Accurate strain determination from digital image correlation of Laue diffraction spots

Accurate strain/stress characterization has important implications in practice, where it is typically connected with safe operation of engineering components. Improving the accuracy and spatial resolution of the measurement techniques can be therefore very beneficial for materials science by helping the understanding of complex material behaviour and the development of novel materials with improved properties. Strain measurement by diffraction methods is based on Bragg’s law, which in the case of a strained crystal predicts a shift of the diffraction peaks compared to their position measured on a reference state. Classically, this shift is determined as the difference between the corresponding absolute peak positions, which requires in many cases accurate knowledge of (i) the geometrical setup and its stability, (ii) the calibration sample, and (iii) a well matching mathematical model of the intensity distribution. In view of this large number of parameters it is intriguing to ask what the accuracy of today’s X-ray diffraction (XRD) methods is and which are the possible ways of improvement. Limiting our survey to methods able to determine the strain tensor at micrometre scale, one can rapidly find that the error of most strain tensor components is about a few times 10 . Transformed to stress (using Young’s modulus of 100 GPa) this represents an uncertainty of tens of MPa, which might be too large for the study of certain phenomena, such as for example the plastic yield of metals. Therefore, efforts are continuously undertaken to ameliorate the precision of the evaluation methods. The majority of the solutions, however, concern point (i), suggesting the use of large area detectors with many pixels and without distortion, or fixing instabilities of the wavelength or micro-spot position by applying more stable optical elements. Progress in this case depends on technical advancement, which sometimes might be slow compared to the needs of the scientific community. Increasing strain/stress accuracy when working with conventional setups needs, therefore, a paradigm change, i.e. a method different from the classical approach based on absolute peak positions. Two recently published articles by Petit et al. (2015) and Zhang et al. (2015) break the tradition and introduce evaluation schemes based on the shift of diffraction peaks determined by digital image correlation (DIC). This new idea, which plays a central role in experimental mechanics, is applied in both papers to white-beam Laue microdiffraction, a popular method often analysed in terms of error sources impeding accurate determination of the deviatoric strain tensor (Hofmann et al., 2011; Poshadel et al., 2012). As argued by Petit et al. (2015), the gain in accuracy of the Laue-DIC method is related to two factors: (a) the smaller uncertainty of the peak shift determined by DIC and (b) the higher sensitivity of the merit function expressing peak positions as a function of reference cell parameters, compared to the sensitivity of the gradient of the merit function, the latter appearing in the formulation of Laue-DIC. From the point of view of the error sources highlighted above it becomes clear that the new approach eliminates the uncertainties related to the choice of an adequate mathematical model describing the experimental intensity distribution. The authors emphasize that relatively good fits can be obtained for the spots of the non-deformed reference specimen using Gaussian or Pearson VII profiles, but already as the specimen is strained, peak quality deteriorates and the uncertainty in peak position increases above 0.1 pixel, characteristic for the reference peaks. Compared to this the uncertainty of DIC is one order of magnitude ISSN 1600-5767