Size effects in the (quasi-)brittle fracture of heterogeneous materials

Abstract:
    Living organisms have evolved biomaterials with remarkable strength and toughness through a hierarchical organization of their microstructure across scales. Transferring these properties to engineering composites necessitates to connect fluctuations of mechanical properties at the microscopic scale to apparent fracture properties at the macro scale. This can only be achieved by pioneering a scale-sensitive homogenization theory of quasi-brittle fracture. Using perturbation approaches in fracture mechanics, we try to untangle the length scale intricacy shaping material toughening by inclusions of fracture properties.
    First, we will explore the interplay between the crack size and that of the heterogeneities by modelling the propagation of a coplanar penny-shaped crack in a material with spatially-varying fracture energy. Building on the result of millions of simulations, we will show that the apparent fracture energy of perfectly brittle composites increases with crack length when the latter exceeds the heterogeneity size. This so-called “R-curve” behaviour, traditionally attributed to the quasi-brittle (damaging) nature of materials, is shown to emerge from the interplay between fracture processes and material disorder. This toughening and its standard deviation can be accurately captured by a mean-field theory of brittle fracture for weakly disordered media.
    Second, we will explore crack propagation in heterogeneous cohesive media. Cohesive-zone models assume that cracking unfolds progressively in a spatially-extended damaged region, called the process zone. The fracture of cohesive composites naturally displays a richer physics, as the finiteness of the process zone introduce size-effects in the interaction of a crack with heterogeneities. By extending perturbation approaches to non-linear fracture mechanics, we investigate the interaction of a dynamic rupture with periodic arrays of tough obstacles. We show that the presence of a process zone results in two competing effects on the deformation of crack fronts: (i) it makes the front more compliant to small-wavelength perturbations, and (ii) it smooths out local fluctuations of strength and process zone size, from which emerge heterogeneities of fracture energy. This interaction mechanisms are further complexified by crack dynamics, as (iii) higher crack velocities leads to an overall stiffening of the crack front, which is further amplified by (iv) the Lorentz contraction of the process zone. Overall, our theory provides a unified framework to predict the variety of front profiles observed in numerical simulations and fracture experiments, even when the small-scale yielding hypothesis of LEFM breaks down.

Short biography:
    Dr. Mathias Lebihain is a permanent researcher at Navier laboratory (École des Ponts, Univ Eiffel, CNRS). After graduating from École polytechnique (X2011) and École des Ponts, he enrolled on a doctorate at the Institut Jean le Rond d'Alembert (Sorbonne Université, CNRS), and defended his thesis in 2019. After a postdoctoral fellowship at EPFL in Switzerland, he joined the Navier laboratory's Geotechnics and Multi-Scale teams late 2021.
    Mathias Lebihain is conducting a research project focusing on the understanding of fracture mechanisms in the presence of heterogeneities and multiphysical couplings. His research covers a diverse topics, from the cracking of materials to the triggering of earthquakes and the adhesion of soft, textured materials. The target applications primarily concern the design of crack-resistant composite materials and the mitigation of seismicity induced by underground fluid injection.

Le mardi 21 mai 2024 à 11h00 / Amphithéâtre François Canac, LMA

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