Predicting the strength of carbon nanotube reinforced polymers using stochastic bottom-up modeling
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Predicting the strength of carbon nanotube reinforced polymers using stochastic bottom‑up modeling Roham Rafiee1 · Hadis Zehtabzadeh1 Received: 8 May 2020 / Accepted: 30 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract It is intended to predict the strength of carbon nanotube reinforced polymer. For this purpose, a sequential multi-scale modeling technique is developed taking into account effective parameters at various scales of micro, meso and macro. CNT-polymer interaction, CNT orientation and CNT waviness are considered at the scale of micro, while formation of CNT aggregates is captured at meso-scale. The occurrence of failure in the form of either matrix failure or CNT and polymer debonding is considered in the modeling as the two prominent failure mechanisms under tensile loading. At the uppermost scale of macro, the investigated material region is partitioned into constitutive blocks using regular tessellation technique accounting for inhomogeneous material behavior. The induced uncertainties during the processing of carbon nanotube reinforced polymers necessitate stochastic modeling. The experienced inconsistencies consisting of CNT length, orientation, waviness pattern and intensity of agglomeration are captured using random parameters. Therefore, the constitutive behavior of each block at macro-scale is randomly picked from the outputs of the conducted modeling at lower scales and full stochastic modeling is implemented. The outputs of the developed modeling are compared with available experimental observations in published data and remarkable agreement is observed. Keywords Multi-scale modeling · Strength · Non-linear behavior · Stochastic modeling · Carbon nanotube
1 Introduction The extraordinary and multifunctional characteristics of carbon nanotube (CNT) have established a new era in the field of the science and technology of composite materials. A new word of nanocomposite has been coined implying on a category of composites where a nano reinforcing agent is incorporated into matrix instead of conventional microsized one. CNT can be viewed as a super material due to its incredible mechanical properties originated from the strong covalent carbon–carbon bonds in its nanostructure. Thus it is an ideal reinforcement for polymeric resin from theoretical point of view. But practically, some uncertainties associated with the processing of CNT reinforced polymers are impeding the full translation of its superb properties into polymers. The interaction between CNT and surrounding polymer and * Roham Rafiee [email protected] 1
Composites Research Laboratory, Faculty of New Science and Technologies, University of Tehran, Tehran 1439955171, Iran
also the quality of CNT dispersion in polymeric resin are two most important issues deviating the efficiency of CNT in enhancing polymer properties from the ideal expectation. The CNT-polymer interaction accounts for load transferring from matrix to resin and hence play a crucial role since no perfect bonding is observed. Th
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