Modified Williamson-Hall Method Research Articles

Planning Mechanical Behavior of A356 Alloy Wheels by Using Distinct Heat Treatments

The aim of this investigation concerns evaluating the mechanical strength and microhardness values of A356 alloy samples in distinctive heat treatments, including those commonly applied to automotive wheels. It is recognized that A356 and Al-Si-based alloys exhibit considerable versatility across numerous industrial applications. The mechanical behavior obtained is intimately associated with different operational parameters (e.g., cooling rates, solution treatment, quenching, and artificial aging). In this study, a group of samples are quenched at 30, 60 and 80 °C. Another set is quenched and subsequently aged at three different temperatures, i.e., 180, 200, and 220 °C for 5 h, and mechanical responses are compared. Microstructural characterization, X-ray diffraction (XRD) analysis, tensile testing, and microhardness measurements are carried out. Using the Rietveld data and based on the modified Williamson–Hall method, the microstrains, crystallite size, and dislocation densities are calculated. Based on this, the resulting mechanical strengths from distinctive quenching and aging are understood. It was found that there exists a “quasi-optimal range” of operational parameters involving different A356 alloy treatments, which vary depending on the manufacturing route. Considering A356 alloy wheels, the planning of the powder coat treatment before or after T6 treating provides better mechanical properties and ductility.

Surface mechanical property and residual stress stability of shot-peened Mg-8Gd-3Y alloy by in-situ X-ray diffraction

Shot peening (SP) treatment is a common surface treatment used to enhance the mechanical properties and stress corrosion resistance of components. However, accurately measuring the mechanical properties of the thin surface deformation layer using conventional techniques is challenging. This study addresses this limitation using an in-situ X-ray diffraction (XRD) test technique in combination with a micro-tensile tester to determine the thin surface layer mechanical properties of the shot-peened Mg-8Gd-8Y (GW83) alloy. The results demonstrated that SP developed a gradient-strengthened layer with ultrafine grains near the surface layer. The minimum domain size was 51 nm using the modified Williamson–Hall method. The yield strength of the strengthened layer was 24% higher than that of the matrix material. The relaxation rule of the surface compressive residual stress (CRS) was explored under tensile–tensile cyclic loading. It was found that the CRS relaxed within five cycles and tended to be relatively stable there after. The relaxation rule was greatly affected by the initial CRS state, external stress amplitude, and cycle numbers.

Effect of pulsed magnetic field on retained austenite of quenched 8Cr4Mo4V steel under cryogenic condition

High-intensity pulsed magnetic field was applied to modify the microstructure and mechanical propertis of quenched 8Cr4Mo4V bearing steel under the cryogenic environment. The microstructual transformation in 8Cr4Mo4V bearing steel was investigated by X-ray diffraction (XRD), Vibrating sample magnetometer (VSM) and Electron Backscatter Diffraction (EBSD) and so on. The results revealed that individual deep cryogenic treatment (DCT) promote the transformation from retained austenite (RA) in quenched steel to martensite. However, this phase transformation will be inhibited by coupling high-intensity magnetic field with deep cryogenic treatment (MDCT). For instance, the relative reduction of RA content in DCT samples was 10 ± 2%, while that in MDCT samples was 3 ± 3%. Furthermore, the modified Williamson-Hall method was utilized to estimate the dislocation characteristics based on XRD profile analysis. It exhibited that the proportion of edge dislocation significantly decrease from 61.8% to 43.7% by DCT, while this type of dislocation remains almost unchanged after MDCT. Moreover, the microhardness of quenched 8Cr4Mo4V steel became more uniform after MDCT than that of DCT. It can be indicated that the martensite transformation is blocked and carbon cluster is dissolved under the condition of coupling pulsed magnetic field treatment.

Dense dislocations enable high-performance PbSe thermoelectric at low-medium temperatures

PbSe-based thermoelectric materials exhibit promising ZT values at medium temperature, but its near-room-temperature thermoelectric properties are overlooked, thus restricting its average ZT (ZTave) value at low-medium temperatures. Here, a high ZTave of 0.90 at low temperature (300–573 K) is reported in n-type PbSe-based thermoelectric material (Pb1.02Se0.72Te0.20S0.08−0.3%Cu), resulting in a large ZTave of 0.96 at low-medium temperatures (300–773 K). This high thermoelectric performance stems from its ultralow lattice thermal conductivity caused by dense dislocations through heavy Te/S alloying and Cu interstitial doping. The dislocation density evaluated by modified Williamson-Hall method reaches up to 5.4 × 1016 m−2 in Pb1.02Se0.72Te0.20S0.08−0.3%Cu. Moreover, the microstructure observation further uncloses two kinds of dislocations, namely screw and edge dislocations, with several to hundreds of nanometers scale in length. These dislocations in lattice can strongly intensify phonon scattering to minimize the lattice thermal conductivity and simultaneously maintain high carrier transport. As a result, with the reduced lattice thermal conductivity and optimized power factor in Pb1.02Se0.72Te0.20S0.08−0.3%Cu, its near-room-temperature thermoelectric performance is largely enhanced and exceeds previous PbSe-based thermoelectric materials.

Assessing the dislocation density in CdSe nanocrystals from XRD peak profile analysis (XDPPA) assisted by first principles method

Nanocrystalline CdSe has been synthesized via a wet chemical technique followed by characterized using XRD and HRTEM. Classical (CWH) and modified Williamson Hall (MWH) techniques have been used for the determination of microstructures based on the X-ray diffraction peak profile analysis (XDPPA). Rietveld refinement of the experimental XRD pattern provides the refined full width at half maximum (FWHM) of CdSe nanocrystals. Here, the output structural information as obtained from the Rietveld refinement method has been fed into the Quantum Espresso (QE) code for the determination of elastic constants of CdSe using the first principles method. Both the FWHM and elastic constants are used in CWH and MWH analysis. Since the MWH method considers the strain anisotropy of the crystals, it can provide a better fit than the CWH method. In addition to this, the MWH method has been used to find out the dislocations character present in the CdSe nanocrystals. Dislocations are important because these are responsible for inducing strain in the nanocrystals.

Сравнение подходов, основанных на методе Вильямсона–Холла, для анализа структуры высокоэнтропийного сплава Al0,3CoCrFeNi после холодной пластической деформации

Introduction. High-entropy alloys (HEAs) belong to a new and promising class of materials that are attracting the attention of both scientists and engineers from all over the world. Among all alloys of the AlxCoCrFeNi system, HEAs with x ≤ 0.3 attract special attention. Materials with this composition are characterized by the presence of only one phase with a face-centered cubic lattice (FCC). Such alloys have high ductility, excellent corrosion resistance and phase stability at high temperatures. The purpose of this work is to compare several methods of profile analysis on the example of plastically deformed ingots of a high-entropy Al0.3CoCrFeNi alloy. The methods of investigation. Using several methods of profile analysis of X-ray diffraction patterns, the structures of the cold-worked high-entropy alloy Al0.3CoCrFeNi are studied. In addition to the classical Williamson-Hall method, the analysis was carried out using a modified one, as well as a method that takes into account the anisotropy of the elastic properties of the crystal lattice. Research material. Ingots of the high-entropy Al0.3CoCrFeNi alloy deformed by cold rolling with a maximum reduction ratio of 80% were used as the object of the study. Samples were cut from the obtained blanks, which were studied by the method of synchrotron radiation diffraction according to the “transmission” scheme along two (longitudinal (RD) and transverse (TD)) directions of rolled products. Results and discussion. It is shown that the use of the classical Williamson-Hall method leads to a significant error in the approximation of experimental results. The modified Williamson-Hall method has the smallest approximation error and can be recommended for studying the Al0.3CoCrFeNi alloy. An analysis of deformed samples using this method made it possible to reveal several features of the formation of defects in the crystalline structure, which are in good agreement with the classical concepts of the mechanisms of plastic deformation. First, an increase in the degree of deformation of the high-entropy Al0.3CoCrFeNi alloy leads to an almost uniform increase in the number of twins and stacking faults. Secondly, with an increase in the degree of reduction, there is a decrease in the fraction of edge dislocations and an increase in the fraction of screw dislocations in the material. The results obtained correlate well with the results of microhardness measurements.

X-ray Line Profile Analysis of Austenitic Phase Transition and Morphology of Nickel-Free Fe-18Cr-18Mn Steel Powder Synthesized by Mechanical Alloying

In this study, microstructural evolution and phase transition of nickel-free Fe-18Cr-18Mn (wt. %) austenitic steel powders, induced by mechanical alloying, were investigated. X-ray diffraction, scanning electron microscopy, and microhardness testing techniques were used to observe the changes in the phase composition and particle size as functions of milling time. The first 30 h of mechanical alloying was performed in an argon atmosphere followed by nitrogen for up to 150 h. X-ray diffraction results revealed that the Fe-fcc phase started to form after 30 h of milling, and its fraction continued to increase with alloying time. However, even after 150 h of milling, weak Fe-bcc phase reflections were still detectable (~3.5 wt. %). Basic microstructure features of the multi-phase alloy were determined by X-ray profile analyses, using the whole powder pattern modeling approach to model anisotropic broadening of line profiles. It was demonstrated that the WPPM algorithm can be regarded as a powerful tool for characterizing microstructures even in more complicated multi-phase cases with overlapping reflections. Prolonging alloying time up to 150 h caused the evolution of the microstructure towards the nanocrystalline state with a mean domain size of 6 nm, accompanied by high densities of dislocations exceeding 1016/m2. Deformation-induced hardening was manifested macroscopically by a corresponding increase in microhardness to 1068 HV0.2. Additionally, diffraction data were processed by the modified Williamson–Hall method, which revealed similar trends of domain size evolutions, but yielded sizes twice as high compared to the WPPM method.

Ni-incorporated cadmium sulphide quantum dots for solar cell: An evolution to microstructural and linear-nonlinear optical properties

Cadmium sulphide (CdS) compounds have attracted interest due to their applications in opto-electronic devices such as solar cell, sensor, photodiode, etc. The performance of such devices are strongly depends on structure, morphology, and optical properties. Here we report, Ni-incorporated CdS quantum dots(QD) synthesized by conventional chemical co-precipitation method. Ni concentration (0, 2, 4, 6 and 8 wt-%) on Ni-incorporated CdS QD and its microstructural and linear-nonlinear optical properties are extensively investigated. Optical studies derived from UV–ViS. are performed to estimate linear-nonlinear parameters of Ni-incorporated CdS QD by utilizing the absorption and reflection spectra. The optical band gap values decrease from 2.53 to 2.33 eV as Ni content increases. On the other hand, the refractive index values increase with increasing Ni content. Additionally, skin depth, electrical-optical conductivity, and nonlinear parameters are effectively influenced by increasing Ni content in CdS QD.XRD studies confirm that the Ni-incorporated CdS QD exhibits a hexagonal crystal structure with a strong (002) preferential orientation. X-ray peak profile analysis by Scherer method and modified Williamson–Hall method is employed to calculate the crystallite size and lattice parameters such as strain, stress, and energy density of the Ni-incorporated CdS QD. The obtained results indicate that the crystallite size of QD estimated from Scherer and Williamson–Hall methods are correlated and in the range of 2.10–17.89 nm. Energy-dispersive X-ray spectroscopy(EDS) confirms the incorporation of Ni in CdS QD.

Recovery of severely deformed ferrite studied by in situ high energy X-ray diffraction

Recovery of severely deformed ferrite was followed in situ by High Energy X Ray Diffraction during heating and isothermal holding experiments. Dislocation densities during annealing were determined by a modified Williamson Hall method. The deduced recovery kinetics was compared to post-mortem hardness measurements. A temperature dependent saturation of recovery was exhibited during holding. Dislocation density drop and saturation behavior cannot be reproduced simultaneously by the classical physically based models.

Influence of prior deformation temperature on strain induced martensite formation and its effect on the tensile strengthening behaviour of type 304 SS studied by XRDLPA

Type 304 stainless steel is a metastable austenitic stainless steel that undergoes strain induced transformation from austenite to α′ martensite during deformation at room temperature. Role of prior deformation, by rolling at room temperature and at 200 °C (a temperature at which the strain induced martensitic transformation does not occur), on the subsequent room temperature tensile deformation behaviour of the austenite phase is investigated. The changes in dislocation density of the parent phase and the volume fraction of the martensite formed due to deformation were estimated by X-ray diffraction line profile analysis of data obtained from Beam Line - 12 of the Indus 2 synchrotron. The contrast caused by dislocations in the austenite phase has been addressed using the modified Williamson-Hall method. The character of dislocations changes from screw to edge above a critical equivalent strain of ~0.14. The influence of martensite formation on the increase in dislocation density in the austenite phase is confirmed from XRDLPA. An alternative approach to determine dislocation density is proposed which is independent of elastic constants of the material and is found to correlate well with the values determined by the Williamson-Smallman approach. The results obtained from XRDLPA are corroborated with EBSD analysis. It is also seen that the composite strength of the steel, which has undergone different levels of deformation, is related to the changes in dislocation density of austenite and volume fraction of martensite based on Taylor's equation enabling correlation of structure-property.

Evolution of dislocation and stacking-fault densities for a Cu-0.7Cr-0.07Zr alloy during cryogenic tensile test: An in-situ synchrotron X-ray diffraction analysis

Processing at cryogenic temperatures is one of the ways of improving mechanical properties of copper alloys. However, such processing routes may result in unstable microstructures, which make it difficult to understand the deformation mechanisms controlling microstructure evolution during cryogenic deformation. In this study, the microstructure evolution of a Cu-0.7Cr-0.07Zr alloy was analyzed as a function of the flow behavior during tensile tests performed at 123 K and 298 K, through in-situ X-ray diffraction (XRD) experiments in a synchrotron source. The tensile behavior was analyzed in terms of the dynamic recovery rate using the Kocks-Mecking model, while the evolution of stacking-fault density, dislocation density and crystallite size during the tests was estimated by the modified Williamson-Hall method. Solution-treated and peak-aged conditions were tested to assess the influence of particles distribution. At 298 K, the strain-hardening rate was controlled by dislocation glide and the flow stress was affected mainly by particle strengthening. At 123 K, a simultaneous increase in strength and ductility was attributed to the twinning induced plasticity (TWIP) effect, promoted by precipitate interfaces acting as nuclei for stacking-faults, thus delaying necking and increasing the plasticity. Based on the evolution of dislocation and stacking-fault densities with increasing plastic strain, it was concluded that, at 123 K, mechanical twinning predominated at strain levels below 0.15, mainly for aged conditions, while dislocation glide between twin boundaries, and its accumulation, started after TWIP mechanism reached its saturation. • In-situ synchrotron X-ray diffraction of Cu-0.7–0.07Zr has been performed. • Solutionized and peak-aged conditions were evaluated at 298 K and 123 K. • Both temperature and precipitates affected the plastic strain regime. • At 123 K, mechanical twinning predominated at strains below 0.15. • Twinning induced plasticity (TWIP) effect occurred during plastic flow at 123 K.

Effect of stress shot peening on the residual stress field and microstructure of nanostructured Mg-8Gd-3Y alloy

The effects of stress shot peening on the residual stress, microstructure and mechanical property of nanostructured Mg-8Gd-3Y alloy were systematacially investigated by the X-ray diffraction stress analysis, modified Williamson–Hall method, transmission electron microscopy and hardness tester. The results indicated that conventional shot peening led to a gradient nanostructured Mg-8Gd-3Y alloy with a size of 60–100 nm at the top surface layer. The formation of nanograins was primarily ascribed to the dynamic rotation recrystallization. Compared with conventional shot peening, stress shot peening significantly improved the residual stress distribution with a maximum value of −215 MPa and the affected depth. In parallel, stress shot peening conferred superior microstructures at the deformation layer, with smaller domain size, more severe lattice distortion and higher-density dislocations. Owing to inducing finer microstructures and higher compressive residual stresses, stress shot peening produced a stiffer deformation layer. It is concluded that stress shot peening was more potent in promoting the surface layer characteristics of nanostructured Mg-8Gd-3Y alloy than conventional shot peening.

Proposal of Analysis Accuracy Improvement Method in Modified Williamson-Hall Method

Proposal of Analysis Accuracy Improvement Method in Modified Williamson-Hall Method

Tensile behavior and microstructural evolution of a Fe-25Ni-20Cr austenitic stainless steel (alloy 709) from room to elevated temperatures through in-situ synchrotron X-ray diffraction characterization and transmission electron microscopy

Uniaxial tensile tests were done on Fe-25Ni-20Cr Austenitic Stainless Steel (Alloy 709) along with in-situ synchrotron measurement at different temperatures (25 °C, 500 °C, 700 °C and 900 °C). The X-Ray diffraction data was collected in-situ in order to follow the phases present as well as to derive the dislocation density as a function of strain through peak broadening analysis based on the modified Williamson-Hall method and see how trends are affected as a function of temperature. The XRD data were complemented by TEM and STEM-EDX characterization done on the post-experiment samples to observe the deformed microstructures. The paper presents a depiction of the tensile behavior of this advanced steel by interpreting the stress-strain curves and the effect of temperature through the information gained by in-situ XRD and TEM observations as well as fractography done ex-situ on the samples tested to rupture.

Correlation in the Parameters Obtained by Direct-Fitting Method and Modified Williamson-Hall Method for Cold Worked Iron

Correlation in the Parameters Obtained by Direct-Fitting Method and Modified Williamson-Hall Method for Cold Worked Iron

On the comparative assessment of ratcheting-induced dislocation density in 42CrMo4 steel by X-ray diffraction profile analysis and hardness measurement

ABSTRACTThe phenomenon of ratcheting occurs under the influence of non-zero mean stress during cyclic loading; it singificantly reduces the low cycle fatigue life of engineering structures. The present investigation deals with a detailed comparison on the estimation of dislocation densities in the 42CrMo4 steel induced by ratcheting using two different methods, i.e. X-ray diffraction (XRD) profile analysis and hardness. The dislocation densities in the ratcheted specimens were assessed using XRD profile analysis following the modified Williamson–Hall method as well as hardness measurements following the modified Nix and Gao model. The results showed that dislocation density increased in the ratcheted specimens as compared to the unratcheted ones and increase in accumulation of ratcheting strain was correlated with the increase in dislocation densities in the ratcheted specimens. It was established that both hardness and X-ray diffraction profile analysis methods can very effectively be used to assess the dislocation densities in the ratcheted specimens.

Strain analysis in ferritic filler weldment by using the modified Williamson-hall method

A strain analysis study of the Fe-Cr-Ni based low carbon steel for welding application prepared by a thermal-induction furnace were performed using a modified Williamson-Hall (MHW) method. Three different models, uniform deformation (UDM), the uniform deformation stress (UDSM), and the the uniform deformation energy density (UDEDM) models. The optimal results showed by calculation result using UDM method indicate that uniform deformation was present on analyzed material. Based on UDM method, the welded material contains smaller grain size than the based materials. The calculated of average microstrain values of 7.6351×10-4 and -9.21×10-4 for based and welded materials respectively suggest different strain phenomena occurs during welding processes. Microstructure analysis by means of transmission electron microscopy reveal that based material consist of grains in 50-100 nm sizes and with planar defects are also detected.

Residual stress and microstructure evolution of shot peened Ni-Al bronze at elevated temperatures

In this work, the relaxation of residual stress and strain hardening effect along with the evolution of microstructure of Ni-Al bronze at elevated temperatures were investigated. The samples were peened and then isothermal annealed at temperatures ranging from 200 to 400°C for different time. The residual stress in the surface layer were determined by X-ray stress analyzer. Variations of domain size and micro-strain were estimated by X-ray line profile analysis in which the modified Williamson-Hall method with uniform deformation energy density model was employed. Experimental results showed that both residual stress and strain hardening effect relaxed dramatically in the initial stages and then gradually reached steady state. Although partially recrystallization occurred at higher temperatures, only part of compressive residual stress relaxed at each fixed temperature. The micro-strain and the dislocation density also declined with the heating temperature and exposure time increasing, which were presumably related to the vacancy transportation and dislocation rearrangement. Meanwhile, as demonstrated by XRD and TEM, the domain size increased significantly. The thermal relaxation activation enthalpies of residual stress and X-ray full width at half maximum were evaluated via Zener-Wert-Avrami relationship. The latter value was larger than that of residual stress, which indicated that the strain hardening effect was more difficult to fade at elevated temperatures. Hardness also reduced continuously during annealing process, which was mainly ascribed to the increased domain size and the weakening strain hardening effect. No phase transition occurred and the crystallinity was improved after annealing treatment. In the present study, the residual stress did not release completely even after annealing at the highest aging temperature for 2h, which meant that shot peening could enable Ni-Al bronze alloys to keep excellent thermal stability of beneficial compressive residual stress.

Determination of contrast factors for cubic slip-systems and their application in the microstructural characterization of binary Fm[formula omitted]m materials

Theoretical attempts to rationalize the strain anisotropy of crystalline systems in terms of dislocations often include the calculation of contrast factors. However, the evaluation of such parameters can be cumbersome because elastic properties and symmetry restraints must be simultaneously taken into account, especially when calculating the distortion tensor and the elastic contributions in slip coordinate systems. In this study, a dislocation-dependent coordinate system is introduced to obtain straightforward expressions for the evaluation of individual contrast factors by a first principles approach. Therein, we report the contrast factors for KCl and NaCl regarding edge and screw dislocations; a further analysis of their microstructure was carried out through the modified Williamson-Hall method.

XRDおよびEBSDを用いた23Cr-45Ni-7W合金溶接部のひずみ評価

The residual strain of 23Cr-45Ni-7W Alloy welds was estimated by the change in the dislocation density and the average misorientation within grains. X-ray diffraction was used to measure the dislocation density by the modified Williamson-Hall method and the modified Warren-Averbach method. EBSD technique was used to measure the orientation in order to calculate the grain orientation spread (GOS) as the average misorientation within grains. Tensile tests were conducted at room temperature and were interrupted to prepare a number of specimens with different residual strain. The changes in the dislocation density and GOS with the strain were investigated using the interrupted specimens and the heat-affected zone in 23Cr-45Ni-7W Alloy welds. The dislocation density and GOS increased approximately linearly with increase in the residual strain. The residual strain of the heat-affected zone in 23Cr-45Ni-7W Alloy welds was evaluated from the linear relationships. The residual strain near the bond line estimated by the dislocation density was 3.7%;the estimated residual strain decreased with increases in the distance from the bond line. At 10 mm away from the bond line, the residual strain became less than 1%. The change in the residual strain near the bond line estimated by GOS showed a similar tendency.