Bridging Stress of Inclined Fiber in Cementitious Composites Based on Large Deflection Beam Theory

Abstract

The behavior of Strain-Hardening Cementitious Composites (SHCC) is strongly affected by the relationship between fiber bridging stress and crack opening width. When the fiber is inclined to the crack surface, the fiber is under the combined action of pulling and bending. This paper treats the fiber on each side of the crack as a continuously supported beam lying on elastic foundation (which represents the matrix) plus a free length protruded into the crack. The protruded part is treated as a cantilever supported at its end by an equivalent spring group representing the part of fiber inside the matrix. The relationship between bridging stress and crack opening width is then calculated by the consideration of axial loading acting on the beam as well as large deflection. From the simulation results on PVA fibers, the peak fiber bridging stress is found to increase with inclined angle due to the increasing bending forces. The trend is similar to that in fiber snubbing models where the fiber is treated as a string over a frictional pulley. The effects of different parameters such as embedded length and fiber to matrix stiffness ratio are then studied. The present work provides the physical explanation of the fiber snubbing effect, and shows how the snubbing factor is affected by various parameters.