This work introduces a novel Augmented Reality (AR) approach to visualize material data alongside real objects in order to facilitate detailed material analyses based on spatial non-destructive testing (NDT) data as generated in X-ray computed tomography (XCT) imaging. For this purpose, we introduce a framework that leverages the potential of AR devices, visualization and interaction techniques to seamlessly explore complex primary and secondary XCT data matched with real-world objects. The overall goal of the proposed analysis scheme is to enable researchers and analysts to inspect material properties and structures onsite and in-place. Coupling immersive visualization techniques with real physical objects allows for highly intuitive workflows in material analysis and inspection, which enables the identification of anomalies and accelerates informed decision making. As a result, this framework generates an immersive experience, which provides a more engaging and more natural analysis of material data. A case study on fiber-reinforced polymer datasets was used to validate the AR framework and its new workflow. Initial results revealed positive feedback from experts, in particular regarding improved understanding of spatial data and a more natural interaction with material samples, which may have significant potential when combined with conventional analysis systems.