X-ray computed-tomography (XCT) is a three-dimensional technique to reveal and quantify internal features and defects in materials. Conventional absorption-based contrast provides information on the attenuation of the X-ray beam intensity and is an invaluable tool in various domains, e.g. medicine and materials science. In the last decade however an important innovation in X-ray technology has emerged by the introduction of Talbot-Lau grating interferometry. This method provides three complementary image modalities in a single scan of the specimen: the absorption contrast (AC), the differential phase contrast (DPC), and the dark-field contrast (DFC). In this contribution we present results of a novel Talbot-Lau grating interferometry desktop μ-XCT-system which are compared to conventional high resolution XCT-results. In the first investigation we characterized polypropylene test specimens that are loaded in tensile testing until final failure. Lower grey levels near the fracture surface in the AC and DPC images indicate pores. Due to increased scattering in these regions DFC images provide high signal intensities, even though the defects are smaller than the spatial resolution. Furthermore we characterized crack-like defects in carbon fiber reinforced laminates that were subjected to impact forces up to 30 Joules using a high-velocity gas gun. Using DFC we are able to detect micro- cracks and delaminations in samples that were subject to low impact forces, whereas these defects are merely detectable using AC. In the third investigation we characterized an unfilled PP test specimen that was cyclically loaded in tensile testing until final failure.