Estimation of dislocation densities in cold rolled Al-Mg-Cu-Mn alloys by combination of yield strength data, EBSD and strength models

Al-Mg-Cu-Mn alloys have been developed for the packaging industry, in which large cold-working deformations are normally applied that can produce high dislocation densities. In this study, we present a simplified model for the yield strength contributions and apply that to obtain the dislocation densities by determining the orientation factors, which can be obtained via the crystal information of electron backscatter diffraction (EBSD). One alloy subjected to three cold-rolling reductions (10%, 40% and 90%) has been analysed by EBSD, and the density of dislocations are estimated using the strengthening model. This assessment suggests that dislocation densities by the Taylor model are roughly consistent but slightly lower than those determined by transmission electron microscopy.     

The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials

The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) × (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.     

Visualization of grain subdivision by analysing the misorientations within a grain using electron backscatter diffraction

The misorientation relative to the average orientation of a grain and the point-to-point relative misorientation along a line across a moderately cold deformed grain, calculated from an electron backscatter diffraction (EBSD) dataset, are analysed in detail by visualizing both the misorientation angle and the misorientation axis. The significance of monitoring the misorientation axis is illustrated by an example of a grain subdivided into a misorientation band structure. A new technique to visualize the subdivision structure by assigning colours to misorientations in such a way that the contrast is maximized within a grain is introduced and discussed. Furthermore, some methods for grain boundary reconstruction from EBSD datasets are compared with the map of the confidence index in order to provide a validation of the accuracy of these methods.     

Quasi-cleavage fracture planes in spheroidized A533B steel

Electron backscattered diffraction (EBSD) has been used to acquire crystal orientation information around unusual microcracks induced by tensile deformation of notched specimens of spheroidized A533B steel. This unusual fracture mode has been called quasi‐cleavage and occurs at relatively low temperatures with fracture energies below that of the upper shelf. EBSD measurements on sectioned samples showed that the quasi‐cleavage cracks were intragranular. A two‐dimensional analysis technique was used in which EBSD measured crystal orientations were combined with secondary electron imaging to obtain the trace of the crack facet on the section plane. The measurements revealed that the observed crack facets were consistent with crack propagation along the {001} and {011} planes.     

Crystallographic analysis of facets using electron backscatter diffraction

Applications of electron backscatter diffraction (EBSD), also known as backscatter Kikuchi diffraction in the scanning electron microscope (SEM) are first and foremost microtexture and grain boundary misorientation analysis on a single polished section in the specimen. A more subtle and revealing approach to analysis of these data is to use EBSD to probe the orientations of planar surfaces, i.e. facets, which bound crystals. These surfaces include: • grain or phase boundaries • fractures • cracks It is of great interest to know the crystallography of such facets since it provides a key to understanding the physical properties of them.
As far as investigation methodology is concerned, surfaces or facets associated with polycrystals are of two types: exposed or unexposed. Exposed facets, such as a fracture surface, can be viewed directly in the SEM, whereas unexposed facets, such as a grain boundary, are usually revealed as an etched trace on a polished surface. Photogrammetric methods can be used to obtain the positional orientation of an exposed facet, and the crystallographic orientation is obtained either directly from the surface or by indirect sectioning. Calibrated sectioning is required to obtain the equivalent parameters for an internal surface. The present paper compares the methods for obtaining and interpreting the crystallography of facets, with illustrations from several materials.     

Combined application of electron backscatter diffraction and stereo-photogrammetry in fractography studies

The main aim of this paper is to report on recent experimental developments that have succeeded in combining electron back-scatter diffraction (EBSD) with stereo-photogrammetry, compared with two other methods for study of fracture surfaces, namely visual fractography analysis in the scanning electron microscope (SEM) and EBSD directly from facets. These approaches will be illustrated with data relating to the cleavage plane orientation analysis in a ferritic and C-Mn steel. It is demonstrated that the combined use of EBSD and stereo-photogrammetry represents a significant advance in the methodology for facet crystallography analysis. The results of point counting from fractograph characterization determined that the proportions of intergranular fracture in C-Mn and ferritic steels were 10.4% and 9.4%, respectively. The crystallographic orientation was determined directly from the fracture surface of a ferritic steel sample and produced an orientation distribution with a clear trend towards the {001} plane. A stereo-photogrammetry technique was validated using the known geometry of a Vickers hardness indent. The technique was then successfully employed to measure the macroscopic orientation of individual cleavage facets in the same reference frame as the EBSD measurements. Correlating the results of these measurements indicated that the actual crystallographic orientation of every cleavage facet identified in the steel specimens is {001}.     

Improving EBSD precision by orientation refinement with full pattern matching

We present a comparison of the precision of different approaches for orientation imaging using electron backscatter diffraction (EBSD) in the scanning electron microscope. We have used EBSD to image the internal structure of WC grains, which contain features due to dislocations and subgrains. We compare the conventional, Hough-transform based orientation results from the EBSD system software with results of a high-precision orientation refinement using simulated pattern matching at the full available detector resolution of 640 × 480 pixels. Electron channelling contrast imaging (ECCI) is used to verify the correspondence of qualitative ECCI features with the quantitative orientation data from pattern matching. For the investigated sample, this leads to an estimated pattern matching sensitivity of about 0.5 mrad (0.03°) and a spatial feature resolution of about 100 nm. In order to investigate the alternative approach of postprocessing noisy orientation data, we analyse the effects of two different types of orientation filters. Using reference features in the high-precision pattern matching results for comparison, we find that denoising of orientation data can reduce the spatial resolution, and can lead to the creation of orientation artefacts for crystallographic features near the spatial and orientational resolution limits of EBSD.     

Phase differentiation via combined EBSD and XEDS

Electron backscatter diffraction (EBSD) and orientation imaging microscopy have become established techniques for analysing the crystallographic microstructure of single and multiphase materials. In certain instances, however, it can be difficult and/or time intensive to differentiate phases within a material by crystallography alone. Traditionally a list of candidate phases is specified prior to data collection. The crystallographic information extracted from the diffraction patterns is then compared with the crystallographic information from these candidate phases, and a best‐fit match is determined. Problems may arise when two phases have similar crystal structures. The phase differentiation process can be improved by collecting chemical information through X‐ray energy‐dispersive spectroscopy (XEDS) simultaneously with the crystallographic information through EBSD and then using the chemical information to pre‐filter the crystallographic phase candidates. This technique improves both the overall speed of the data collection and the accuracy of the final characterization. Examples of this process and the limitations involved will be presented and discussed.     

A preliminary electron backscattered diffraction study of sintered NdFeB-type magnets

This paper reports, for the first time, the use of electron backscattered diffraction (EBSD) to study orientation in sintered NdFeB type magnets. The magnetic properties of NdFeB magnets are greatly improved if a strong crystallographic texture is firstly achieved, namely, the direction of the c‐axis is along the direction of magnetization. A systematic survey of sample preparation techniques showed that samples that were mechanically polished and then etched gave the most reliable EBSD data. Analyses were made using both fully automated EBSD scans and by EBSD measurements taken after manual movement of the beam. The EBSD results are presented as secondary electron SEM micrographs, orientation images and 001 pole figures. For the selection of grains investigated, the deviation of the c‐axis was shown to be between 10° and 30° from the ideal [001]//magnetization direction. It is demonstrated that EBSD is a valuable tool for characterizing the microstructure and texture relationships and for assessing the performance of the processing routes of NdFeB magnets.     

基于EBSD技术构建弹性各向异性粗晶材料超声仿真模型的研究

针对弹性各向异性粗晶材料晶粒结构和取向定量描述困难,导致超声检测仿真结果与试验符合程度较差的问题,提出基于电子背散射衍射(Electron back-scatter diffraction,EBSD)技术确定晶粒形态及晶体取向的建模思路。利用EBSD技术实测得到了尺寸为96 mm×12 mm的离心铸造奥氏体不锈钢(Centrifugally cast austenitic stainless steel,CCASS)轴-径向截面的晶体取向图谱,选择15°取向相(差)角定义EBSD图谱的晶粒结构,并对晶体取向进行归一化处理。在此基础上借助Bond变换法赋以晶粒在对应晶体取向下的刚度矩阵,对模型中晶粒的弹性特征进行量化表征,建立CCASS超声检测模型。采用时域有限差分法进行数值计算,结果表明:利用该方法能够较好地重现CCASS超声检测特有的结构噪声和主频降低等现象,为揭示超声波在弹性各向异性粗晶结构中的散射机理提供了解决思路。     

Orientation effects on indexing of electron backscatter diffraction patterns

Automated Electron Backscatter Diffraction (EBSD) has become a well-accepted technique for characterizing the crystallographic orientation aspects of polycrystalline microstructures. At the advent of this technique, it was observed that patterns obtained from grains in certain crystallographic orientations were more difficult for the automated indexing algorithms to accurately identify than patterns from other orientations. The origin of this problem is often similarities between the EBSD pattern of the correct orientation and patterns from other orientations or phases. While practical solutions have been found and implemented, the identification of these problem orientations generally occurs only after running an automated scan, as problem orientations are often readily apparent in the resulting orientation maps. However, such an approach only finds those problem orientations that are present in the scan area. It would be advantageous to identify all regions of orientation space that may present problems for automated indexing prior to initiating an automated scan, and to minimize this space through the optimization of acquisition and indexing parameters. This work presents new methods for identifying regions in orientation space where the reliability of the automated indexing is suspect prior to performing a scan. This methodology is used to characterize the impact of various parameters on the indexing algorithm.     

Polycrystal orientation maps from TEM

Determination of topography of crystallite orientations is an important technique of investigation of polycrystalline materials. A system for creating orientation maps using transmission electron microscope (TEM) Kikuchi patterns and Convergent beam electron diffraction patterns is presented. The orientation maps are obtained using a step-by-step beam scan on a computer-controlled TEM equipped with a CCD camera. At each step, acquired diffraction patterns are indexed and orientations are determined. Although, the approach used is similar to that applied in SEM/electron back scattered diffraction (EBSD) orientation imaging setups, the TEM-based system considerably differs from its SEM counterpart. The main differences appear due to specific features of TEM and SEM diffraction patterns. Also, the resulting maps are not equivalent. On these generated by TEM, the accuracy of orientation determination can be better than 0.1 degrees. The spatial resolution is estimated to be about 10nm. The latter feature makes the TEM orientation mapping system an important tool for studies at fine scale unreachable by SEM/EBSD systems. The automatic orientation mapping is expected to be a useful complement of the conventional TEM contrast images. The new technique will be essential for characterization of fine structure materials. To illustrate that, example maps of an aluminum sample produced by severe plastic deformation are included.     

Is fast mapping good mapping? A review of the benefits of high‐speed orientation mapping using electron backscatter diffraction

Orientation mapping using automated electron backscatter diffraction (EBSD) is now a common technique for characterizing microstructures. Improvements in software and hardware have resulted in high‐speed mapping capabilities above 80 000 points h^?1. For ‘routine’ microstructural analyses of materials such as steel and aluminium (e.g. texture and grain size measurements and high angle boundary characterization), high‐speed orientation mapping is an ideal approach with minimal penalty on the final statistics. However, for the accurate analysis of very low angle boundaries and for routine analyses of more difficult materials (e.g. most rock samples), we advocate a more patient approach to orientation mapping with an emphasis on data accuracy and reliability. It is important that the objectives of any EBSD analysis are carefully considered before starting – in this way the maximum potential of an EBSD system can be achieved.     

Correlation of microscopic structures to the strain rate hardening of SPCC steel

The high strain rate properties of steel have been studied for accurate crashworthiness of vehicles. The mechanical properties at high strain rates show different characteristics from those at the quasi-static state. In order to seek for the physical phenomenon of the strain rate hardening, a microscopic investigation has been conducted for the texture evolution and dislocation behavior of steel.Tensile tests were performed at strain rates ranged from 0.001/s to 100/s, which is the common range in practical vehicle crashes to investigate the microstructural variation and dislocation behavior. According to experimental results of the EBSD and TEM experiment, the texture evolution does not develop remarkably with the variation in strain rates, while dislocation structure and behavior investigated by TEM experiments show significant difference with the variation in strain rates. The change in the dislocation structure, behavior, and density with the variation of strain rates clearly explains the mechanism of the strain rate hardening showing that round half-loop dislocations are replaced by straight and crossing dislocations and then by cell structured dislocations.     

The characterization of low-angle boundaries by EBSD

A method of accurately measuring misorientations by electron backscatter diffraction (EBSD), which is an extension of that proposed by Wilkinson and based on the comparison of diffraction patterns, is described. The method has been applied to linescans, and found to improve the angular resolution by a factor of more than 30. The consequent improvement in determining misorientation axes is also analysed. Small changes of orientation very close to some low-angle boundaries were investigated and found to be artefacts of the analysis. Measurements of the area from which diffraction patterns are generated show this to be much larger than the effective spatial resolution of EBSD, and it is concluded that this may be a limiting factor in the use of EBSD for microstructural characterization.     

The complementary use of electron backscatter diffraction and ion channelling imaging for the characterization of nanotwins

On the example of electrodeposited nickel films, it is shown that unique information on twins with dimensions on the nanoscale can be obtained by suitable combination of ion channelling imaging and electron backscatter diffraction analysis, whereas both (routine) single techniques cannot meet the requirements for analysis of these films. High‐resolution electron backscatter diffraction is inadequate for full characterization of nanotwins, but image quality maps obtained from electron backscatter diffraction at least yield a qualitative estimation of the location and number of nanotwins. Complementing this information with ion channelling imaging provides more representative insights into the microstructure, because it supplements the quantitative investigation of the number and width of twin lamellae with additional crystallographic orientation analysis provided by EBSD. To this end, two methods for adjusting EBSD data based on ion channelling images are proposed. Thorough selection of the complementary techniques opens future perspectives for the investigation of other challenging samples with nanoscale features in the microstructure.     

A statistical analysis of the variation in measured crystal orientations obtained through electron backscatter diffraction

Electron backscatter diffraction (EBSD) techniques are used to determine the crystallography of individual metal grains. This paper examines the variability in the orientation of measurements obtained by EBSD. Although precision and statistics of orientation have been explored in the literature, little attention has been paid to formal statistical inference for quantifying variation in orientation measurements. Our intention is to study precision by developing statistical analyses for quantifying multiple sources of orientation variation, given repeat scans of a metal sample. Three sources of variability are simultaneously explored: variation in repeat measurements at a fixed location, variation among locations within a grain, and grain-to-grain variation. Bayes statistical methods will be applied to a hierarchical model with the uniform-axis-random-spin (UARS) components of Bingham et al. [1] to quantify these sources of variation. Repeat scans of a Inconel 600 specimen will be used to provide an illustrating example of how the statistical methods can be used to arrive at precision estimates.     

Microstructural and microtextural characterization of oxide scale on steel using electron backscatter diffraction

High‐temperature oxidation of steel has been extensively studied. The microstructure of iron oxides is, however, not well understood because of the difficulty in imaging it using conventional methods, such as optical or electron microscopy. A knowledge of the oxide microstructure and texture is critical in understanding how the oxide film behaves during high‐temperature deformation of steels and more importantly how it can be removed following processing. Recently, electron back‐scatter diffraction (EBSD) has proved to be a powerful technique for distinguishing the different phases in scales. This technique gives valuable information both on the microstructure and on the orientation relationships between the steel and the scale layers. In the current study EBSD has been used to investigate the microstructure and microtexture of iron oxide layers grown on interstitial free steel at different times and temperatures. Heat treatments have been carried out under normal oxidation conditions in order to relate the results to real steel manufacturing in industry. The composition, morphologies, microstructure and microtexture of selected conditions have been studied using EBSD.     

Anti-plane elastodynamic analysis of a cracked orthotropic strip

Stress analysis is carried out in an orthotropic strip containing a Volterra-type screw dislocation. The distributed dislocation technique is used to construct integral equations for an orthotropic strip weakened by multiple smooth cracks under time-harmonic anti-plane deformation. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determine stress intensity factors for multiple smooth cracks under anti-plane deformation. Several examples are solved and the stress intensity factors are obtained. The effects of the geometric parameters, cracks location and orientation on the stress intensity factors of cracks are investigated.     

EBSD characterization of carbide–carbide boundaries in WC–Co composites

A sample of WC‐6wt%Co was investigated for grain boundary character distribution and occurrence of coincidence site lattice (CSL) boundaries on a statistical basis. For this purpose orientation measurements of the grains were carried out using electron back‐scattered diffraction (EBSD). The dominant misorientation relationships were determined by complementary EBSD data representation tools such as orientation maps, misorientation angle distribution histograms and the sectioned three‐dimensional misorientation space. It was found that the grain boundary character distribution of the material is nearly random and the CSL boundaries are not present in statistically significant amounts. It was also found that the amount of binder phase does not play a role in the formation of special boundaries. The paper focuses on the methodology of characterizing grain boundaries in a hexagonal material using EBSD.