3.2.1 Single-lap direct-shear tests

In order to foster the discussion on the quasi-brittle nature of the debonding mechanism, comment on the strain limits provided in guidelines and codes, and eventually highlight the need for future research, in this section part of the previous experimental work conducted by the author in collaboration with Prof. Kolluru V. Subramaniam (Indian Institute of Technology, Hyderabad, India) will be briefly revisited (Subramaniam et al., 2007). Single-lap direct-shear tests were used to evaluate the FRP–concrete debonding using the classical pull–push configuration. The tensile load was applied to the FRP sheet, while the concrete block was restrained against movement. This set-up is also referred to as the near-end supported single-shear test (Yao et al., 2005).

Figure 3.1 shows the specimen dimensions and the loading arrangement (Carloni and Subramaniam, 2012b). The nominal dimensions of the prismatic concrete block were as follows: length L = 330 mm, width b = 125 mm, height h = 125 mm. The coarse aggregates consisted of gravel with a maximum size of 10 mm. River sand was used as fine aggregate. The 28-day compressive strength of concrete, determined as per ASTM C 39 (2011), was 39 MPa. The nominal thickness t_f of the carbon fibers contained in the FRP composite sheet was equal to 0.167 mm. The tensile strength and the Young’s modulus E_f of the composite sheet based on the fiber thickness were equal to 3.83 and 230 GPa, respectively. The FRP sheet was bonded in the center on one side of the concrete block using the wet-layup procedure. The bonded length of the sheet was kept fixed at 152 mm for all specimens. A length (n) of the FRP equal to 35 mm was left unbonded to provide an initial notch. Different nominal widths, b_f, of the FRP sheet equal to 12, 19, 25, 38, and 46 mm were tested. Two linear variable differential transducers (LVDTs) were mounted on the concrete surface close to the edge of the bonded area. The LVDTs reacted off of a thin aluminum Ω-shaped plate, which was glued to the FRP surface at the beginning of the bonded area as shown in Fig. 3.1. The average of the two LVDT readings was named global slip. Tests were conducted in displacement control by increasing the global slip at a constant rate equal to 0.00065 mm/s, up to failure. The modality of failure of all direct-shear test specimens was associated with progressive debonding of the FRP sheet from the concrete substrate.

The strain components on the surface of the FRP and surrounding concrete during the monotonic quasi-static tests were determined from the displacement field, which was measured using a full-field optical technique known as digital image correlation (DIC). Details about DIC can be found in Sutton et al. (1983, 2009). The strain analysis reported in the next section refers to the Cartesian system shown in Fig. 3.1.

Figure 3.2 shows a typical load vs global slip response obtained from a direct-shear test. The load response of Fig. 3.2 corresponds to test W_6 (b_f = 25 mm) reported in Subramaniam et al. (2007). The load responses obtained from specimens with different FRP widths were nominally similar in shape. Additional tests were published by the same authors (Subramaniam et al., 2011) using the same test set-up and concrete blocks with a different width (b = 52 mm) and height (h = 100 mm). The load responses of those specimens were also similar in shape. The load response was initially linear up to point A. A nonlinear behavior was observed in the region AC. The strain analysis, presented in the next section, showed that the interfacial crack initiated in the nonlinear part AC of the load response (Ali-Ahmad et al., 2006; Subramaniam et al., 2007, 2011. The difference between crack initiation and crack propagation in a strengthened beam is outlined in Sebastian (2001). A sudden drop (CC’) in the load marked the onset of the interfacial crack propagation. Load drops before point C (for example at point B) indicated that the debonding process initiated. As the crack propagated (after C), the load remained nominally constant and its value P_crit was determined as the mean value of the load corresponding to the range of the global slip (g₁ = 0.35 mm, g₂ = 0.75 mm). The global slip range (g₁, g₂) slightly varied for each test and was identified on the basis of the strain analysis results that will be presented in the next section. The load response between points H and I will be justified by the strain analysis that follows. The load P_crit is often termed load-carrying capacity or bond strength. Bond strength is probably used improperly in this context, because strength is usually associated with a stress component rather than a load, which depends on the size of the specimen.

To provide a rational basis for comparison, the load-carrying capacity was expressed in terms of the ultimate nominal stress (σ_crit) in the FRP at debonding:

${\sigma }_{\mathrm{crit}}=\frac{P_{\mathrm{crit}}}{b_f{t}_f}$ [3.1]

[3.1]

The variation of σ_crit with the ratio b_f/b is reported in Subramaniam et al. (2007). σ_crit increased linearly with the ratio b_f/b, suggesting the existence of a width effect. This relationship appeared to be independent of the width of the concrete block (Subramaniam et al., 2011). In Subramaniam et al. (2007), it was found that the specimens with b_f = 12 mm exhibited significant scatter and provided results that did not agree with the trend. The reason for the nonconformity of the b_f = 12 mm specimens became clear with the results of the strain analysis.

3.2.2 Strain analysis in direct-shear tests

Figure 3.3 shows the variation of the axial strain ε_yy on the surface of the FRP along the bonded length for point E of the load response of Fig. 3.2. The axial strain distribution along the FRP obtained from all specimens tested was nominally similar. The experimental strain values are represented by ‘×’s. The axial strain values were determined along the center line of the FRP sheet by averaging the strain across a 10-mm-wide strip for each value of y. Averaging the strain across a 10 mm width allows for taking into account the variation of the strain due to the presence of a non-homogeneous substrate and local material variations in the FRP sheet (Ali-Ahmad et al., 2006). A 10-mm strip was chosen based on the size of the aggregate. It can be noticed that at y = 116 mm the axial strain has a relative maximum. The axial strain along the FRP at point E was approximated using the procedure outlined in Ali-Ahmad et al. (2006). The experimental nonlinear strain distribution along the bonded length of Fig. 3.3 was approximated using the following expression (solid line in Fig. 3.3):

${\mathit{\epsilon }}_{\mathit{yy}}={\epsilon }_0+\frac{\mathit{\alpha }}{1+{\mathrm{e}}^{-\frac{\mathit{y}-{\mathit{y}}_0}{\mathit{\beta }}}}$ [3.2]

[3.2]

where α, β, y₀, and ε₀ were determined using nonlinear regression analysis of the strains obtained from DIC. The choice of the function [3.2] is not unique (Dai et al., 2005; 2006; Zhou et al., 2010; Liu and Wu, 2012) and its influence on the results presented in the next section was not investigated in the study. The observed strain distribution along the FRP was essentially equal to zero close to the unloaded end. There was a rapid increase in strain upon approaching the loaded end. The strain leveled off at a value ${\overline{\mathit{\epsilon }}}_{\mathit{yy}}$ approximately equal to 5520 με. The observed strain distribution was divided into three main regions: (1) the stress-free zone (SFZ); (2) the stress-transfer zone (STZ); and (3) the fully-debonded zone (FDZ). In the FDZ, the strains were essentially constant and were found to remain unchanged as the global slip increased, which is consistent with the observation that the load remained nominally constant (P_crit) after the debonding process propagated. Analysis of the strain data revealed that the STZ was fully established when the load response attained P_crit. In other words, the ‘S’ shape of the strain profile was fully established for points of the load response after C. For each test, the global slip range (g₁, g₂) within which the STZ was fully established was determined and used to compute the load-carrying capacity P_crit. The fitting curves, obtained using Equation [3.2], for points D, F, G, and H, are shown in Fig. 3.3 for comparison. It can be observed that a simple translation of the STZ further along the length of the FRP sheet occurred as the global slip increased while its shape remained constant. The translation of the STZ indicated self-similar crack growth.

The STZ at point H reached the end of the bonded length. Any further increment of the global slip corresponded to a different fracture path that involved a larger amount of concrete as the crack kinked in the direction of the concrete block. The portion of the load response H-I in Fig. 3.2 is related to this different behavior of the FRP–concrete interface (Carrara et al., 2011). It is important to notice that the best-fit curve provided a maximum strain ${\overline{\mathit{\epsilon }}}_{\mathit{yy}}$ that varied slightly from point to point along the load response. These variations were consistent with the variation of the load. The mean values of the maximum strain ${\overline{\mathit{\epsilon }}}_{\mathit{yy}}$, calculated from ten points of the load response in the range (g₁, g₂), are shown in Fig. 3.4 and reported in Table 3.1 for all the tests published in Subramaniam et al. (2007). The mean value (5560 με) of test W_6 is shown with a black-filled marker in Fig. 3.4.

Table 3.1

Fracture parameters of the tests published in Subramaniam et al. (2007)

Test	bf (mm)	Pcrit (kN)	LSTZ (mm)	${\overline{\mathit{\epsilon }}}_{\mathit{yy}}$ (με)	GF (MPa × mm)
W_1	46	12.90	80	7210	0.874
W_2	46	12.05	76	6180	0.634
W_3	46	13.20	75	5890	0.563
W_4	38	10.09	81	6430	0.692
W_5	38	10.02	73	6240	0.652
W_6	25	5.54	80	5560	0.546
W_7	25	5.44	76	5630	0.530
W_8	25	5.36	69	6490	0.705
W_9	19	4.27	75	6400	0.686
W_10	19	4.05	78	5890	0.579

The progressive debonding of the FRP composite sheet from concrete is associated with a STZ of a fixed length L_STZ, which translates as the crack advances (Fig. 3.3). L_STZ is also termed the effective bond length (Chen and Teng, 2001) or the development length (ACI 440.2R-08, 2008). Values of L_STZ are reported in Table 3.1 and summarized in Fig. 3.5. Each value plotted in Fig. 3.5 represents the mean value for each test and was calculated from ten points of the load response within (g₁, g₂). Some of the proposed formulas for L_STZ (Nuebauer and Rostasy, 1999; Chen and Teng, 2001; Monti et al., 2003; Karbhari et al., 2006) are plotted in Fig. 3.5 for comparison. The experimental values of L_STZ are not affected by the width of the FRP sheet.

Figure 3.6 shows the variation of the axial strain ε_yy across the width of the specimen W_6 (Subramaniam et al., 2007) at point E (Fig. 3.2) for different values of y. Figure 3.6 reveals the presence of a central region of the FRP where the axial strain is nominally constant across the width b_s is the measurement of the central region of the FRP. The width b_d of the concrete strip involved in the stress transfer is larger than the FRP width. Only for those specimens with b_f > 12 mm the central region was observed; therefore, it was concluded that specimens with b_f = 12 mm did not follow the trend of σ_crit vs b_f/b due to the absence of the central region. A plot of the strain ε_yy for a specimen with b_f = 12 mm can be found in Subramaniam et al. (2007). The width of the central region of the FRP increased as the FRP width increased, while the quantity (b_d − b_s) remained constant. Hence, the increase in the nominal stress at debonding with an increase in the FRP width was explained by the increase of the central region. Available results in the literature (Chen and Teng, 2001; Yao et al., 2005) did not confirm the conclusions reported in Subramaniam et al. (2007). Chen and Teng (2001) reported a decrease of the normalized load-carrying capacity with an increase of the FRP-to-concrete width ratio. A coefficient β_p that takes into account the effect of the FRP-to-concrete width ratio was proposed by the authors. It should be noticed, however, that the specimens considered by the authors (Chen and Teng, 2001) to validate the model had a minimum FRP width equal to 25.4 mm. Size effect was not considered in their study, and some of the data, obtained from the literature and used to calibrate the model, were from bond tests between steel plates and concrete.

Subramaniam et al. (2007) showed that the plot of the shear strain ε_xy across the width of the specimen for different values of y also revealed the presence of edge regions in the FRP sheet that were characterized by high-shear strain gradients. The central region in which the axial strain was constant coincided with the central region of the strip where the shear strain was zero.

3.3.1 Cohesive material law

Several researchers attempted to study the ICD phenomenon and the debonding in direct-shear tests as a Mode-II fracture problem (Anderson, 2004) where the interface region is idealized to be of zero thickness with well-defined material properties (Ali-Ahmad et al., 2006; Wu and Niu, 2007; Mazzotti et al., 2008). In this idealization, the interfacial crack, associated with initiation and propagation of debonding, is subject to a Mode-II loading condition. The quasi-brittle behavior of the interfacial crack, in the spirit of the cohesive crack model, is described by introducing a cohesive material law, which relates the interfacial shear stress (τ_zy) to the relative slip (s) between FRP and concrete. It is important to highlight that the cohesive material law τ_zy –s represents the constitutive law of a fictitious material that links the FRP strip to the concrete substrate (interface). The shear stress should not be associated with the shear stress that occurs in concrete at a particular distance from the concrete surface. Researchers (Abdel Baky et al., 2012) attempted to describe the variation of the shear stress through the depth of the concrete substrate, and observed that the normal stress σ_yy in concrete influences the value of the maximum shear stress (τ_max). Although it is reasonable to assume that the stress field in concrete near the interface has an important role in the stress transfer, and therefore in the debonding mechanism, the cohesive material law herein introduced aims to describe the interfacial debonding at the macro-scale; hence its parameters should not refer to the actual stress state in concrete at the microscopic level.

Fracture along the interface does not occur on an ideal plane parallel to the FRP strip but follows a tortuous path, which is in part controlled by the distribution of the aggregates and in part by the mixed-mode nature of the fracture process at the microscopic level. In fact, the crack continuously kinks to follow the path that requires the least amount of energy, and is related to the fracture properties of the two materials (Hutchinson and Suo, 1992; Gunes, 2004; Gunes et al., 2009). At the macroscopic level, the microscopic mixed-mode fracture can be considered a Mode-II fracture at the FRP–concrete interface.

Several analytical/numerical procedures to estimate the cohesive interface behavior from the load response of direct-shear tests were developed. For example, Ali-Ahmad et al. (2006) established an experimental procedure to directly determine the Mode-II interfacial fracture law using DIC measurements. The cohesive material law for the interface, when implemented in a numerical analysis procedure, allowed for predicting the load response of concrete beams strengthened with externally bonded FRP sheets (Wu and Yin, 2003; Ali-Ahmad et al., 2007; Wu and Niu, 2007). Among others, Ferracuti et al. (2007), Mazzotti et al. (2008), and Carrara et al. (2011) used a procedure similar to Ali-Ahmad et al. (2006). In those studies, the authors used strain gage readings along the FRP surface to obtain the interfacial law. Pellegrino et al. (2008) and Pellegrino and Modena (2009) used a double-lap shear test and a small-beam test to investigate the effect of the axial stiffness of the composite on the cohesive material law and indicated the need of more research to study this aspect.

From the measured strain ε_yy along the bonded length, the interface shear stress was calculated as (Taljsten, 1996, 1997):

${\tau }_{\mathit{zy}}=E_f{t}_f\frac{d{\epsilon }_{\mathit{yy}}}{\mathit{dy}}$ [3.3]

[3.3]

The following assumptions were made: (1) the FRP sheet was homogenous and linear elastic; (2) the thickness and the width of the FRP sheet were constant along the bonded length; (3) the interface was subject only to shear loading; (4) the interface between the FRP and the concrete was assumed to be of infinitesimal thickness; and (5) the concrete substrate was rigid. The relative slip, s(y), between FRP and concrete at a given location on the FRP was obtained by integrating the axial strain in the FRP up to that point. Lu et al. (2005) commented on the possible ways to obtain the τ_zy –s curves, observing that the violent local variations of strain measured by strain gages entailed substantial differences in the fracture parameters. The procedure followed by Subramaniam et al. (2007, 2011) used the strain contours obtained from DIC, which allowed to identify the fluctuations of the strain profile due to the local variations of the FRP and the substrate (Ali-Ahmad et al., 2006). The cohesive material law curves corresponding to points D, E, F, and G of the load response of Fig. 3.2 are shown in Fig. 3.7. An important aspect of this procedure should be pointed out. The cohesive material law is a local constitutive law and should be obtained from strain measurements at a specific point along the bonded length for the entire load response and eventually compared with the constitute laws obtained from other points along the bonded area. Conversely, the procedure adopted in Ali-Ahmad et al. (2006) and in Subramaniam et al. (2007) used the strain values along the bonded length. Inherently, points along the bonded length have different interfacial properties, as suggested by the load response depicted in Fig. 3.2.

Several expressions of the cohesive material law are available in the literature. For example, Ferracuti et al. (2007) proposed the following relationship:

${\tau }_{\mathit{zy}}\left(s\right)=\overline{\tau }\frac{s}{\overline{s}}\frac{n}{\left(n+1\right)+{\left(\frac{s}{\overline{s}}\right)}^n}$ [3.4]

[3.4]

where $\overline{\tau }$ is the maximum shear stress and $\overline{s}$ is the corresponding slip. Other researchers indicated these parameters as τ_max and s₀, respectively. The parameter n (>2) mainly governs the softening branch of the softening curve.

3.3.2 Interfacial fracture energy

The interfacial fracture energy G_F is the energy required to create and fully break the elementary unit area of the cohesive crack. G_F corresponds to the area under the entire τ_zy–s curve (Bazant and Planas, 1997):

$G_F={\displaystyle {\int }_0^{s_f}{\tau }_{\mathit{zy}}\left(s\right)ds}$ [3.5]

[3.5]

where s_f is the slip corresponding to complete separation of the interface. The mean values of G_F for all tests published in Subramaniam et al. (2007) are shown in Fig. 3.8 and reported in Table 3.1. The values plotted in Fig. 3.8 were obtained for each test by processing the same ten images corresponding to ten points of the load response used to calculate the values of Figs 3.4 and 3.5. The experimental data in Fig. 3.8 are compared with some of the available formulas in the literature for G_F. Some of the formulas used as comparison in Fig. 3.7 include a width effect coefficient that depends on b_f/b.

The relationship between the interfacial fracture energy and the fracture energy of concrete (Mode-I) is still an open discussion among researchers (Achintha and Burgoyne, 2008, 2011; Carrara et al., 2011). Although the fracture process in ICD occurs in concrete, it propagates in a mortar-rich thin layer (Carloni and Subramaniam, 2010) in which the mechanical and fracture properties are not easily defined. Undoubtedly, the two fracture energies are related, although a convincing relationship has not yet been found. Rabinovitch (2004) successfully used the Mode-I fracture energy of concrete to study the EPD using the fracture mechanics concept of energy release rate. In the context of EPD, the energy required to create and fully break the elementary unit area of cohesive crack should be closely related to the fracture energy of concrete as the debonding typically occurs in the concrete cover and peeling stresses are not negligible.

Taljsten (1996) obtained a relationship between the interfacial fracture energy and the load-carrying capacity in direct-shear tests by considering the energy release during the advancement of the interfacial crack a by an amount da (Fig. 3.9). The energy release rate G per unit width b_f of the composite is obtained as:

$G=\frac{1}{b_f}\left[\frac{d}{\mathit{da}}\left(F-U_e\right)\right]$ [3.6]

[3.6]

where F is the work done by the external load P and U_e is the elastic energy. When debonding propagates, G = G_f.

If δ is the displacement of the point of application of the applied force P (Fig. 3.9) and C is the compliance of the system, then:

$U_e=\frac{1}{2}{P}^{2}C$ [3.7]

[3.7]

and when the interfacial crack propagates:

$G_F=\frac{1}{b_f}\left[P\frac{d\delta }{\mathit{da}}-\frac{d{U}_e}{\mathit{da}}\right]=\frac{1}{b_f}\frac{P^2}{2}\frac{\partial C}{\partial a}$ [3.8]

[3.8]

Therefore:

$P=\sqrt{\frac{2G_F{b}_f}{\partial C/\partial a}}$ [3.9]

[3.9]

If the substrate is considered rigid and the adhesive layer is idealized as a zero-thickness layer:

$\frac{\partial C}{\partial a}=\frac{1}{E_f{b}_f{t}_f}$ [3.10]

[3.10]

E_f and t_f are the elastic modulus and the thickness of the composite, respectively. From Equations [3.9] and [3.10], the interface fracture energy G_F is related to the load-carrying capacity (Hearing, 2000; Yuan et al., 2001; Wu et al., 2002; Liu and Wu, 2012; Wu et al., 2012):

$P_u=b_f\sqrt{2G_F{E}_f{t}_f}$ [3.11]

[3.11]

Equation [3.11] can be obtained through an energy balance approach (Focacci et al., 2000; Hearing, 2000; Liu and Wu, 2012) and is based on the assumption that a pure Mode-II interfacial crack propagation occurs across the entire width of the composite. The theoretical load-carrying capacity under pure Mode-II was indicated as P_u in Equation [3.11] to distinguish it from the experimental value P_crit. Wu et al. (2002) used an equilibrium approach to show how the load-carrying capacity depends only on the fracture energy and not on the shape of the τ_zy –s curve. An analytical approach can be found in Wu et al. (2012) in which a cohesive material law τ_zy (s) was assumed. The authors were able to predict the snapback phenomenon observed by other researchers (Ali-Ahmad et al., 2007). The load-carrying capacity calculated from Equation [3.11] should not be expected to match the experimental results (P_u ≠ P_crit). In fact, the width effect shown in Fig. 3.6 indicated that only in the central region of the strip the axial strain is constant (and the shear strain is zero), which entailed that the Mode-II loading condition should be assumed only in the central region of the FRP sheet.

It is interesting to notice that different experimental set-ups are available in literature (Yao et al., 2005) for direct-shear tests that might lead to significantly different results and complicate the analysis of the data. It was shown that the cohesive material model developed from direct-shear tests is directly applicable to beam tests (Chen and Teng, 2003). However, Gunes et al. (2009) observed that the Mode-II fracture energy G_F under flexural loading should be higher than that measured from direct-shear tests, due to the curvature effect.

3.3.3 Discussion of interfacial fracture energy as a true fracture parameter

Contradictory results (Chen and Teng, 2001; Subramaniam et al., 2007; Mazzotti et al., 2008; Carloni and Subramaniam, 2012b) complicate the interpretation of the interfacial fracture energy G_F as a true fracture parameter. Han (2009) reported that G_F increases with decreasing ratio b_f/b. Similarly, Czaderski et al. (2010) reported that G_F increases with decreasing width of the FRP. The interfacial cohesive law was obtained by measuring the strain along the FRP strip close to the edge. The authors also questioned whether G_F is a material property by making a parallelism with the Mode-I and Mode-II fracture energies of concrete (Carpinteri et al., 1993; Gunes, 2004). Chen and Teng (2001) reviewed some of the fracture mechanics approaches, which provided a value of G_F that depended on the width of the FRP and concrete. Conversely, Dai et al. (2006) affirmed that G_F is a material property and has a certain value for a particular combination of FRP and concrete types. Mazzotti et al. (2008) obtained the fracture energy from the load-carrying capacity of the interface of near-end supported single-shear tests. They observed that the interfacial fracture energy did not scale with the width of the FRP sheet due to the small size of the aggregate. Ching and Buyukozturk (2006) conducted direct-shear tests to study the influence of the effect of moisture on G_F. It was concluded that a different debonding mechanism occurred if the specimens were conditioned at relative humidity (RH) 100%, with a progressive decrease of the fracture toughness with increasing exposure. Subramaniam et al. (2007, 2011) indicated that the interfacial fracture parameters do not scale with the width if determined from measurements in the central region of the FRP sheet.

The discussion on the nature of the interfacial fracture energy as a true fracture parameter in part arises from the misuse of Equation [3.11]. From Equation [3.11], researchers used the experimental load-carrying capacity P_crit to determine the fracture energy by assuming that P_u = P_crit:

$G_F=\frac{P_{\mathrm{crit}}^2}{2b_f^2{E}_f{t}_f}$ [3.12]

[3.12]

This approach led to an erroneous evaluation of G_F, because the experimental value of the load-carrying capacity includes the width effect and in particular the mixed-mode behavior of the edges (Subramaniam et al., 2007). The fracture energy cannot be directly related to the experimental load-carrying capacity of the interface. The values of G_F determined via Equation [3.12] scale with the width of the FRP sheet. Hence, the experimental values of the fracture energy determined through Equation [3.12] should not be considered as true values. The experimental values in Fig. 3.8 indicated that the fracture energy is nominally invariant with the width of the FRP sheet. Therefore, G_F is a true fracture parameter, provided that it is obtained from strain measurements in the central region of the FRP sheet where a Mode-II fracture occurs.

3.3.4 Mode-I interfacial loading and alternative fracture approaches

In addition to the discussion regarding the nature of the fracture energy, concerns remain on the applicability of the direct-shear test results to describe ICD, mainly because of the presence of a Mode-I component (peeling stresses). The Mode-I should not be confused with the one observed before at the microscopic level, but in the spirit of the macroscopic approach of the fictitious interface. The Mode-I opening is described by the relationship between the normal stress (peeling) σ_zz and the opening of the crack w (Martinelli et al., 2011; Carrara and Ferretti, 2013). The Mode-I interfacial fracture energy, corresponding to the area of the σ_zz –w curve, is considerably lower than the Mode-II fracture energy (Taljsten, 1996; Gunes, 2004), thus even a small component of the load perpendicular to the FRP sheet could potentially reduce the load-carrying capacity of the interface. A Mode-I component is always present in the direct-shear test measurements, due to the relationship between shear and moment. A limited number of experimental works reported the study of Mode-I and mixed-mode debonding (Wan et al., 2004; Davalos et al., 2006; Alam et al., 2012). Some authors (Yao et al., 2005) recognized that the effect of a small loading angle (offset) was insignificant for relatively long bonded lengths. The presence of a Mode-I condition in beams can be explained by considering the opening of a flexural/shear crack as illustrated in Fig. 3.10 (Garden and Hollaway, 1998). As the crack opens, the two faces of the crack will undergo a relative vertical displacement that will cause a mixed-mode condition for the FRP–concrete interface. Rabinovitch (2008, 2012) used a fracture mechanics approach that considered the Mode-I and Mode-II cohesive material laws and their coupling. A set of nonlinear differential equations was derived by considering a multi-layer description of the strengthened beam. A different length of the STZ for Mode-I and Mode-II can be observed in these studies. Mazzucco et al. (2012) used a similar approach to capture the coupling of the shear and peeling stresses, but introduced a contact-damage model for the adhesion between layers. Gunes et al. (2009) reported that if the strengthened beam was sufficiently strong in shear, the flexural/shear crack mouth displacement would be limited and consequently the mixed-mode nature of debonding fracture would quickly merge into a Mode-II condition. It is interesting to notice that the results published by Alam et al. (2012) showed that the effective bond length increases if the Mode-I component is significant.

Alternative approaches within the framework of fracture mechanics are available in the literature. Achintha and Burgoyne (2008, 2011), for example, studied the debonding phenomenon as a Mode-I problem, by considering that the debonding often occurs in the concrete just above the interface. The Mode-I fracture energy of concrete was used in their approach. The authors observed that none of the existing studies available in the literature provided a reliable estimate of the interfacial fracture energy G_F. Gunes et al. (2009) proposed a global energy balance model to predict FRP debonding failure. The amount of energy dissipated in the system during debonding was determined by calculating the change in the potential energy of the system. The component of the energy dissipation due to the debonding process was calculated by means of the interfacial fracture energy. An expression of G_F was provided that included the geometric factor k_b to take into account the influence of the width of the FRP sheet.

3.6.1 Unresolved issues

Durability studies of the FRP strengthening technique are still limited, and additional data are necessary. Among the others, the effect of environmental conditions on the interfacial fracture properties was studied in Green et al. (2000), Ching and Buyukozturk (2006), and Subramaniam et al. (2008). It was recognized that freeze–thaw cycles determined a reduction of the load-carrying capacity. Conversely, a recent study by Dash et al. (2013) showed that the combined effect of moisture, temperature, and sustained loading could be beneficial for the ultimate load-carrying capacity of the interface.

The fatigue behavior of the FRP interface has still not been fully investigated (Kim and Heffernan, 2008; Carloni et al., 2012; Carloni and Subramaniam, 2013). The limited studies available in the literature are contradictory; however, it appears that fatigue loading even at low ranges could be detrimental for the stress transfer between FRP and concrete (Aidoo et al., 2004). The influence of the frequency (Diab et al., 2009) and the explicit dependence of the fatigue life on the load range and its mean value are not fully understood. Carloni and Subramaniam (2013) observed that fatigue-induced debonding could occur at the epoxy–fiber interface rather than in a thin layer of concrete. The shift of the debonding interface entails reduction of the effective bond length.

The relationship between the results of direct-shear tests and the actual performance of FRP strips bonded to RC beams is still an open issue. The effect of the curvature of the beam and the relative vertical displacement at flexural/shear cracks on the interface behavior is not easily captured by direct-shear tests. Sebastian (2001) observed that a strain distribution is present in the FRP strip prior to initiation of debonding, which is not taken into account in direct-shear tests. He also observed that measuring the strain on the FRP surface could be misleading in beams because of the presence of curvature. Rosenboom and Rizkalla (2008) pointed out that the strain limit provided in codes might not be sufficient to prevent debonding and noticed that the width effect in beams and direct-shear tests could be different. The relationship between the debonding mechanism in direct-shear tests and beams is also complicated by the fact that several direct-shear test set-ups are available and a standardized test is not available.

3.6.2 Fiber-reinforced cementitious matrix (FRCM) composites

Newly-developed composites that represent a sustainable alternative to FRPs are the so-called FRCM composites. In FRCM composites, fibers are typically bundled, and modified cement-based mortar is used instead of epoxy as matrix. The limited available literature (D’Ambrisi and Focacci, 2009; Ombres, 2012) suggests that FRCM composites can be used effectively for strengthening of RC structures. However, in FRCM composites debonding is typically observed at the matrix–fiber interface rather than in the substrate or at the matrix–concrete interface, which is typically observed in FRP composites. A complete understanding of the interfacial stress-transfer mechanism in FRCM composites is not available yet, although researchers have applied the concept of cohesive crack to describe the matrix–fiber interfacial behavior (D’Ambrisi et al., 2012; D’Antino et al., 2013). The studies available in the literature indicate that the effective bond length of FRCMs is much longer than that typically observed for the FRP–concrete interface. Moreover, friction between fibers, and between fibers and matrix, during the debonding process complicate the phenomenon. If these observations are confirmed, the debonding would not be governed by the properties of the concrete but rather by the combination of fibers and mortar used in the application.