Fracture Surfaces as Multiscaling Graphs

Eran Bouchbinder, Itamar Procaccia, Stéphane Santucci, Loïc Vanel
2006 Physical Review Letters  
Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs h(x) of height h as a function of length x. We show that these are multiscaling, in the sense that n^th order moments of the height fluctuations across any distance ℓ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class
more » ... of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.
doi:10.1103/physrevlett.96.055509 pmid:16486953 fatcat:6b3kficj5fb5jgx6hmrzrymgpu