Dai et al. [10] extended his bond-slip model developed for ambient temperature [24] to make it applicable for elevated temperature. This model utilized two keys parameters: (1) the interfacial fracture energy (Gf); (2) the interfacial brittleness index (B). Despite the simplicity of the proposed model (only two parameters need to be determined from the test data), it also has some weakness in attaining the highly accurate shape description of nonlinear bond-slip curves. In addition, the value of B was determined based on the load-strain distribution not based on the load-displacement curves due to the limited experiments reporting the load-displacement curves. Using the measured strain can show considerable variations from one place to another due to the discrete nature of concrete cracks and heterogeneity of concrete.
Dai et al proposed the following expressions to determine interfacial fracture energy and interfacial brittleness index.
\(\frac{G_f\left(T\right)}{G_{fo}}=\frac{1}{2}\tanh\left[-b_2\left(\frac{T}{T_{g,a}}-b_3\ \right)\right]+\frac{1}{2}\)
\(\frac{B\left(T\right)}{B_o}=\frac{\left(1-c_1\right)}{2}\tanh\left[-c_2\left(\frac{T}{T_{g,a}}-c_3\right)\right]+\frac{\left(1+C_3\right)}{2}\)
Where Gf (T) and B(T) are the interfacial fracture energy and brittleness index at the elevated temperature, respectively; Gf0 (N/mm) and B0 (mm-1) are the interfacial fracture energy and brittleness index at the ambient temperature; and b2 = 3.206, b3 = 1.313, c1 = 0.485, c2 = 14.053, and c3 = 0.877 are constant derived from the available experimental data then. The value of Gf0 and Br should be determined from the shear test because they change from one system to another depending on the concrete strength and properties of adhesive[23] [22][25]. If such test cannot be performed, Dai et al. [10] reamended use the values from Lu et al. [23] model Gf0 = 0.545 N/mm (for normal compressive strength of 35 MPa and commonly used adhesive) and Br is within the range of 8 to 14.1 (for normal concrete with cylindrical compressive strength ranging from 15 MPa to 50 MPa)
Dai et al. [10] also revised Bisby’s model [26] for the degradation of modules of elasticity at elevated temperature
of prefabricated FRP to account for the degradation of the FRP sheets (wet layup strengthening system). It is important to mention that the revised model was only validated with data from Chowdhury et al. [27] [28] due to the limited available test data (therefore, it is need to be validated with a bigger data to check its accuracy).
\(\frac{E_p\left(T\right)}{Epo}=\left(\frac{1-a_1}{2}\right)\tanh\left[-a_2\left(\frac{T}{T_{g,p}}-a_3\right)\right]+\left(\frac{1+a1}{2}\right)\)
Where Ep0 and Ep(T) are the elastic modulus of FRP at the ambient temperature and elevated temperature T(oC), respectively; a1 = 0.729, a2 = 9.856, a3 = 0.609 are empirical factors.
The ultimate load that the FRP can resist before failure can be determined using the following formula:
\(P_{uT}=bp\sqrt{\frac{2G_fE_{pT}t_p}{\left(1+\alpha\right)}}-\frac{E_pt_pb_p}{\left(1+\alpha\right)}\left(\alpha_p-\alpha_c\right)\ \Delta T\)
\(\alpha=\frac{E_pt_pb_p}{E_ct_cb_c}\)
Were PuT is the ultimate thermotical pull load due to both mechanical and thermal effects; Gf is the interfacial fracture energy at a specified temperature; bp and tp are the width and thickness of the FRP plate/sheet, respectively; bc and tc are the width and thickness of the concrete prism; αp and αc are the thermal expansion coefficient of FRP and concrete, respectively.
Dai et al. [10] proposed the following formulas to determine the bond-slip relationship
\(\tau\left(x\right)=2G_fB\left(e^{-B\delta\left(x\right)}-e^{-2B\delta\left(x\right)}\right)\)
\(\delta\left(x\right)=\frac{1}{B}\ln\left[e^{B\left(Ax+c_e\right)}+1\right]\)
\(c_e=\frac{1}{B}\ln\left\{\frac{\frac{1}{A}\left(\frac{P\left(1+\alpha\right)}{E_{p\left(T\right)}t_pb_p}+\left(\alpha_p-\alpha_c\right)\Delta T\right)}{1-\frac{1}{A}\left[\frac{P\left(1+\alpha\right)}{E_{p\left(T\right)}\ t_p\ b_p}+\left(\alpha_p-\alpha_c\right)\right]}\right\}\ -\ A.L\)
\(A=\ \sqrt{\frac{2G_f\left(1+\alpha\right)}{E_{p\left(T\right)}t_p}}\)
\(\epsilon\left(x\right)=\frac{A}{1+\frac{e^{BA\left(L-x\right)}\left(P_{uT}-P\right)}{P+\frac{E_pt_pb_p}{\left(1+\alpha\right)}\left(\alpha_p-\alpha_c\right)\Delta T}}\)
Where τ(x) is the shear stress at distance x from the loaded end; δ(x) is the slip at the same distance x ; ε(x) is the strain at the same distance x; P is the experimental load acting at the load end of the FRP; A is the area underneath the τ ⁓ δ curve which is equal to the interfacial fracture energy [ ; B is the brittleness index.
Vast number of studies dedicated to study the structural failure, design parameters, and failure modes of externally bonded FRP. The performance of this system is dominated by the bond behavior between FRP and concrete. This bond behavior can be greatly influenced by the environmental factors that can lead into premature failure. Understanding the long-term behavior and degradation of this system under various environmental factors is as important as the short-term performance. Despite of the extensive literature dedicated for studying the durability of the FRP system, most of these studies focused on the effect of an isolated degrading agent such solar radiation (UV), freeze and thaw, moisture and temperature. Thus, less attention was given to the combined effect of two or more agents, which represents the real case situation. The hygrothermal environment including the combined effect of moisture and temperature is considered the most aggressive environment for FRP [7] [8] [13]. On one hand, moisture can plasticize and degrade the epoxy bonding between FRP and concrete through the hydrolytic breakdown between matrix and FRP. Moreover, it can reduce the Tg. On the other hand, temperature close or higher than the Tg can significantly reduce the bond strength [14][3][4]. Temperature coupled with moisture can accelerate the degradation by increasing the rate of moisture absorption.
In this research, the behavior of FRP sheets bonded with epoxy resin in wet layup technique is going to be investigated. There are two reasons for investigating this system (1) this system is widely used in the rehibition and strengthening of the masonry wall and infrastructure that is commonly exposed to hygrothermal environment; (2) since It has a lower Tg, it is expected to be more effected
by hygrothermal environment especially in a temperature close to the service temperature.
The experimental program will explore the degradation of the bond after exposure into two hygrothermal conditions which are (1) moisture combined with different ranges of temperature; (2) water immersion combined with various range of temperature. Single-lap shear and pull-off test will be used to investigate bond degradation as shown in the Figure. The effect of the hygrothermals conditions on the modules of elasticity of the FRP and Tg will be also evaluated and measured. Finally, an analytical model is going to be proposed to determine the degradation of the bond strength.