As far as the F R P / c o n c r e t e interfacial behaviour of shear-strengthened beams is con- cerned, it is generally accepted t h a t debonding propagation is governed by mode II frac- ture behaviour (in-plane shear/sliding). Bond-slip curves were identified experimentally or theoretically by an ascending branch before reaching the bond strength ( rm a x) , followed by softening behaviour. As shown earlier, the bilinear bond-slip model may be used to characterize the F R P / c o n c r e t e interfacial behaviour. In this model, initiation and prop- agation of debonding can be represented with three parameters: interfacial stiffness (ks), local bond strength ( rm a x) , and interfacial fracture energy (Gf), as shown in Figure 7.1.
In this section, the numerical predictions of a Pellegrino and Modena beam having steel stirrups and strengthened with a single layer of F R P sheets (TR30D3) is used to gain a clear understanding of FRP/concrete interfacial properties on the performance of shear- strengthened beams. T h e numerical aspect for the interfacial behaviour is investigated by modifying the order of the bond-slip model of Lu et al. [2005].
7.2.1.1 Effect of I n t e r f a c i a l Stiffness
Interfacial slip suppose to have a direct effect on the stress transfer rate from the con- crete to the F R P sheets. After concrete cracking, low interfacial stiffness may result in a slow stresss flow into F R P sheets causing debonding. Three values for the corresponding interfacial slip to the maximum interfacial shear stress (so) were investigated: 0.02 mm, 0.04 m m and 0.05 mm. The analyses were stopped when the first delamination occurred.
The reason for this is to investigate the effect of such parameters on the strengthening performance. T h e comparison is presented in terms of load-deflection relationships. As shown in Figure 7.2, the interfacial stiffness (ks) has no effect on the overall structural performance and also, the debonding point remains almost the same. In the figure, the same ultimate load carrying capacity and the corresponding midspan deflection are ob- tained despite the variation in the interfacial stiffness, where the debonding initiated at the same load value.
Bond stress (MPa)
(mm) F i g u r e 7 . 1 : Typical bond-slip relationship
400
300
12 Central deflection (mm)
F i g u r e 7 . 2 : Effect of interfacial stiffness on t h e applied load-central deflection relationship
7.2. PARAMETRIC STUDIES
400
300
tmax=4 MPa tmax=6 MPa tmax=8 MPa
12
Central deflection (mm)
Figure 7.3: Effect of interfacial bond strength on the applied load-central deflection relationship
7.2.1.2 Effect of Interfacial Bond Strength
To clearly demonstrate the effect of FRP/concrete interfacial bond strength (rm a x), local bond strengths ranged between 4 MPa, 6 MPa and 8 MPa were considered. As seen in Figure 7.3, increase of bond strength has a low effect on the global structural stiffness. If keeping other parameters constant, high bond strength presents more stress transfer, which resulted in small increase of ductility of the beam. Generally, this means that interfacial bond strength does not have a significant influence on the load carrying capacity and also the stress in the FRPs. This may be due to the fact that the debonding occurs at the softening branch of the interfacial bond curve.
7.2.1.3 Effect of Interfacial Fracture Energy
The larger interfacial fracture energy (Gf) the harder debonding becomes. The influence of the interfacial fracture energy (Gf) is investigated through various values of maximum interfacial slip ((smax). The following values were considered for the comparison of inter- facial fracture energy: smax = 0.2 mm, smax = 0.4 mm and smax = 0.8 mm. With the increase of interfacial fracture energy, the ultimate load carrying capacity and the struc- tural ductility can be enhanced, as shown in Figure 7.4. Low interfacial fracture energy resulted in early debonding and limited the transferable stresses to the FRPs leading to
400
^ 300
smax=0.2 mm smax=0.4 mm smax=0.8 mm
12
Central deflection (mm)
Figure 7.4: Effect of interfacial fracture energy on the applied load-central deflection relation- ship
crushing of the concrete.
To have insight into the trend of the FRP/concrete interfacial behaviour, the above comparison values is extended to investigate bond-slip interfacial relationships for the various fracture energy values. The investigation is conducted for an interface element corresponds to the location of first debonding occurrence. This element is taken at the top edge near the loading point. The influence of the interfacial fracture energy on the interfacial bond-slip relation is depicted in Figure 7.5(a)-(c). For a maximum interfacial slip (smax) is 0.2 mm (Figure 7.5a), the debonding occurred at the descending branch after few iterations. W i t h the increase of the maximum interfacial energy, this leaded to delay the debonding. It is of interest to mention t h a t the increase in the predicted debonding load when using high interfacial fracture energy is similar to the assumption of full bond between the concrete and F R P s .
In conclusion, the interfacial fracture energy (G/) rather t h a n the interfacial stiff- ness (ks), and interfacial bond strength ( rm a x) has a significant influence on the global behaviour of F R P shear-strengthened beams.
7.2. PARAMETRIC STUDIES
0.05 0.1 0.15 0.2
Interfacial slip (mm) (a) smax=0.2 mm
2
o 03
0.1 0.2 0.3 0.4
Interfacial slip (mm) (b) smax=0.4 mm
0 0.2 0.4 0.6 0.8 1
Interfacial slip (mm)
F i g u r e 7.5: Comparison between t h e provided and predicted shear stress-slip curves for various values of interfacial fracture energy