Simple Fiber Poullout Model for Aligned Hook Eneded Stell Fibre

Cement based material such as mortar and concrete are brittle in nature and crack under low tensile stress and strain levels. Adding discontinuous fibers as reinforced concrete remedy some concern related to cement based material brittleness and poor resistance to crack growth. After cracking the fibers arrest between two crack faces and provide mechanisms that abate their unstable propagation []. Fibers bridging force is achieved by transmission of the bond interfacial stress between the fiber and surrounding matrix. The resistance of the section to further crack opening depends largely on the fiber pullout mechanisms and related possibilities including complete fiber pullout or fiber fracture []. The high levels of interfacial shear strength may prevent fibers from complete debonding and result in fiber fracture. Although the strength of composite may increase, its toughness reduces significantly and failure is brittle. On contrary the low interfacial shear strength causes complete fiber debonding from matrix and fiber pullout. The effectiveness of fiber is often assessed by using single fiber pullout test. The experiments have shown that in improving the pullout resistance, hook-end fiber is more effective than straight fiber [,, ].The pullout process of hooked-end fibers is more complex than that of straight steel fibers and there is one additional deformation mechanism because of mechanical anchorage. So the analytical models for straight fiber are not valid for the fibers having mechanical anchorage. The main objective of this paper is to develop an analytical model for hook-end steel fiber pullout behavior. In this model the concept of bond shear stress versus slip relation between fiber and matrix has been used to develop fiber force and bond stress. Also the interfacial stress has been supposed that to be distributed uniformly. Based on two mentioned assumption a theoretical relation have been developed for aligned straight fiber at first. Then this relation is promoted for hook ended steel fiber pullout response. In order to do this, the effect of hooks on force and stress distribution has been analyzed along the fiber length and utilized for developing the pullout response of hook ended steel fiber. Based on obtained relation, the hooks change the fiber along the fiber length at the hooks and this force will be decreased with constant coefficient which is the function of fiber geometry. Despite that a normal force and its frictional force will be occurred at the hook bent. Decreasing the fiber force and creating a normal force at the hook bend are the factors that create an extra resistance force against the pullout in hook-end fiber. This study investigates these factors and develops the relations in order to calculating the maximum load required for pulling out the hook-end fiber. Finally the model has been validated by experimental results on the hook-end steel fiber. Proposed model is able to estimate the main pullout mechanism due to mechanical anchorage of hooks.