Dislocation Density Measurements Research Articles

Influences of Vanadium and Silicon on Case Hardness and Residual Stress of Nitrided Medium Carbon Steels

Medium carbon steels alloyed with two levels each of V and Si were heat treated to form tempered martensite and bainite, followed by nitriding to evaluate their effects on case hardness and residual stress. Microstructures were quantitatively characterized with Vickers microhardness testing, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), X-ray diffraction (XRD), conventional transmission electron microscopy (CTEM), and scanning transmission electron microscopy (STEM). Measurements of subgrain size, cementite size, dislocation density, and volume fractions of nitride precipitates were combined in a strength model to predict the contributions of V and Si to maximum case hardness after nitriding. Higher V contents lead to increases in maximum case hardness by increasing the volume fraction of MX precipitates. Increases in Si content lead to increased maximum case hardness by increasing the volume fraction of amorphous (Si and Mn)-containing nitride precipitates; the presence of Mn in these precipitates has not been previously reported. Higher Si contents also lead to increases in solid solution strengthening because the majority of Si remains in solution in the ferrite matrix. Greater volume fractions of MX and (Si and Mn)-containing nitrides both lead to higher magnitudes of compressive residual stress. The results presented here demonstrate that alloying can improve the properties after nitriding, providing insight into advanced nitriding steel grades and potentially enabling a wider range of steel microstructures to be nitrided without a debit in performance.

On the mechanistic understanding of annealing-induced strength enhancement of ultrafine-grained high-Mn steel

Severe plastic deformation (SPD) introduces both high dislocation density and profound grain refinement in metals, triggering metastable microstructures associated with non-equilibrium boundaries and vacancy agglomerates. Subsequent solute migration induced by low-temperature annealing has the potential to release complex microstructures, and thereby increase strength. However, a mechanistic understanding of the annealing-induced strength enhancement in the SPD-processed high-Mn steel with ultrafine grains has remained elusive, particularly at the nanoscale. Here, the impact of subsequent annealing on the tensile properties of the SPD-processed high Mn steel with ultrafine grains was investigated. C detection and dislocation density measurements proved that both severe lattice distortion and high density of dislocations (resulting from the SPD route) are the precursors of C-clusters during the subsequent annealing. Formation of the nano-sized C-clusters in the SPD-annealing-treated samples interrupts dislocation gliding upon loading, increasing the yield strength by 15% at comparable ductility compared to those of the SPD-processed samples with same grain sizes. We attribute the increased strength to dislocation forest hardening via annealing-driven C-clusters, qualifying a low-temperature annealing step as a replicable strategy for further improving the strength of the SPD-processed nanostructured materials.

Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale

The equations of dislocation transport at finite crystal deformation were developed, with a special emphasis on a vector density representation of dislocations. A companion thermodynamic analysis yielded a generalized expression for the driving force of dislocations that depend on Mandel (Cauchy) stress in the reference (spatial) configurations and the contribution of the dislocation core energy to the free energy of the crystal. Our formulation relied on several dislocation density tensor measures linked to the incompatibility of the plastic distortion in the crystal. While previous works develop such tensors starting from the multiplicative decomposition of the deformation gradient, we developed the tensor measures of the dislocation density and the dislocation flux from the additive decomposition of the displacement gradient and the crystal velocity fields. The two-point dislocation density measures defined by the referential curl of the plastic distortion and the spatial curl of the inverse elastic distortion and the associate dislocation currents were found to be more useful in deriving the referential and spatial forms of the transport equations for the vector density of dislocations. A few test problems showing the effect of finite deformation on the static dislocation fields are presented, with a particular attention to lattice rotation. The framework developed provides the theoretical basis for investigating crystal plasticity and dislocation patterning at the mesoscale, and it bears the potential for realistic comparison with experiments upon numerical solution.

Effect of Gd on Dynamic Recrystallization Behavior of Magnesium During Hot Compression

Dynamic recrystallization (DRX) behavior of two binary Mg–0.5Gd and Mg–1.5Gd alloys and pure Mg were studied by hot compression in the temperature range of 300–450 °C to explore the role of Gd on DRX grain size refinement and kinetics. The dependency of DRX grain size on the Gd content during hot compression was quantified and expressed based on the Zener–Hollomon parameter. While the exponent of the Zener–Hollomon parameter was obtained as − 0.118 independent of the Gd content, the proportionality constant varied by Gd concentration. The developed expression revealed significant reduction in the DRX grain size of the Mg–Gd alloys. The volume fraction of dynamically recrystallized grains was calculated by applying the Johnson–Mehl–Avrami–Kolmogorov type model, which resolved the faster kinetics for DRX of the Mg–1.5Gd alloy compared to ones for the Mg–0.5Gd alloy and pure Mg. The higher driving pressure for DRX of the Mg–1.5Gd alloy was justified based on dislocation density measurements at the onset of DRX through the Williamson-Hall method. The role of Gd on dynamic recrystallization behavior of Mg during hot compression was studied. A linear relationship between the DRX grain size and Gd content was developed and dislocation density of the binary Mg-Gd alloys and pure Mg at the onset of DRX during hot compression was measured.

In situ high energy X-ray diffraction measurement of strain and dislocation density ahead of crack tips grown in hydrogen

The deformation fields near fatigue crack tips grown in hydrogen and in air were measured using high-energy x-ray diffraction. A larger magnitude of elastic strain was observed in the hydrogen case compared to the air case. The magnitude of elastic strain was quantified through an effective crack tip stress intensity factor. The dislocation profile ahead of the crack was probed via x-ray line broadening and electron back-scatter diffraction was used to assess the crack path (intergranular vs. transgranular). Ahead of the crack tip grown in hydrogen, an order of magnitude lower dislocation density, compared to a baseline density far from the crack, was observed. This decrease in dislocation density was not observed in the air case. These differences are discussed in terms of two leading hydrogen embrittlement mechanisms, Hydrogen Enhanced Localized Plasticity (HELP) and Hydrogen Enhanced Decohesion (HEDE). We have observed a decrease in transgranular cohesion (transgranular HEDE), as well as an increase in intergranular fracture. The measurements of dislocation activity support a model of a decrease in intergranular cohesion (intergranular HEDE) which is likely facilitated by the HELP mechanism. This suggests that the increase in fatigue crack growth rate is due to a sum of the two effects of hydrogen, in which the crack grows faster in the transgranular fracture mode and faster due to an increase in a new mode of intergranular fracture.

Effect of second-phase particles evolution and lattice transformations while ultrafine graining and annealing on the corrosion resistance and electrical conductivity of Al–Mn–Si alloy

Al–Mn–Si specimens were subjected to constrained groove pressing, cold-rolling and annealing, respectively. Microstructure characterizations indicated that second-phase particles were arranged along the material flow direction and did not orient at grain boundaries. Analysis of x-ray diffraction patterns exhibited that severe straining led to dynamic restoration and lattice swelling. Since findings for annealed specimens did not follow a linear trend; however, they were in good agreement with corrosion characteristics and electrical conductivity results. Outputs of electrochemical polarization test revealed that corrosion rate has direct correlation with lattice distortion and dislocation density measurements. As most of the particles have not remarkable open circuit potential with aluminum matrix along with other existent particles and also did not contain required size to act as origin of pitting corrosion, they would capable of forming the passive layer porous and subsequently could prevent encouraging uniform passive layer. In the case, they let the aggressive ions to penetrate beneath the passive layer and react with talented sites like dislocations and grain boundaries. Scrutiny of lattice d-spacing proved that by imposing deformation, electrical conductivity alters by change in d-spacing since by annealing at elevated temperature conductivity follows the winner of competition between d-spacing, lattice distortion and particles transformations.

Short communication: Assessment of the dislocation density using X-ray topography in Al single crystals annealed for long times near the melting temperature

Earlier work by the authors determined the dislocation density as a function of time in aluminum single crystals annealed near the melting temperature using etch-pits. It was found that the dislocation density is stable and unchanged even with annealing times up to one year for statically annealed Al single crystals with an initially low dislocation density. As several investigators have suggested that etch-pits are not reliable compared to transmission electron microscopy in assessing the dislocation density, the current study utilized x-ray topography at a synchrotron for dislocation density measurements. This work, then, is a short paper complementing the authors earlier work by using a new, reliable, but rarely utilized non-destructive technique to measure the dislocation density. The results confirm the trend of the earlier study using etch-pits by the authors.

Experimental evaluation and prediction of end-forming behavior of friction stir processed Al6063T6 tubes at different tool traverse speeds

In the present work, end forming of friction stir processed (FSPed) Al 6063T6 tubes at varying traverse speeds has been studied. End expansion, reduction, and beading experiments are conducted to evaluate the effect on the mechanical properties of the processed zone, forming load evolution, and tube thinning. Finite element simulations of the end-forming processes are done and the results like load requirement and instabilities are validated. The traverse speed affects the tensile behavior and end forming of tubes significantly. The dislocation density measurement confirms its relation with strain hardening exponent of the processed zone. The tensile properties, end-forming behavior, and energy absorption capacity of the FSPed Al tube encourage the use of such tubes in place of raw tube for end-forming applications, with appropriate parametric optimization. Occurrence of instabilities during end forming needs attention so that the applicability is not restricted. Finally, finite element simulation results on load requirement correlate well with experimental data. The predictions from thickness strain mapping method, specifically the displacement at the onset of instabilities, in beading are acceptable, while considerable difference is seen in tube expansion. Wrinkling predictions during end reduction are encouraging.

Lower-bound dislocation density mapping in microcoined tantalum using high-resolution electron backscatter diffraction

High-resolution electron backscatter diffraction (HR-EBSD) is used to map the geometrically necessary dislocation (GND) density in the cross-sections of annealed, rolled, and microcoined tantalum foils that are typical targets used in modern laser-induced compression materials science studies. The microcoined samples are characteristic of microforming, where the deformation length scale is on the order of the grain size (~50 μm). In particular, inhomogeneities in dislocation density maps across 0.1–1 mm regions of interest are compared with expectations from slip line field approximations. The average HR-EBSD GND dislocation density measurements in various annealed and cold worked tantalum samples are compared with corresponding dislocation density approximations from microhardness measurements. GND densities in the range 1013 − 1015 m−2 are typical.

Comparison of electron backscatter and X-ray diffraction techniques for measuring dislocation density in Zircaloy-2

Two methods for measuring dislocation density were applied to a series of plastically deformed tensile samples of Zircaloy-2. Samples subjected to plastic strains ranging from 4 to 17% along a variety of loading paths were characterized using both electron backscatter diffraction (EBSD) and synchrotron X-ray line profile analysis (LPA). It was found that the EBSD-based method gave results which were similar in magnitude to those obtained by LPA and followed a similar trend with increasing plastic strain. The effects of microscope parameters and post-processing of the EBSD data on dislocation density measurements are also discussed. The typical method for estimating uncertainty in dislocation density measured via EBSD was shown to be overly conservative, and a more realistic method of determining uncertainty is presented as an alternative.

Effects of alloying and processing modifications on precipitation behavior and elevated temperature strength in 9% Cr ferritic/martensitic steels

Two low-carbon 9-Cr ferritic-martensitic steels were designed with the aim of decreasing M23C6 and maintaining or increasing MX phase fraction. A low-carbon (LC) alloy and a low-carbon, zero-niobium (0Nb) alloy were fabricated, their designs based upon the P92 alloy system. Solutionizing temperatures to maximize V and Nb in solution while avoiding δ-ferrite were determined to be 1170 °C for the P92 alloy and 1050 °C for LC and 0Nb, significantly lower than predicted using ThermoCalc® modeling. As was intended, the M23C6 phase fraction was reduced for LC and 0Nb alloys after both heat treating and aging relative to the base P92 alloy, as determined by wide angle x-ray scattering (WAXS) analysis. Dislocation density measurements from x-ray line broadening in P92 and LC suggest these alloys had more stable dislocation substructures than 0Nb at lower temperature and shorter time aging conditions. While LC exhibited lower microhardness than P92 at room temperature, the tensile properties were comparable at 650 °C, suggesting that elevated temperature strength can be achieved with lower carbon contents. Aging studies showed that P92 had a more stable microstructure for higher temperature and longer time aging conditions. The P92 alloy also had a longer stress rupture life, implying that the M23C6 precipitate contribution to thermal stability is important. Evidence of Z-phase was discovered for the LC alloy aged 10,000 h at 650 °C, corresponding to decreased strength and increased ductility. Overall, the stress rupture lives of the modified heat-treatment variations of P92 and LC compare favorably to literature values for 9% Cr steels with conventional heat treatments.

Comparison of thermal stress computations in Czochralski and Kyropoulos growth of sapphire crystals

Thermal stress computations during sapphire growth are compared between a resistive Czochralski furnace and a Kyropoulos inductive furnace. 2D – axisymmetric global simulations are performed to compute the thermal field in the furnace and the convection in the melt. Temperatures carried out from global modeling at a given stage of the growth process, are used for thermal stress computations in the crystal. Three-dimensional stress analysis, which takes into account the anisotropic elastic constants of sapphire, shows nearly axisymmetric von Mises stress distribution in the crystal. It is shown that applying 2D – axisymmetric modeling of thermal stress may result in significant errors. Computations performed for a crystal of 10 cm in diameter grown in a Kyropoulos furnace show only a thin region of 2–3 mm with high thermal stress located at the crystal periphery. The model predicts very low thermal stresses in the central part of the crystal. Simulations of an ingot grown by Czochralski technique, show higher thermal stresses in almost the whole volume of the crystal. Numerical computations are in agreement with our previous measurements of dislocation density in sapphire crystals grown by the Kyropoulos method. The present numerical results can explain the experimental observations showing that sapphire crystals grown by Czochralski technique have a much higher dislocation density than Kyropoulos grown ingots.

Guidelines for establishing an etching procedure for dislocation density measurements on multicrystalline silicon samples

With multicrystalline silicon becoming the main material used for photovoltaic applications and dislocations being one of the main material limitations to better solar cell efficiency, etch pit density measurements are gaining more importance. Traditionally, etch pit density measurements are based on selective etching of silicon samples. The majority of the etchants have been developed for monocrystalline samples with known orientation, while those developed for multicrystalline samples have been less investigated and might need some optimization. In this study, we use and compare the PVScan tool, which provides a quick way to assess dislocation density on selectively etched samples, and microscope image analysis. We show how the etching methods used for dislocation density measurements can affect the results, and we suggest how to optimize the Sopori etching procedure for multicrystalline silicon samples with high dislocation densities. We also show how the Sopori etchant can be used to substitute Secco while maintaining a high precision of dislocation density measurements, but without the toxic hexavalent chromium compounds.

On the evaluation of dislocation densities in pure tantalum from EBSD orientation data

We analyze measurements of dislocation densities carried out independently by several teams using three different methods on orientation maps obtained by Electron Back Scattered Diffraction on commercially pure tantalum samples in three different microstructural states. The characteristic aspects of these three methods: the Kernel average method, the Dillamore method and the determination of the lattice curvature-induced Nye’s tensor component fields are reviewed and their results are compared. One of the main features of the uncovered dislocation density distributions is their strong heterogeneity over the analyzed samples. Fluctuations in the dislocation densities, amounting to several times their base level and scaling as power-laws of their spatial frequency are observed along grain boundaries, and to a lesser degree along sub-grain boundaries. As a result of such scale invariance, defining an average dislocation density over a representative volume element is hardly possible, which leads to questioning the pertinence of such a notion. Field methods allowing to map the dislocation density distributions over the samples therefore appear to be mandatory.

PERC Solar Cell Performance Predictions From Multicrystalline Silicon Ingot Metrology Data

The influence of the as-grown material quality on the performance of multicrystalline silicon PERC solar cells is investigated using recently developed spectral photoluminescence imaging techniques on ingot level, i.e., on bricks, and is examined in conjunction with photoluminescence measurements on as-cut wafers. The effect of material parameters, including bulk lifetime, dislocation density, and resistivity, is studied with regard to their effect on cell output across a sample set of three directionally solidified production bricks of widely varying bulk lifetime and dislocation density. The data are analyzed statistically using a linear mixed model. Bulk lifetime is found to be a statistically significant predictor of the cell performance across the studied sample set. The prediction accuracy is found greatest for material with low dislocation density where a linear correlation between cell performance and as-grown bulk lifetime is found. The dislocation densities measured on as-cut wafers remain a more accurate predictor for medium to highly dislocated material, but predictions are improved by adding bulk lifetime as an additional predictor in the model. Dislocation density measurements taken on the side facets of silicon bricks were identified as not being significant predictors for this dataset. However, the detection may enable the classification of bricks into broad dislocation defect classes, which is expected to further improve the overall prediction accuracy for models which use brick metrology only. With increasing cell efficiencies and an ongoing trend of reducing the dislocation density in industrial multicrystalline wafers, our findings suggest that the bulk lifetime, measurable on bricks, i.e., directly after ingot growth, becomes an increasingly relevant parameter.

Dynamic strain aging in DP steels at forming relevant strain rates and temperatures

Mechanical testing of dual phase (DP) steels at low strain rates (10−3s−1) have shown that they are susceptible to dynamic strain aging (DSA) between 100°C–400°C. During industrial forming processes at intermediate strain rates (1–102s−1), the local temperatures may rise to the DSA range due to deformation heating which may disturb the exceptional formability of these steels. In this study, two grades of DP steel (DP590 and DP800) are tested at thermomechanical conditions relevant to forming and the effects of DSA on the formability are established. Test results show that the DSA controls the deformation between 200°C–300°C through serrations in the stress-strain curves of both grades. With increasing strain rates (up to 1s−1) and temperatures, DSA intensifies and results in severe drops in uniform and total ductility with negative strain rate sensitivity, indicating poor formability at these conditions. A detailed analysis of the serrations coupled with dislocation density measurements by x-ray analysis suggests that the serrations can be linked to a periodic microstructural feature.

Geometrically necessary dislocation density measurements at a grain boundary due to wedge indentation into an aluminum bicrystal

An aluminum bicrystal with a symmetric tilt Σ43 (3 3 5)[1 1 0] coincident site lattice grain boundary was deformed plastically via wedge indentation under conditions that led to a plane strain deformation state. Plastic deformation is induced into both crystals and the initially straight grain boundary developed a significant curvature. The resulting lattice rotation field was measured via Electron Backscatter Diffraction (EBSD). The Nye dislocation density tensor and the associated Geometrically Necessary Dislocation (GND) densities introduced by the plastic deformation were calculated. The grain boundary served as an impediment to plastic deformation as quantified through a smaller lattice rotation magnitude and smaller GND density magnitudes in one of the crystals. There is evidence that the lattice rotations in one grain brought a slip system in that grain into alignment with a slip system in the other grain, upon which the impediment to dislocation transmission across the grain boundary was reduced. This allowed the two slip systems to rotate together in tandem at later stages of the deformation. Finite element crystal plasticity simulations using classical constitutive hardening relationship capture the general features observed in the experiments.

Microstructure, accumulated strain, and mechanical behavior of AA6061 Al alloy severely deformed at cryogenic temperatures

The combination of Severe Plastic Deformation (SPD) and cryogenic temperatures can be an efficient way to obtain metals and alloys with very refined microstructure and thus optimize the strength-ductility pair. However, there is still a lack of studies on cryogenic SPD process and their effects on microstructure and mechanical properties, especially in precipitation-hardenable aluminum alloys. This study describes the effect of low temperature processing on microstructure, aging kinetic and tensile properties of AA6061 Al alloy after cryo-SPD. Samples of AA6061 Al alloy in the solutionized state was processed by Equal-channel angular pressing (ECAP) at 77 K and 298 K, up to accumulate true strains up to 4.2. Results indicated that the aging kinetic is accelerated when deformation is performed at cryogenic temperature, dislocation density measurement by x-ray and diffraction analysis at TEM achieved a saturation level of 2×1015 m−2 by ECAP at 298K and 5×1015 m−2 after cryogenic ECAP plus precipitation hardening. The same level of yield strength was observed in both deformation procedures but an improvement in uniform elongation was achieved by cryogenic ECAP followed by a T6 treatment

Dislocation density and mechanical threshold stress in OFHC copper subjected to SHPB loading and plate impact

The dislocation density and mechanical threshold stress (MTS) of oxygen-free high-thermal-conductivity (OFHC) copper loaded at strain rates in the range of 102 to 106s−1 were measured. Moderate-strain-rate (102 to 104s−1) experiments were performed using a Split Hopkinson Pressure Bar (SHPB). A steel collar was placed around each specimen to control the maximum loading strain. High-strain-rate (105 to 106s−1) experiments were carried out using a 57-mm-bore single-stage gas gun. The radial release effect was eliminated using the momentum trapping technique. The loaded samples were recovered, and the dislocation characteristics and dislocation density were determined by X-ray diffraction profile analysis. The fraction of the screw dislocation was found to decrease with increasing loading strain and strain rate. The dislocation density was found to lie between 1.8×1014 and 2.2×1015m−2. Quasi-static reload compression tests were performed on the recovered samples at room temperature. The mechanical threshold stress (or the flow stress at 0K) was obtained by fitting the reload stress–strain data to the MTS model. The results of analysis of the equivalent strain, mechanical threshold stress, and dislocation density measurements suggest that the relation between the mechanical threshold stress and the dislocation density can be described well by the Taylor relationship.

Constrained groove pressing and subsequent annealing of Al-Mn-Si alloy: Microstructure evolutions, crystallographic transformations, mechanical properties, electrical conductivity and corrosion resistance

Al-Mn-Si specimens were severe plastic deformed (SPDed) through constrained groove pressing (CGP) by εeff=1.16, 232, and 3.48. CGPed sheets were subsequently annealed at 150, 250 and 350°C to investigate complementary treatment route on macro- and microscale properties of heavily strained alloy. Microstructure evolutions in deformed and post-annealed states along with their associated mechanisms such as recovery, recrystallization and strain induced grain boundary migration (SIGBM) were studied and analyzed. SIGBM as an indication for inhomogeneous grain growth was traced by transformations in grains' aspect ratio. Microanalysis of crystallographic characteristics by means of X-ray diffraction (XRD) patterns revealed that (111) planes were the main crystallographic index in CGPed and annealed alloys since preservation up to 350°C had amplified the (200) and deteriorated the intensity of (311) planes. Dislocation density measurements implied the dynamic recovery occurrence in CGP (εeff=2.32) which had affected mechanical characteristics, electrical conductivity and corrosion resistance of the utilized alloy. Mechanical properties through tension and hardness tests had been examined since the maximum YS, UTS, and hardness of 118MPa and 141MPa, 52Hv obtained for CGPed specimen (εeff=3.48) compared with annealed alloy with the values of 85MPa and 112MPa, and 29Hv, respectively.