Fracture mechanics and mechanisms of a carbon fiber reinforced carbon matrix lamina composite are studied. The importance of microfracture processes of first matrix cracking, fiber bridging, and fiber pullout processes for toughening C/C-composites is emphasized, and then, the fiber bridging process of the composite is mainly focused through the measurement of the R-curve. The fiber bridging tractions are estimated by the Dugdale approach from which the superb stress shielding and excellent notch tolerance of the composite are demonstrated.