Cohesive fracture model for functionally graded fiber reinforced concrete

a r t i c l e i n f o Keywords: Concrete (E) Fiber reinforced concrete (FRC) (E) Constitutive relationship (C) Cohesive fracture (C) Fracture energy (C) A simple, effective, and practical constitutive model for cohesive fracture of fiber reinforced concrete is proposed by differentiating the aggregate bridging zone and the fiber bridging zone. The aggregate bridging zone is related to the total fracture energy of plain concrete, while the fiber bridging zone is associated with the difference between the total fracture energy of fiber reinforced concrete and the total fracture energy of plain concrete. The cohesive fracture model is defined by experimental fracture parameters, which are obtained through three-point bending and split tensile tests. As expected, the model describes fracture behavior of plain concrete beams. In addition, it predicts the fracture behavior of either fiber reinforced concrete beams or a combination of plain and fiber reinforced concrete functionally layered in a single beam specimen. The validated model is also applied to investigate continuously, functionally graded fiber reinforced concrete composites. Fiber reinforced concrete (FRC) composites have been utilized to improve the performance of plain concrete materials and to repair and retrofit structures [1–8]. Fibers can be spatially (or functionally) distributed to improve structural performance while minimizing the amount of fibers. These spatially varied microstructures created by nonuniform distributions of reinforcement phase are called functionally graded materials (FGMs) [9]. Recently, functionally graded fiber-reinforced cement composite have been developed by using the extrusion technique [10] and the Hatschek process [11] in order to improve the structural performance of a component while reducing its material cost. In order to explicitly consider the larger fracture process zone in cementitious materials, Hillerborg et al. [12] expanded the cohesive zone model concept [13,14] to concrete by combining fracture mechanics and the finite element method. The major challenge in the cohesive zone model is the determination of the traction– separation relationship, which represents the nonlinear fracture process zone of a material. For plain concrete, a linear softening model was employed by Hillerborg et al. [12], and a bilinear softening model was introduced by Petersson et al. [15]. Since then, a bilinear softening model has been widely utilized to investigate plain concrete fracture behavior [16]. The nonlinear fracture process zone of FRC has been specifically investigated by various methods such as (a) direct tension tests [17–19], (b) fiber pull-out tests [20–24], (c) indirect methods [25,26], and (d) …