Micromechanical modeling of crack-bridging relations of hybrid-fiber Strain-Hardening Cementitious Composites considering interaction between different fibers

As tensile crack-bridging constitutive relations play an important role in the multiple cracking behaviors of Strain-Hardening Cementitious Composites (SHCCs), careful control of the crack-bridging relations is the key to a successful design of the materials. This study theoretically explores the crack-bridging relations of SHCCs with fixed total volume fraction (2.5%) of hybrid polyvinyl alcohol (PVA) and steel fibers. Since a large number of experiments at the single-fiber level are needed to determine the parameters for the micromechanical model, the snubbing coefficient, fiber strength reduction factor and Cook-Gordon parameter for mono-fiber composites were theoretically calibrated rather than experimentally obtained in this study. With these calibrated parameters, the crack-bridging relations of hybrid-fiber SHCCs were then modeled and compared to the test results. The superposition principle was used to address the contributions of different types of fibers, and the interaction between PVA and steel fibers was considered through the matrix micro-spalling in the modeling. The theoretically modeled crack-bridging relations of hybrid-fiber SHCCs were in good agreement with the test curves in terms of the tensile strength and the corresponding crack opening. The findings in this study provide a better understanding of fiber hybridizations in SHCCs.