A novel analytical model for fiber reinforced cementitious matrix FRCM coupons subjected to tensile tests

Abstract

A much enhanced -with respect to existing literature- analytical model for FRCM coupons subjected to standard tensile tests is proposed. One fourth of the coupon is idealized considering two layers, matrix and fiber, subjected to a uniaxial stress state, mutually interacting at the interface through tangential stresses. The matrix is assumed elastic-perfectly fragile and the fiber linear elastic. The shear stress-slip relationship at the interface is tri-linear, with the first phase elastic, the second exhibiting linear softening followed by a third phase at possible non-null residual strength. The longitudinal equilibrium equations written for the two layers, suitably re-arranged, allow deducing a field problem governed in the three phases by a single second order linear differential equation where the independent variable is the interface slip, with solution retrievable analytically. Since the location of the points where the interface is in the different phases is not a-priori known, a discretization with small length elements is adopted. For each element the solution of the field problem is known in closed form and the only variables to determine are the integration constants coming from the solution of the differential equation. After a standard assemblage, all constants are derived imposing the boundary conditions at the extremes of the elements, which depend on the state of cracking of the matrix layer. The model is validated against two sets of experimental data on coupons tested in two different University laboratories in Italy. A satisfactory predictivity of both the global and local behavior is found.