Nanoscale Weibull statistics

Abstract

In this paper a modification of the classical Weibull statistics is developed for nanoscale applications. It is called nanoscale Weibull statistics. A comparison between nanoscale and classical Weibull statistics applied to experimental results on fracture strength of carbon nanotubes clearly shows the effectiveness of the proposed modification. A Weibull's modulus of similar to 3 is deduced for nanotubes. The approach can treat (also) a small number of structural defects, as required for nearly defect-free structures (e.g., nanotubes) as well as a quantized crack propagation (e.g., as a consequence of the discrete nature of matter), allowing to remove the paradoxes caused by the presence of stress intensifications.