Hall-Petch Type Research Articles

Grain growth kinetics in CoCrFeNi and CoCrFeMnNi high entropy alloys processed by spark plasma sintering

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 Cr7C3 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.

Diagnostics of the Engineering State of Steam Pipelines of Thermal Power Plants by the Hardness and Crack Resistance of Steel

We propose a nondestructive method for the diagnostics of the current state of heat-resistant steels after long-term operation in the steam pipelines of thermal power plants (TPP). It is based on measuring the sizes of ferrite grains and the hardness of 15Kh1M1F heat-resistant steel directly on the pipe surface and on the use of the deduced relationship between these characteristics (of the Hall–Petch type). The plot of this relationship contains two rectilinear parts. The first part agrees with the physical ideas concerning the correlation between the grain size and the strength (hardness) of the material. The second part with a rapid decrease in the hardness of steel is connected not only with the subsequent changes in the microstructure of steel but also with the development of the in-service defects scattered in the volume of the metal. To determine the limiting state of degraded steel, we used one of the parameters of fracture mechanics, namely, the effective threshold amplitude of the stress intensity factor (SIF) ΔKth eff determined with regard for the effect of fatigue crack closure. The application of this parameter is substantiated by the detected inversion of the influence of hydrogen on ΔKth eff (from positive to negative) observed as the degree of in-service degradation of steel increases. The indicated inversion is caused by the transformation of the mechanism of fatigue crack growth in the subthreshold part of the fatigue crack growth diagram from transgranular (caused by microshears at the crack tip in each loading cycle) into a brittler mechanism accompanied by the formation of intergranular fragments of mode I fracture in the damaged areas. Therefore, the threshold of cyclic crack-growth resistance corresponding to this inversion is taken as the critical value $$ \varDelta {K}_{\mathrm{th}\;\mathrm{eff}}^c $$ below which the probability of brittle fracture of the exploited steel becomes much higher. By using the constructed correlation dependence between ΔKth eff and the hardness of the metal and the determined critical value $$ \varDelta {K}_{\mathrm{th}\;\mathrm{eff}}^c, $$ we estimate the critical value of hardness. Below this value, the hazard of uncontrolled brittle fracture noticeably increases due to the presence of defects scattered in the bulk of the metal.

Near-eutectic Zn-Mg alloys: Interrelations of solidification thermal parameters, microstructure length scale and tensile/corrosion properties

Zn-Mg alloys are considered to have potential application in bone implants, since both metals are biocompatible and have biodegradable characteristics. Adding Mg to Zn can boost mechanical and corrosion resistances. However, the literature is very limited on quantifying the interrelation of solidification parameters, microstructural features and mechanical/corrosion properties of Zn-Mg alloys. The present study examines the interrelations of alloy Mg content, macrosegregation effects, morphology and scale of the matrix and eutectic phases, nature of intermetallics and tensile and corrosion properties of near-eutectic Zn-Mg alloys. The alloys samples are obtained by unsteady-state directional solidification resulting in a wide range of solidification thermal parameters and microstructures. We examine microstructural features of both dendritic and complex regular eutectic phases. It is shown that the eutectic exhibits a bimodal pattern with neighboring areas of coarse and fine lamellae. Experimental growth laws relating the primary, secondary and eutectic spacings to the solidification cooling rate and growth rate are proposed. Hall-Petch type equations are derived expressing tensile strength and elongation to dendritic and eutectic spacings. Electrochemical parameters determined by polarization curves during corrosion tests and SEM analyses of corroded areas have shown that the alloy having an essentially eutectic microstructure is associated with better corrosion resistance.

Structural representation of additively manufactured 316L austenitic stainless steel

Three 316L stainless steel materials are studied and reported upon; wrought, as-built additively manufactured (AM), and heat-treated AM material. The AM material was produced from the laser engineered net shaping (LENS) process. Macroscopic uniaxial compression stress-strain curves were obtained for all three materials. The curves were similar for the wrought and heat-treated AM materials but the as-built AM material demonstrated approximately 1.7 times greater flow stress at any given level of strain than the other two materials. Electron-backscatter diffraction analysis of the materials also showed that the microstructures of the three materials differed; with complex grain morphology for the as-built AM material. The mean grain size of each of the three materials also differed. The initial dislocation density was also measured with neutron diffraction and line-profile analysis for both wrought and as-built AM materials with the density in the AM material approximately 2.5 times greater. A single crystal model was proposed to represent the essential features of the three FCC materials accounting for dislocation interactions and representation of grain size via a simple Hall-Petch type term. The strength of this term is evaluated through independent experimental results on traditionally manufactured materials. The model was applied to each of the three materials by simulation of the uniaxial compression experiments by direct numerical simulation of electron-backscatter diffraction images. This allowed for representation of the size of each grain in the simulations. The results suggest that the difference in initial dislocation density of the three materials is the primary factor causing the difference in stress-strain response. Although the differences in grain size contribute to a higher stress for the as-built AM material, the effect is small. Other factors such as internal stress and grain morphology could play a role in mechanical behavior difference and these two factors are also discussed.

Horizontally Solidified Al–3 wt%Cu–(0.5 wt%Mg) Alloys: Tailoring Thermal Parameters, Microstructure, Microhardness, and Corrosion Behavior

In the present experimental investigation, Al–3 wt%Cu and Al–3 wt%Cu–0.5 wt%Mg alloys castings are produced by a horizontal solidification technique with a view to examining the interrelationship among growth rate (GR), cooling rate (CR), secondary dendrite arm spacing (λ2), Vickers microhardness (HV), and corrosion behavior in a 0.5 M NaCl solution. The intermetallic phases of the as-solidified microstructures, that is, θ-Al2Cu, S–Al2CuMg, and ω-Al7Cu2Fe, are subjected to a comprehensive characterization by using calculations provided by computational thermodynamics software, optical microscopy, and scanning electron microscopy/energy-dispersive spectroscopy. Moreover, electrochemical impedance spectroscopy and potentiodynamic polarization tests have been applied to analyze the corrosion performance of samples of both alloys castings. Hall–Petch-type equations are proposed to represent the HV dependence on λ2. It is shown that the addition of Mg to the Al–Cu alloy has led to a considerable increase in HV; however, the Al–Cu binary alloy is shown to have lower corrosion current density (icorr) as well as higher polarization resistance as compared to the corresponding results of the Al–Cu–Mg ternary alloy.

Microstructure and mechanical properties of stainless steel 316L vertical struts manufactured by laser powder bed fusion process

Stainless steel 316L (SS316L) vertical struts with various diameters ranging from 0.25 mm to 5 mm were manufactured by laser powder bed fusion (LPBF) process. A systematic investigation was conducted on the microstructure and mechanical properties of the produced struts. The struts possessed hierarchical microstructures consisting of cellular sub-grain structures inside columnar grains. The primary dendrite arm spacing (PDAS) of the cellular sub-grains decreased monotonically with increasing strut diameter until reaching a plateau after 1 mm. In contrast, the columnar grain width did not show a clear relationship with respect to the variation in the strut diameter. A <110> to <100> texture transition along the building direction (BD) of the struts was observed as the strut diameter decreased from 5 mm to 0.25 mm, which was attributed to the change of the heat extraction direction. Microstructure-property relations were established via Hall-Petch type correlations between the PDAS and the microhardness as well as the PDAS and the strengths of the struts, suggesting the importance of the role played by the cellular sub-grain structures in the strengthening of LPBF manufactured SS316L. Electron backscatter diffraction (EBSD) analysis confirmed that the strong <110> texture within the thicker struts promoted the twinning-induced plasticity, and thus resulted in a better strength-ductility combination compared with that of the thinner struts with <100> texture or weak <110> texture.

Combined Effects of Texture and Grain Size Distribution on the Tensile Behavior of α-Titanium.

This work analyzes the role of both the grain size distribution and the crystallographic texture on the tensile behavior of commercially pure titanium. Specimens with different microstructures, especially with several mean grain sizes, were specifically prepared for that purpose. It is observed that the yield stress depends on the grain size following a Hall–Petch relationship, that the stress–strain curves have a tendency to form a plateau that becomes more and more pronounced with decreasing mean grain size and that the hardening capacity increases with the grain size. All these observations are well reproduced by an elasto-visco-plastic self-consistent model that incorporates grain size effects within a crystal plasticity framework where dislocations’ densities are the state variables. First, the critical resolved shear stresses are made dependent on the individual grain size through the addition of a Hall–Petch type term. Then, the main originality of the model comes from the fact that the multiplication of mobile dislocation densities is also made grain size dependent. The underlying assumption is that grain boundaries act mainly as barriers or sinks for dislocations. Hence, the smaller the grain size, the smaller the expansion of dislocation loops and thus the smaller the increase rate of mobile dislocation density is. As a consequence of this hypothesis, both mobile and forest dislocation densities increase with the grain size and provide an explanation for the grain size dependence of the transient low work hardening rate and hardening capacity.

Microstructure and Tensile/Corrosion Properties Relationships of Directionally Solidified Al–Cu–Ni Alloys

Al–Cu–Ni alloys are of scientific and technological interest due to high strength/high temperature applications, based on the reinforcement originated from the interaction between the Al-rich phase and intermetallic composites. The nature, morphology, size, volume fraction and dispersion of IMCs particles throughout the Al-rich matrix are important factors determining the resulting mechanical and chemical properties. The present work aims to evaluate the effect of the addition of 1wt%Ni into Al–5wt%Cu and Al–15wt%Cu alloys on the solidification rate, macrosegregation, microstructure features and the interrelations of such characteristics on tensile and corrosion properties. A directional solidification technique is used permitting a wide range of microstructural scales to be examined. Experimental growth laws relating the primary and secondary dendritic spacings to growth rate and solidification cooling rate are proposed, and Hall–Petch type equations are derived relating the ultimate tensile strength and elongation to the primary dendritic spacing. Considering a compromise between ultimate tensile strength and corrosion resistance of the examined alloys samples from both alloys castings it is shown that the samples having more refined microstructures are associated with the highest values of such properties.

The microstructural evolution and hardness of the equiatomic CoCrCuFeNi high-entropy alloy in the semi-solid state

The semi-solid slurries of the CoCrCuFeNi high entropy alloy (HEA) were fabricated through the recrystallization and partial melting (RAP) process by cold-rolling and partial remelting. Based on Kim's theory, the solidus-liquidus temperature range and the fraction of the liquid phase as a function of temperature were examined from the Differential Scanning Calorimetry (DSC) curve. The effect of isothermal temperature and soaking time on the microstructural evolution of the CoCrCuFeNi HEA in a semi-solid state were analyzed. The results showed that the globular structure was obtained without the new phase formed for the semi-solid slurries, containing two face-centered-cubic (FCC) solid-solution phases. The average grain size of the globular grain and the globular degree increased with increasing the isothermal temperature and soaking time. The study of the coarsening kinetics indicated that the coarsening process could be described by the modified liquid film migration model. The sluggish diffusion effect of the current HEA leaded to the low coarsening rate, compared with other conventional alloys. However, the existence of the liquid phase in the semi-solid state resulted in a higher grain growth rate for the CoCrCuFeNi HEA with a lower activation energy of 206.9 kJ/mol, compared with the diffusion couple and the grain growth process for the other HEAs at low temperatures. To evaluate the mechanical properties, Vickers hardness was measured to represent the strength of the CoCrCuFeNi HEA. The CoCrCuFeNi semi-solid slurries showed a Hall-Petch type relationship of the average grain size dependence on Vickers hardness.

Correlations of microstructure and mechanical properties of the ternary Sn-9wt%Zn-2wt%Cu solder alloy

The microstructure length-scales (dendritic and eutectic), morphologies and tensile properties of a ternary Sn-9wt.%Zn-2wt.%Cu alloy are compared with those of a binary eutectic Sn-9wt.%Zn alloy. The following experimental/analytical steps were performed: transient directional solidification experiments of the Sn-9wt.%Zn-2wt.%Cu alloy; measurements of secondary dendrite arm (λ2) and interphase spacing (λ); morphology of the eutectic α-Zn phase; determination of thermal parameters such as cooling rate (ṪL) and their evolutions during solidification; and, finally, interrelations of microstructure vs. tensile properties. The addition of 2wt.%Cu causes significant refinement of the eutectic structure. Hall-Petch type experimental expressions outlined the variations of strength and ductility with both λ2 and λ. Very fine Zn globules and needles forming the eutectic in the ternary alloy seems to cause a reversal on ductility behavior, as compared to the tendency observed for the binary Sn-9wt.%Zn alloy. Here, for the ternary Sn-9wt.%Zn-2wt.%Cu alloy ductility increases with decreasing interphase spacing.

Microstructure evolution and mechanical properties of hot deformed Mg9Al1Zn samples containing a friction stir processed zone

Abstract During the last decade, FSP of magnesium alloys has become more popular due to the potential microstructure refinement of their eutectic phases, and interest has increased around the AZ1 that is one of the most commercially used magnesium alloys. In this work, high pressure die cast AZ91 plates were tensile tested at high temperatures after friction stir processing (FSP), with the stirred region in the middle of the gauge length. Samples deformed at 350 °C revealed an increment of ductility that was doubled as compared to those deformed at 300 °C and a strengthening of the nugget was measured by Vickers microhardness (HV). The correlation of HV average values to local grain size confirmed the validity of the Hall–Petch type equation where stress is replaced by hardness. X-rays diffraction and electrical conductivity highlighted the potential increment of solute atoms in solid solution during FSP. Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) investigations performed on as-FSPed and hot deformed samples determined MgAlZn and AlMn particles type evolution through statistical analysis that supported mechanical properties and the strengthening mechanisms.

Tailoring microstructure, tensile properties and fracture process via transient directional solidification of Zn-Sn alloys

The aim of the present study is to determine interrelations of microstructure length-scale, tensile properties and fracture mechanisms of hypoeutectic Zn-Sn alloys. Three compositions were subjected to transient directional solidification: Zn-10, 20 and 40wt%Sn. Grainy-faceted cleavage has been observed as the predominant mode of fracture, which propagated across the Zn-rich plate cells. A clear influence of the formed microstructure and proportion of eutectic may be noted in the fracture features, with alveolar structures also appearing in fracture surfaces. Growth laws relating the eutectic spacing with the growth rate are proposed, which are able to encompass both steady-state and transient solidification conditions. Hall-Petch type equations are developed relating the yield and ultimate tensile strengths, σy and σu, respectively, to the cellular spacing, λ, in which smaller λ values resulted in higher σy and σu.

Properties and microstructure changes in Au-Cu-based alloy with indium addition

In this work, the effects of indium addition on the microstructure, corrosion resistance and hardness in as-cast Au-Cu-based alloys were investigated. The experimental results indicated that as-cast Au-Cu-based shown a typical dendritic structure, and the secondary dendrite arm spacing of alloy was significantly decreased by adding indium element, especially when the In-rich phase existed at interdendritic region. The as-cast samples without indium and with 1 wt.% In were a single Au-Cu-based solid solution with face-centered cubic (f.c.c.) structure. Moreover, the In-rich phase of the alloy with 3 wt.% In shown granular structure, but with 5 wt.% In was network structure. With the indium content increasing, the hardness of alloy was significantly increased and exhibited better Hall-Petch type relationship with the secondary dendrite arm spacing. Minor indium addition enhanced the corrosion resistance of alloy, but when an In-rich phase generated at interdendritic region, the corrosion rate was increased due to the micro-galvanic effect and also affected by the structure of the In-rich phase.

Examination of Thermal Parameters, Primary Dendritic Spacings and Microhardness of a Horizontally Solidified Al-Cu-Mg Ternary Alloy

In this paper, the Al-3wt.%Cu-0.5wt.%Mg alloy was grown by the transient horizontal directional solidification method in a water cooled stainless steel chill. A temperature monitoring system in the metal was used and the registered time-temperature data during the solidification process were applied to determine tip growth rates (VL) and cooling rates (TR) which have been correlated with both primary dendrite arm spacings (λ1) and Vickers microhardness (HV). Characterization techniques by optical and scanning electron microscopy (OM and SEM) were employed and the observed microstructures show an Al-rich dendritic matrix (a-Al) and θ (Al2Cu) and S (Al2CuMg) intermetallic phases within the interdendritic regions. Power and Hall-Petch type experimental equations were proposed to describe the HV profile as a function of the thermal and microstructural parameters (VL, TR, and λ1). In order to investigate the effect of the Mg alloying, a comparative analysis was also performed between the experimental values of this article and the results of previous studies carried out with the Al-3wt.%Cu binary alloy.

Molecular dynamics simulations for responses of nanotwinned diamond films under nanoindentation

We performed molecular dynamics (MD) simulations for the responses of single crystal (SC) and nanotwinned (nt) diamond films under nanoindentation, respectively, aimed to uncover the effects of twin boundary (TB) and twin thickness (δ) on hardness (H) and the corresponding deformation mechanisms. We found the Hall-Petch type relationship between H and δ. We also found that the inelastic deformation of SC-diamond under indentation could mainly be attributed to the nucleation and propagation of 〈110〉{111} dislocation loops. It showed that dislocation blockage and pile up at the TBs may induce additional hardening of the nt-diamond, while the softening of the material could be attributed to: (i) the formation and movement of the dislocation loops parallel with the surface, and (ii) the breakage of TBs, which may serve as new sites for dislocations nucleation.

Dislocation versus grain boundary strengthening in SPD processed metals: Non-causal relation between grain size and strength of deformed polycrystals

In metals that are heavily cold deformed, for instance by a severe plastic deformation process, significant strengthening is caused by the high density of defects such as grain boundaries and dislocations. In this work a model for volume-averaged dislocation and grain boundary (GB) creation is used to show that unless significant annihilation of defects post deformation occurs, the dislocation densities and GB densities in the deformed material are closely correlated. The dislocation strengthening effect thus shows a strong correlation with GB strengthening, and correlation of strength or hardness with d−1/2, where d is the grain size, as in a Hall-Petch type plot, can not be taken as an indication that GB strengthening dominates. Instead, in many SPD processed metals and alloys, dislocation strengthening is the dominant strengthening effect, even though a Hall-Petch type plot shows a good linear correlation.

Interrelationship of thermal parameters, microstructure and microhardness of directionally solidified Bi–Zn solder alloys

Due to the health and environmental concerns associated with lead usage, the research on alternative lead-free alloys for replacing lead-based solders is a global demand. Despite numerous studies on Sn-based lead-free solders in recent years, there is not yet a standard solder alloy able to cover the spectrum of properties furnished by the classic Sn-Pb alloy. In this sense, particular lead-free alloys compositions have been suited for specific needs and the options have been broadening when elements other than tin are used as the base component, such as indium, gold and bismuth. The later element is well known in the hall of lead-free alloys as an alloying option rather than as a base component. This study aims to establish interrelations of solidification thermal parameters (growth and cooling rates), microstructure features (primary and secondary dendrite arm spacings – λ1 and λ2; eutectic spacing – λE and interphase spacing – λint) and hardness of Bi-Zn alloys (1.5wt% Zn-hypoeutectic, 2.7wt% Zn-eutectic, and 5wt% Zn-hypereutectic alloys) samples, which were directionally solidified in unsteady-state conditions under cooling rates similar to those of found in industrial soldering practice. Examination of the resulting microstructures by scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS) permitted the different phases morphologies to be characterized: Bi-rich trigonal dendrites and long Zn fibers, as primary phases of, hypoeutectic and hypereutectic alloys, respectively, immersed in a fiber-like eutectic mixture. The combined effects of macrosegregation, Zn alloying and representative scales of the phases forming the microstructure (λint, λ2 and λE) on hardness of the Bi-Zn alloys are evaluated and Hall–Petch type equations relating λint, λ2 and λE to hardness are proposed.

Dependence of hardness on interlamellar spacing of discontinuous precipitates in cast AZ91 magnesium alloy

The relationship between the hardness and interlamellar spacing of discontinuous precipitates was investigated for a cast AZ91 (Mg–9%Al–1%Zn–0.3%Mn) alloy. After the specimens were solution-treated at 693 K for 24 h, the specimens were isothermally aged for 48 h at different temperatures ranging from 403 K to 473 K, in order to obtain discontinuous precipitates with various interlamellar spacings. It was found that aging below 423 K yielded nodular discontinuous precipitates as the only observed structure at the grain boundaries, while aging above 423 K yielded both discontinuous and continuous precipitates. The hardness of the discontinuous precipitates decreased with an increase in the aging temperature, while the interlamellar spacing of the discontinuous precipitates increased with increasing aging temperature. The hardness of the discontinuous precipitates in the AZ91 alloy was correlated with the interlamellar spacing and can follow a Hall-Petch type relation as in the case of lamellar-structured pearlite in steel.

Phase transformation behaviors and properties of a high strength Cu-Ni-Si alloy

High strength and high electrically conductivity Cu-Ni-Si alloys are important candidate materials for extending the life of currently used elastic-conductor materials. Phase transformation behaviors and properties of a synthesized Cu-6.0Ni-1.0Si-0.5Al-0.15Mg-0.1Cr alloy were investigated systematically. After homogenized for 4h at 940°C, hot rolled by 80% at 850°C, solution treated for 6h at 970°C, cold rolled by 50%, and annealed for 60min at 450°C, the studied alloy approached physical properties of 1097.5MPa in tensile strength and 26.4%IACS in electrical conductivity. Transmission electron microscope observations showed that four precipitation phases including δ-Ni2Si, β-Ni3Si, β-NiAl, and γ′-Ni3Al were formed in the studied alloy, which was subjected to different annealing temperatures. A detailed diagram for isothermal decompositions has been established. The high strength of the studied alloy was primarily attributed to the Orowan precipitation strengthening, and secondary attributed to the solid solution strengthening, the Hall-Petch type grain boundary strengthening, and the work hardening. Multi-precipitation phases of Ni2Si, γ′-Ni3Al, β-Ni3Si played significantly into the strengthening effects, and the low electron diffraction influence of Mg and Cr contributed to both solution strengthening and maintaining a high electrical conductivity. Multi-phase precipitation strengthening and using trace amount alloying elements for solution strengthening will be a new strategy to develop high strength and high electrical conductivity copper alloys.

Measurement of spatial stress gradients near grain boundaries

A correlative method based on electron back scattered diffraction and focused ion-beam–digital image correlation slit milling technique was used to quantitatively determine spatially resolved stress profiles in the vicinity of grain boundaries in pure titanium. Measured local stress gradients were in good agreement with local average misorientation and experimentally calculated geometrically necessary dislocation densities. Stress profiles within few hundred to thousand nanometers near the grain boundary display a local minimum, followed by a typical Hall-Petch type variation of “one over square root of distance”. The observed trends allude to local stress relaxation mechanisms active near grain boundaries.