This paper presents a novel quantitative approach for characterizing evolution of cracks in carbon fiber-reinforced polymer (CFRP) composites subjected to opening loads using in situ synchrotron radiation X-ray computed tomography (nanoscopic SR X-CT) with spatial resolution of \(\sim\) 50 nm. Topological data analysis (TDA), specifically persistent homology (PH) and its distance metric, the p-Wasserstein distance ( \({\hbox {W}_{p}}\) ), is employed to quantitatively describe the distinct three-dimensional (3D) shapes of cracks in samples with “thin” and “thick” resin regions. The 3D crack shapes correspond to different cracking modes, with “thin” resin regions displaying brittle behavior and “thick” regions exhibiting more ductile characteristics. This topological method, which tracks changes in crack shape across two-dimensional (2D) slices, effectively distinguishes between brittle and ductile cracking modes and quantifies the cracking mechanism autonomously. Additionally, the method identifies trigger sites and the timing of crack propagation by correlating the crack’s progression along the length of the carbon fiber/epoxy composites with its temporal evolution. From a materials perspective, this methodology allows integration of not just crack length but also 3D crack shape into predictive models, offering valuable insights for optimizing the performance and extending the lifetime of carbon fiber/epoxy composites.
