A New Analytical Model for FRCM Coupons

Abstract

An analytical approach to describe FRCM coupons subjected to standard tensile tests is presented. The coupon is idealized assuming a mono-axial stress state and considering both matrix and fiber. Matrix and fiber interact at the common interface by means of tensile stresses. The fiber is supposed linear elastic, mortar is elastic perfectly brittle and the interface is characterized by a trilinear tau-slip law, where the first stage is elastic, the second involves linear softening and the third exhibits a constant tangential strength. A single second order linear differential equation - deduced from simple longitudinal equilibrium equations - governs the field problem in the three stages of the interface. The only independent variable is the slip at the interface and the solution can be obtained analytically. A priori it is not possible to know the position of the points where the interface exits one phase to enter into another and consequently a discretization with small elements is implemented. The closed-form solution is known for each element where the only variables to be defined are the integration constants of the differential equation solution of the differential equation. Depending on the state of cracking of the mortar, all the constants are derived by imposing suitable boundary conditions at the edges of the elements. The model is successfully validated against available experimental results and previously presented numerical models.