Radial cracks in perforated thin sheets

Romain Vermorel (1) , Nicolas Vandenberghe (1) , Emmanuel Villermaux (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

When a rigid cone is slowly pushed through a thin elastic sheet, the material breaks, exhibiting a network of cracks expanding in the radial direction. Experiments conducted with aluminum sheets show that the number of cracks is selected at the beginning of the perforation process and then remains stable. A simple model predicts the number of cracks as the result of a competition between the elastic energy stored in the sheet, and the energy dissipated during crack extension. We also evidence the subtle rearrangements of randomly distributed cracks into uniform radial patterns with fewer cracks. In that respect, this study exemplifies how relaxation mechanisms in fragmenting solids can attenuate the influence of defects in the material.

Mots clés: radial cracks; thin sheets; elasticity; fragmentation; perforation; fracture energy

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Physique Classique [physics.class-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Physique Générale [physics.gen-ph]

Romain Vermorel, Nicolas Vandenberghe, Emmanuel Villermaux. Radial cracks in perforated thin sheets. Physical Review Letters, 2010, 104, pp.175502. ⟨10.1103/PhysRevLett.104.175502⟩. ⟨hal-00566658⟩