A probability model for the strength of carbon nanotubes

A longstanding controversy exists on the form of the probability distribution for the strength of carbon nanotubes: is it Weibull, lognormal, or something else? We present a theory for CNT strength through integration of weakest link scaling, flaw statistics, and brittle fracture. The probability distribution that arises exhibits multiple regimes, each of which takes the form of a Weibull distribution. Our model not only gives a possible resolution to the debate but provides a way to attain reliable estimates of CNT strength for materials design from practical-sized (non-asymptotic) data sets of CNT strength. Last, the model offers an explanation for the severe underestimation of CNT strength from strength tests of CNT bundles.