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Stiffness threshold of randomly distributed carbon nanotube networks

Yuli Chen's picture

For carbon nanotube (CNT) networks, with increasing network density, there may be sudden changes in the properties, such as the sudden change in electrical conductivity at the electrical percolation threshold.  In this paper, the change in stiffness of the CNT networks is studied and especially the existence of stiffness threshold is revealed.  Two critical network densities are found to divide the stiffness behavior into three stages: zero stiffness, bending dominated and stretching dominated stages.  The first critical network density is a criterion to judge whether or not the network is capable of carrying load, defined as the stiffness threshold.  The second critical network density is a criterion to measure whether or not most of the CNTs in network are utilized effectively to carry load, defined as bending-stretching transitional threshold. 

Based on the geometric probability analysis, a theoretical methodology is set up to predict the two thresholds and explain their underlying mechanisms.  The stiffness threshold is revealed to be determined by the statical determinacy of CNTs in the network, and can be estimated quantitatively by the stabilization fraction of network, a newly proposed parameter in this paper.  The other threshold, bending-stretching transitional threshold, which signs the conversion of dominant deformation mode, is verified to be well evaluated by the proposed defect fraction of network.  According to the theoretical analysis as well as the numerical simulation, the average intersection number on each CNT is revealed as the only dominant factor for the electrical percolation and the stiffness thresholds, it is approximately 3.7 for electrical percolation threshold, and 5.2 for the stiffness threshold of 2D networks.  For 3D networks, they are 1.4 and 4.4 respectively.  And it also affects the bending-stretching transitional threshold, together with the CNT aspect ratio.  The average intersection number divided by the fourth root of CNT aspect ratio is found to be an invariant at the bending-stretching transitional threshold, which is 6.7 and 6.3 for 2D and 3D networks, respectively.  Based on this study, a simple piecewise expression is summarized to describe the relative stiffness of CNT networks, in which the relative stiffness of networks depends on the relative network density as well as the CNT aspect ratio.  This formula provides a solid theoretical foundation for the design optimization and property prediction of CNT networks.


Guoxiang Zu's picture

Dear Prof.Yuli Chen,

When I click the link, it will go to ""

Actually I need to remove the "For", then the hyperlink would work.


Maybe you could remove the "For".



Yuli Chen's picture

Dear Guoxiang,

Thanks, I have removed "for" and the link works now.

Best wishes,

Yuli Chen

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