A probabilistic damage model of the dynamic fragmentation process in brittle materials

Pascal Forquin (1) , François Hild (2)

1 LPMM - Laboratoire de physique et mécanique des matériaux
2 LMT - Laboratoire de Mécanique et Technologie

Dynamic fragmentation is observed in brittle materials such as ceramics, concrete, glass or rocks submitted to impact or blast loadings. Under such loadings, high-stress-rate tensile fields develop within the target, and produce fragmentations characterized by a high density of oriented cracks. To improve industrial processes such as blast loadings in open quarry or ballistic efficiencies of armours or concrete structures against impact loadings, it is essential to understand the main properties of such damage processes (namely, characteristic time of fragmentation, characteristic density, orientation and extension of cracking, ultimate strength) as functions of the loading rate, the size of the structure (or the examination volume), and the failure properties of the brittle material concerned. In the present contribution, the concept of probability of non-obscuration is developed and extended to predict the crack density for any size, shape of the loaded volume, stress gradients, and stress-rates. A closed-form solution is used to show how a brittle and random behaviour under quasi-static loading becomes deterministic and stress-rate-dependent with increasing loading rates. Two definitions of the tensile strength of brittle materials are proposed. As shown by Monte-Carlo simulations, for brittle materials, the “ultimate macroscopic strength” applies under high loading rate or in a large domain whereas the “mean obscuration stress” applied in a small domain or under low stress rate. Next, a multi-scale model is presented and used to simulate damage processes observed during edge-on impact tests performed on an ultra-high strength concrete. Last, the fragmentation properties predicted by modelling of six brittle materials (dense and porous SiC ceramics, a micro-concrete, an ultra-high strength concrete, a limestone rock and a soda-lime silicate glass) are compared.

Mots clés: Probability of obscuration; Weakest-link hypothesis; Anisotropic damage model; Dynamic tensile strength; Edge-On Impact tests; Single; multiple fragmentation process

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Pascal Forquin, François Hild. A probabilistic damage model of the dynamic fragmentation process in brittle materials. Advances in Applied Mechanics, 2010, 44, pp.1-72. ⟨10.1016/S0065-2156(10)44001-6⟩. ⟨hal-00521184⟩