Characteristic tensile strength and Weibull shape parameter of carbon nanotubes

Recently, it has been argued [N. M. Pugno and R. S. Ruoff, J. Appl. Phys. 99, 024301 (2006)] that available carbon-nanotube (CNT) tensile strength data do not obey the “classical” Weibull statistical model. In this paper we formulate Weibull’s theory in a manner suitable for assessing CNT fracture-strength data and demonstrate that, on taking into account the area S subjected to uniform tensile stresses, the data are consistent with Weibull’s model. Based on available data, a characteristic strength σC (S=1μm2) equal to 17.6±2.5GPa in conjunction with a shape parameter m equal to 2.77±0.34 provides a good description of the CNT fracture strength. In terms of effective strengths, and on assuming that the relevant area-scaling laws apply, carbon nanotubes and diamond nanofilms exhibit similar features for stressed areas ranging from 1to104μm2.