The Path To Absolute Strain Measurement

  • Author : Prof David Dingley, BLG Vantage
  • Field : Technique > Software solutions to measure absolute strain using HR EBSD techniques.
  • Summary : This document describes the state of the art in approaches to measure absolute strain using HR EBSD and pattern simulation.
  • First Published : September 2019
  • References : See references below.

Introduction

As leaders in the field of HR EBSD the team here at BLG Vantage has naturally been working towards a solution for absolute strain measurement. Numerous attempts by others have run into limitations and problems  -as discussed below. In summary, HR EBSD or High angular Resolution EBSD is the tool by which residual elastic strain and stress maps can be mapped within polycrystalline samples.  The original robust method established by Wilkinson Meaden and Dingley in 2006 (1) provides only relative stress strain measurements.  This is because the technique relies on cross correlating a High Resolution EBSD pattern from a test area of the sample with a pattern obtained from an area assessed to be of minimal strain. The strain level assessment typically uses prior analysis of the Kernel Average Map (KAM) of the sample.

 

Simulated Patterns

From the very beginning, methods have been explored to assign an absolute figure for the strain at the reference point by cross correlating the EBSD pattern obtained from the reference point with a computer simulated pattern generated for the case of zero or known strain and at the same orientation as that of the reference pattern. This is a sensible approach but is fraught with difficulties and as yet no perfect solution has been found.

There are three major problems:

  1. The simulated pattern must be very similar to the real pattern.
  2. The EBSD pattern centre and the pattern centre to screen distance (or z) must be the same within a few tenths of a camera pixel for both the experimental case and the computer simulation, S Villert et al (2). They came to this conclusion comparing a simulated EBSD pattern with a reference simulated pattern calculated with different pattern centre and specimen to screen distance parameters. The case for comparison of a simulated pattern and an experimental pattern would be even worse.
  3. The crystal orientation used in the simulation must also be correct to a few 100ths of a degree as rotational errors result in large movements of the diffraction bands.

 

Simulation Comp

Experimental and simulated EBSD patterns from Ge as recorded in our current research. The patterns are of resolution 2050x2050pixels.  The simulated pattern was formed using dynamical diffraction theory without contrast asymmetry correction.  It can be seen that the upper Kikuchi lines of the [200] band are brighter than background in the experimental image and darker than background in the simulated image.  This anisotropy has an effect on the cross correlation of the two images and requires attention.

 

The original attempt by Kacher et al (3) using kinematical electron diffraction theory to generate the computer simulations fails on counts 1 and 2, Maurice et al.  (4).

Since then all other simulation methods have used the dynamical diffraction theory with the principle authorities on this being Winkelman (5-6), De Graef (7).

The procedure follows a set path.

  • Use the approximate pattern centre and specimen to screen distance determined, for example, using the standard Hough based routine.
  • Use the approximate value for the crystal orientation as also calculated from the Hough based procedure.
  • Compute the EBSD pattern for the case of zero strain.
  • Perform a cross correlation between real and simulated patterns.
  • Vary the PC and specimen to screen values, the orientation and the assumed strain. Repeat the cross correlation.
  • Select a measure of the quality of the image correspondence, the cross-correlation coefficient for example.
  • Change the variables in a minimisation routine until the image correspondence criterion is minimised.
  • Use the strain value at this minimum position as the strain of the reference pattern.

It is acknowledged that the number of variables is large: 3 for the PC and specimen to screen values, 3 for the orientation and 6 for the strain values, a total of 12.  Under these circumstances proving that the method is robust and accurate is a difficult task and as yet, there is no agreement as to which is the best minimisation procedure or what is the resultant accuracy.

 

Solutions

There is one open-source site that offers a means of using computer simulated EBSD patterns as an aid in orientation and strain measurement (8). It uses kinematical electron diffraction theory in simulating the patterns which suffers from all three of the problems mentioned above.  A second open source site (9) concentrates on the use that can be made of simulating patterns at very low resolution and hence is not suitable for measurement of residual strain.  The aim of this approach is to improve speed and accuracy of indexing for low-quality diffraction patterns.

As leaders in the field of HR EBSD the team here at BLG Vantage has naturally been working towards a solution for absolute strain measurement.  Our approach is different from other published methods due to the challenges already identified and our in depth knowledge acquired over the years. Preliminary results are encouraging and our findings are being prepared for publication in the near future.

 

References

  1. J. Wilkinson, G. Meaden, and D. J. Dingley, “ High resolution mapping of strains and rotations using electron backscatter diffraction”, Mater. Sci. Technol. (2006), 22(11), 1271.
  2. S Villert, C Maurice, C Wyon and R Fortunier, “Accurate assessment of Elastic Strain Measurement by EBSD”. Journal of Microscopy 233, (2009), 290-301
  3. J Kacher, C Landon, B L Adams, D Fullwood, “Bragg’s Law Diffraction Simulations for Electron Backscatter Diffraction Analysis”, Ultramicroscopy 109, (2009) 1148-156.
  4. C Maurice, R Fortunier, D H Driver, A Day, K Mingard, G Meaden, “Comments on the paper ‘Bragg’s Law Diffraction Simulations for Electron Backscatter Diffraction Analysis’ by J Kacher, C Landon, B L Adams, D Fullwood,  Ultramicroscopy 110, (2010) 758-759
  5. Winkelmann, “Dynamical Simulation of Electron Backscatter Diffraction Patterns” in Electron Backscatter Diffraction. Mater. Sci., Springer US, Boston, MA, 2009: pp. 21–33.
  6. Nolze, A. Winkelmann, “A.P. Boyle, Pattern matching approach to pseudosymmetry” problems in electron backscatter diffraction”, Ultramicroscopy. 160 (2015) 146–154.
  7. Singh, M. De Graef, “Orientation Sampling for Dictionary-Based Diffraction Pattern Indexing Methods”, Sci. Eng. (2016) 1–22.
  8. https://github.com/BYU-MicrostructureOfMaterials/OpenXY.git
  9. https://github.com/marcdegraef