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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2011002456
pages 279-295


X. Frank Xu
Department of Civil, Environmental and Ocean Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
Keqiang Hu
Department of Civil, Environmental & Ocean Engineering, Stevens Institute of Technology, Hoboken, New Jersey, 07307, USA
Irene J. Beyerlein
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
George Deodatis
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY


In modeling and simulation of material failure, a major challenge lies in the computation of stress redistributions during the stochastic propagation of localized failures. In this study, an nth-order generalized local load sharing (GLLS) model is introduced to account for the complexity of such local interactions in an efficient way.The rule is flexible, covering a wide range of load sharing mechanisms between the equal load sharing and local load sharing types. A Monte Carlo simulation model employing various orders of this GLLS rule is used to study the effect of such load redistributions on the failure of a micron-scale carbon nanotube (CNT) fiber. These CNT fibers exhibit a hierarchical structure. At the lowest length scale are single- or multi-walled CNTs with nanoscale diameters (e.g., 1–10 nm), which are aligned and clustered to form small bundles at the next higher length scale (15–60 nm in diameter). Thousands of these CNT bundles aggregate and align to create CNT fibers with micron-scale diameters. The results of this study indicate that the mean strength of the CNT fibers reduces by approximately two-thirds of an order of magnitude when up-scaling from an individual CNT to a CNT fiber. This dramatic strength reduction occurs at three different stages of the up-scaling process: (1) from individual CNTs of length lt to CNT bundles of the same length; (2) from a CNT bundle of length lt to a CNT bundle of length lb(lb = 10lt); and (3) from CNT bundles of length lb to CNT fibers of the same length. The specific strength reductions during these three stages are provided in the paper. The computed fiber strengths are in the same general range as corresponding experimental values reported in the literature. The ability of the GLLS model to efficiently account for different mechanisms of load sharing, in combination with the multi-stage up-scaling Monte Carlo simulation approach, is expected to benefit the design and optimization of robust structural composites built up from carbon nanotubes.