Fiber bundle models and their extension for special failure modes
By: Frank Raischel
From: CFTC
At: Complexo Interdisciplinar, Anfiteatro
[2010-03-03]
The fracture and failure of fiber reinforced materials such as GFRP (glass fiber reinforced polymers), wood, or reinforced concrete, is considerably determined by the interplay of matrix and fiber constituents, and the disorder present. A comprehensive understanding of their degradation and failure requires the inclusion of statistical methods.
The class of fiber bundle models (FBM) holds an eminent position among these statistical approaches, due to the FBMs ability to describe the stochastic nature of heterogeneous materials, the presence of orientational order, and the dynamical rearrangements upon partial failure. In their simplest representation, the classical FBM models a bundle of parallel fibers under longitudinal strain, where each fiber is characterized by modulus of elasticity and a statistically sampled failure threshold. Under increasing load, individual fibers fail and redistribute their load upon neighboring fibers according to a load sharing law, thus potentially triggering avalanches of further failures.
I will present recent extensions to fibre bundle models which help to understand the failure of fiber reinforced materials under shear. It will then be shown how the classical FBM can be modified to describe the appearance of plasticity. Fiber bundle models also allow to capture the appearance of statistical precursors of imminent failure. In addition, I will highlight how to improve already existing fibre bundle models for continuous damage, in order to account for the failure of materials with a pronounced hierarchical setup. Finally, an outlook on recent developments will be given.