Effect of the inherent eccentricity in single-lap direct-shear tests of PBO FRCM-concrete joints

Composite Structures 142 (2016) 117–129

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Effect of the inherent eccentricity in single-lap direct-shear tests of PBO FRCM-concrete joints Tommaso D’Antino a, Lesley H. Sneed b,⇑, Christian Carloni c, Carlo Pellegrino d a

Politecnico di Milano, Piazza Leonardo da Vinci, 20133 Milan, Italy Missouri S&T, 1401 North Pine Street, Rolla, MO 65409, USA c University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy d University of Padova, via Marzolo 9, 35131 Padova, Italy b

a r t i c l e

i n f o

Article history: Available online 22 January 2016 Keywords: Bond Cementitious matrix Digital image correlation Direct-shear test FRCM composite

a b s t r a c t Investigation of the bond between fiber reinforced composites and the substrates onto which they are applied is of critical importance to understand their failure mechanisms. The bond behavior can be studied using different experimental test set-ups; the most commonly used are the single-lap and double-lap direct-shear tests. Although single-lap shear tests are simpler to carry out than double-lap shear tests, the presence of an eccentricity between the pulling and restraining forces leads to a mixed mode fracture process at the interface, which may influence the results. This study investigates the eccentricity effect on the bond behavior of fiber reinforced cementitious matrix (FRCM) composite–concrete joints. FRCM composite strips with the same bonded length were applied to concrete blocks of different lengths and tested using the single-lap shear test. The use of digital image correlation (DIC) allowed for studying the strain field on the surface of the bonded composite. Results were compared with those from double-lap shear tests of the same composite. The results obtained confirm that the eccentricity effect is negligible for bonded lengths longer than the effective bond length. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Direct-shear tests are commonly used to study the debonding at the composite–concrete interface because load is applied parallel to the interface, and stresses out of plane are minimized [1]. Direct-shear tests are convenient and enable various instrumentation layouts and innovative measurement techniques including spatially continuous measurement of surface displacements, which can be used to determine surface strains in the composite and concrete from gradients of the displacement fields [2]. Single-lap and double-lap (direct) shear tests have been used extensively to study the fiber reinforced polymer (FRP) – concrete interface (e.g., [2– 10]). Recently, single-lap and double-lap shear tests have been used to study the fiber reinforced cementitious matrix (FRCM) – concrete interface [11–18]. Single-lap and double-lap shear tests each have their advantages and disadvantages in studying the debonding of a composite–concrete interface [19,20]. An advantage of the single-lap ⇑ Corresponding author. Tel.: +1 573 341 4553. E-mail addresses: [email protected] (T. D’Antino), [email protected] (L.H. Sneed), [email protected] (C. Carloni), [email protected] (C. Pellegrino). http://dx.doi.org/10.1016/j.compstruct.2016.01.076 0263-8223/Ó 2016 Elsevier Ltd. All rights reserved.

shear test is its simplicity; because force is applied directly to the composite, the force in the composite can be measured directly rather than determined indirectly from a local strain measurement or from measured displacements. Despite its simplicity, devising a method to restrain the concrete substrate may provide some challenges. The test fixture should be designed so that the load is applied directly and uniformly to the composite while minimizing eccentricity of the applied load with respect to the support restraint, which cannot be fully eliminated. Researchers have reported that the bonded length of composite influences the failure mode of the FRP-concrete interface in single-lap shear tests [10]. Carrara et al. [10] found that as the bonded length decreases, fracture tends to be mixed mode instead of pure Mode-II (shear). In this case the measured Mode-II fracture energy, which is the area enclosed by the interfacial cohesive law [14], decreases or increases due to the presence of out-of-plane displacements (Mode-I peeling or compression) of the FRP plate. Double-lap shear tests, whether pushed or pulled apart, utilize a symmetrical system to apply load simultaneously to two bonded composite strips. Because of the specimen’s symmetry, load can be applied to the concrete substrate to which the composites are bonded, instead of to the composite as in the case of single-lap shear tests. Double-lap shear tests require very accurate specimen fabrication

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and testing to achieve concentric loading between the concrete prism(s) and the two composite strips bonded to the concrete surfaces. However, because debonding generally does not occur equally and simultaneously in both composite strips, load redistribution occurs during the test [18]. Limitations of this system include its requirement for stable equilibrium, i.e. small displacements in plane do not cause large movements out of plane. Complete debonding of one of the two composite strips leads to unstable equilibrium. Furthermore, the composite strip that debonds first would be expected to have the lower bond capacity of the two strips. In general, this would suggest that results from double-lap shear tests tend towards a lower bound estimate of the composite bond capacity [18]. Several authors have attempted to study the debonding phenomenon in FRP-concrete joints considering both Mode-I and Mode-II loading conditions [1,21,22]. The Mode-I loading is described by the relationship between the normal stress (peeling) rzz and crack opening w [1,22]. The Mode-I interfacial fracture energy, corresponding to the area of the rzz–w curve, is considerably lower than the Mode-II fracture energy [3,23], 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 single-lap direct-shear test measurements due to the relationship between shear and moment. A limited number of experimental works reported the study of the Mode-I and mixed mode debonding [24–27]. Some authors [28] recognized that the effect of a small loading angle (offset) was insignificant for relatively long bonded lengths. However, other authors [29] indicated that during crack growth the Mode-I component is dominant for any angle of loading. The presence of a Mode-I condition in strengthened beams can be explained by considering the opening of a flexural/shear crack [30,31]. As the crack opens the two faces of the crack undergo a relative vertical displacement that causes a mixed-mode condition for the FRP-concrete interface. Rabinovitch [32,33] 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 stress transfer zone (STZ), which defines the zone in which the stress is transferred from the concrete substrate to the composite, for Mode-I and Mode-II can be observed in these studies. Mazzucco et al. [34] 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. Günes et al. [35] 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 note that the results published by Alam et al. [24] showed that the effective bond length increases if the Mode-I component is significant. Dai et al. [36] observed experimentally an opposite trend, although they used a different set-up. In FRCM-concrete joints a distinction should be made between the possible interfaces at which debonding can occur: (1) At the FRCM-concrete interface Mode-I and Mode-II are coupled, and the fracture parameters should depend on the characteristics of the two materials and whether the crack propagation occurs in concrete or at the interface (delamination). (2) At the fiber-internal matrix layer interface Mode-I and Mode-II are coupled, and the fracture parameters should depend on the characteristics of the chemical and mechanical bond between the fibers and matrix.

(3) At the fiber-external matrix layer interface Mode-I and Mode-II are coupled; however the Mode-I component is negative (compression) since the external layer acts as a restraint for the fibers. The beneficial effect of a negative normal stress component is taken into account, for example, in the model presented by Carrara and Ferretti [1]. The interfaces that appear to be critical are (1) and (2). The authors reported that for shorter bonded lengths [15], delamination (interface 1) of the entire composite strip occurred. For interface 2 the Mode-I loading component could influence the interfacial crack growth if the external layer is sufficiently thin to deform and therefore to allow significant out of plane displacements (w) of the fibers. It is interesting to note that for those specimens cast without the external layer of matrix the Mode-I component is not restrained, and therefore the coupled modes should imply a lower value of the applied force. This, in turn, entails that the role of the matrix layers studied by authors [17], discussed in Section 2, is a lower bound case of what in reality occurs in direct-shear tests and beam applications. Some authors proposed uncoupled cohesive laws for FRPconcrete joints [21] and determined the local failure by introducing a mixed mode fracture criterion, typically in the form of Eq. (1):



GI GIF

k



þ

GII GIIF

k

¼1

ð1Þ

The parameter k is usually assumed equal to 1, although the available literature does not seem to provide sufficient discussion in this regard. GI and GII are the Mode-I and Mode-II components of the energy release rate, respectively. GIF and GIIF are the fracture energy related to pure Mode-I and Mode-II, respectively. Other authors have proposed coupled cohesive laws [1] associated with a fracture criterion. The results, although promising, do not seem to fully capture the phenomenon. For example, the different effective bond lengths for Mode-I and Mode-II should entail that in the portion of the STZ where the Mode-I is not active the shear stresses are determined from a pure Mode-II cohesive law. In addition, most of the fracture criteria proposed assume that the softening stages of the cohesive laws end together. This paper examines the results of an experimental investigation conducted to study the bond behavior and stress-transfer mechanism of FRCM composites externally bonded to a concrete substrate using single-lap direct-shear tests of different dimensions. The objective of this work is to study the effect of the eccentricity between the pulling and restraining forces on the composite bond behavior. The FRCM composite investigated in this study is comprised of a polyparaphenylene benzobisoxazole (PBO) fiber net and a polymer modified cement-based matrix. Results of single-lap shear tests with FRCM composite strips bonded to concrete prisms with different prism lengths, namely L = 375 mm and L = 510 mm, are presented and discussed. Strains measured on the composite surface using digital image correlation (DIC) are examined to study the bending induced in the composite. Findings are compared with those from double-lap shear tests of the same composite previously reported by the authors [18] to examine the influence of the different direct-shear test types on the bond behavior of the FRCM composites applied to concrete supports. 2. Background Failure of PBO FRCM-concrete joints with one layer of fibers is reported to be debonding of the fibers from the embedding matrix [12,15]. PBO FRCM-concrete joints subjected to direct-shear tests are characterized by an initial linear applied load P-global slip g

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behavior, where the global slip g is defined as the relative displacement between the fibers and the concrete substrate at the loaded end. When microcracks start to occur at the matrix–fiber interface, the applied load-global slip response becomes non-linear until the onset of matrix–fiber debonding, which corresponds to the debonding load Pdeb. As in the case of FRP composites, the debonding load of FRCM-concrete joints is also referred to as the loadcarrying capacity [15]. After the debonding load Pdeb is attained, the STZ, which in the case of FRCM composites defines the region where only the bond stress-transfer mechanism occurs [37], is fully established and simply translates toward the composite free end with increasing global slip. The applied load P increases due to the presence of friction (interlocking) between the matrix and the portion of fiber net that has debonded, between fiber filaments, and between longitudinal and transversal fiber bundles. When the STZ reaches the composite free end, the maximum (peak) applied load P⁄ is attained. Further increase in the global slip corresponds to a decrease in the applied load until the constant applied load Pf, which is associated with friction only, is attained [14]. In general, when the STZ reaches the composite free end, the applied load can increase further due to the presence of friction at the matrix– fiber interface. However, assuming that the shear stress due to friction is small relative to the shear stress associated with a Mode-II interfacial loading condition, the applied load increase after the STZ reaches the free end can be neglected. The authors are currently studying this phenomenon, which will be described in a future publication. For reference, Fig. 1 shows the applied loadglobal slip response of specimen DS_330_60_B_D_1 (discussed in the next section) with points Pdeb, P⁄, and Pf identified on the response. In a previous paper by the authors [17], some single-lap shear specimens with the same FRCM composite were cast without applying the external matrix layer in order to investigate the role of the internal and external matrix layers in the stress-transfer mechanism. Failure of specimens without the external matrix layer was characterized by debonding of the fiber at the matrix–fiber interface, and the load response observed resembled the load response observed in specimens with the external matrix layer (Fig. 1). Comparison between the results obtained from specimens with and without the external matrix layer allowed the authors to identify the contribution of each matrix layer to the stress-transfer mechanism. In particular, it was observed that the load-carrying capacity of specimens without the external matrix layer was on average very similar to the load-carrying capacity of specimens with both the internal and external layers of matrix. Assuming a pure Mode-II loading condition, the internal and external matrix layer-fiber bond behaviors can be characterized by different shear

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stress-slip relationships [14,17]. The area enclosed by each shear stress-slip relationship is the Mode-II fracture energy GIIF. Assuming that the interfacial behavior between the fibers and the internal matrix layer is not influenced by the presence of the external matrix layer [17], analysis previously conducted by the authors showed that the internal matrix layer fracture energy GiIIF is 6.4 times higher than the external matrix layer fracture energy GeIIF . It is probably more reasonable to assume that the internal and external matrix layer-fiber bond behaviors have the same shear stress-slip relationship. In this case, different slips occur between the two matrix layers and the fibers, and once debonding occurs at one interface the other relationship cannot be fully utilized. 3. Materials and methods 3.1. Materials The FRCM composite material consisted of a PBO fiber net and a cementitious matrix. The PBO fiber net was made of bidirectional rovings spaced at 10 and 20 mm on center in the two orthogonal directions. The total weight of fibers in the net was 88.0 g/m2, with 70.2 g/m2 and 17.8 g/m2 in the longitudinal and transversal directions, respectively. The nominal width b⁄ and average thickness t⁄ of one fiber bundle were 5 mm and 0.092 mm, respectively. It should be noted that the definition of average thickness t⁄ in this paper is different from the equivalent thickness of the fabric given by the manufacturer [38], and therefore the values are different. The equivalent thickness provided by the manufacturer is obtained by assuming the fibers are spread evenly over the entire width of the composite rather than bundled. In this paper t⁄ represents the thickness of a single fiber bundle, which is assumed to have a rectangular cross section of width b⁄. All transversal bundles of the fiber net were on one side of the longitudinal bundles. Tensile strength, ultimate strain, and elastic modulus of the fibers measured by the authors were 3015 MPa, 0.0145, and 206 GPa, respectively. Additional information on the fiber tensile tests is reported in [13] and [15]. The matrix employed in this study, which was designed to attain high bond with PBO fibers, was comprised of high-fineness cement binder, adhesion promoter, inorganic nanoparticles, micro aggregates, and new-generation higheffectiveness polycarboxylic water-reducing admixtures [39]. The average compressive strength [40] and splitting tensile strength [41] of the matrix was measured with at least two 50  100 mm cylinders cast from each batch of mortar used to cast the composites and were 28.4 MPa and 3.5 MPa, respectively. Two batches of normalweight concrete with portland cement (Type 1) without admixtures, one for each block length, were used to construct the concrete blocks. Twelve (6 + 6) 100 mm  200 mm concrete cylinders were cast from the two batches of concrete. The average compressive strength [40] and splitting tensile strength [41] were 42.5 MPa (CoV = 0.013) and 3.4 MPa (CoV = 0.113) for the blocks with L = 375 mm, and 33.5 MPa (CoV = 0.085) and 3.0 MPa (CoV = 0.042) for the blocks with L = 510 mm. 3.2. Methods

Fig. 1. Applied load P – global slip g curve of specimen DS_330_60_B_D_1.

Twenty specimens presented in this paper were tested using the single-lap (direct) shear test set-up. FRCM composite strips were externally bonded to concrete blocks (prisms). The push–pull configuration was adopted where the concrete prism was pulled while the fibers were restrained (Fig. 2). Two different sizes of concrete prisms were used, both of which had the same cross section (b = 125 mm width x h = 125 mm depth), but different lengths (L = 375 mm or L = 510 mm). The faces of the concrete blocks were sandblasted prior to applying the first (internal) layer of matrix.

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Fig. 2. Single-lap shear test set-up (a) front view, (b) side view, (c) top view.

Only the formed faces of the prisms were used to bond the composite strips; the face of each prism that was troweled smooth after casting was disregarded. The matrix was applied only in the bonded area to embed the fibers and bond the composite to the concrete substrate (Fig. 2). The matrix was applied from the edge of the external longitudinal bundle on one side of the fiber strip to the edge of the external longitudinal bundle on the other side of the fiber strip. Fibers were bare outside the bonded area. A 4 mm thick layer of matrix (internal layer) was applied to the concrete using molds to control the composite width and thickness [15]. A single layer of PBO fiber net was applied onto the internal matrix layer, and the fibers were pressed delicately onto the matrix to maintain their alignment and assure proper impregnation by the matrix. The fiber strip was positioned such that it extended slightly beyond the end of the matrix at the free end of the composite strip

as shown in Fig. 3. A second (external) 4 mm thick layer of matrix was applied over the PBO fiber net. The thickness of the composite strip t = 8 mm was in accordance with the manufacturer’s recommendations [38]. The bonded width b1 and bonded length ‘ of the composite were 60 mm and 330 mm, respectively. The composite was bonded starting at a distance d = 38 mm from the prism edge at the loaded end (Fig. 2). Table 1 lists the test specimens presented. Specimens were named following the notation DS_X_Y_(S and/or B and/or D)_Z(T), where DS indicates that the specimen was tested in single-lap direct shear, X = bonded length (‘) in mm, Y = bonded width (b1) in mm, S indicates that strain gages were mounted on the specimen, D indicates that the specimen was tested until a constant applied load resulted at the end of the test, B indicates that the 330 mm long composite strip was applied to a concrete block with L = 510 mm, and Z = specimen number. Superscript T after the specimen number indicates that the fiber net was oriented with the transversal bundles directly against the matrix internal layer. Aluminum plates were attached to the end of the fiber strip with a thermosetting epoxy resin to grip the bare fibers during

Table 1 Single-lap shear test specimens.

Fig. 3. Photo of single-lap direct-shear test (a) L = 375 mm, (b) L = 510 mm. Note the fibers extending beyond the bonded area at the free end.

Name

L (mm)

P⁄ (kN)

r⁄ (MPa)

DS_330_60_1T DS_330_60_2T DS_330_60_3T DS_330_60_4T DS_330_60_5T DS_330_60_6 DS_330_60_7 DS_330_60_S_1 DS_330_60_S_2 DS_330_60_D_1 DS_330_60_D_2 DS_330_60_D_3 DS_330_60_D_4 DS_330_60_D_5 DS_330_60_D_1 DS_330_60_B_1 DS_330_60_B_2 DS_330_60_B_D_1 DS_330_60_B_D_2 DS_330_60_B_D_3

375 375 375 375 375 375 375 375 375 375 375 375 375 375 375 510 510 510 510 510

7.05 6.56 6.06 6.50 6.28 7.01 6.73 6.30 7.31 8.29 7.12 6.56 5.24 6.69 8.29 6.27 6.30 6.39 6.90 6.72

2190 2040 1880 2020 1950 2180 2090 1960 2270 2570 2210 2040 1630 2080 2570 1950 1960 1990 2140 2090

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testing (Fig. 2). The aluminum plates were also bolted together with four through-bolts at the plate corners to assure a uniform pressure on the gripped fibers and to prevent slippage within the plates. The concrete prism was restrained against movement by a steel frame bolted to the testing machine base. The steel frame was made with flat bars with width ws = 48 mm and thickness ts = 9 mm. A steel plate was inserted between the steel frame and the top of the prism to distribute the pressure provided by the frame restraint to the concrete prism. Tests were conducted under displacement control using a close-loop servo-hydraulic universal testing machine. The global slip g was increased at a constant rate of 0.00084 mm/s until failure. Global slip was measured using two linear variable displacement transducers (LVDTs) that were attached to the concrete surface near the edge of the bonded area. The LVDTs reacted off of a thin aluminum X-shaped bent plate that was attached to the PBO transversal fiber bundle surface adjacent to the beginning of the bonded area as shown in Fig. 2. The average of the two LVDT measurements was used to control the displacement rate. The strain on the surface of the FRCM composite was measured on one specimen using a full-field optical technique called digital image correlation (DIC). DIC is a non-contact measuring technique that allows for obtaining the surface displacement field. DIC mathematically correlates images of the specimens, taken during testing, that correspond to different applied load and global slip values. DIC recognizes and correlates points on the surface and computes their displacement with respect to the initial undeformed image. The surface strains are then determined as the gradients of the displacements after interpolating the displacement contours with a quintic B-spline collocation method [42]. In order to enable the DIC measurements, the composite surface of specimen DS_330_60_7 was covered uniformly with white nonreflective paint prior to testing. Black paint was then sprayed on the composite surface to create a speckle pattern, which is recognized and employed by the DIC software to obtain the displacement field. During testing the specimen was illuminated with normal white light to assure uniform light intensity on the composite surface. Images were taken at a frequency of 0.17 Hz and were processed considering the origin of the Cartesian axes located at the bottom left corner of the FRCM composite shown in Fig. 2.

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transversal pattern, and in some cases they extended in the composite longitudinal direction. The presence of shrinkage cracks introduced discontinuities of the matrix–fiber interface, thus affecting the stress-transfer mechanism. Shrinkage cracks opened with increasing slip and, in some specimens previously reported by the authors [37], penetrated the thickness of the matrix causing partial detachment of the composite strip at the composite–concrete interface. As mentioned in Section 2, the authors previously tested some single-lap shear specimens with the same FRCM composite but without the external matrix layer in order to study the role of the different matrix layers in the stress-transfer mechanism [17]. Testing of FRCM-concrete joints in which the external matrix layer was omitted also allowed for visual observation of the effect of the load-restraint eccentricity associated with the use of the single-lap direct-shear test set-up. After the onset of debonding, the fiber net lifted up with increasing global slip (Fig. 4), which clearly indicates the presence of a fracture mechanics Mode-I peeling component.

4. Experimental results 4.1. General behavior and failure mode Failure of the specimens presented in this paper was characterized by considerable slippage between the fibers and matrix. In general, no damage was observed at the matrix-concrete interface, and debonding occurred at the matrix–fiber interface. The load response of specimen DS_330_60_B_D_1 is illustrated in Fig. 1 and is representative of the response of all specimens. The longitudinal fiber bundles were observed to gradually pull out of the composite at the loaded end of the bonded area, and, after the peak load was reached, the longitudinal fibers beyond the free end of the bonded area (Fig. 3) advanced slowly into the matrix. The peak load P⁄ of each specimen is presented in Table 1. Table 1 also includes the peak stress r⁄ defined in Eq. (2), where n is the number of longitudinal fiber bundles:

r ¼

P  nb t

ð2Þ

Although all specimens were cast under the same external conditions following the same procedure, shrinkage cracks appeared on the matrix surface of some specimens before they were tested. Shrinkage cracks were characterized mainly by a

Fig. 4. (a) Lift up of fibers observed in specimens where the external layer of matrix is omitted, (b) side-view sketch showing lift up of fibers.

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4.2. Applied load vs. global slip response The applied load P – global slip g behavior of representative specimens with the same composite bonded length and different block lengths L is shown in Fig. 5. The load responses resemble the idealized load response described in Section 2 [14], and no significant differences are observed between specimens with different block lengths. The P–g curves shown in Fig. 5 are consistent up to values of the applied load of approximately 5 kN, whereas they become more scattered afterwards. This phenomenon is attributed to the stochastically distributed matrix–fiber bond properties that induce nonuniform microcracking (and subsequent debonding) of the matrix–fiber interface of the different bundles, which in turn is responsible for the differences observed between load responses. Further discussion about the influence of the bond properties of the different bundles on the applied load is provided in Section 5.1. 4.3. Surface strains Digital image correlation (DIC) was used to measure the field of displacement on the matrix surface of specimen DS_330_60_7. Displacements and strains were obtained for different square areas (subsets) for a 5 pixel step size, which provided points spaced at approximately 0.81 mm. Different subsets were used to study the influence of subset dimension on the results obtained. Strain profiles were analyzed for representative points of the load response,

which are reported in Fig. 6: point A corresponds to the end of the applied load – global slip elastic branch; point B corresponds to the onset of debonding (Pdeb in Fig. 1); point C denotes the peak load (P⁄ in Fig. 1). Points I and X were added to study the strain behavior during the establishment of the stress-transfer mechanism and after the peak load, respectively. Fig. 6 also plots the displacements ga and gb measured by LVDTa and LVDTb (Fig. 2), respectively, throughout the load response. The longitudinal strains eyy for the representative points of the load response are shown in Fig. 7. Values of eyy were obtained with subsets with edges equal to 21 pixels (Fig. 7a), 29 pixels (Fig. 7b), 40 pixels (Fig. 7c), and 60 pixels (Fig. 7d). For each value of y the strain is computed as the average over the range 19.5 mm < x < 23.5 mm, where x = 21.5 mm corresponds to the center of the third longitudinal fiber bundle from the fiber net left-hand side. The range of x employed, which was slightly less than the width of a single fiber bundle, was selected taking into account that the composite lefthand side was more loaded than the right-hand side for points of the load response between points A and B and after the peak load P⁄ was attained (Fig. 6). Additional discussion on the non-uniform load distribution among longitudinal fiber bundles is included in Section 5.1. The longitudinal strain eyy distribution on the surface of the external matrix layer, obtained with the 21  21 pixel subset, is also shown in Fig. 8 for point B of the load response, which corresponds to the onset of debonding (Fig. 6). 5. Analysis and discussion 5.1. Distribution of applied load among longitudinal fiber bundles

Fig. 5. Applied load P – global slip g responses of representative specimens with different concrete block lengths L.

Due to the stochastically distributed matrix–fiber bond properties, the applied load is not evenly distributed among the longitudinal fibers along the composite width [17]. Comparison of displacements ga and gb measured by LVDTa and LVDTb, respectively, which were attached to the concrete surface on the two sides of the composite, allows for examining the load distribution along the composite width to obtain an indication of which composite side is more loaded and to determine whether the nonuniform distribution compromised the reliability of the results. The difference between displacements ga and gb of each singlelap shear test in Table 1 was compared with the average value of the slip corresponding to the complete debonding of the fibers, sf ¼ 1:57 mm, which was computed through a fracture mechanics approach [17]. Only specimens for which jg a  g b j 6 sf for values of the applied load P lower than the peak load P⁄ were considered reliable. All single-lap direct-shear tests included in Table 1 were determined to be reliable using this criterion. For illustration, Fig. 6 shows the P–g, P–ga, and P–gb curves of specimen DS_330_60_7. The displacements measured by LVDTa and LVDTb differ slightly for applied load values up to the peak load P⁄, which indicates a relatively even distribution of the applied load among the longitudinal fiber bundles. However, further increasing of the global slip g after P⁄ was attained resulted in a greater increase of ga with respect to gb, which indicates that the composite left-hand side was more loaded than the right-hand side. 5.2. Effect of the load-restraint eccentricity on single-lap shear test results

Fig. 6. Applied load P versus LVDT measurements of specimen DS_330_60_7.

5.2.1. Single-lap direct-shear test set-up used in this study Single-lap direct-shear test set-ups always present an inherent eccentricity between the pulling and restraining forces. During testing this eccentricity entails for a fracture mechanics mixed mode condition [1] that may affect the results. In the single-lap direct-shear test set-up employed in this work, two steel frames

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Fig. 7. Strain measured along the bonded length of specimen DS_330_60_7 for points of the load response depicted in Fig. 6 using a subset edge of 21 pixels (a), 29 pixels (b), 40 pixels (c), and 60 pixels (d). Note: compression is depicted as positive.

Fig. 8. Strain measured on the matrix surface of specimen DS_330_60_7 for point B of the load response depicted in Fig. 6 using subset edge of 21 pixels. Note: compression is depicted as positive.

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with elements of the same cross-section and different lengths were bolted to the machine base to restrain concrete blocks with different lengths, namely L = 375 mm and L = 510 mm. When applying the force to the bare fibers, deformation of the concrete block and steel frame causes the rotation of the concrete block. The restraining effect provided by the steel frame on the concrete block can be represented by two springs with axes oriented in the y- and z-directions located at the block’s top mid-point as shown in Fig. 9 (the axes are defined in Fig. 2). The restraining effect provided by the machine base to which the steel frames were bolted is represented by roller supports in the y- and z-directions acting on the block’s right hand corner (Fig. 9). For simplicity it is assumed that the deformation of the concrete block is negligible, and its rigid rotation is governed by the deformation of the steel frame, which is assumed to behave as a cantilever with length L. In this paper, as in previous papers by the authors that describe the results of single-lap shear tests, the applied load P refers to the vertical force applied by the testing machine, whereas in the remainder of this paper F represents the force applied in the direction of the fibers. When load P is applied by the testing machine base, it is quasi-statically transferred from the concrete block to the FRCM composite, whose bare fibers are restrained by the testing machine. The steel frame reacts restraining the concrete block with y- and z-direction components and undergoes elongation Dy and displacement Dz, which in turn allow the concrete block to rotate. If the deformations are small and the matrix thickness is neglected (with respect to the concrete block thickness h), Eqs. (3) and (4) hold:

Dy ¼

Ry  L ky

ð3Þ

Dz ¼

Rz  L3 3  kz

ð4Þ

where ky = E2A, and kz = E2I1. Ry and Rz are the restraining components provided by the springs, E is the elastic modulus of the steel, A = tsws is the cross-sectional area, and I1 = tsw3s /12 is the principal moment of inertia about the axis parallel to x of each vertical element of the steel frame. Since the concrete block is assumed to rotate rigidly, the ratio between the elongation Dy and displacement Dz can be expressed by:

Dy h ¼ Dz 2L

ð5Þ

Substituting Eqs. (3) and (4) into Eq. (5), the ratio q between the z- and y-direction steel frame restraining components can be obtained:

q¼

Rz 6I1 ¼ Ry ALh

ð6Þ

Hence, enforcing the equilibrium conditions the steel frame restraining components are given by Eqs. (7) and (8):

Ry ¼

2Fh h þ 2qL

Rz ¼ q

2Fh h þ 2qL

ð7Þ

ð8Þ

Increasing the length of the concrete block L will result in an increase of Dy and Dz and, as a consequence, a larger rotation of the concrete block that entails for a higher Mode-I loading condition. The components of the applied force F parallel and orthogonal to the composite strip are indicated in Fig. 9 by PII and PI, respectively. The vertical (y-direction) and horizontal (z-direction) components of the applied force F are the applied load P, which was used to construct the applied load-global slip curves described in previous sections, and Fh, respectively. b and a are the angles between the y-direction and the direction of the bare fibers and

Fig. 9. Sketch of the forces applied on concrete block and fibers during the single-lap direct-shear tests: (a) test set-up employed, sketch of the concrete block rotation with (b) L = 375 mm and (c) L = 510 mm, (d) detail of the loaded end, (e) force diagram.

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the concrete block, respectively (Fig. 9). Note that in the sketch of Fig. 9e angles a and b are exaggerated with respect to the sketches of Figs. 9b–d. Assuming small displacements and deformations, angles a and b can be approximated by Eqs. (9) and (10), respectively:

a¼

Dz L

b ¼ Dz

ð9Þ Ld Ll

ð10Þ

It should be noted that in the case of FRP-concrete joints, as debonding occurs the stress transfer zone STZ translates toward the composite free end, and the distance between the point where the fiber strip is gripped and the point of the composite strip along the bonded area where F is fully developed, which coincides with l until the onset of debonding, increases. This phenomenon, which causes a decrease of the angle b, is not present in the case of FRCM-concrete joints where the presence of the external matrix layer prevents the debonded fibers from lifting up. The components of the applied force F parallel (PII) and orthogonal (PI) to the composite strip depend on the rotation of the concrete block and bare fibers and can be computed from the applied load P (Fig. 9):

PI ¼ P

sinða þ bÞ cos b

ð11Þ

PII ¼ P

cosða þ bÞ cos b

ð12Þ

From Eqs. (10) and (11) it may be noted that for a fixed concrete block length L the peeling component PI can be limited by increasing the length of the bare fibers l, which results in a decrease of the angle b while the angle a remains constant. As a reference, angles a and b were computed for an applied load P = 6.80 kN, which is the average of the peak load values of specimens reported in Table 1, for concrete block lengths equal to 375 mm and 510 mm. The steel elastic modulus E was assumed equal to 200 GPa whereas the length of the bare fibers l, which was held approximately constant during the experimental campaign, was equal to 270 mm. The elongation and displacement obtained were Dy = 0.026 mm and 0.0035 mm and Dz = 0.154 mm and 0.285 mm for L = 375 mm and L = 510 mm, respectively, which correspond to a = 0.0004 rad and 0.0006 rad and b = 0.0005 rad and 0.0010 rad for L = 375 mm and L = 510 mm, respectively. The peeling component PI was 0.1% and 0.2% of the applied load P for L = 375 mm and L = 510 mm, respectively, whereas the component parallel to the composite strip PII was approximately equal to P (difference in the order of 107%). These results confirm the assumption of small displacements and deformations and show that, provided that the stress-transfer mechanism is fully established, the applied load P can be assumed equal to the applied force F, i.e. the peeling component PI can be neglected. It should be noted that in previous publications by the authors the applied load P was always assumed equal to the applied force F. The z restraining component of the machine base is generated by friction between the concrete block and the machine base, and thus it is proportional to the y restraining component. Hence, when the ratio between the machine base z and y restraining components exceeds the coefficient of friction l, the system would no longer be in equilibrium. Enforcing the rigid rotation of the concrete block as per Eq. (5), and assuming l = 0.5 according to EN 1994-1-1 [43], the equilibrium condition can be expressed by Eq. (13):

l¼

w2s h 2

Lðh  w2s Þ

6 0:5

ð13Þ

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Eq. (13) clearly shows that the width of the steel frame ws, which can be regarded here as the steel frame stiffness, plays the main role in determining the rotation of the concrete block. Comparison of the experimental results obtained from FRCMconcrete joints with the same composite bonded length ‘ = 330 mm and different block lengths L = 375 mm and L = 510 mm allowed for evaluating the global effect of the inherent eccentricity of the single-lap shear test set-up employed on the peak load (or stress). Fig. 10 shows the peak stress r of the specimens included in Table 1 along with the average values (Avg) and corresponding coefficients of variation (CoV) for specimens with the same test type and block length. Although the use of the longer blocks entails for a higher Mode-I loading condition with respect to the case of shorter blocks, the average peak stress of the single-lap tests performed on blocks with different lengths is very similar (4% difference). Results of double-lap shear tests previously reported by the authors [18] with the same FRCM composite, the same composite bonded length and width, and block length L = 375 mm (the DDS_330_60 series in [18]) are also plotted in Fig. 10 along with the corresponding average and coefficient of variation values. The load response up to the peak load and the failure mode of the composite tested in double-lap shear was similar to that tested in single-lap shear [18]. Values of peak stress determined by the single-lap shear test with both block lengths are slightly higher than values determined by the double-lap shear tests with the same composite bonded length (16% and 12% difference for single-lap tests with L = 375 mm and L = 510 mm, respectively), which confirms that double-lap shear tests tend towards a lower bound estimate of the composite bond capacity [18], and suggests that the effect of the inherent eccentricity in the single-lap shear tests is not significant. As mentioned in Section 4.1, the presence of a Mode-I loading condition affects the response of FRCM-concrete joints in which the external layer of matrix is omitted. Although the contribution of the external layer to the load-carrying capacity is limited, the external matrix layer plays an important role in limiting the effect of the Mode-I loading condition. When the external layer of matrix is omitted, the effect of the peeling component PI on the embedded fibers is not contrasted by the restraining effect provided by the external matrix layer, as is clearly visible from the lift up of the debonded fibers (Fig. 4). Since the external matrix layer may reduce the effect of the peeling component PI, peak load values obtained with specimens without the external matrix layer should be substantially lower than peak load values obtained with specimens with the same characteristics but with the external matrix

Fig. 10. Peak stress of single-lap and double-lap specimens with different concrete block lengths L.

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layer. However, as discussed in Section 2, the load-carrying capacity and consequently the peak load of specimens with and without the external layer of matrix were very similar. Therefore, values of the internal layer fracture energy GiIIF obtained from specimens without the external matrix layer [17], which are affected by the presence of a non-contrasted Mode-I loading condition, are lower than corresponding values of the internal layer Mode-II fracture energy for specimens with the external matrix layer. Assuming a pure Mode-II loading condition, the load carrying capacity of specimens with and without the external matrix layer would be even more similar than that measured by the authors using single-lap shear tests [17], where the presence of an inherent eccentricity affected the results. In summary, in the case of FRCM-concrete joints the Mode-I component at the fiber–matrix interfaces can be probably neglected given the beneficial effect of the external layer of matrix. On the other hand the coupled effect of Mode-I and Mode-II should be studied at the matrix-concrete interface especially in the case of stiff composites, i.e. multiple layers of fibers. In fact, delamination or interlaminar delamination appears to occur more often when multiple layers of FRCM composite are applied to the beam tension face [44]. 5.2.2. Alternative single-lap direct-shear set-ups Different single-lap direct-shear test set-ups have been used to investigate the bond behavior of composite–concrete joints [28]. When using the push–pull configuration, the concrete block can be restrained using a steel frame constraining the loaded and free end faces of the block, as shown in this study (Fig. 2), or employing a stiff steel plate and two restraints in directions parallel and orthogonal to the applied load direction (Fig. 11). In the case of the latter, displacement and rotation of the concrete block are hindered by the restraint in the direction parallel to the applied load direction (named restraining plate in Fig. 11a) and by the combined effect of the steel plate and the restraint orthogonal to the applied load direction (named restraining frame in Fig. 11a), respectively. This test set-up was employed with a push–pull configuration to reduce the rotation of the concrete block [10], and when used in a pull–pull configuration it provided FRP-to-concrete bond capacity values 10–15% higher than values obtained with a pull–pull set-up where the specimen was restrained only by clamping the steel rebar embedded in the concrete block [45]. However, when the load P is applied to the

composite (Fig. 11), the concrete block tends to rotate due to the eccentricity between the applied force and the restraints, thus inducing a peeling force on the composite strip. Assuming restraints as depicted in Fig. 11b, the concrete block rotates about the top edge of the restraining plate due to axial elongation of the restraining frame Dr (for simplicity the restraining plate bending deformation is neglected):

Dr ¼

Rr  h kr

ð14Þ

where Rr is the reaction, kr = AE is the stiffness, and A and E are the area and the elastic modulus of the restraining frame. Assuming that the horizontal component of the reaction provided by the steel plate is generated by friction with the concrete block and that the concrete block rotates rigidly, enforcing the equilibrium conditions it holds that:

Rr ¼

Fðh  hr Þ

lhr þ r þ d

ð15Þ

where F is the force applied in the direction of the fibers, h is the concrete block height, hr is the length of the restraining plate, l is the steel–concrete friction coefficient, and r is the distance between the restraining frame and the point of the composite strip where F is fully developed (Fig. 11). It should be noted that the concrete block can rotate only if the horizontal steel plate component is equal to the steel–concrete static friction for a given vertical component provided by the steel frame. Thus, it seems reasonable to assume l = 0.5 as indicated in EN 1994-1-1 [43]. The force components orthogonal (peeling component PI) and parallel (PII) to the composite strip depend on the angle a between the initial and rotated position of the concrete block and b between the initial and rotated position of the bare fibers (note that in the sketches of Fig. 11c and d the forces and angles a and b depicted are exaggerated with respect to other sketches in the same figure):

a¼

Dr rþd

b ¼ Dr

d lðr þ dÞ

ð16Þ ð17Þ

PI ¼ F  sinða  bÞ

ð18Þ

PII ¼ F  cosða  bÞ

ð19Þ

Fig. 11. Sketches of the forces applied on concrete block and fibers with an alternative push–pull single-lap test set-up: (a) test set-up employed, (b) sketch of the concrete block rotation, (c) detail of the loaded end, (d) force diagram.

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When employing the test set-up depicted in Fig. 11 for FRPconcrete joints, after debonding occurs the STZ translates toward the free end causing a decrease of the distance r and, in turn, an increase of Dr for the same applied force F. Therefore, provided that the stress-transfer mechanism is still fully established, a higher peeling force is applied to the composite strip when the bonded length is reduced. However, in the case of FRCM-concrete joints, the presence of the external matrix layer prevents the lift up of the debonded fibers and r remains constant. It should be noted that, although increasing the length of the restraining plate hr would result in a decrease of Dr, hr should be short enough not to induce compressive stress close to the composite-support interface, which would affect the results [28]. The influence of Mode-I loading condition of the test set-up depicted in Fig. 11 can be reduced by increasing the length of the concrete block, which would result in decreasing Dr for the same applied force F, or by increasing the length of the bare fibers, which would reduce the angle b. The test set-up of Fig. 11 was used to study the bond behavior of FRP-concrete joints through numerical modeling in which the concrete block was restrained by roller supports along the steel plate- and restraining plate-concrete interfaces. The results obtained showed compression of the FRP composite, orthogonal to the composite plane, at the beginning of the bonded length [1,46]. This negative Mode-I (compression) component is not present in experimental tests where unintended loading offsets are avoided, i.e. b = 0 at the beginning of test, and is due to the restraints applied to the concrete block that do not reproduce the actual restraining condition and thus provides misleading results. Although using stiff restraints may reduce the Mode-I loading condition, a peeling force is always present in single-lap direct-shear tests due to inherent eccentricity between the applied and restraining forces. 5.3. Significance of surface strain results It should be emphasized that the DIC results presented in this paper are the displacements and strains on the surface of the external matrix layer, not the displacements and strains of the fibers. Previous work by the authors showed that the stress-transfer mechanism between the fibers and the internal and external matrix layers is different [17], and therefore the displacement and strain field is not uniform through the thickness of the composite. Furthermore, the stress-transfer between the fibers and matrix is more pronounced at the interface between the fibers and the internal matrix layer, which indicates that the magnitudes of the measurements on the external matrix layer surface should not be used to determine the magnitude of the strains on the fibers. However, the surface measurements in this case were useful to study the bending of the matrix induced by the Mode-I peeling effect. The strains depicted in Figs. 7a and 8, which were obtained using a subset with 21 pixels (approximately 3.40 mm) edge, show compression of the external matrix layer at the loaded end and, for point C, at the free end (note: in Figs. 7 and 8 compression is depicted as positive). Compressive strains are the result of ModeI peeling effect, which causes bending of the matrix with compression on the exterior surface. The maximum strain values observed in Figs. 7a and 8 are slightly higher than the ultimate compressive strain of the matrix em = 0.004, which was computed from the average matrix compressive strength (Section 3.1) and matrix elastic modulus (declared by the manufacturer [38]) assuming linear behavior up to failure. Strain values higher than em may be caused by formation and opening of cracks in the matrix. Furthermore, it should be noted that the presence of shrinkage cracks, which may open during testing, on the matrix surface affects the optical

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measurements performed by DIC. Values of strain measured by DIC on the bonded length central portion, i.e. excluding loaded and free ends, oscillate within approximately 0.001 and 0.001. This behavior, clearly shown in Fig. 7, is in part due to the presence of the transversal fiber bundles that influence the external matrix– fiber stress-transfer mechanism [17]. Oscillations in the DIC measurements were observed in all subsets adopted, though peak values of the oscillations decrease from approximately 0.001 (21 pixels subset) to approximately 0.0006 (60 pixels subset) when larger subsets are employed. These oscillations are due to the presence of transversal fiber bundles placed toward the external matrix layer, which affected the longitudinal displacement v and strain eyy on the matrix surface. Displacements of the matrix surface vary from point to point due to pattern of the embedded fiber net. Points on the matrix surface that correspond to longitudinal fiber bundles, which are stressed during testing, have displacements different from points corresponding to transversal fiber bundles and fiber net spaces. Fig. 7 shows the differences in longitudinal strain eyy obtained with different subsets. When employing large subsets, differences in displacement within the same subset are levelled off and the oscillations are reduced. DIC is well-suited for metals and homogeneous materials, whereas its use is particularly challenging in the case of cohesive materials. In general, the subset dimension is a function of the speckle size and spacing. However, when studying cohesive materials, the subset and step dimensions have to be defined taking also into account the size of the material components. The use of subsets with dimension comparable with the size of the material components may lead to high displacement gradients, which does not comply with the homogeneity assumption adopted in the case of cohesive materials. Although the mortar employed for the FRCM composite studied in this paper includes high-fineness cement and micro aggregates, it cannot be regarded as a homogeneous material at a scale of the same order of magnitude of the particles comprising the matrix. Results obtained with subsets and steps with dimensions less than 1 mm are affected by the inhomogeneity of the material. The use of subsets with greater dimensions allows for reducing the noise due to the matrix granularity, although the measurement precision is reduced. The displacements in the y direction v obtained by DIC at the peak load P⁄ (point C in Fig. 6) of specimen DS_330_60_7 are depicted in Fig. 12a. For each value of y the displacement is obtained as the average over the range 19.5 mm < x < 23.5 mm, which corresponds to the position of the third bundle from the fiber net left-hand side, as discussed in Section 4.3. Fig. 12a shows that v does not vary significantly along the bonded length and, hence, the displacement of the matrix surface can be regarded as rigid body motion. Local variations of v can be attributed to the inhomogeneity of the matrix surface as previously explained. The average value of the displacements v measured along the  = 5.05 mm. Fig. 12b bonded length at peak load P⁄ is equal to v shows the relationship between P and the testing machine stroke d, i.e. the displacement of the piston recorded by an LVDT embedded within the machine, during testing. The stroke d corresponding to the peak load P⁄ was equal to 5.20 mm, which is comparable to the displacements v measured on the matrix surface by DIC for the same applied load value (Fig. 12a). The differ is due to ence between the stroke d and average displacement v the deformation of the elements between the machine LVDT and the composite strip (e.g. machine piston and head, steel frame, joints). These results show that the external matrix layer displacement is mainly due to rigid body motion due to the testing configuration adopted in this study (Section 3.2), not deformation of the matrix.

128

Fig. 12. Displacement

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v obtained by DIC at peak load P⁄ (subset edge = 21 pixels) (a) and applied load – testing machine stroke curve (b) of specimen DS_330_60_7.

6. Conclusions This paper describes the results of an experimental study conducted to investigate the behavior and stress-transfer mechanism of PBO-FRCM composites externally bonded to a concrete substrate. FRCM composite strips with the same bonded length were applied to concrete blocks of different lengths to investigate the effect of the eccentricity between the applied load and the restraint on the composite bond behavior. The use of digital image correlation (DIC) allowed for studying the strain field on the surface of the bonded composite. Results were compared to those of double-lap shear tests of the same composite previously reported by the authors. The following conclusions are made based on the findings of this study: 1. The load-restraint eccentricity did not significantly influence the load response for the single-lap shear tests with different block lengths. 2. The peeling component PI in the single-lap shear test set-up employed in this study can be limited by increasing the length of the bare fibers for a fixed concrete block length L, which results in a decrease of the angle b while the angle a remains constant. 3. The use of an alternate single-lap test set-up where a steel plate is used to restrain the concrete block face opposite to the strengthened face does not fully prevent the presence of a Mode-I loading condition. 4. Very small differences in displacement were observed on the external matrix layer surface. The external matrix displacement is mainly due to rigid body motion due to the testing configuration adopted in this study, not deformation of the matrix. 5. The average peak stress of the single-lap tests performed on blocks with different lengths L = 375 mm and L = 510 mm was very similar (4% difference). Values of peak stress determined by the single-lap shear test were slightly higher than values determined by the double-lap shear tests (16% and 12% difference for single-lap tests with L = 375 mm and L = 510 mm, respectively). 6. For FRCM-concrete joints the Mode-I component at the fiber– matrix interfaces can be probably neglected given the beneficial effect of the external layer of matrix.

Acknowledgements The experimental work discussed in this paper was conducted at Missouri University of Science and Technology (Missouri S&T).

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