## 5 Experimental Characterization of the Cohesive Law  
The simplified approaches reported in the previous section may give, in several cases, very conservative ultimate values for the maximum FRP stress allowable to avoid debonding failure. For this reason, experimental evaluation of the debonding mechanisms is suggested for high-performance reinforcing systems. More specifically, the identification of a cohesive law requires the evaluation of shear slip between the FRP and the structural elements along the loading direction. The former is conventionally measured by means of either linear variable displacement transducers (LVDTs) or laser meter devices installed on the composite plate, located at the beginning of the bonded area. The latter is commonly measured using strain gauges positioned along the longitudinal plane. While no international standards are currently available, several experimental setups have been proposed in literature [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26], based on a concrete block reinforced with an FRP laminate subject to a traction force, \(F\) (Figure 5). Starting from strains in the FRP recorded at fixed points along the x axis, \(\varepsilon_{\text{i}}\), the mean tangential stresses between two subsequent points (\(x_{\text{i}}\) and \(x_{\text{i+1}}\)) are given by the following expression:  
\[\tau_{\text{i,i+1}}=-\frac{E_{\text{f}}\,A_{\text{f}}\left(\varepsilon_{\text{ i+1}}-\varepsilon_{\text{i}}\right)}{b_{\text{f}}(x_{\text{i+1}}-x_{\text{i}})}, \tag{9}\]  
where \(b_{\text{f}}\) and \(A_{\text{f}}\) are the FRP width and cross-sectional area, respectively. The relative displacement between the FRP and the top concrete face (slip), \(s\), provides us with the interface law, which can be modelled using a bilinear or exponential law (Figure 6). The bilinear law is typically used in the analytical modelling of junctions, while the exponential law is used in their numerical modelling based on FEM codes, due to the continuity of the first derivative. Figure 5: Bond test setup. Starting from the interface law, the fracture energy of the FRP-concrete interface is obtained as follows:  
\[\Gamma_{\text{F}}=\int\limits_{0}^{\infty}\tau_{\text{b}}(s)\,ds. \tag{10}\]  
The corresponding specific fracture energy can be obtained by identifying the value below which no more than 5% of test results can be expected to fall. Some recent studies have proposed the use of Digital Image Correlation (DIC), a non-contact optical technique, to obtain the relative displacement, with measurements made over an extended area of the specimens being tested, rather than measuring only from the beginning of the bonded area [19; 20; 21; 22; 23; 24; 25; 26]. This promising method also allows the estimation, with good accuracy, of the strain field acting on the FRP and the external surfaces of concrete core. However, it also exhibits some disadvantages: (i) it requires extensive computing resources, and (ii) it is inaccurate close to the region characterized by displacement discontinuity (e.g., the FRP-substrate slip area). The latter limitation may be overcome by setting suitable parameters for the geometry and position of regions of interest (ROIs) in the DIC analysis (Figure 7). A recent methodology [25] allows a direct evaluation of fracture energy without fixing the interface law, by investigating the relationship between the cohesive traction and the J-integral. Figure 6: Interface laws. Figure 7: Experimental bond test (**left**), Region of Interest placed on the composite (**right**) [25]. More specifically, this approach assumes that:  
* The concrete block is rigid, due to its negligible compliance compared to that of GFRP laminate; this is also confirmed by recordings from the concrete strain gauges;
* The unbounded portion of the GFRP laminate is subject to a pure axial load;
* The bonded interface carries a pure shear load;
* The interface shear is constant over the width of the GFRP laminate;
* The adherends behavior is linear elastic.