Tension Stiffening Modeling of Steel Fiber Reinforced Concrete

Adding steel fibers to reinforced concrete improves the active mechanisms on crack surface including tension and shear transfer mechanisms. In Steel Fiber Reinforced Concrete (SFRC), tensile stresses are developed in fibers and deformed reinforcing bars just after crack initiation. With this beneficial effect, concrete tensile strength is improved and crack spacing decreases. In this research, SFRC member behavior is analytically investigated under pure tension and in order to verify the model, the results are compared with some recent experimental results. From the viewpoint of constitutive modeling of RC elements, there are two main approaches, discrete crack and continuum level models. The major disadvantage that adheres to discrete crack models is the fact that these models focus on the local crack behavior and seek to detect the crack paths which of course requires a high computational cost. By contrast, continuum level models taking advantage of the spatially averaged models between two primary transverse cracks. In a process of developing average constitutive models, it is important to model local mechanisms, these mechanisms in a reinforced concrete domain are related to initiation and propagation of cracks.
In this article, the tension stiffening model is developed considering all effective local stress transfer mechanisms including tension behavior of deformed bar, fibers pullout, tension softening of plain concrete and bond slip-stress between the reinforcing bar and concrete matrix. Straight and end hooked fibers have different mechanisms during pullout such as debonding, friction and mechanical anchorage of end hooked fibers. To predict the fiber tensile behaviors, it is necessary to define fiber stress transfer mechanism on the crack surface. The most important parameters that affect fibers behavior are material, size and geometry, distribution and orientation of fibers. The model used in this research considers a uniform random distribution for fiber’s geometrical location and inclination angle. In this model, the slip occurred in the fiber is considered in both sides of fiber embedded in concrete. The bond slip- stress behavior of straight fiber is defined as linear before the bond stress reaches to the bond strength then the bond stress is considered constant until complete pullout. In end hooked fibers, in addition to debonding and friction, end mechanical anchorage of the fiber has also an important effect on the bearing capacity. In fact, in the process of fiber pullout, hooked part of fiber most have plastic deformation.To simulate it, a parabolic model is used. In order to solve the algorithm, an iterative analysis method is applied to calculate tension stress-elongation of specimen. To increase the accuracy of the model, the local yielding of reinforcing bars and matrix damage at the crack surface are also numerically simulated. Model verification is carried out by comparing computational predictions with available experimental results. The results show good agreement with test results. The proposed model is also shown to be useful in considering the effect of various percentage of fibers on average stress strain behavior of deformed bar, total load elongation of specimen, crack spacing and concrete tension stiffening. By increasing fiber percentage, crack spacing will decrease so the average stress strain behavior of deformed rebar become more likely to bare bar.