Radial Elastic Modulus for the Interface between FRP Reinforcing Bars and Concrete

Abstract

The surface structure of reinforcing elements within a matrix can produce a complex mechanical interaction including mechanical interlocking along the interface. This interaction can be modeled using an interface idealization at a scale in which the details of the surface structure are omitted and the actual interface traction is homogenized over a length characteristic of the surface structure. For some applications such as the reinforcement of concrete with FRP bars, the reinforcing element can be idealized as being a circular cylinder, and the radial elastic interaction can affect the overall behavior, e.g., the “bond response” and failure mode of the composite system. The definition of the radial elastic modulus for the interface of the “homogenized model” requires static equivalence of the actual and homogenized tractions and equal amounts of strain energy in the domains. A unit cell approach is taken idealizing the traction distribution as periodic, and an analytical solution for the strain energy in the reinforcing element is presented. The analytical expression for the elastic modulus reflects its dependence upon the traction distribution, material properties, and bar geometry. To study the effects of these parameters, three bond specimens of an FRP bar in a concrete matrix are examined. As the actual traction distribution becomes more concentrated, the interface of the homogenized model becomes more compliant. With respect to material properties, the radial elastic modulus is usually most sensitive to changes in the transverse Young’s modulus of the FRP bar; for lightweight concrete the modulus is equally sensitive to changes in Young’s modulus of the concrete. The elastic moduli are applied to accurately reproduce the effects of a non-uniform traction distribution even when the concrete is split longitudinally and snap-back behavior occurs in the radial response. The traction distribution and compliance of the FRP bar have a significant effect on the snap-back behavior which indicates the potential for a very sudden failure due to concrete cracking.