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Extensive development of the Arctic, rich in various natural resources, requires a lot of cheap ecologically safe construction materials preferably using local renewable sources. Ice being easily available in regions with a cold climate meets all the above criteria but has low strength, high fragility and a tendency to creep. Known strengthening techniques using macroscopic and microfiber additives have many drawbacks. This paper describes a new approach to ice strengthening by adding organic or inorganic 50–100 nm nanoparticles (NPs) to the water to be frozen and presents experimental results and possible mechanisms analysis of polycrystalline ice strengthening using NPs. Cellulose and silica NPs have been tested as typical representatives of such additives. Both are hydrophilic, ecologically safe, widespread, cheap and can be produced from local renewable raw materials. It is shown that the addition of 0.01 to 5 wt.% of NPs results in a reduction of ice composite average grain size by a factor of 5.3 ± 0.7 and an increase of its compression strength by a factor of 2.5 ± 0.3. The highest sensitivity of ice strength to NPs concentration is between 0.1 and 1 wt.%. In this concentration range, the increase in strength is reversely proportional to the square root of the average grain size. Experimental data fit Griffith's relation better than Hall–Petch, so ice strength is limited by cracks with the length proportional to average grain size. [ABSTRACT FROM AUTHOR]

The phenomenon of the strain-rate sensitivity of metallic materials has been a topic of interest since the first mechanical tests at different strain rates were performed. The problem of its theoretical description appeared simultaneously. Despite the significant number of studies covering this issue, it is necessary to rule out a few drawbacks of previously reported models, which is the goal of this work. Herein, an extension of the elastic–viscoplastic model to a generalized state of stress is proposed while aiming to describe the strain rate sensitivity of Armco-iron samples that were pulled in tension within the framework of the finite-difference method. A mathematical model was formulated using equivalent stress and strain, which alleviated the complexity of the relaxation-type constitutive equations. The critical shear stress (CSS) function describes S-type instability with a single equation. The plastic strain rate was calculated based on the well-known Orowan equation, which is related to dislocation dynamics. In addition, the model took the material's microstructure into account based on the design of a representative volume element (RVE) using the step-by-step packing (SSP) method. The results of the modeling were compared with the available experimental data and were found to satisfactorily correlate with them. The results suggest that the misfit error between the model and experimental data did not exceed 10% in the range of strain rates under study, which is a reliable outcome. [ABSTRACT FROM AUTHOR]

The effect of grain size on tensile deformation behaviors at room- and cryogenic-temperatures was examined using extruded Mg–Al–Zn (AZ31) alloys with different average grain sizes of 3.7, 14.0, and 38.7 μm. The mechanical properties were influenced by the grain size as well as the testing temperature. Strength increased with a finer grained structure and a lower testing temperature. Regarding the elongation-to-failure in tension, all the alloys tested at cryogenic-temperature exhibited about half the values of those at room-temperature. Deformed microstructural observations revealed that deformation twins formed in the alloys with coarse- and meso-grained structures, but decreased with grain refinement. The reduction of twin formation at both room- and cryogenic-temperatures is due to enhancement of grain boundary plasticity. Contrary to our expectation, it is interesting to note that grain boundary compatibility contributes to activation of non-basal dislocation slips, irrespective of testing temperatures. In addition, dislocation slips lead to occurrence of strain hardening after yielding even at 77 K. [ABSTRACT FROM AUTHOR]

The effects of grain size (GS) and distance between twin boundaries (d) on the tensile properties of nanocrystalline (NC) face-centered cubic Cu50Ni50 alloy are studied using the molecular dynamics simulations. The common neighbour analysis, dislocation extraction algorithm, shear strain, and von Mises stress configurations together with the total dislocation length, stress–strain relation, and tensile strength diagrams are presented to investigate the mechanical characteristics of the NC Cu50Ni50 specimens. The results exhibits that the twin boundaries significantly restrict the formation and propagation of the stacking faults. The integral deformation occurs under a combination of displacement, breakage, and self-destruction of the twin boundary along with the contraction and expansion of the grains. The tensile strength increases as the GS and the d increase, which agrees with the inverse Hall-Petch relation. The tensile strength of the conventional NC is higher than that of the twinned NC for each pair of specimens with the same GS. [ABSTRACT FROM AUTHOR]

A brief history and update are given in four examples demonstrating that polycrystals are generally stronger than their individual component crystal grains because of obstructed dislocation pile-ups at grain boundaries. The example cases constitute diverse applications of a Hall–Petch dependence involving one or another aspects of the full polycrystal stress–strain behavior: (1) a Hall–Petch based description for a compilation of delayed yielding measurements compiled for steel; (2) computations for an H-P grain size dependent, tensile, plastic instability behavior of copper; (3) an H-P relationship for the true maximum stress for the limit of uniform straining of aluminum; and (4) the onset of a ductile-to-brittle transition in steel cleavage fracturing measurements that are connected to the material fracture toughness properties. [ABSTRACT FROM AUTHOR]

This work studied the relationship between biodegradation rate and grain size itself, excluding other structural factors such as segregations, impure inclusions, second phase particles, sub-structures, internal stresses and textures caused by alloying additions and deformation processing for pure Mg. A spectrum of grain size was obtained by annealing through changing the annealing temperature. Grain boundary influenced the hardness and the biodegradation behavior. The hardness was grain size-dependent, following a typical Hall–Petch relation: HV = 18.45 + 92.31 d − 1 2 . The biodegradation rate decreased with decreasing grain size, following a similar Hall–Petch relation: P i = 0.17 − 0.68 d − 1 2 or P w = 1.34 − 6.17 d − 1 2 . This work should be helpful for better controlling biodegradation performance of biodegradable Mg alloys through varying their grain size. [ABSTRACT FROM AUTHOR]

The phenomenon of the strain-rate sensitivity of metallic materials has been a topic of interest since the first mechanical tests at different strain rates were performed. The problem of its theoretical description appeared simultaneously. Despite the significant number of studies covering this issue, it is necessary to rule out a few drawbacks of previously reported models, which is the goal of this work. Herein, an extension of the elastic–viscoplastic model to a generalized state of stress is proposed while aiming to describe the strain rate sensitivity of Armco-iron samples that were pulled in tension within the framework of the finite-difference method. A mathematical model was formulated using equivalent stress and strain, which alleviated the complexity of the relaxation-type constitutive equations. The critical shear stress (CSS) function describes S-type instability with a single equation. The plastic strain rate was calculated based on the well-known Orowan equation, which is related to dislocation dynamics. In addition, the model took the material’s microstructure into account based on the design of a representative volume element (RVE) using the step-by-step packing (SSP) method. The results of the modeling were compared with the available experimental data and were found to satisfactorily correlate with them. The results suggest that the misfit error between the model and experimental data did not exceed 10% in the range of strain rates under study, which is a reliable outcome.

The mechanical properties of Ti49.8Ni50.2 (at %) alloy under tension at room temperature are studied in dependence on the true strain (e = 1.84–9.55) specified during isothermal multi-axial forging (abc-pressing). It was found that the stress at the beginning of the pseudoyield plateau does not depend on the value of the true abc-strain. It was found that after abs-pressing, already at a true strain e = 1.84, the yield stress σy was 900 ± 25 MPa, which is more than twice as high as compared to σy in the initial state of the specimens. With a further increase in the abc-strain, the yield stress continues to increase slightly and reaches 1000 ± 25 MPa at e = 9.55. In this case, the ultimate tensile strength of the samples increases by about 15%. The strain-hardening coefficient ϴ = dσ/dε at the III (linear) stage of the σ(ε) curve has a similar dependence on e. It is shown that after abc-pressing with e from 1.84 to 9.55, the yield stress and ultimate tensile increase linearly with increasing d−1/2 in accordance with the Hall–Petch relation, where d is the average grain–subgrain size. [ABSTRACT FROM AUTHOR]

The results on investigations of mechanical properties of high-purity titanium with grains ranging from tens of nanometers up to a few micrometers subjected to uniaxial tension, compression and microindenting are presented. Different structural states in high-purity titanium were formed by severe plastic deformation according to the scheme «upsetting – extrusion – drawing» in combination with annealing at temperatures of 250–550° C and quasi-hydrostatic extrusion at room and liquid nitrogen temperatures. The values of yield strengths and microhardness for samples of high-purity titanium with grains of different sizes are determined. It was shown that the combination of severe plastic deformation with cryogenic quasi-hydrostatic extrusion allowed to create high-purity nanocrystalline titanium with high mechanical properties. The obtained experimental data were analyzed for the implementation of the Hall-Petch relation and discrepancy between the values of yield strengths in tension and compression (strength differential or S-D effect). Satisfactory fulfillment of the Hall-Petch relation for high-purity titanium in the whole range of the studied grain size values was shown and a noticeable difference in the yield values for compression and tension was found. The values of the coefficients in the Hall-Petch equation for deformation by tension, compression and microindenting were determined. These coefficients are noticeably lower than the corresponding values for the industrial grades of titanium, i.e. in high-purity titanium, the grain boundaries are weaker barriers for moving dislocations than in the industrial titanium, whose boundaries are enriched with impurities. The features of the acoustic waves emission during compression of samples in various structural states were studied. It was concluded that the deformation of titanium in all the investigated structural states was carried out by dislocation slip.

A brief history and update are given in four examples demonstrating that polycrystals are generally stronger than their individual component crystal grains because of obstructed dislocation pile-ups at grain boundaries. The example cases constitute diverse applications of a Hall–Petch dependence involving one or another aspects of the full polycrystal stress–strain behavior: (1) a Hall–Petch based description for a compilation of delayed yielding measurements compiled for steel; (2) computations for an H-P grain size dependent, tensile, plastic instability behavior of copper; (3) an H-P relationship for the true maximum stress for the limit of uniform straining of aluminum; and (4) the onset of a ductile-to-brittle transition in steel cleavage fracturing measurements that are connected to the material fracture toughness properties.

Structural material AA-7075-T6, an aluminium-based alloy, was subjected to thermal exposure for 60 min in the temperature range 100–300 °C with an interval of 20 °C. Harris analysis of the XRD patterns of specimens showed that the un-exposed AA-7075-T6 material was texture free, but upon thermal exposure, it developed texture. The crystallite size and lattice strain of the specimens were evaluated by Williamson-Hall analysis of the XRD patterns. Thermal exposure in the temperature range 100‒200 °C had no noticeable effect on the surface hardness. However, it decreased rapidly with the increase in temperature from 200 to 300 °C. This behaviour was accounted for in terms of dislocation glide by Orowan mechanism in an atmosphere of semi-coherent ή precipitates (MgZn2) in the main matrix. Breakdown of Hall–Petch relation established that crystallite boundaries do not make any significant contribution to the surface hardness, but the resistance to glide dislocations is offered by the semi-coherent ή precipitates (MgZn2) present in the matrix. [ABSTRACT FROM AUTHOR]

The mechanical properties of Ti49.8Ni50.2 (at %) alloy under tension at room temperature are studied in dependence on the true strain (e = 1.84–9.55) specified during isothermal multi-axial forging (abc-pressing). It was found that the stress at the beginning of the pseudoyield plateau does not depend on the value of the true abc-strain. It was found that after abs-pressing, already at a true strain e = 1.84, the yield stress σy was 900 ± 25 MPa, which is more than twice as high as compared to σy in the initial state of the specimens. With a further increase in the abc-strain, the yield stress continues to increase slightly and reaches 1000 ± 25 MPa at e = 9.55. In this case, the ultimate tensile strength of the samples increases by about 15%. The strain-hardening coefficient ϴ = dσ/dε at the III (linear) stage of the σ(ε) curve has a similar dependence on e. It is shown that after abc-pressing with e from 1.84 to 9.55, the yield stress and ultimate tensile increase linearly with increasing d−1/2 in accordance with the Hall–Petch relation, where d is the average grain–subgrain size.

Zinc single crystal specimens were irradiated with pulsed Nd:YAG laser in vacuum. Keeping the number of laser shots constant (10 shots), laser energy was varied from 50 to 150 mJ, whereas the corresponding laser fluence was 97 to 292 J cm−2, respectively. Using optical microscope, the dimensions (area and perimeter) of laser ablated region on the surface of each specimen were measured. Both parameters increased, in general, on increasing laser pulse energy. Examination of surface morphology by scanning electron microscope revealed formation of pores, grooves, cracks, bubbles, micron-size rods, ripples, ridges, cavities, microcones, and solid flakes, etc. Surface roughness had no systematic dependence on the laser pulse energy. Structural parameters, i.e., texture coefficient, lattice strain, and crystallite size, were determined by means of Harris analysis as well as Williamson–Hall analysis of the XRD patterns of specimens. The variation of lattice strain and crystallite size with laser fluence or laser pulse energy was alike. Surface hardness decreased on increasing laser fluence, and followed classical Hall–Petch relation. [ABSTRACT FROM AUTHOR]

Beeswax and beeswax hydrocarbon-based oleogels were studied to evaluate the quantitative relationship between their yield strength and crystal size distribution. With this aim, oleogels were prepared using four different cooling regimes to obtain different crystal size distributions. The microstructure was evaluated by polarized light microscopy. The yield strength is measured by the cone penetration test. Oleogels were characterized by average grain size, microstructure entropy, grain boundary energy per unit volume, and microstructure temperature. We have provided the theoretical basis for interpreting the microstructure and evaluating the microstructure-based hardening of oleogels. It is shown that the microstructure entropy might be used to predict the yield strength of oleogels by the Hall-Petch relationship.

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 length-scale effect on the hardness of Al/Si 3 N 4 multilayered composites were investigated via combined experimental and machine learning approaches. It was found that the hardness decreases with increase of the individual layer thickness, in agreement with the classic Hall-Petch relation. However, the hardness decrease became moderate when the individual layer thickness was less than 80 nm. The individual critical layer thickness of metallic/ceramic multilayered composites for the change in deformation mechanism was obtained by machine learning methods. The prediction results indicated that the individual critical transition layer thickness was mainly determined by the metal layer, and the corresponding critical transition hardness was positively correlated with the elastic modulus of the ceramic layer. Importantly, it was confirmed that the hardness of other metallic/ceramic multilayered composite systems could be predicted by the machine learning approach, especially the optimized random forest regression (RFR) model. [Display omitted] [ABSTRACT FROM AUTHOR]

The hot rolled 60Si2MnA spring steel was transformed to obtain different proeutectoid ferrite morphologies by different cooling rates after finish rolling through dynamic thermal simulation test. The coexistence relationship between proeutectoid ferrite and pearlite, and the effect of proeutectoid ferrite morphology on mechanical properties were systematically investigated. Results showed that the reticular proeutectoid ferrite could be formed by the cooling rates of 0.5–2 °C/s; the small, dispersed and blocky proeutectoid ferrite could be formed by the increased cooling rates of 3–5 °C/s; and the bulk content of proeutectoid ferrite decreased. The pearlitic colony and interlamellar spacing also decreased, the reciprocal of them both followed a linear relationship with the reciprocal of proeutectoid ferrite bulk content. Besides, the tensile strength, percentage of area reduction, impact energy and microhardness increased, which all follow a Hall–Petch-type relationship with the inverse of square root of proeutectoid ferrite bulk content. The fracture morphologies of tensile and impact tests transformed from intergranular fracture to cleavage and dimple fracture, and the strength and plasticity of spring steel were both improved. The results have been explained on the basis of proeutectoid ferrite morphologies–microstructures–mechanical properties relationship effectively.

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]

The yield strength σ0.2 of titanium polycrystals in tension and in the temperature range of 4.2–395 K is studied as a function of grain size (d) ranging from micro- to nanometer dimensions. It was found that at temperatures below ∼180 K, the σ0.2 (d) dependences are not described by the classical Hall–Petch relation, shifting instead to higher stresses at nanometer size (d). The characteristics of grain-boundary hardening observed at low temperatures are explained using theoretical models, according to which in nanometer-size grains, the diameter of a dislocation loop originating at a grain boundary is proportional to d, with the nucleation stress being σ ∼ 1/d. The critical value dnc is estimated, below which the ratio σ0.2 ∼ 1/d holds at a fixed temperature. It is established that the dnc value decreases with an increase in the temperature of the experiment. [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]

In this work, we investigate the tensile strength and ductility of bulk Cu/Nb nanolaminates after exposure to high temperatures. We show that the interface transforms from flat to wavy at a transition temperature of 700 °C, and tensile strength is linearly proportional to H-1/2 (H = layer thickness). Moreover, the wavy interfaces give rise to a higher slope of the Hall-Petch law. This result can be attributed to greater resistance to slip transmission across wavy interfaces compared to planar interfaces. After 1000 °C for 1 h, the material still exhibits a high strength of 468 MPa and enhanced elongation. Unlabelled Image [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]

The Frank-Read model, as a way of generating dislocations in metals and alloys, is widely accepted. In the early 1960s, Li proposed an alternate mechanism. Namely, grain boundary sources for dislocations, with the aim of providing a different model for the Hall-Petch relation without the need of dislocation pile-ups at grain boundaries, or Frank-Read sources inside the grain. This article provides a review of his model, and supporting evidence for grain boundaries or interfacial sources of dislocations, including direct observations using transmission electron microscopy. The Li model has acquired new interest with the recent development of nanomaterial and multilayers. It is now known that nanocrystalline metals/alloys show a behavior different from conventional polycrystalline materials. The role of grain boundary sources in nanomaterials is reviewed briefly.

When metal is subjected to extreme strain rates, the conversation of energy to plastic power, the subsequent heat production and the growth of damages may lag behind the rate of loading. The imbalance alters deformation pathways and activates micro-dynamic excitations. The excitations immobilize dislocation, are responsible for the stress upturn and magnify plasticity-induced heating. The main conclusion of this study is that dynamic strengthening, plasticity-induced heating, grain size strengthening and the processes of microstructural relaxation are inseparable phenomena. Here, the phenomena are discussed in semi-independent sections, and then, are assembled into a unified constitutive model. The model is first tested under simple loading conditions and, later, is validated in a numerical analysis of the plate impact problem, where a copper flyer strikes a copper target with a velocity of 308 m/s. It should be stated that the simulations are performed with the use of the deformable discrete element method, which is designed for monitoring translations and rotations of deformable particles.

A theoretical model is developed to describe the influence of recovery and recrystallization on the macroelastic limit, the yield strength, and the grain-boundary hardening coefficient of the submicrocrystalline (SMC) metals fabricated by severe plastic deformation. The anomalous hardening and the increase in the grain-boundary hardening coefficient upon annealing of the SMC metals are shown to be related to defect accumulation in migrating grain boundaries in them. Equations are derived to relate the Hall-Petch relation parameters to the grain-boundary migration velocity, the nonequilibrium state of grain boundaries, the lattice dislocation density, and the annealing temperature and time. The results of the numerical calculations performed using the developed model are compared with the experimental results obtained in part I of this work. [ABSTRACT FROM AUTHOR]

We investigated the Hall-Petch relations in Al-ZnO composites with different matrix grain size ( D ) relative to interparticle spacing ( L ). For samples with D  >  L , it was found that grain refinement as described by Hall-Petch relation and particle strengthening by Orowan mechanism both significantly contribute to the strengthening of the composites. For samples with D  ≤  L , variation of microhardness with grain size was found to follow a good Hall-Petch relation with an enhanced Hall-Petch slope. Our study indicates the different coupling of strengthening mechanisms in metal matrix composites with different microstructure length scales. [ABSTRACT FROM AUTHOR]

A model is developed to calculate the Hall-Petch relation parameters for the submicrocrystalline (SMC) metals fabricated by severe plastic deformation (SPD) methods. The model is based on the assumption that the flow stress in SMC metals includes both conventional contributions (caused by lattice dislocations, impurity atoms, etc.) and a contribution related to the long-range internal stress fields created by the SPD-induced defects distributed over grain boundaries. Equations are derived to calculate the Hall-Petch relation parameters as functions of the strain and the strain rate. The results calculated by the derived equations agree well with the experimental data. The low resistance of grain boundaries to the motion of grain boundaries in SMC materials (see part I of this work) is found to be related to a violation of the Hall-Petch relation in SMC metals. [ABSTRACT FROM AUTHOR]

The effects of minor additions (0.2, 0.4 and 0.8 wt%) of Ti on the thermal stability of both Cu nanograins and Y 2 O 3 particles in nanostructured Cu-5 vol%Y 2 O 3 composite powder particles were investigated via 1 h isochronal annealing at temperatures ranging from 300 to 1000 °C. It was found that a small amount addition of 0.4 wt%Ti effectively inhibits the coarsening of the Y 2 O 3 particles during annealing at a very high homologous temperature of 0.87T m , where T m is the melting point of Cu, which, in turn, stabilizes Cu nanograins and retains the hardness value of the as-milled powder sample. However, this is in clear contrast with the significant decrease in hardness of the Ti-free and 0.2 wt%Ti doped milled powder samples annealed at the same condition, resulting from the coarsening of the Y 2 O 3 particles and growth of Cu nanograins. The energy dispersive X-ray spectrometry elemental analysis shows that the stabilizing mechanisms responsible for the improved thermal stability of the Y 2 O 3 particles are associated with the chemical reactions between Ti, O and Y 2 O 3 . [ABSTRACT FROM AUTHOR]

We investigated the effects of the grain size on the yield strength of aluminum using a group of samples with grains successively refined by equal-channel angular pressing (ECAP) and another group of samples produced by 8 ECAP passes and subsequently annealed step by step to produce coarser grains. Tensile tests were performed on all the samples. Adopting a linear addition model for different strengthening contributions, the observed yield strength was resolved into dislocation-related and grain size-related strengthening contributions. The former was directly evaluated using the Taylor equation with dislocation densities determined by the Williamson–Hall method, and the latter was quantified by subtracting the former and the friction stress from the observed yield strength. It was found that for the as-ECAP-processed samples, the amount of the grain size-related strengthening was consistent with an extrapolation of the conventional Hall–Petch relation, and marked extra strengthening, which was clearly related to the grain refinement, appeared after annealing. [ABSTRACT FROM AUTHOR]

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

Mg-3Al-1Zn (AZ31) alloy sheets with various thickness reductions from 10% to 60% were fabricated in a single pass at 150 °C by hot-roller-cold-material rolling. The rolled sheets were then evaluated by microstructural characterization and tensile testing. The strength shows an increase with increasing thickness reduction from 10% to 40%, but the further increase in thickness reduction leads to a decrease in strength. Yield strengths of 273 MPa along the rolling direction and 357 MPa along the transverse direction are obtained for the sheet with 40% thickness reduction, which is characterized by highly elongated grains and high density dislocations, together with a few ultrafine, recrystallized grains in microstructure. The variation in strength with thickness reduction is discussed in light of the strengthening contributions from grain size and dislocation density. [ABSTRACT FROM AUTHOR]

The mechanical strengths of nano-scale individual crystal or nanopolycrystalline metals, and other dimensionally-related materials are increased by an order of magnitude or more as compared to those values measured at conventional crystal or polycrystal grain dimensions. An explanation for the result is attributed to the constraint provided at the surface of the crystals or, more importantly, at interfacial boundaries within or between crystals. The effect is most often described in terms either of two size dependencies: an inverse dependence on crystal size because of single dislocation behavior or, within a polycrystalline material, in terms of a reciprocal square root of grain size dependence, designated as a Hall-Petch relationship for the researchers first pointing to the effect for steel and who provided an enduring dislocation pile-up interpretation for the relationship. The current report provides an updated description of such strength properties for iron and steel materials, and describes applications of the relationship to a wider range of materials, including non-ferrous metals, nano-twinned, polyphase, and composite materials. At limiting small nm grain sizes, there is a generally minor strength reversal that is accompanied by an additional order-of-magnitude elevation of an increased strength dependence on deformation rate, thus giving an important emphasis to the strain rate sensitivity property of materials at nano-scale dimensions. [ABSTRACT FROM AUTHOR]

The Sistaninia-Niffenegger Fatigue (SNF) model, a mesoscale hysteresis energy-based model of fatigue crack initiation, is calibrated and validated both by experiments and numerical modeling. The simulations are able to reproduce the fatigue life curves for the AISI 316L austenitic stainless steel of different grain sizes. In addition, it’s shown that the model captures the crack initiation site and the subsequent propagation through the anisotropic microstructure in a real multi-notched sample subjected to high cycle fatigue (HCF) loading. The microstructure of the polycrystal is determined by electron back scattering diffraction (EBSD), whereas the material properties of the polycrystal and the parameters of the model are obtained by inverse analysis using the Levenberg-Marquardt algorithm, based on the tensile stress-strain curves and the HCF test results, respectively. The model can be applied to different microstructures under HCF loading and evaluate crack initiation and its evolution with precision within the intrinsic scattering of HCF tests. [ABSTRACT FROM AUTHOR]

The mechanical properties of copper foils electroplated with (200) and (220) preferred orientations and thicknesses of 8–24 μm were assessed at various temperatures. It was found that the yield strength and elastic modulus both decrease with increasing temperature to 150 °C, and that the greater susceptibility of a columnar structure to defects makes it more sensitive to temperature than an equiaxed structure. Thus, for a given grain size, a columnar structure has a lower yield strength. A modified Hall-Petch relation was subsequently developed to take into account the effect of micro-structure on material strength by introducing a structure factor ( S ) : σ y = σ 0 + kd − 1/2 + S . As the slope ( k ) of this equation is constant, it can be used for copper thin films of any thickness, provided they are at room temperature and above the micro-level in scale. This structure factor concept, however, is only valid at room temperature. In the modified Hall-Petch relation, the new variable related to the equiaxed and columnar structures in the copper thin films was abstracted from the Hall-Petch relation. Then, if the materials are the same, the k value and the σ 0 value are constant regardless of the scale, and the relationship between the grain size and the yield strength can be shown by only changing the structure factor. [ABSTRACT FROM AUTHOR]

The hot rolled 60Si2MnA spring steel was transformed to obtain different proeutectoid ferrite morphologies by different cooling rates after finish rolling through dynamic thermal simulation test. The coexistence relationship between proeutectoid ferrite and pearlite, and the effect of proeutectoid ferritemorphology onmechanical properties were systematically investigated. Results showed that the reticular proeutectoid ferrite could be formed by the cooling rates of 0.5-2 °C/s; the small, dispersed and blocky proeutectoid ferrite could be formed by the increased cooling rates of 3-5 °C/s; and the bulk content of proeutectoid ferrite decreased. The pearlitic colony and interlamellar spacing also decreased, the reciprocal of themboth followed a linear relationship with the reciprocal of proeutectoid ferrite bulk content. Besides, the tensile strength, percentage of area reduction, impact energy and microhardness increased, which all follow a Hall-Petch-type relationship with the inverse of square root of proeutectoid ferrite bulk content. The fracture morphologies of tensile and impact tests transformed from intergranular fracture to cleavage and dimple fracture, and the strength and plasticity of spring steel were both improved. The results have been explained on the basis of proeutectoid ferrite morphologies-microstructures-mechanical properties relationship effectively. [ABSTRACT FROM AUTHOR]

Depth sensing nanoindentation experiments were performed to investigate the strain rate dependent-independent behaviors of nanotwinned microcrystalline Cu. The specimens were electro-deposited using three different additives, which resulted in controlled variations in microstructural parameters, viz., grain size, and twin spacing. One of the three samples with the lowest twin lamella spacing showed a lower stress exponent, which might result in enhanced ductility. The stress exponent and activation volume increased with increasing twin spacing. In contrast, the hardness revealed a dependence on the effective length scale considering the weighted average of the twin spacing and grain size. The mechanical properties obtained by introducing nanotwins in coarser initial grain size are comparable to nanotwinned nanocrystalline materials. Thus, the possibility of using a coarser initial grain size for nanotwinned materials paves the way for a new paradigm with a broader range of nanotwinned materials. • Effective length scale equation proposed based on twin spacing and grain size. • Strain rate-dependent behavior exhibited dependence on twin spacing. • nt-mc-Cu exhibited lower stress exponent than ufc-Cu and nc-Cu. • Complexity involved in grain refinement can be avoided by incorporating nt in mc-Cu. [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]

Herein, we showed that the grain size, rather than the domain size, controlled room-temperature properties of a B2-ordered refractory Al 15 Nb 40 Ti 40 V 5 medium-entropy alloy. Grain refinement to 20 μm at any size of B2 domains resulted in elongation of ∼50%, which was superior to all the reported refractory high/medium-entropy alloys. [ABSTRACT FROM AUTHOR]

In the present study, the microscopic deformation mechanism and tensile properties of Al 0.1 CoCrFeNi nanocrystalline high-entropy alloys (HEAs) during uniaxial tension were studied through molecular dynamics simulation, and the dependence of mechanical properties on grain size and strain rate has been explored. As the tensile strain increases from 0 to 0.1, the atoms undergo a phase transformation from the face-centered cubic (FCC) structure into the hexagonal close-packed (HCP), body-centered cubic (BCC) and amorphous structure, and the dislocation density increases gradually due to dislocation annihilation and interaction. HEA grains undergo the transformation of the inverse Hall-Petch (H–P) relation into the H–P relation after exceeding one critical size of 14.77 nm at a strain rate of 5 × 107/s, and this critical size increases with increasing strain rate. The microscopic deformation mechanism of the H–P relation is that the accumulation of dislocations at the grain boundaries leads to an increase in the strength of HEAs. In contrast, the inverse H–P relation is caused by the migration of grain boundaries, and the rotation and merging of HEA grains. The increase of strain rate positively affects the tensile properties of nanocrystalline HEAs, and the flow stress and yield strength exhibit sensitive dependence on the extremely high strain rates. In addition, the amorphization of atoms has become an important way for HEAs to deform plastically at high strain rates. The microstructure evolution and deformation mechanism of Al 0.1 CoCrFeNi nanocrystalline high-entropy alloys have been revealed from atomic level and the effects of grain diameters and strain rate on the tension properties of the Al 0.1 CoCrFeNi nanocrystalline high-entropy alloys have been studies quantitatively. [Display omitted] • MD study on the deformation mechanism and tensile properties of HEAs. • The dynamic evolution of ESF, ISF, dislocation, etc. causes stress fluctuations. • HEAs grain have a critical size below which the inverse H–P relation occurs. • The critical size of HEAs grain increases with the increase of strain rate. • High strain rate helps to improve tensile properties of nanocrystalline HEAs. [ABSTRACT FROM AUTHOR]

To get a range of crystallite size, 5 N pure polycrystalline zinc specimens were shined with 50–100 Nd:YAG laser shots. Williamson-Hall, Size-Strain Plot, Halder-Wagner, and Wagner-Aqua models were employed to evaluate the crystallite size and lattice strain of pristine and laser-treated specimens. Surface hardness of the specimens were measured under 0.2 and 0.3 kgf indentation loads for 10 s. In each case, the surface hardness followed inverse Hall – Petch Relation. For a fixed number of laser shots, the surface hardness was greater for 0.2 kgf indentation load than that for 0.3 kgf. The surface hardness of pristine zinc specimen increased on treatment with 50 laser shots. With further rise in laser shots up to 80, the surface hardness progressively decreased close to that of pristine specimen. Later, it again increased for 90 laser shots and then slightly decreased for 100 laser shots. • 5 N pure zinc specimens were shined with 50–100 Nd:YAG laser shots. • Williamson-Hall, Size-Strain, Halder-Wagner, Wagner-Aqua models provided structural parameters. • Surface hardness was measured under 0.2 and 0.3 kgf indentation loads for 10 s. • Surface hardness followed inverse Hall – Petch Relation. • Surface hardness was greater for 0.2 kgf indentation load than that for 0.3 kgf. [ABSTRACT FROM AUTHOR]

The effect of grain size and strain rate on the room-temperature compression of pure magnesium was investigated. Samples with equiaxed grains and grain size ranging over 1.4–88 µm were obtained by extrusion at different temperatures. The extruded samples were compressed at strain rate between 1 × 10−2 s−1 and 1 × 10−6 s−1. In microstructures with grain size greater than 15 µm, the deformation mechanism was dominated by twinning; while in those with grain size smaller than 8 µm, the dominant deformation mechanism was dislocation slip. In addition, significant grain-boundary sliding was observed with decreasing grain size and strain rate. The Hall-Petch relationship broke down with mean grain size smaller than a critical grain size, which increased with decreased strain rate. Further, the deformation mode (compression or tension) had a negligibly small effect on the critical grain size for changes in the dominant deformation mechanisms and the Hall-Petch breakdown. The changes in deformation mechanisms with grain size were understood in terms of the strain-rate sensitivity exponent m. When the grain size decreased from 88 µm to 1.4 µm, m increased to approximately 0.3 from 0.01. The increase in m with grain refinement was consistent with enhanced grain-boundary sliding, in addition to dislocation slip and the suppression of deformation twinning. It thereby reduced the asymmetry of the tension-compression yield strength. • Inverse Hall-Petch relationship (H-P) is seen in ultrafine grain size pure Mg. • Critical grain size for break-down of H-P is independent of deformation mode. • Deformed structures show grain boundary sliding (GBS) in low-strain rates. • GBS strain contribution to overall strain increases with decrease in grain sizes. [ABSTRACT FROM AUTHOR]