Measurement of Residual Elastic Strains in a Titanium Alloy Using High Energy Synchrotron X-Ray Diffraction

Abstract

Residual elastic strains in a bent bar of titanium alloy Ti-6Al-4V were measured using high energy diffraction on station 16.3 at SRS Daresbury. Using a single bounce Laue crystal monochromator, diffraction peaks were collected for reflections (00.2), (10.1), (10.2) and (11.0) from the hcp alpha phase of the titanium alloy. Reference values of the lattice spacing for each of the reflections were found from the diffraction pattern collected from a stress-free sampling volume. The residual elastic strain values calculated on the basis of each reflection were then computed and plotted as a function of position across the bent bar. The average macroscopic residual elastic strain was computed using an averaging procedure taking into account the multiplicity of each reflection. Energy dispersive white beam diffraction from the same bent bar was used to collect diffraction patterns over the range of lattice spacings between 0.8 and 2.2 Å . Detector calibration was carried out using the procedure described in Liu et al. (2005) and detailed interpretation of the energy dispersive profiles was carried out allowing the identification of average residual elastic strains in the two principal phases present in the titanium alloy considered, the a-Ti hcp and the b-Ti bcc phases. Peak-specific residual strain profiles computed on the basis of monochromatic measurements show significant differences reflecting the variation in the elastic and plastic properties with grain orientation, i.e., crystal anisotropy. Using the contrast between the elastic and plastic properties of different directions within the a-Ti hcp lattice, the difference between residual elastic strains measured for (00.2) and (11.0) reflections was plotted, as well as the Fdifference strain_ between (00.2) and (10.1) reflections. These profiles show a good qualitative correlation with the plastic strain profile introduced by inelastic bending that was computed from the analysis of Pawley refinement of the energy-dispersive diffraction measurements.

Measurement, analysis and reconstruction of residual stresses

“…The analytical method for reconstructing the residual stresses does not use the eigenstrain or inherent strain concepts developed by Korsunsky and others. 16,17 As will be shown later, the region of interest that contains the residual stress field is a section through a rectangular beam, in Figure 1, with depth 2 h. For inplane stresses the equilibrium equations are…”

“…The reconstruction analysis is similar to that used by the authors in earlier work. [13][14][15] Similar approaches for reconstruction of residual stresses have been developed by Korsunsky et al 16 An analytical solution for the residual strains, as a function of an arbitrary eigenstrain distribution, was derived for the analysis of residually stressed bars. Jun and Korsunsky 17 used a finite element based formulation to determine the eigenstrain distribution in a shot-peened sample and friction stir welds, from a set of measurements of residual stresses.…”

Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

“…Quantifying the residual stress field within a component using lab source x-rays relies on removing layers of materials from the surface and investigating the newly exposed layers [39], [32], which introduces a significant uncertainty to the stress solution. Penetration through moderate thicknesses (mm-cm) of metallic samples combined with the advantages of high speed area detectors and short collection times have enabled a new generation of high energy synchrotron x-ray diffraction experiments [34], [48], [30], [49], [13], [33], [23], [5]. This large number of lattice strain measurements can be assembled into lattice strain pole figures [15], [46], [36], [33], which can be "inverted" to calculate the orientation-dependent strain and stress tensors within the polycrystalline diffraction volume [3], [47], [6].…”

BL-02: a versatile X-ray scattering and diffraction beamline for engineering applications at Indus-2 synchrotron source

“…Due to good collimation of the source, synchrotron X-ray diffraction is capable of providing high spatial resolution ($ 500 mm). Thus, 3D mapping of the strain distribution in engineered components up to millimetre depths (Steuwer et al, 2004;Korsunsky et al, 2006;Pyzalla, 2000;Collins et al, 2017) is possible.…”