Integrated cyclic fiber-bridging model encompassing buckling characteristics of both steel and PE fibers

The response of fiber-reinforced concrete (FRC) members to cyclic or seismic loading has been extensively studied in recent years. However, these experiments cannot fully elucidate the impact of cyclic fiber-bridging criteria on the macroscopic mechanical properties of FRC, particularly for hybrid fiber FRC after cracking. To explicit the cycling fiber-bridging behavior of steel fibers in the ultra-high-performance concrete (UHPC) and polyethylene (PE) fibers in the engineered cementitious composite (ECC), a series of single fiber pull-out test programs considering fiber types, embedding length, and loading scheme were carried out. The test results indicate that the relatively high flexural stiffness of steel fiber results in the bridging force becoming negative upon reaching a certain degree of unloading, with its maximum value governed by the compressive buckling critical. Distinctly, the fiber-bridging behavior of flexible PE fiber exhibits a nonlinear rapid decrease to zero during unloading and tends to return along a similar path during reloading. Further, an integrated cyclic fiber-bridging model encompassing the buckling characteristics of steel and PE fibers is proposed. The introduction of the elastic modulus reducer factor greatly enhances the accuracy of fiber-bridging model prediction. The proposed unloading law that introduces the modified compression buckling criterion could accurately calculate the unloading-reloading behavior, critical buckling load, and post-peak behavior of steel fiber when unloading at any slip deformation. Meanwhile, a simple formulation can quickly and effectively calculate the unloading-reloading process by simply changing the parameter values is proposed for flexible fibers. Finally, the simulated cycling fiber-bridging relationship for both steel and PE fibers agree well with their actual cyclic fiber pull-out behavior.