken into account, a Hall-Petch relation describes the hardness evolution nicely, except a deviation of the K-doped tungsten sheet rolled to highest strain with its much higher hardness. The similar structural and mechanical properties of both materials in the as-rolled condition allow further studies of recrystallization behaviour of the new K-doped material with a benchmark against the equivalent pure tungsten sheets. Isochronal annealing for 1 h was performed at different temperatures between 700 °C and 2200 °C. A sharp decrease in hardness to intermediate values is observed at around 900 °C for both materials, presumably reflecting extended recovery. A second decrease is observed at 1400 °C for pure tungsten, approaching the hardness of a single crystal and indicating recrystallization and severe growth of grains. For K-doped tungsten, however, the occurrence of the second decrease is shifted to higher temperatures from 1400 °C to 1800 °C with increasing strain and an intermediate hardness is maintained up to 1800 °C. We refer this dependence of the recrystallization resistance on strain in the K-doped material to the dispersion of K-bubbles, resulting in increased Zener pinning forces retarding boundary motion. • Cold-rolling down to 50 μm sheets leads to a very strong texture and high hardness. • Small grain size of <180 nm, no saturation in grain size reduction observed. • LABs are significantly influencing the hardness following the Hall-Petch relation. • Restoration mechanism leads to softening at 900 °C, presumably by extended recovery. • K-bubbles inhibit RX at higher temperatures, more effectively with increasing strain. [ABSTRACT FROM AUTHOR]

Single-phase equiatomic CoCrFeMnNi high-entropy alloy (HEA) specimens with three different grain sizes (0.65 μm, 2.1 μm and 105 μm) were processed by cold rolling and annealing treatment. Tensile properties were investigated over a broad temperature range from 77 K to 873 K. Superior strength-ductility balance can be achieved by refining grain size and decreasing temperature. The Hall-Petch relationship was well fitted, and the fitting parameters have a negative relation with temperature. The thermal and athermal contributions to the yield strength were revealed. This work has unveiled the superior mechanical property of HEAs at cryogenic temperatures. • The Hall-Petch relationships for CoCrFeMnNi high-entropy alloys (HEAs) were well fitted in large temperature range. • The Hall-Petch slope and friction stress of the CoCrFeMnNi HEAs have a negative relation with temperature. • Athermal contribution and grain size (d) follow a Hall-Petch relation, while thermal part is related to temperature and d. • Superior strength and ductility for CoCrFeMnNi HEAs were achieved by refining grain size and decreasing temperature. [ABSTRACT FROM AUTHOR]

Al–Sn based alloys are widely used as plain bearings in several engineering applications, particularly in internal combustion engines. The microstructures of these alloys are composed by two main phases, α-Al and β-Sn. The latter provides the low friction coefficient required for bearing applications. The new combustion engines and hybrid systems impose harder working conditions to plain bearings, thus the bearing materials need to be stronger with improved friction properties. The conventional Al20Sn1Cu (wt.%) alloy produced at different cooling rates by means of different casting processes such as Belt Casting, Twin Roller and Single Roller Melt Spinning techniques was studied. The effects of the cooling rate and of the Mn addition on the microstructure and properties were studied. The samples produced by the melt-spinning technique with cooling rates higher than ∼5 × 105 K/s conducts the alloy to a solidification pathway in a metastable condition through a miscibility gap. A microstructure characterized by an homogeneous small rounded β-Sn particles distributed in a refined α-Al grain size matrix is obtained. Samples produced with cooling rate higher than ∼1.4 × 106 K/s show an anisotropic microstructure of a <100> α-Al crystallographic texture in a columnar microstructure. The melt-spun samples with an isotropic microstructure reach a Vickers hardness 86% higher and an improved wetting property than the alloy produced by the traditional Belt-Casting technique. However the melt-spun samples with crystallographic texture showed a downfall in the properties. The addition of Mn leads to a more homogeneous and refined microstructure independently of the casting technique used. • Hardness increases following a Hall-Petch relation as the α-Al crystallite decreases. • Wettability increases as the α-Al crystallite decreases. • Crystallographic texture is formed when the solidification rate is higher than 106 K/s. • The crystallographic texture downfall hardness and wetting properties. • Rapid solidification can be applied in the bearing manufacturing process. [ABSTRACT FROM AUTHOR]

Nanocrystalline CoCrFeNi and CoCrFeMnNi high entropy alloys have been processed by mechanical alloying followed by spark plasma sintering. Grain growth kinetics has been estimated for both the alloys by subjecting them to heat treatment in the temperature range 1073–1373 K. These alloys possess a thermally stable single phase FCC structure along with Cr 7 C 3 contamination. Electron back scattered diffraction (EBSD) has been used to determine grain size of all the heat treated samples. Both CoCrFeNi and CoCrFeMnNi alloys exhibit a grain growth exponent, n = 3, suggesting long-range diffusion-controlled grain growth in these alloys. Activation energies for grain growth are 134 and 197 kJ/mol for CoCrFeNi and CoCrFeMnNi, respectively, which are significantly lower than the activation energy of lattice diffusion in these alloys. Hardness is measured for CoCrFeMnNi alloy as function of grain size and is found to follow the Hall-Petch type relation. The strength coefficient (slope of Hall-Petch relation) is calculated as 1.92 GPa, which is nearly three times that of the value reported in literature for coarse grained CoCrFeMnNi. Presence of carbides enhances the hardness of these HEAs. The maximum contribution to strengthening comes from the FCC-carbide phase boundaries. • SPSed CoCrFeNi and CoCrFeMnNi HEAs show thermally stable FCC and Cr 7 C 3 phases. • Grain growth activation energy is lower than the energy barrier for bulk diffusion. • Coarsening of carbide particles is the rate controlling step for grain growth. • Hardness of SPSed CoCrFeMnNi follows Hall-Petch behaviour. • Maximum contribution to strengthening comes from FCC-carbide phase boundaries. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Interaction stress between flow defects plays key role in deformation of NG-MG laminate composite. • Peak stress follows inverse Hall-Petch relation. • The shear band width scales with the intrinsic length scale associated with interaction stress. • Material length with respect to MG layer thickness governs transition from shear banding to necking. Abstract Nanolaminate composites consisting of alternate layers of Nanoglasses (NGs) and metallic glasses (MGs) have shown enhanced tensile ductility without great penalty on strength. Recent atomistic simulations on such NG-MG nanolaminate composites have revealed that peak stress attained in these materials do not follow rule of mixture. Also, a transition in deformation behaviour takes place when MG layer thickness is reduced below a threshold level which is correlated with average size of glassy grain in NG layer. However, the mechanistic reasons for this correlation is not well understood. Therefore, continuum simulations of tensile loading on NG-MG laminate composites are performed using thermodynamic consistent non-local plasticity model. Results show that interaction stress associated with flow defects such shear transformation zones (STZs) plays a pivotal role in the deformation response of laminate composites. Also, shear band width in these materials, scales with intrinsic material length associated with the interaction stress. Further, the material length with respect to MG layer thickness governs the transition in deformation behaviour. The present work may provide guidelines in developing highly ductile NG-MG laminate composites for practical engineering applications. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • The dislocation mechanism inside the grain is related to the grain size. • The time of dislocation nucleation is affected by temperature. • The motion of the grain boundary affects the grain size at high temperature. • The dislocation density inside grains will change due to temperature. Abstract A molecular dynamic method was utilized to analyze the microscopic deformation mechanism of polycrystalline TiAl alloy under the influence of grain size and temperature. The results showed that, for a grain size of <8 nm, the yield stress of the nano-polycrystalline TiAl alloy increased with increasing grain size (inverse Hall-Petch relation). Such a plastic deformation was mainly the result of the migration of grain boundaries (GB) and grain rotation. When the grain size exceeded 8 nm, the sensitivity of yield stress on the grain size decreased. The dislocation slip and the deformation twin in the interior of the grain gradually dominated the plastic deformation. With increasing grain size, the Young's modulus also increased. The temperature also influenced the Young's modulus. Increasing the temperature resulted in an increase of the distance between atoms, which decreased the bonding force between atoms, and thus decreased the Young's modulus. With increasing temperature, the dislocation density decreased and the dislocation emission on the GB delayed. [ABSTRACT FROM AUTHOR]

Abstract Considering the greatly significance of high quality billet in industrial manufacture and subsequent deformation process, special casting technologies are employed usually. In this present work, traditional fixed-frequency ultrasonic field (FUF), low frequency electromagnetic field (LEF), variable-frequency ultrasonic field (VUF) and the combinational field of VUF + LEF were introduced to refine the as-cast microstructure and promote the mechanical properties of AZ80 magnesium alloy during the semi-continuous casting. The results showed that all kinds of the external field treatments have their ability to refine the grain, while the combinational field represents the best efficiency in terms of grain refinement with the grain size of 116–141 μm decreased from 679–1454 μm (untreated billet) in the ∅ 255 mm billet. The homogeneity of grains was improved dramatically as well. The main role of VUF was to promote heterogeneous nucleation and generate the large number of nuclei by enlarging cavitation area and acoustic pressure, while the main contribution of LEF was to transport these nuclei in the entire liquid cave. The same as grain size, the Mg 17 Al 12 phases were also refined showing the increase of area fraction of tiny phase. The YS and UTS were remarkably increased after the combinational field treatment, showing the values of 96.8–105 MPa (YS) and 165.5–214.3 MPa (UTS) increased from 73.1 to 84.4 MPa (YS) and 138–153.7 MPa (UTS) of the untreated billet. Finally, the relation between UTS and grain size was established using Hall–Petch relation as a bridge. Highlights • The VUF and LEF were firstly used in semi continuous casting of AZ80 Mg alloy. • The grain was refined dramatically after VUF + LEF treatment. • The mechanism of grain refinement was discussed in detail. • The relation between grain size and ultimate tensile strength was established. [ABSTRACT FROM AUTHOR]

Abstract The deformation and strengthening behavior of an ultra-fine grained (UFG) Al fabricated via powder metallurgy was investigated over a wide range of homologous temperatures (T H). Our results reveal that the presence of a high density of γ-Al 2 O 3 nanoparticles, located primarily at high angle grain boundaries (HAGBs), promoted remarkable stabilization of the Al grain structure up to T H = 0.94. The 0.2% strain offset yield stress (YS 0.2) of the materials annealed at 600 °C for 24 h with grain sizes (d 3D) of 0.57, 1.67, 2.33 and 2.99 μm was systematically studied from room temperature (RT) to 600 °C. Our study reveals that with decreasing d 3D the strain hardening ability of the materials gradually decreased, and this behavior became pronounced at elevated T , which was attributed to the onset of plastic instability. The YS 0.2 of the materials at all T followed the relation YS 0.2 = a + k d 3D −0.5. As determined on the basis of data interpolation, a positive transition from an established Hall-Petch (HP) relation at RT occurred at d 3D = ∼8 μm. As the parameter a was negative at RT and 300 °C the documented strength–structure relationship cannot be explained on the basis of a Hall-Petch relation. The γ-Al 2 O 3 particles located at HAGBs did not contribute notably to RT strengthening, whereas GBs played a significant role in the overall strength. The materials showed a high YS 0.2 up to a T H of 0.94. The YS 0.2 was observed to be linearly correlated with the reciprocal square root of the d 3D and the coefficient k followed k = 224.4–0.376 T relation. The HP model overestimated the YS 0.2 values at elevated T namely for the materials with a smaller d 3D. It is proposed that softening occurred as a result of the γ-Al 2 O 3 particles densely distributed within a 3D network, which were included in Hansen's strengthening model; particle strengthening played a role at elevated T. Highlights • Deformation and strengthening of a stable ultra and fine-grained Al at 25–600 °C. • Al grain structure effectively stabilized by a 3D network of Al 2 O 3 nanoparticles. • Yield stress at all temperatures shows a linear dependence with Al grain size. • A major contribution occurs due to grain boundary strengthening. • A strength–structure relationship that cannot be rationalized using Hall-Petch law. [ABSTRACT FROM AUTHOR]

Abstract: Metallic multilayers exhibit a very pronounced size effect where the mechanical strength depends on the layer thickness. Traditionally the Hall–Petch relation is used to account for the size effect. However, rigorous application of dislocation pileup theory predicts significant deviation from the Hall–Petch relation due to elastic inhomogeneity, discreteness of dislocations and dislocation source operation. Elastic inhomogeneity leads to anomalous scaling where the scaling exponent deviates from 1/2 of the classical Hall–Petch relation. The discrete dislocation effect is properly accounted for by a piecewise approach that can be applied at all length scales. In this article, a key step in the formulation is taken: the dislocation source characteristics are taken into consideration. Thus, all the three effects are accounted for. Analytic formulas linking yield stress to microscopic interface strength, dislocation source activation stress and other easily obtainable parameters (the Burgers vector, the elastic constants of constituent materials, crystal structure and layer thickness) are provided for all length scales. The model is then applied to Cu/Ni multilayers and the predicted strength is compared with experimental data. [Copyright &y& Elsevier]

Phase pure and 25 % Sb incorporated Bi 2 Te 3 compounds with a rhombohedral crystal structure are synthesized by mechanical alloying the stoichiometric mixtures of elemental powders within 3 h under an inert atmosphere. The structure and microstructure of the synthesized samples are revealed by analyzing XRD patterns with Rietveld refinement, FESEM, HRTEM images, and EDX spectra. The increment of lattice parameter 'c' with increasing milling time is associated with the increased [Bi/Sb Te ] type antisite defects. Optical bandgaps of the pure and Sb-alloyed Bi 2 Te 3 samples of different sizes are determined from the FTIR spectra. The transition of undoped n-type to Sb-alloyed p-type semiconducting nature is revealed from the photo responses of the samples. The ac electrical conductivity as well as complex impedance spectra in the temperature range 303–403 K reveal the semi-metallic, non-Debye type behavior of the samples and temperature-dependent relaxation phenomena. The change in electrical conductivity and the corresponding activation energies due to Sb alloying and for different grain sizes are explained in terms of antisite defects and porosity of materials. The temperature variation of the frequency exponent has been demonstrated with the small polaron hopping transaction. The Mott VRH model is used to explain the electrical conduction mechanism of the synthesized samples. The variation of Vickers microhardness with the grain size of milled samples corroborates well with the Hall-Petch relation. The normal indentation size effect (ISE) is depicted from Meyer's law. The photocatalytic activity of 10 h milled Sb-alloyed sample to degrade Rhodamine B cationic dye in wastewater is ∼ 91 %. The correlations of electrical and mechanical properties with the photocatalytic activity of the samples have been established. [Display omitted] • Bi 1.5 Sb 0.5 Te 3 of different sizes have been fabricated via facile mechanical alloying. • A transition from n-type to p-type semiconductor is observed upon Sb inclusion. • Mott's VRH model and SPH model is applied to explain the conduction mechanism. • Grain size and porosity dependent microhardness is measured to find normal ISE. • Improved photocatalytic activities against organic dyes are observed for the first time. [ABSTRACT FROM AUTHOR]

The difference in the mechanical behaviors of dilute solid solutions, complex solid solutions and their corresponding strengthening mechanisms, is an evolving field of study. An understanding of the mechanisms and formulation of theories of strengthening in the complex atomic energy landscapes could eventually lead to a better understanding of the fundamental behavior of condensed matter itself. In this work we attempt to extract the effect of thermo–mechanical processing on the microstructure–mechanical property linkages of complex concentrated alloys (CCAs) by training machine learning (ML) models using processing information / parameters as features. The effect of processing on the phase morphology and the mechanical properties is studied. The stacking fault energy (SFE) predicted based on CCA composition is used as a benchmark to identify deformation mechanisms that are activated based on the arrangement of the component elements within the distorted CCA lattice. This work presents a novel method that attempts to establish ML based process–structure–property (PSP) linkages that could help capture higher order dependencies that may not be adequately captured by existing relations between mechanical properties, phase evolution, composition and processing information. An assortment of Bayesian–learning models are used to create a framework that captures the evolution of phases, their volume fractions, grain sizes and the corresponding change in mechanical properties of a diverse set of CCA compositions as they encounter various processing conditions. The evolution of the mechanical property with grain size is captured as Hall–Petch relations as an example of possible PSP linkage representations. • Effect of thermo-mechanical processing on the microstructure-mechanical properties. • A hierarchical model for determining properties over multiple length scale. • Bayesian learning models for predicting phases and their volume fractions. • Hall-Petch relation is verified as an example of PSP linkage representations. [ABSTRACT FROM AUTHOR]