Phase contrast stereometry: fatigue crack mapping in three dimensions

Abstract

The work reported below describes development of a novel method, termed X-ray phase contrast stereometry, for reconstructing the three-dimensional (3D) positions of features within a specimen. The approach takes measured positions of a given feature in phase microradiographs recorded at different viewing angles and refines that feature's position numerically. The approach is designed to address limitations in conventional laboratory or synchrotron X-ray absorption micro computed tomography (microCT), particularly those inherent in studying plate-like samples. The phase stereometric reconstruction technique was applied to a small compact tension sample of aluminium alloy AA 2090 (20.3 mm wide from notch tip to back face and 2.7 mm thick) containing a fatigue crack and was used to map the 3D crack surface non-invasively. Up to ten viewing angles were used for each of 2269 points mapped on the approximately 2.7 mm × 6.0 mm surface. The 3D stereometry-derived crack surface agreed with the surface map from absorption microCT of the same sample. The phase technique was superior in terms of its crack sensitivity; the phase images allowed the crack to be followed to its tip, even with zero applied load while absorption microCT could only detect about 5 mm of the crack 6 mm long when loaded to 40 kgf. The origin of the contrast used for stereometric mapping was confirmed to be from the peaks on the crack face; phase microradiographs from a second (intact) sample showed a pattern of features identical with those revealed on the surface when the sample was split open. Crack opening as a function of in-situ load was measured for the same points on the crack surface using both phase stereometry and absorption microCT; the openings were in good agreement.

Acknowledgements

The authors dedicate this article to the memory of Professor Howard K. Birnbaum, recently deceased, the thesis supervisor of the corresponding author. His long-time advocacy of synchrotron X-ray imaging, even though he did not work extensively in this field, will be missed. This article summarizes some of the results from the PhD thesis of Ignatiev [51]. The authors thank Dr J.C. Elliott and Dr G.R. Davis (Queen Mary, University of London) for their collaboration on the absorption microCT measurements of sample CT-41M, reported earlier, which allowed the phase stereometric results to be verified. The authors also thank Dr E. Lautenschlager (Northwestern University) for his help fracturing sample CT-33M and Dr J.D. Almer (XOR APS) for his help setting up the in-situ load frame used in this study. The initial stages of this research were partially supported by the US Office of Naval Research (grants N00014-89-J-1708 and N00014-94-1-0306). Use of the APS was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract W-31-109-ENG-38.

Notes

One should note that high-resolution synchrotron microCT images from third-generation sources almost invariably include components of phase contrast that produce edge enhancement in the reconstructions (in the more subtle manifestations) or even anomalously high values of linear attenuation coefficient away from surfaces [3]. These effects become more pronounced as spatial resolution increases.

Strictly speaking, voxels should be described in terms of the lengths of their three orthogonal edges but, when these edges are equal and the voxels can be termed ‘isotropic’, one often only gives one of the three-dimensions.