Issue 41

M.F. Funari et alii, Frattura ed Integrità Strutturale, 41 (2017) 524-535; DOI: 10.3221/IGF-ESIS.41.63 532 concerning the potential cohesive zone model are reported in Tabs. 3-6, respectively. In the present study, comparisons with results arising from the literature [18, 19] are developed. The main model refers to a steel beam, strengthened with FRP strip elements. The model is based on two cohesive interface elements, which are introduced between adhesive-steel and adhesive-FRP strip elements. As a consequence, debonding phenomena may affect the layered structures at two different interface levels. The interface law utilized to reproduce the debonding process is consistent with the model proposed by [20]. 1 E s [GPa] 12 G s [GPa] L s [mm] 1 L s [mm] 2 L s [mm] c s [mm] a s [mm] B s [mm] H s [mm] s  [kg/mc] 190 79.3 280 30 20 35 105 50 20 7500 Table 3 : Geometrical and mechanical properties of the steel beam. 1 E adh [GPa] 12 G adh [GPa] L adh [mm] B adh [mm] h adh [mm] adh  [kg/mc] 5 0.350 160 50 3 2000 Table 4 : Geometrical and mechanical properties of the adhesive layer. 1 E frp [GPa] 12 G frp [GPa] L frp [mm] B frp [mm] h frp [mm] frp  [kg/mc] 165 60 160 50 1.2 2000 Table 5 : Geometrical and mechanical properties of the Frp strip. Adhesive-Steel interface ( as ) Adhesive-Frp interface ( af ) as  [N/mm] as n  [mm] as  [N/mm] as n  [mm] 0.350 0.01 0.350 0.01 Table 6 : Interfaces parameters of the Adhesive-Steel interface ( as ) and Adhesive-Frp interface ( af ). In order to obtain a stable crack propagation, the structure is loaded under a displacement control mode. In particular, to avoid the dynamic effects due to the external load, a very small loading rate equal to 1 mm/s is assumed. However, time steps are modified during the computation from 1E-3 to 1E-7 sec, before and after the activation of the debonding phenomena, to capture accurately the effects produced by crack growth. In Fig. 7, results in terms of resistance curve and crack speed time histories for different thickness of the FRP strips are reported. At first, the structure presents a linear, stable and quasi-static behavior. Subsequently, when the crack growth criterion is satisfied in the adhesive-steel interface, the ALE interface is activated to reproduce the debonding phenomena. During the activation of debonding mechanisms, the resistance curve presents an oscillatory and variable behavior which varies very fast. In the same figure, a detail of the resistance curve at the point in which the crack onset is activated is also reported. This trend is quite in agreement with similar experimental results available from the literature [21], which show the importance of the dynamic effects during the crack growth. It is worth nothing that the resistance curves are quite dependent from the thickness properties of FRP strip. In particular, an increase of the FRP strip thickness reveals a similar impact on the critical displacement and load at the onset of the dynamic process (Fig. 7). Increasing the thickness of the FRP strip, the edge debonding strength of the beam is reduced (Fig. 7a). This effect is attributed to the increased amount of energy that is accumulated in the stiffened FRP layer and the corresponding increment of the edge stresses. Once the dynamic process is activated, the influence of the FRP strip thickness produces an increase of the crack speeds, which leads to more severe failure mechanisms. Contrarily to the properties of the FRP layer, which are well documented in the literature, the influence of the adhesive on the debonding phenomena is not completely investigated. To this end, in Fig. 8, results in terms of resistance curves and crack speed time histories for different values of the thicknesses of the adhesive layer are presented. In particular, an increment of the adhesive thickness reveals a different impact with respect the previous analyses in terms of FRP strip characteristics, i.e. Fig. 7. As a matter of fact, the results show how by using thin adhesive layers, an increase of the dynamic debonding strength is observed (Fig. 8a) leading the structure to be affected to a more severe dynamic state (Fig. 8b), since the observed crack tip speeds tend to be increased. From the results reported in Fig. 7 and 8, a good agreement with the data available from the literature is also observed [18].