Please go through the review article entitled :Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: A review", by Peng-Cheng Maa etal published in Composites: Part A 41 (2010) 1345–1367
It depends on the type of Nanotube (SWNT/DWNT/MWNT). It depends on the purity too. There are varying values reported in the literature from 0.15TPa to 1.8 TPa
For MWNT, refer this paper: doi:10.1016/S0921-5093(01)01807-X
Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes
Here is another paper explaining the dependence of elastic moduli based on structural details: Elastic Properties of Carbon Nanotubes and Nanoropes
Phys. Rev. Lett. 79, 1297 – Published 18 August 1997
Here is another excellent review paper: doi:10.1016/S0266-3538(01)00094-X
Advances in the science and technology of carbon nanotubes and their composites: a review
Young's modulus is around 300-1000 GPa and tensile strnegth 10-60 GPa.
However don't forget that the mechanical in the radial direction display rather lower values than those mentioned. Much "softer" material in that direction. One shouldk simply just measure tghe mechanical properties for the batch that you have.
It is around 1TPa but is dependent on composition and chirality. For single CNTs you can always use a mdified atomic force microscope (AFM), and for composites, a normal tensile testing machine using the same standardized "dogbone shaped" geometry as for other materials. Since the CNTs in a composite will have a statistical distribution of orientations etc. you dont have to worry so much about the directional properties of each single CNT. Hope this helps :)
If you are still conducting research on CNTs, you might find the following article helpful.
Ahmed, Shahrior, Nivesh Karna, Jenny Zhou, Hsing-Wei Chu, Mark Placette, Xuejun Fan, and Liangbiao Chen. "Investigation of affecting parameters on the effective modulus and natural frequency of wavy carbon nanotubes." Journal of Physics and Chemistry of Solids 121 (2018): 121-127.