Brittle to ductile transition in democratic fiber bundle model

Hudson Borja da Rocha¹; Lev Truskinovsky¹

¹ Ecole Polytechnique

doi:10.20906/CPS/COB-2015-0571

Resumo

Fiber bundle model (FBM) has been used for years as a prototypical description of brittle fracture in systems with random failure thresholds. The model describes a parallel connection of breakable units with piece-wise quadratic elastic energy. The democratic or mean-field version of the FBM assumes that after breaking of a single unit the loads are redistributed equally. The democratic FBM has been previously studied only in a soft loading setting. The ensuing behavior is always brittle and the main result was that near the global fracture threshold the model exhibits a power law distribution of failure avalanches. To capture ductile behavior in the same prototypical framework, we augment the FBM by adding internal (series to fibers) and external (series to the bundle) springs and study the resulting system in a hard device. By changing the stiffness of the series springs we were able to simulate a crossover from brittle to ductile response. While the former is characterized by intermittent avalanche distribution near the global failure threshold, the latter shows predominantly Gaussian statistics. Near the brittle-to-ductile transition point correlation length diverges and the whole transition bears a strong resemblance to the athermal phase change of the second order (critical point). Our observations regarding the structure of fluctuations can be used for the development of reliable acoustic-emission-based precursors of global failure and for non-destructive acoustic monitoring of the remaining life of fracturing samples.

Palavras-chave: Fiber bundle model; criticality; fracture; brittle; ductile