Topological data analysis for roughness surfaces of bonding assembly - Canot, Hélène; Durand, Philippe; Frénod, Emmanuel; Hassoune, Bouchra; Nassiet, Valérie; Tramis, Olivier (Discrete and Continuous Dynamical Systems - S, 2024)
Testing the reliability of bonded joints in material assemblies is one of the major subjects in the aeronautical industry. One of the methods for characterizing adhesion is based on the study of the roughness of the fracture surfaces of assemblies. In this study, the interest is focused on the quantification of the adhesion of the bonded structure by the corner cleavage test, allowing the study of crack propagation within bonded assemblies. Optical profilometry measurements, obtained by scanning the surface of the fractured surfaces of monoadhesives: ABT M52, copolymer-doped and non-nanostructured AHT are used. The aim of the profilometric study is to quantify surface roughness. To go further than traditional methods of characterizing roughness, we analyze the profiles using mathematical methods to confirm the experimental studies and extract more geometric information. We apply various techniques of topological data analysis (TDA) to extract the topological features of the profiles. These techniques recover experimental elements in a quantitative manner. Persistence diagrams give us a multi-scale characterization of the rupture facies, attesting the voids, micro-cracks at nano-level, quantifying the maximum amplitude of the peaks at micro level. We extract features vectors using persistent images for each profile and we look for similarities in persistence diagrams using Bottleneck and Wasserstein distances in perspective of a machine learning application in a future study. Then the profiles were studied by Takens embedding which will produce a point cloud analyzed by homological persistence in order to produce indications of periodicity or quasi-periodicity. This computational topological approach makes it possible to extract the essential characteristics of the surface and roughness of the profile of the adhesives in order to conclude on their toughness and fracture resistance.
Keywords: journalArticle