Stochastic fracture mechanics and size effect

report

English

Quasibrittle materials such as concrete, fiber composites, rocks, tough ceramics, sea ice, dry snow slabs, wood and some biomaterials, fail at different nominal strengths with respect to their structural size. Smaller structures fail in a ductile manner which usually involves distributed cracking with strain-softening. The stress redistribution that is caused by fracture and distributed cracking engenders an energetic size effect, i.e., decrease of the nominal strength of structures with increasing structure size. A structure far larger than the fracture process zone (FPZ) fails in an almost perfectly brittle manner and, if the failure occurs right at the crack initiation,the failure load is governed by the statistically weakest point in the structure, which gives a basis to the statistical size effect. Strategies for capturing the statistical size effect using the stochastic finite element method in the sense of extreme value statistics are presented. They combine feasible types of Monte Carlo simulation based on nonlinear fracture mechanics. This is exemplified by various cases of size effect in plain concrete structures. A special attention is devoted to size effects of concrete reinforcement in the form of yarns made of glass fibers (a new composite material called textile reinforced concrete). The interdisciplinary field of stochastic fracture mechanics is accessed by utilizing new advanced software developments which progress beyond the traditional approach and attempt to treat in a combined manner the reliability theory with fracture nonlinearity. This approach automatically yields not only the statistical part of size effect at crack initiation, but also the energetic part of size effect. Examples of statistical simulations of size effect with nonlinear fracture mechanics software ATENA combined with probabilistic software FREET are presented. Capturing the statistical size effect is made possible by (1) incorporating the analytical results of extreme value statistics into the stochastic finite element calculations, (2) implementing an efficient random field generation, and (3) exploiting small-sample Monte-Carlo type simulation called Latin Hypercube Sampling. The necessary steps towards the results were the development of mathematical tools and algorithms (with their theoretical and numerical validation) and finally software development (FREET). Next, the applications of the methods and software follow aiming at study of size effects in various materials and loading conditions.

Probabilistic-based assessment, failure probability, reliability, reliability, software, Latin Hypercube Sampling, sensitivity analysis, quasibrittle materials, concrete,multi-filament yarn, fiber bundle models, delayed activation,nonlinear fracture mechanics, cohesive crack, size effect, theory f extreme values, Weibull theory, random field simulation, stochastic finite element method

VOŘECHOVSKÝ, M.

1. 7. 2004

VUT v Brně

Brno

80-214-2695-0

Doktorská dizertační práce

170