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A Note on Statistical Strength of Carbon Nanotubes

X. Frank Xu1,2, Yuxin Jie3, Irene J. Beyerlein4
School of Civil Engineering, Beijing Jiaotong University,
Corresponding author.
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA. Email:

Computers, Materials & Continua 2013, 38(1), 17-30.


This note aims to relate the measured strength statistics of individual carbon nanotubes (CNTs) to the physics of brittle fracture and the weakest link model. By approximating an arbitrary flaw size distribution with a segmented power law, an effort is made to extend applicability of the Weibull distribution to arbitrary flaw populations, which explains why the Weibull distribution fits the experimental data of CNTs and many other brittle materials, and why in other cases it is not so clear. A generalized Weibull distribution is proposed to account for all non-asymptotic cases. The published CNT testing data are analyzed, and finally a major issue present in existing interpretation of CNT bundle testing data is clarified.


Strength, Power law, Weibull distribution, Carbon nanotubes.

Cite This Article

X. F. . Xu, Y. . Jie and I. J. . Beyerlein, "A note on statistical strength of carbon nanotubes," Computers, Materials & Continua, vol. 38, no.1, pp. 17–30, 2013.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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