Wrapping and unwrapping multifractal fields: Application to fatigue and abrupt failure fracture surfaces - Samy Lakhal; Laurent Ponson; Michael Benzaquen; Jean-Philippe Bouchaud (Physical Review Research)
We develop a spectral procedure to generate multifractal random fields in any dimensions d, parameterized by their roughness exponent H, intermittency exponent λ, and multifractal range ξ. We retrieve all the salient features of the log-normal multifractal random walk introduced by E. Bacry et al. [Phys. Rev. E 64, 026103 (2001)1063-651X10.1103/PhysRevE.64.026103], namely, a quadratic scaling exponent spectrum ζ_{q}, and fat-tailed and spatially correlated fluctuations. Such construction procedure is then used in d=2 to “unwrap” experimental fracture surfaces of an aluminum alloy obtained by abrupt and fatigue failure. Our analysis demonstrates the presence of anisotropic and filamental structures, ascribed to the dissipative nature of the damage mechanisms that underlie material failure.