Bridging Toughening and Fracture Energy of X-type Fiber Reinforced Cementitious Composites

摘要

Based on the fiber bridging model and constant frictional interface stress, this paper derived the P-δ relation for the X-type fiber pulled out of cementitious matrix. By considering the random distributions of the bridging fibers and supposing that rupture of fiber never occurs, it derived the σ_B-δ relation of a single macro-crack, from which the fracture energy equation was deduced by integral. The derived toughening equations have continuous and explicit forms and are convenient for the approximate estimate of the fracture toughness of the composite. The fracture energy expression suggests that increasing fiber volume fraction, utilizing longer fibers or slender fibers and improving interface bonding are effective methods for improving the composite fracture toughness, while adopting fibers with higher elastic modulus is not a preferred suggestion. It is also found that when using X-type fibers to replace cylindrical fibers with same section area, one can obtain 3～8 times of fracture energy (corresponding leg length-width ratio of the X-type fiber cross section is 5～50).