X-rays can provide images when an object is visibly obstructed, allowing for motion measurements via x-ray digital image correlation (DIC). However, x-ray images are path-integrated and contain data for all objects between the source and detector. If multiple objects are present in the x-ray path, conventional DIC algorithms may fail to correlate the x-ray images. A new DIC algorithm called path-integrated (PI)-DIC addresses this issue by reformulating the matching criterion for DIC to account for multiple, independently-moving objects. PI-DIC requires a set of reference x-ray images of each independent object. However, due to experimental constraints, such reference images might not be obtainable from the experiment. This work focuses on the reliability of synthetically-generated reference images, in such cases. A simplified exemplar is used for demonstration purposes, consisting of two aluminum plates with tantalum x-ray DIC patterns undergoing independent rigid translations. Synthetic reference images based on the “as-designed” DIC patterns were generated. However, PI-DIC with the synthetic images suffered some biases due to manufacturing defects of the patterns. A systematic study of seven identified defect types found that an incorrect feature diameter was the most influential defect. Synthetic images were re-generated with the corrected feature diameter, and PI-DIC errors were improved by a factor of 3-4. Final biases ranged from 0.00-0.04 px, and standard uncertainties ranged from 0.06-0.11 px. In conclusion, PI-DIC accurately measured the independent displacement of two plates from a single series of path-integrated x-ray images using synthetically-generated reference images, and the methods and conclusions derived here can be extended to more generalized cases involving stereo PI-DIC for arbitrary specimen geometry and motion. This work thus extends the application space of x-ray imaging for full-field DIC measurements of multiple surfaces or objects in extreme environments where optical DIC is not possible.
Understanding temperature-dependent material decomposition and structural deformation induced by combined thermal-mechanical environments is critical for safety qualification of hardware under accident scenarios. Seeing in with X-rays elucidated the physics necessary to develop X-ray strain and thermometry diagnostics for use in optically opaque environments. Two parallel thermometry schemes were explored: X-ray fluorescence and X-ray diffraction of inorganic doped ceramics– colloquially known as thermographic phosphors. Two parallel surface strain techniques–Path-Integrated Digital Image Correlation and Frequency Multiplexed Digital Image Correlation–were demonstrated. Finally, preliminary demonstration of time-resolved digital volume correlation was performed by taking advantage of limited view reconstruction techniques. Additionally, research into blended ceramic-metal coatings was critical to generating intrinsic thermographic patterns for the future combination of X-ray strain and thermometry measurements.
X-ray imaging offers unique possibilities for Digital Image Correlation (DIC), opening the door for full-field deformation measurements of a test article in complex environments where optical DIC suffers severe biases or is impossible. While X-ray DIC has been performed in the past with standard DIC codes designed for optical images, the path-integrated nature of X-ray images places constraints on the experimental setup, predominantly that only a single surface of interest moves/deforms. These requirements are difficult to realize for many practical situations and limit the amount of information that can be garnered in a single test. Other X-ray based diagnostics such as Digital Volume Correlation (DVC) and Projection DVC (P-DVC) overcome these obstacles, but DVC is limited to quasi-static tests, and both DVC and P-DVC necessitate high-resolution computed tomography (CT) scan(s) and often require a potentially invasive pattern throughout the volume of the specimen. Here this work presents a novel approach to measure time-resolved displacements and strains on multiple surfaces from a single series of 2D, path-integrated (PI) X-ray images, called PI-DIC. The principle of optical flow or conservation of intensity—the foundation of DIC—was reframed for path-integrated images, for an exemplar setup comprised of two plates moving and deforming independently. Synthetic images were generated for rigid translations, rigid rotations, and uniform stretches, where each plate underwent a unique motion/deformation. Experimental specimens were fabricated (either an aluminum plate with tantalum features or a plastic plate with steel features) and the two specimens were independently translated. PI-DIC was successfully demonstrated with the synthetic images and validated with the experimental images. Prescribed displacements were recovered for each plate from the single set of path-integrated, deformed images. Errors were approximately 0.02 px for the synthetic images with 1.5% image noise, and 0.05 px for the experimental images. These results provide the foundation for PI-DIC to measure motion and deformation of multiple, independent surfaces with subpixel accuracy from a single series of path-integrated X-ray images.
Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.
