Classical Hall-Petch Relationship Research Articles

Obtaining Symmetrical Gradient Structure in Copper Wire by Combined Processing

Traditionally, structural wire is characterized by a homogeneous microstructure, where the average grain size in different parts of the wire is uniform. According to the classical Hall–Petch relationship, a homogeneous polycrystalline metal can be strengthened by decreasing the average grain size since an increase in the volume fraction of grain boundaries will further impede the motion of dislocations. However, a decrease in the grain size inevitably leads to a decrease in the ductility and deformability of the material due to limited dislocation mobility. Putting a gradient microstructure into the wire has promising potential for overcoming the compromise between strength and ductility. This is proposed a new combined technology in this paper in order to obtain a gradient microstructure. This technology consists of deforming the wire in a rotating equal-channel step die and subsequent traditional drawing. Deformation of copper wire with a diameter of 6.5 mm to a diameter of 5.0 mm was carried out in three passes at room temperature. As a result of such processing, a gradient microstructure with a surface nanostructured layer (grain size ~400 nm) with a gradual increase in grain size towards the center of the wire was obtained. As a result, the microhardness in the surface zone was 1150 MPa, 770 Mpa in the neutral zone, and 685 MPa in the central zone of the wire. Such a symmetrical spread of microhardness, observed over the entire cross-section of the rod, is a direct confirmation of the presence of a gradient microstructure in deformed materials. The strength characteristics of the wire were doubled: the tensile strength increased from 335 MPa to 675 MPa, and the yield strength from 230 MPa to 445 MPa. At the same time, the relative elongation decreased from 20% to 16%, and the relative contraction from 28% to 23%. Despite the fact that the ductility of copper is decreased after cyclic deformation, its values remain at a fairly high level. The validity of all results is confirmed by numerous experiments using a complex of traditional and modern research methods, which include optical, scanning, and transmission microscopy; determination of mechanical properties under tension; and measurement of hardness and electrical resistance. These methods allow reliable interpretation of the fine microstructure of the wire and provide information on its strength, plastic, and electrical properties.

Effects of different ions irradiation on the electrochemical corrosion and hardness of pure iron

Pure iron (Fe) was subjected to singly charged 1 MeV Gold (Au+1), Nickel (Ni+1), Cobalt (Co+1), Copper (Cu+1), and Yttrium (Y+1) ions irradiation at a constant dose of 5 × 10 14 ions/cm2. X-ray diffraction analysis revealed polycrystalline nature of Fe with ions-induced changes in its crystallinity. Improvement in the crsytallinity of Fe due Au+1 irradiation was more significant as compared to the others. Similarly, the crystallinity of Fe was greatly decreased due to the impact of Y+1 ions. The Fe surface morphology indicated the surface defects in the form of pits, cavities and protruded structures after ions irradiation. Potentiodynamic Polarization (PDP) revealed an increase in the corrosion resistance of Fe after irradiation. The Au+1 ions irradiated specimen was found more effective in terms of high corrosion resistance than other specimens. The surface hardness of Fe exhibited Classical Hall–Petch relation, which demonstrated that the larger the crystallite size (26–83 nm), the smaller would be the surface hardness (190–182 HV) and vice versa.

Length-scale effect on the hardness of metallic/ceramic multilayered composites: A machine learning prediction

The length-scale effect on the hardness of Al/Si3N4 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.

Microstructure design and mechanical properties of grain-gradient graphene/aluminum composites

The metal matrix with mixed grain-gradient structure and the graphene with different characteristics could be designed and prepared to ameliorate the plasticity and toughness reduction of the metal matrix composites (MMCs) caused by graphene reinforcement. However, the relationship between the microstructure and the mechanical properties of composites needs to be investigated. In this paper, a self-developed structural modeling program is employed to design and establish a single-edge notch tensile finite element model of the graphene reinforced grain-gradient aluminum (Al) matrix composites, where the distribution and morphology of graphene and grains can be redistributed. Then, the grain size dependence of yield strength is introduced into the developed crystal plasticity finite element method (CPFEM) according to the classical Hall-Petch relationship, the damage mechanism of the graphene/Al composites with various designed novel microstructures is analyzed in combination with the cohesive zone model (CZM), and the microstructure of the graphene/Al composites with optimal mechanical properties is obtained. In addition, it is found that the failure mode, strength and toughness of the composites could be ameliorated by adjusting the bonding state of graphene-Al interface. This study provides a new insight into the microstructure design and fabrication of the graphene/Al composites with optimal comprehensive properties.

Eutectoid lamellar structure strengthened ultra-strong Al13Fe29Co29Ni29 high-entropy alloy

Alloys with a lamellar structure exhibit excellent mechanical properties as a large number of interfaces hinder dislocation motion. Here, an ultra-strong Al13Fe29Co29Ni29 high-entropy alloy (HEA) reinforced by a pearlite-like lamellar structure is studied. The results show that the Al13Fe29Co29Ni29 alloy decomposes into submicron lamellar (face-centered cubic (FCC) + L12) and (body-centered cubic (BCC) + B2) phases during heat treatment between 560 °C and 600 °C. The layer thickness is determined to decrease with decreasing transformation temperature in the Al13Fe29Co29Ni29 alloy, and it is proportional to the reciprocal of the undercooling of the phase transition. Strengthened by the submicron lamellar structure, the yield strength of the alloy after annealing at 600 °C reaches 1301 MPa with a ductility of 6.1%. In addition, the yield strength increases with the refinement of the lamellar structure, and it follows the classical Hall–Petch relationship. Furthermore, the lamellar FCC and lamellar BCC phases are strengthened by the nanosized L12 and B2 phases, respectively. This lamellar-structure-strengthened alloy possesses a higher strength than other metallic nanolaminates with the same layer thickness, such as Cu–Ni, Ti–Al, and Cu–Ag alloys. Thus, it is envisaged that the proposed alloy will be useful for technological applications.

Uncovering the softening mechanism and exploring the strengthening strategies in extremely fine nanograined metals: A molecular dynamics study

• Softening and strengthening in extremely fine nanograined metals are governed by grain boundary (GB) stability. • Atomic sliding in GB layer induces the softening while dislocation activity in grain interior plays the role of coordinator to fit the deformation dominated by GBs. • The solid solution exerts the negative strengthening (the softening) effect to the nanoscale metals. • The GB segregation gives rise to a notable improvement in strength, and this improvement can be further enhanced by optimizing solute concentration and GB excess. The strength of polycrystalline metals increases with decreasing grain size, following the classical Hall-Petch relationship. However, this relationship fails when softening occurs at very small grain sizes (typically less than 10 to 20 nm), which limits the development of ultrahigh-strength materials. In this work, using columnar-grained nanocrystalline Cu-Ag ‘samples’, molecular dynamics simulations were performed to investigate the softening mechanism and explore the strengthening strategies (e.g., formation of solid solution or grain boundary (GB) segregation) in extremely fine nanograined metals. Accordingly, the softening of pure metals is induced by atomic sliding in the GB layer, rather than dislocation activities in the grain interior, although both occur during deformation. The solid solution lowers the stacking fault energy and increases the GB energy, which leads to the softening of NC metals. GB segregation stabilizes GB structures, which causes a notable improvement in strength, and this improvement can be further enhanced by optimizing the solute concentration and GB excess. This work deepens the understanding of the softening mechanism due to atomic sliding in the GB layer and the strengthening mechanism arising from tailoring the GB stability of immiscible alloys and provides insights into the design of ultrahigh-strength materials.

Size-dependent yield stress in ultrafine-grained polycrystals: A multiscale discrete dislocation dynamics study

In this study, the effects of grain size and dislocation source properties on the yield stress of ultrafine-grained (UFG) polycrystals were examined using three-dimensional multiscale discrete dislocation dynamics (DDD). A polycrystal model containing multiple grains with randomly distributed orientations was constructed within a multiscale DDD framework. Grain boundaries (GBs) were assumed to be penetrable by dislocations, with two dislocation-GB interaction mechanisms, i.e., dislocation absorption at GBs and dislocation emission from GBs, being considered. The simulation investigated the dislocation source effect and demonstrated a non-monotonic dependency of flow stress on dislocation source length, where the lowest flow stress corresponds to a Frank-Read (FR) source length of d/4 where d is the grain size. When the length of a FR source in the polycrystalline sample exceeds this value, the simulated yield stress increases owing to the constraining effect of grain boundaries on dislocation movement. The grain size dependence of the yield stress shows deviations from the classical Hall–Petch relationship as the exponent in the Hall–Petch type relation ranges from about 0.91 to about 0.98, depending on the initial dislocation density in the samples. Detailed analysis indicates that the grain size dependence of the yield stress is mainly controlled by the effect of grain boundary constraints on dislocation activation. A secondary effect arises from grain size dependent dislocation accumulation and the resulting Taylor hardening. The activation and operation of FR sources were quantitatively examined to further understand the origins of source length and grain size effects. A theoretical model is proposed to account simultaneously for the effects of source length, grain size, and initial dislocation density on the yield stress of polycrystals in the UFG regime.

Effect of Fe on the Hall-Petch relationship of (CoCrMnNi)100-x Fex medium-and high-entropy alloys

In the present study, a systematic investigation on the effect of Fe content on the Hall-Petch coefficient of (CoCrMnNi)100-x Fex (x = 20, 40, 50, and 60) medium- and high-entropy alloys (M/HEAs) was carried out. The cold-rolled alloys were annealed at 900 °C and 1000 °C between 3 min and 10 h for recrystallization. Scanning electron microscope with a backscattered detector was used to obtain micrographs of recrystallized specimens for grain size calculation. Tensile testing was used to evaluate the mechanical properties of the alloys. The microstructure showed that regardless of the alloy composition, the grain size was approximately similar when subjected to the same heat treatment condition. Moreover, all the alloys obeyed the classical Hall-Petch relationship. Friction stress (solid solution, SS strengthening) decreased with an increase of Fe content, which was attributed to weak lattice distortion caused by the reduction of the atomic size misfit. The Hall-Petch coefficient, which represents grain boundary (GB) strengthening, also decreases as the Fe content increases. A linear relationship between intrinsic stacking fault energy and Hall-Petch coefficient was found not to exist. However, it is proposed that the monotonic decrease of the Hall-Petch coefficient is directly related to the unstable stacking fault energy (γUSFE). As a result, an increase of Fe content in (CoCrMnNi)100-x Fex alloy system leads to an increase of γUSFE, which in turn weakens GB strengthening (Hall-Petch coefficient). Moreover, HEAs and MEAs with higher Fe content tend to have low yield strength due to weak contributions from both SS and GB strengthening. Therefore, to design superior MEAs and HEAs with enhanced strength, the choice of principal elements and their respective contents is imperative for an optimized contribution from both SS and GB strengthening mechanisms.

Impact of Carbon Ion Implantation on the Crystal Structure, Surface Morphology, Vickers Hardness and Electrochemical Corrosion of Zirconium

Specimens of polycrystalline zirconium were irradiated with 1 MeV singly charged carbon ions using Pelletron accelerator. The ion doses used were in the range 1013 ions/cm2-1015 ions/cm2. The pristine specimen had preferred orientation for (002) and (004) crystallographic planes, which remained unaffected on irradiation with carbon ions. The crystallite size and lattice strain initially increased on irradiation with carbon ion dose 1013 ions/cm2 and later on decreased monotonically with further increase in ion dose till 1015 ions/cm2. Lattice strain increased linearly with the crystallite size. FESEM micrographs showed that carbon ion irradiation on the smooth surface of pristine zirconium specimens produced surface defects in the form of pits, cavities, agglomers and protruded structures of height ≈ 26 µm, which modified the surface properties, such as surface roughness, surface hardness and corrosion resistance. The surface roughness increased substantially on irradiation with carbon ions till 1014 ions/cm2 and later on decreased a little bit from the peak value. The surface hardness followed the classical Hall–Petch relation. The corrosion resistance is significantly improved on irradiation with carbon ions; greater the ion dose better is the corrosion resistance.

Impact of Laser Fluence in Modifying the Surface Characteristics of Laser-Treated Monocrystalline Zinc

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.

Microstructural and Hardness Evolution in a Duplex Stainless Steel Processed by High-Pressure Torsion

The duplex stainless steel 2205, designated DSS2205 and having a duplex structure comprising ferrite and austenite phases, was processed by high-pressure torsion (HPT) and the microstructural and hardness evolutions were investigated after various HPT revolutions and at different positions within the specimens. The results show that the grain refinement induced by severe deformation processing is different in the ferrite and austenite phases such that the ferrite grains are refined via dislocation subdivision, whereas grain refinement in the austenite phase depends mainly on the interaction of dislocations and twin boundaries at relatively low strains. When the numbers of revolutions increases, the grain refinement in austenite restricts the occurrence of deformation twinning so that dislocation slip becomes dominant. During HPT processing, the effect of the phase boundaries on the mechanical properties of the alloy is very significant. The results show the average width between two adjacent phases and the hardness of the alloy are generally consistent with the classical Hall–Petch relationship.

Microstructure and mechanical properties of fine grained uranium prepared by ECAP and subsequent intermediate heat treatment

Abstract The microstructure and mechanical properties of fine grained uranium prepared by equal channel angular pressing (ECAP) and subsequent intermediate heat treatment were investigated systematically by the confocal laser scanning microscope (CLSM), electron backscatter diffraction (EBSD) and split Hopkinson pressure bar (SHPB). The results show that the initial coarse grained uranium was refined from about 1000 to 6.5 μm prepared by ECAP at 3 passes and subsequent heat treatment, and the corresponding dynamic yield strength increased from 135 to 390 MPa. For the ECAPed uranium samples, the relationship between grain size and yield strength could be described by classical Hall–Petch relationship, and the fitting Hall–Petch relationship for the fine grained uranium samples prepared by ECAP was drawn.

Tailoring grain growth and solid solution strengthening of single-phase CrCoNi medium-entropy alloys by solute selection

In the present study, we selected solutes to be added to the CrCoNi medium-entropy alloy (MEA) based on the mismatch of self-diffusion activation energy (SDQ) between the alloying elements and constituent elements of the matrix, and then investigated their grain growth behavior and mechanical properties. Mo and Al were selected as the solutes for investigation primarily because they have higher and lower SDQ, respectively, than those of the matrix elements; a secondary factor was their higher and lower shear modulus. Their concentrations were fixed at 3 at.% each because previous work had shown these compositions to be single-phase solid solutions with the face-centered cubic structure. Three alloys were produced by arc melting, casting, homogenizing, cold rolling and annealing at various temperatures and times to produce samples with different grain sizes. They were (a) the base alloy CrCoNi, (b) the base alloy plus 3 at.% Mo, and (c) the base alloy plus 3 at.% Al. The activation energies for grain growth of the CrCoNi, CrCoNi-3Mo and CrCoNi-3Al MEAs were found to be ∼251, ∼368 and ∼219 kJ/mol, respectively, consistent with the notion that elements with higher SDQ (in this study Mo) retard grain growth (likely by a solute-drag effect), whereas those with lower values (Al) accelerate grain growth. The room-temperature tensile properties show that Mo increases the yield strength by ∼40 % but Al addition has a smaller strengthening effect consistent with their relative shear moduli. The yield strength as a function of grain size for the three single-phase MEAs follows the classical Hall-Petch relationship with much higher slopes (＞600 MPa μm−0.5) than traditional solid solutions. This work shows that the grain growth kinetics and solid solution strengthening of the CrCoNi MEA can be tuned by selecting solute elements that have appropriate diffusion and physical properties.

Nanostructured Ti29.7Ni50.3Hf20 high temperature shape memory alloy processed by high-pressure torsion

High-pressure torsion (HPT) processing under a pressure of 6.0 GPa was applied to Ti29.7Ni50.3Hf20 (at.%) alloy. Two types of structure were observed after HPT with 3 revolutions: first one is the mixture of amorphous phase and retained nanocrystalline; second is the alternating bands of amorphous phase and high defect density crystalline. As a result, post deformation annealing (PDA) at 500−700 °C leads to the non-uniform distribution of martensite and parent phase grains. The grains of martensite are twice larger compared to that of parent phase. The nanocrystalline and ultrafine grains form after annealing at 500−600 °C and 700 °C, respectively. The twinning mechanism does not change with the reduction of martensitic grains up to ∼35 nm. The relationship between strength and grain size in Ti29.7Ni50.3Hf20 alloy obeys the classical Hall-Petch relationship with a coefficient of 10.80 ± 0.39 GPa nm1/2.

Effect of local stresses of primary twinning on double twinning, twin intersection and their competition

Taking into account the local stresses resulting from the primary twinning with transformation strains, the competition between double twinning {10–11}–{10–12} and (10–12)–(–1012) (CDTW and EDTW) is theoretically modeled. Using electron backscatter diffraction technique, the statistical fractions, thickness-length ratios and their critical values of CDTW and EDTW within grains of as-cast AZ31 magnesium alloy sheets at the low strain stage of hot rolling processing are obtained to validate the theoretical results. In addition, the competition between the DTW and twin intersection are also discussed in detail. The results show that: (1) The secondary twin growth complies with the classical Hall-Petch relationship. Due to the difference in the driving forces resulting from different transformation strains between the primary extension and contraction twinning, the secondary extension twin of EDTW is more difficult to grow compared to that of CDTW for primary twin bands with small thickness-length ratios, which is contrary to the regulation for primary twin bands with large thickness-length ratios; (2) The greater the thickness-length ratio of the primary twinning is, the smaller the critical shear stress of the secondary twinning is. This is opposite to the effect of thickness-length ratio on the critical shear stress of the incident twinning in the twin intersection. It is indicated that the thickening of the primary twinning provides the higher driving force for the formation of DTW, however hinders the twin intersection more evidently; (3) Within coarse grains, at the low strain stage, the formation of DTW can dominantly induce dynamic recrystallization and continue plastic deformation, while the stress concentration resulting from the twin intersection is inclined to cause brittle fracture. Therefore, based on the effect of the local stress, the selection mechanism of the thickness-length ratio on the DTW and twin intersection is of great significance to determining the plastic performance of magnesium alloys during hot working. In the current study, massive control factors of the thickness-length ratio of the primary twinning are concluded, which provides some corresponding schemes of material design.

Effect of bimodal microstructure on the tensile properties of selective laser melt Al-Mg-Sc-Zr alloy

Selective laser melting (SLM) has become a promising manufacturing route for the aluminum alloy models and parts in automotive and aircraft industries. In this work, an Al-4.0Mg-0.7Sc-0.4Zr-0.5Mn alloy was fabricated by SLM and near-full densification (relative density 99.7%) was obtained. A fine equiaxed grain regions and columnar grain regions alternately distributed characteristic is observed in the as-fabricated sample. The results of microstructural analyses show that the rapid solidification process and the precipitation of Al3Mg2, Al6(Fe, Mn), and Al3(Sc, Zr) particles lead to the fine grain structure, which provides a combination of high yield strength and excellent ductility. The mechanical properties of the as-fabricated sample were analyzed based on the typical microstructural feature of a combination of coarse columnar grain regions and fine grain regions. The strengthening effect is mainly attributed to the grain boundaries and the effect of grain boundaries on yield stress is according with the classical Hall-Petch relationship.

Low-Temperature feature of grain-boundary hardening of nanocrystalline titanium

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.

Obtaining hexagon-shaped billets of copper with gradient structure by twist extrusion

Processing by twist extrusion was used to produce copper billets with a hexagonal cross-section. A special feature of the billets is their gradient microstructure owing to a specific strain pattern: an undeformed core and a deformed outer sheath. The initial sample with a 40 mm diameter was processed at room temperature by four twist extrusion passes through a twist die having a hexagonal cross-section and a small twist-line slope angle β = 40° with a back-pressure of 100 MPa. The results showed that the processed sample had an undeformed core 20 mm in diameter and a deformed outer sheath with a gradient microstructure in which the average grain size decreased gradually from 50 μm to 0.5 μm towards the periphery along a radius direction. The microstructure gradient represented the various stages of the grain refinement process corresponding to increasing shear strain. The texture revealed two different shear deformation modes whose shear planes were perpendicular and parallel to the extrusion axis. The measured Vickers hardness showed good agreement with the microstructure. In the deformation zone, the classical Hall-Petch relation between the hardness and the grain size of the various characteristic areas formed by twist extrusion was found.

Size Dependence of Grain Boundary Migration in Metals under Mechanical Loading

The greatly increased grain boundary (GB) mobility in nanograined metals under mechanical loading is distinguished from that in their coarse-grained counterparts. The feature leads to softening of nanograined materials and deviation of strength from the classical Hall-Petch relationship. In this Letter, grain size dependences of GB migration in nanograined Ag, Cu, and Ni under tension were investigated quantitatively in a wide size range. As grain size decreases from submicron, GB migration intensifies and then diminishes below a critical grain size. The GB migration peaks at about 80, 75, and 38nm in Ag, Cu, and Ni, respectively. The suppression of GB migration below a critical size can be attributed to GB relaxation during sample processing or by postthermal annealing. With relaxed GBs the governing deformation mechanism of nanograins shifts from GB migration to formation of through-grain twins or stacking faults.GB relaxation, analogous to GB segregation, offers a novel approach to stabilizing nanograined materials under mechanical loading.

A 3D crystal plasticity model of monotonic and cyclic simple shear deformation for commercial-purity polycrystalline Ti with a harmonic structure

A micromechanical model was developed to describe the monotonic and cyclic simple shear deformation behavior of commercial-purity polycrystalline titanium (CP-Ti) with a harmonic structure (HS) design. The crystalline plasticity theory was implemented to model the constitutive behavior of the hexagonal close-packed (HCP) polycrystals. The grain size effect on the plastic yielding and hardening properties was considered by means of the classic Hall-Petch relation. Multiscale analyses were carried out for a representative volume element (RVE), including an fine-grained (FG) phase and a coarse-grained (CG) phase. This model was implemented into a finite element code (Cast3M) by means of a user subroutine. Monotonic simple shear tests and cyclic shear tests with imposed increasing strain amplitudes were carried out for CG and HS samples. Comparisons between the numerical results and the experimental data revealed the model's ability to describe the overall response correctly for both the HS CP-Ti and the homogenous CG CP-Ti under monotonic and cyclic shear loading.