Nanoindentation derived elastic constants of carbon fibres and their nanostructural based predictions

Elastic constants of single carbon fibres were estimated by a novel nanoindentation based method and subsequently predicted by modified two- and three-phase Eshelby-Mori-Tanaka (EMT) micromechanical models which takes into account both crystalline, amorphous phases and microvoids of the fibre structure. This case study was carried out on a T-300 PAN-based carbon fibre reinforced SiC composite material at room temperature. Transversal and longitudinal cross-sections of individual fibres were indented by a sharp Berkovich tip up to the maximum depth of 150 nm. Assuming transverse isotropy of the fibres, their five elastic constants were deduced from the measured indentation moduli using numerical (Vlassak-Nix) and analytical (Delafargue-Ulm) models, and finite element method simulations. The elastic constants were estimated to c11 = 30.9, c12 = 9.7, c13 = 12.2, c33 = 237.3 and c44 = 10.9 GPa. The complete set of measured elastic constants were analyzed and then predicted by the proposed modified EMT models. The application of anisotropic nanoindentation coupled with the amorphous-crystalline structure model is unique to carbon fibre which revealed that an anisotropic ‘amorphous′ matrix should be assumed to achieve an appropriate fit with experimental results. This matrix was considered as a mixture of microvoids and aligned graphite planes, and their volume ratio was determined.