Diffracting-grain identification from electron backscatter diffraction maps during residual stress measurements: a comparison between the sin2ψ and cosα methods

Abstract

X-ray diffraction (XRD) is a widely used technique to evaluate residual stresses in crystalline materials. Several XRD measurement methods are available. (i) The sin2ψ method, a multiple-exposure technique, uses linear detectors to capture intercepts of the Debye–Scherrer rings, losing the major portion of the diffracting signal. (ii) The cosα method, thanks to the development of compact 2D detectors allowing the entire Debye–Scherrer ring to be captured in a single exposure, is an alternative method for residual stress measurement. The present article compares the two calculation methods in a new manner, by looking at the possible measurement errors related to each method. To this end, sets of grains in diffraction condition were first identified from electron backscatter diffraction (EBSD) mapping of Inconel 718 samples for each XRD calculation method and its associated detector, as each method provides different sets owing to the detector geometry or to the method specificities (such as tilt-angle number or Debye–Scherrer ring division). The X-ray elastic constant (XEC) ½S 2, calculated from EBSD maps for the {311} lattice planes, was determined and compared for the different sets of diffracting grains. It was observed that the 2D detector captures 1.5 times more grains in a single exposure (one tilt angle) than the linear detectors for nine tilt angles. Different XEC mean values were found for the sets of grains from the two XRD techniques/detectors. Grain-size effects were simulated, as well as detector oscillations to overcome them. A bimodal grain-size distribution effect and `artificial' textures introduced by XRD measurement techniques are also discussed.