Keywords: carbon nanotube, polymer composites, stochastic analysis, mechanical properties, multi-scale analysis.

The carbon nanotube (CNT) is considered to be a new generation of material possessing superior mechanical, thermal and electrical properties. The applications of CNT, especially in form of the CNT composites have received great attention and interest in recent years. Most of investigations used a deterministic approach to obtain the mechanical properties of CNT composites and big differences between the experimental observations and theoretical models are observed. This discrepancy can be attributed to the existence of real random parameters in contrast with the deterministic parameters employed.

The main goal of this research is to determine the properties of CNT-Epoxy by considering three random parameters such as volume fractions, lengths and orientations of the CNT. Random volume fractions simulate the randomness of the CNT dispersion at the macro level. Different lengths of the CNTs lead to variable efficiencies of load transfer from the matrix to the CNT resulting in different reinforcement capabilities. For this purpose, a stochastic multi-scale modeling technique is developed. The developed modeling technique consists of two phases: model preparation on the basis of top-down scanning and simulation based on bottom-up modeling. In the model preparation, the material region on a macro scale is portioned into smaller square blocks on a meso-scale. Random volume fractions are assigned to each block. This represents the random dispersion of the CNTs in the matrix. Each block includes a different portion of the CNTs oriented randomly in various directions with random lengths on micro-nano scale. In the modeling, a hierarchical multi-scale method is developed starting from the nano scale and finally to the macro-scale. Effective parameters associated with each scale are identified and an appropriate modeling technique is used to simulate them. Finite element analysis (FEA) is performed to study properties of the CNT and its interaction with surrounding polymer at the nano-micro-scale, while an improved micromechanics equation is used for the meso-scale on the basis of the developed equivalent fiber concept. An averaging technique is used at macro-scale and its accuracy is examined by comparing the result with a FEA on a macro-scale.

The results obtained for random volume fractions with the same mean value and different distribution show a very small fluctuation. Therefore, one can simply replace the random volume fraction with its mean value. On the other hand, it was observed that the random length of the CNTs, which has significant influence on the results, can also be substituted by its average value with a very good approximation. Therefore, both the volume fraction and the length of CNTs can be treated as deterministic variables by replacing them with their mean values. Although, the volume fraction and the length of the CNTs as random parameters can not be ignored, but mean values can be used for both of them as an alternative approach.

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