1. Introduction
Externally bonded fiber reinforced polymer (FRP) is widely used as a proven reinforcement technique for masonry structures [
1,
2,
3,
4,
5]. Practical applications and numerous studies have found that the debonding of FRP from the surface of substrates (e.g., concrete, clay brick and mortar) is the principal failure mode of reinforced structures [
1,
6,
7,
8,
9]. The bond–slip relationship between FRP and substrate is the basis for understanding the process of interfacial debonding. The masonry structure is likely to be subjected to dynamic loads such as earthquakes, explosions and impacts. Experimental studies of the FRP-to-substrate interface show that the dynamic interfacial strength is significantly higher than that of static [
10,
11,
12,
13], and the dynamic bond–slip relationship is naturally different from that of static [
14,
15,
16,
17,
18]. An accurate bond–slip relationship can be used for strength calculations of FRP-reinforced structures, helping to design safer and more economical FRP-reinforced solutions. Therefore, the study of the bond–slip relationship at the FRP-to-brick interface under dynamic loading is of great significance.
Almost all the methods for deriving the bond–slip relationship at the FRP-to-substrate interface are based on the pull test [
19] (including the single-lap shear test, the double-lap shear test and the beam test) or its numerical simulation. According to the differences in the test data used, the methods for calculating the bond–slip relationship are roughly divided into three: one direct method and two indirect methods.
The direct method is most commonly used. The method directly applies the differential and integral of the axial strain of the FRP to calculate the bond stress and slip, respectively, and then derive the bond–slip relationship by synthesizing the data from different loading stages [
20]. Based on the direct method of using strain data, different models have been established to fit the bond–slip relationship. These bond–slip models all conform to the tendency of tensile softening, but with different shapes: (1) bilinear [
21,
22], e.g., Monti et al.’s model [
22]; (2) multilinear [
23,
24], e.g., Ghiassi et al.’s model [
24]; (3) single curve type [
25,
26,
27,
28,
29,
30,
31], e.g., Popovics et al.’s model [
25] and its development of Nakaba et al.’s model [
26] and Savioa et al.’s model [
27]; (4) double curve type, e.g., Dai and Ueda’s model [
32] and Lu et al.’s model [
33]; (5) mixed type with line and curve, e.g., Pan and Wu’s model [
34]. All of these five types of models appear in the study of the bond–slip relationship at the FRP-concrete interface.
Some studies have suggested that there are three main reasons why a consistent, reliable and accurate bond–slip relationship cannot be derived with the direct method. First, the debonding process is difficult to capture due to the highly nonlinear and brittle nature of local fractures [
35]. Second, the irregularities in the surface treatment and adhesive layer cause an irregular fluctuation in strain measurements [
36]. Third, the random distribution of cracks and aggregates in concrete also induces irregular fluctuations in strain measurements, resulting in a drastic variation in bond stress calculated from strain data [
33]. To overcome this issue, Ueda and Dai et al. [
35,
37,
38] ignored the dense strain information, fitted the load–slip curve at the loading end and then derived the bond–slip relationship indirectly based on a simple and rigorous analytical method. To further eliminate the chance errors of the experimental measurements and improve the accuracy of the analysis results, Wu et al. [
36,
39,
40] fitted the slip distribution curves at different loading stages simultaneously to calculate the bond–slip relationship indirectly.
Summarizing the concerns of the above references, it can be found that the research on the bond–slip relationship is mainly focused on the FRP-to-concrete interface, while there is less research on the FRP-to-brick interface. The research on the bond–slip relationship at the FRP-to-brick interface under dynamic loading is even more limited. Besides, due to the harsh requirements of the dynamic loading control on the experimental equipment, most of the studies are on the tensile strength of the interface and lack the study of the bond–slip relationship.
Accordingly, the bond–slip relationship at the FRP-to-brick interface under dynamic loading is investigated in this paper. Firstly, a numerical model of the FRP-to-brick interface was constructed based on the single-lap shear tests under two different loading rates. Secondly, the effects of FRP stiffness and brick strength on the bond–slip relationship were studied numerically. Finally, the dynamic enhancement effect on material performance was integrated to study and analyze the dynamic bond–slip relationship under different slip rates.
2. Single-Lap Shear Tests
The digital image correlation (DIC) method was adopted to implement full-field strain measurements, and a special fixture was designed to ensure stability during the dynamic loading. The CFRP-to-brick (CFRP, carbon fiber reinforced polymer) single-lap shear tests under two different loading rates were performed on a universal testing machine.
2.1. Materials and Specimen Preparation
The bricks used in the tests are standard commercial clay bricks with a size of 240 × 115 × 53 mm
3. The carbon cloth is a unidirectional woven carbon fiber fabric UT30-30G produced by Toray Japan. The epoxy adhesive HM-180C3P is a two-component fiber adhesive produced by Horse China specifically for structural reinforcement. Their specific material parameters are shown in
Table 1.
The CFRP-to-brick specimens are shown in
Figure 1. The carbon cloth with a width of 40 mm was bonded on the centerline of the brick, which contains a 160 mm long bonded region and a 40 mm long unbonded region. The surface of the bricks was sanded smooth and cleaned previously. Then the unbonded region was covered with tape to prevent impregnation by the adhesive. Finally, the carbon cloth was bonded to the brick by the wet lay-up method.
2.2. Instruments and Test Procedures
With the fixture as shown in
Figure 2, the single-lap shear tests were performed on an MTS universal testing machine (MTS, Eden Prairie, MN, America). The loading rate of the MTS universal testing machine with an ultimate load of 100 KN ranges from 1 to 1000 mm/min. Two groups of tests were performed, Group A: 10 mm/min and Group B: 1000 mm/min. Each group contains five specimens.
The strain was measured by a two-dimensional digital image correlation (DIC) method combined with a high-speed camera (iX Cameras, Rochford Essex, UK). As shown in
Figure 3, the debonding process was recorded by a high-speed camera (ix cameras i-SPEED716) with a maximum frame rate of 500,000 fps. The required light was provided by two 200 W LED lights. The high-speed camera was triggered by a TTL (Transistor-Transistor Logic) pulse from the testing machine.
2.3. Test Results and Analysis
The test results revealed that all specimens exhibited the peeling of CFRP and a thin layer of brick, as shown in
Figure 4, the fracture of the brick dominated the failure of FRP-to-brick interface. The test results are in agreement with the related literature [
30,
41].
The load–slip curves at the loading end are shown in
Figure 5. The loading process can be roughly divided into three stages: linear growth stage, softening stage and stable stage. With the increase of slip, the tensile force first goes through the linear growth stage and the softening stage to reach the ultimate load
Fu, then into the stable stage. In the stable stage, the slip further increases, the tensile force remains basically unchanged.
Comparing the average of the two groups of curves, it can be found that the linear growth rate of both groups is the same, but the linear growth stage of group B is longer so that the ultimate load is larger, which is 1.2 times of that of group A. Besides, Group B also has a longer stable stage and ends up with a larger slip.
To deeply understand the process of interfacial failure, the strain at different loading stages marked in
Figure 5 was analyzed. The corresponding strain contours obtained by the DIC method are shown in
Figure 6, in which the process of strain develops from the loading end to the free end can be clearly seen. Before the ultimate load
Fu, the strain increases while it develops from the loading end to the free end. After the ultimate load
Fu, the strain continues to develop towards the free end while the strain at the loading end hardly increases, indicating that the interface at the loading end may have been damaged.
The strain on the median line marked in
Figure 6 was extracted. The strain distribution data and the fitted curves of specimen A4 and B2 are shown in
Figure 7a,b, respectively. The strain development at the loading end (X = 160 mm) matches their load–slip relationships shown in
Figure 5. The development of strain from the loading end to the free end can be clearly seen in
Figure 7. By comparing
Figure 7a,b, it can be found that the final strain of B2 (1000 mm/min) is larger than that of A4 (10 mm/min). There are irregular fluctuations in strain measurements, as shown in
Figure 7. It is because of the irregularities in the surface treatment and the random distribution of cracks and aggregates in brick. The formula for fitting the curves in the figure will be given in the next section along with the derivation of the bond–slip relationship.
2.4. Bond–Slip Relationship
The slip distribution data derived by integrating the strain is shown in
Figure 8. To eliminate the chance errors of the experimental measurements and improve the accuracy of the analysis results, the method proposed by Wu et al. [
36,
39,
40] was applied to calculate the bond–slip relationship. The following mathematical function was used to fit the slip distribution curves at different loading stages simultaneously:
where
s is the slip,
x is the distance from the free end,
α and
β are the shared fitting parameters and
x0 is the fitting parameter that varies with different loading stages. The fitted results are shown in
Figure 8.
The strain distribution can be derived from the slip distribution [
36]:
Then, the distribution of the bond stress can be obtained as follows [
36]:
where
is called the FRP stiffness,
is the FRP modulus of elasticity and
is the FRP thickness.
Equation (1) can be expressed as [
36]:
Substituting Equation (4) into Equation (3) yields the bond–slip relationship [
36]:
Further, parameters such as the maximum bond stress
, the local slip
at the maximum bond stress and the interfacial fracture energy
can be derived [
40]:
The bond–slip parameters obtained by using the aforementioned method are listed in
Table 2, and the bond–slip curves for Specimens A4 and B2 are shown in
Figure 9. It can be found that the maximum bond stress and the corresponding slip are greater for Group B (1000 mm/min) compared with Group A (10 mm/min), and the curve coverage area i.e., interfacial fracture energy is greater for Group A as well.
It should be noted that the interfacial fracture energy is the energy consumed for FRP peeling from the substrate per unit area of FRP, not the fracture energy of cracks in the substrate material. The fracture energy of cracks in the substrate material is strain-rate-independent [
42,
43]. However, the corresponding fracture surface under the FRP is not flat, as shown in
Figure 4, and it may change with the loading rate [
18]. The variation of the fracture surface may be responsible for the dynamic enhancement of the interface, but the specific microscopic mechanism requires further investigation based on more specimens.
By comparing the load–slip curves, strain distribution, slip distribution and bond–slip curves of group A and group B, it is indicated that the interface behavior of FRP-to-brick has a significant dynamic enhancement effect. This may be related to the strain rate effect on the mechanical performance of materials such as FRP and brick under dynamic loading.