2. The relationship between micro-texture and strain

Standard SEM-based EBSD primarily provides maps of the spatial distribution of crystal orientation, i.e. crystallographic texture, and nearest neighbour disorientation, i.e. meso-structure. It is widely understood  both factors contribute to the mechanical properties of polycrystalline materials and this arises from the orientation relationship between the internal stress state and the crystal slip systems. The Taylor and Schmidt models have been the standard method of estimating likely consequences; however, estimates are approximate because internal stress state details are poorly known, particularly in the more anisotropic materials and where loading conditions other than simple uniaxial tension apply.

Accurate knowledge of the internal stress state is important in understanding and controlling the recrystallization process, the precursor to determining texture.

This estimation challenge is further compounded when we are dealing with materials with multiple phase and high degrees of precipitation.

3. Conventional EBSD: Only a partial picture

Many attempts using conventional EBSD have been made to try to assess a material’s internal stress state. These attempts have been indirect and only produced qualitative results because of:

• The relatively poor angular resolution possible in conventional EBSD, 0.5 degrees as determined using the Hough Kikuchi band detection algorithm.
• Distortions within individual patterns, which occur because of elastic strain, being completely inaccessible.

Therefore, although the spatial resolution of the EBSD technique is capable of detecting crystallographic changes within individual grains, the measurements are not precise enough to interpret residual stress or dislocation density. To date, the best measurements achieved are the mapping of EBSD pattern quality and an assessment of the average disorientation between an individual point within a grain with its next nearest neighbours, the latter known as the metric, ‘Kernel Average’. Kernel Average Maps (KAM) became the norm for assessing internal strain. However, as shown in Figure 1 below,

the conventional KAM approach to assessing strain is limited by its low precision and the presence of artifacts from the Hough transform which can lead to inaccurate results.

High Angular Resolution EBSD (HREBSD) offers a more precise measurement of strain, addressing effectively the shortfalls of the KAM approach.

4. Bridging the Gap: HREBSD gives a rigorous measure of strain

HREBSD gives a rigorous quantitative measure of residual strain, ranging from  elastic strains as small as 0.01% to measurement of dislocation density distributions over the GND range 1x1012m-2 to 1014m-2.

The HREBSD evidence-based and tested technique is based on a cross-correlation procedure or XCF between an EBSD pattern recorded from a reference region within a grain, normally that with the lowest KAM value as measured using conventional EBSD, and all other points within the grain. This technique determines the full strain tensor and from there, through application of the generalised Young’s modulus, i.e. complete elastic stiffness tensor, to a measure of the stresses and the energy density distribution/von Mises’ stress metric. For example, it is possible to correlate slip line observations and the shear stresses acting on these lines to tensile stress concentrations at grain boundaries and to then relate both to a set of sample reference axes or to the three reference axes defining the crystal orientation. A good example of this is shown in Figure 1 below.

Figure 1. Sample HR EBSD maps of stress and GND density map at tensile loading of 138N

a) stress map in tensile loading direction, (b) and (e) transverse normal stresses,  (c) and (f) shear stresses,  (d) SEM micrograph showing slip line distribution

(g) total GND density map.

5. HREBSD: Reveals inaccuracies in conventional EBSD

Using the HREBSD technique improves the angular resolution to 0.0006˚  leading to far higher quality KAM values than otherwise possible; the example in Figure 2 below shows how the normal KAM map can be very misleading. However, what is of far more value is that HREBSD enables an analysis  which reveals the distribution of the residual geometrically necessary dislocation (GND) density; these dislocations are needed to assess the measured disorientations. This HREBSD  analysis encompasses the separate contributions from edge and screw dislocation components together with the total GND density as shown in Figure 1(g) above; measurements are based on the Nye dislocation tensor and, therefore, are dependent on the criterion of minimum residual energy. The HREBSD result is a lower bound case as the disorientations in the direction normal to the surface, which cannot be measured without serial sectioning, are set to zero.

  Standard Kernel Average Misorientation Map (KAM)                                                                                High Resolution Misorientation Map (HR KAM) using CrossCourt

                                                                              Figure 2. Comparison of standard KAM and HR KAM EBSD maps

6. Engineering Measures: The von Mises Stress

Often it is asserted that a simpler metric could be used  to assimilate all the information contained in the 9-component stress tensor measured by the HREBSD technique. Metrics proposed are:

• Principal stresses, commonly used in mechanics to define the set of orthogonal directions parallel to the axes which remain unchanged in direction under the imposed strain condition.
• The von Mises’ stress, a scalar stress signifying a critical internal energy density which, when exceeded, will cause the material to yield plastically.

The HREBSD method can map both the principal stresses and the von Mises’ stress; no other electron diffraction based technique, used because of its high special resolution, retrieves this data.

See examples in Figure 3 below.

Figure 3.  Top row: rotation maps.
Bottom row: Von Misses maps at different tensile loads, (scaled so that mean Von Misses stress equal tensile load at that level)

Thermal scale, green zero GP. Yellow 0.2 GP, Red 0.4 GP.

7. Conclusion: HREBSD a leap forward in Microstructural Characterisation

EBSD was foundational in microstructural characterisation; the inception of HREBSD is the next key stage of development. HREBSD gives EBSD a new dimension, moving us forward in fully understanding the role of crystal orientation and neighbour disorientation in determining the mechanical properties and recrystallization processes.