  This work presents a model that successfully describes the tensile properties
of macroscopic fibres of carbon nanotubes (CNTs). The core idea is to treat
such a fibre as a network of CNT bundles, similar to the structure of
high-performance polymer fibres, with tensile properties defined by the CNT
bundle orientation distribution function (ODF), shear modulus and shear
strength. Synchrotron small-angle X-ray scattering measurements on individual
fibres are used to determine the initial ODF and its evolution during in-situ
tensile testing. This enables prediction of tensile modulus, strength and
fracture envelope, with remarkable agreement with experimental data for fibres
produced in-house with different constituent CNTs and for different draw
ratios, as well as with literature data. The parameters extracted from the
model include: CNT bundle shear strength, shear modulus and tensile strength.
These are in agreement with data for commercial high-performance fibres,
although high compared with values for single-crystal graphite and short
individual CNTs. The manuscript also discusses the unusually high fracture
energy of CNT fibres and exceptionally high figure of merit for ballistic
protection. The model predicts that small improvements in orientation would
lead to superior ballistic peformance than any synthetic high-peformance fiber,
with values of strain wave velocity ($U^{1/3}$) exceeding $1000 m/s$.
