Influence of fiber orientation on the behavior of macro synthetic fiber in short- and long-term pullout tests

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G. Bitencourt, Daniel Cardoso This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4261406/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Sep, 2024 Read the published version in Materials and Structures → Version 1 posted 5 You are reading this latest preprint version Abstract Synthetic fibers deforming over time can be a concern in structural design, particularly in serviceability limit states. Short-term pullout tests are commonly used to predict fiber–matrix interactions, but even in this case, an individualized evaluation of the pullout behavior of single fibers oriented parallel to the load direction may not be sufficient to predict the efficiency of the composite. In the present work, short- and long-term pullout tests were performed with fibers oriented at angles of 15°, 30°, and 45° with respect to the direction of the load to investigate the influence of macro synthetic fibers orientation on fiber–matrix interactions. In short-term tests, optical microscopy images were obtained on the pulled-out fibers to correlate the surface degradation of the fibers with the stress versus strain curves. In quasi-static pullout (short-term), small reductions in pullout strength were observed for all fibers and angles, in addition to an intensive degradation of their surfaces owing to the significant snubbing effect of this type of fiber. In contrast, for the long-term tests, a creep reduction was observed with increasing fiber inclination angle caused by the creep reduction of the fiber due to non-axial loading and additional force components produced by the deviation of the axial force. The parameters of Burgers rheological model were written as a function of the fiber orientation angle, with excellent adjustment to the experimental data. fiber orientation cement composites macro synthetic fiber pullout creep Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Synthetic macrofibers have been widely used in cementitious matrix reinforcement applications. However, some of their characteristics and effects have yet to be elucidated. Notably, polymeric materials tend to respond to short-term loads elastically, although they present a viscous behavior with sustained loads over time, deforming indefinitely [ 1 ]. As structures need to be designed for a specific working life, the creep behavior of these materials should be investigated, considering that the structural life span is limited by the time to creep failure [ 1 ]. Pullout tests are commonly used to investigate fiber–matrix interactions, as they can measure the force required to extract embedded fibers. The pullout and flexural strength curves of the composite, although extremely representative of the real behavior, are influenced by various fiber and matrix characteristics, such as the angle of inclination of the fiber concerning the direction of the load. In real composites, the distribution and orientation of fibers are generally random with respect to possible fracture planes, primarily influenced by factors such as the placement point and direction, element geometry, and the use of vibrators [ 2 ]. In addition, fibers often tend to assume angles other than 0° with respect to the direction of the load, affecting the overall composite strength. The angle of inclination of the fibers can influence the pullout behavior in several ways. However, these responses are primarily dependent on fiber shape and properties, mainly whether the fiber is steel or synthetic [ 3 ]. The pulling process, as suggested by Li et al. [ 3 ] and Wu & Li [ 4 ], is analogous to a cable passing over a friction pulley. A concentration of stresses occurs on the pullout surface, close to the support point, increasing the frictional resistance due to the high contact pressures (snubbing effect) [ 3 , 5 ]. Owing to the tensions applied to the matrix at the fiber exit point, a local fragmentation may occur as the angle increases [ 3 , 6 ]. The snubbing effect is more significant in polymeric fibers than in steel fibers owing to premature matrix fragmentation caused by the high stiffness and elastic resistance of steel fibers [ 3 ]. In addition, the fibers are obliged to slip through this fragmented region, causing plastic deformations in the fiber [ 6 ] and increasing its probability of failure [ 7 ], especially in the case of deformed fibers with superficial corrugation [ 6 ]. The pullout behavior under a sustained load can also depend on the angle of inclination of the fibers. Considering steel has negligible creep at ambient temperature [ 1 , 8 ], its long-term load-carrying capacity is not a concern. However, owing to their viscoelasticity, polymeric materials exhibit high deformations over time [ 1 , 8 – 10 ]. Therefore, some studies have extensively investigated the pullout mechanisms of polymeric macrofibers under a sustained load [ 9 – 13 ]. Their results show that pullout creep is caused by a combination of fiber creep and pullout creep [ 9 – 11 ], with the shape, surface corrugation of the fiber and its modulus of elasticity [ 12 ] being the main parameters that govern the behavior under sustained load. However, none of these studies considered the effects of fiber orientation over time. The mechanical behavior of fiber-reinforced composites is significantly related to the pullout behavior of an individual fiber. If inclined fibers behave differently from aligned fibers during the pullout, the performance of these composites cannot be evaluated solely based on fiber-aligned results. As the fibers are embedded into the matrix to bridge the cracks, an inclination concerning the direction of the load can impair the overall toughness of the composite. Therefore, the snubbing and matrix fragmentation effects for inclined fibers must be considered when modeling the pullout behavior under sustained load, especially when polymeric fibers are used. This study performed pullout tests with fibers inclined at angles at 15°, 30°, and 45° for three different synthetic macrofibers. First, a quasi-static test was conducted. Then, using the results, a sustained load of 50% of the maximum peak load was applied for 10 days. Finally, the influence of fiber orientation on the pullout test under sustained loading with inclined fibers was investigated and correlated with the quasi-static pullout mechanisms already established in the literature. In addition, a four-parameter Burgers rheological model that correlates pullout displacement, apparent bond stress, and time is used to predict pullout behavior over time. Expressions to obtain the rheological model parameters as a function of fiber orientation are also proposed and can be applied to simulate the behavior of these composites in mesoscale models. 2. Experimental procedure 2.1. Materials and concrete mix The mortar mix is similar to that reported by Souza et al. [ 14 ], who studied concrete reinforced with polyvinyl alcohol (PVA) fibers in applications on industrial concrete floors. The composition, together with the dosage, is presented in Table 1 . The Portland cement CPV ARI PLUS (equivalent to ASTM type III cement) supplied by Lafarge Holcim and the superplasticizer additive ADVA® 753, by GCP Applied Technologies were used to produce the cementitious matrix. A water/cement factor of 0.42 was adopted in the mix, with 380 kg/m³ of cement content. Gravel with particle sizes of 12.5 mm and 19 mm were used as coarse aggregate, whereas natural quartz sand with particle size and fineness modulus of 2.40 mm and 2.58, respectively, was adopted as fine aggregate, determined according to the Brazilian standard NBR 17054 [ 15 ] (equivalent to ASTM C136-01 [ 16 ]). Table 1 Mixture proportions [ 17 ]. Material Content (kg/m³) Cement (CPV ARI) 380 Fine aggregate 811 Coarse aggregate (12.5 mm) 250 Coarse aggregate (19 mm) 650 Water 160 Superplasticizer 3.80 The mortar was produced following a procedure described in previous works [ 14 ] [ 17 ]. A slump of approximately 60 mm was obtained for the plain matrix, according to the Brazilian Standard NBR 16889 [ 18 ] (equivalent to ASTM C143/C143M-12 [ 19 ]). The compressive strength and the initial tangent modulus of the fiber-free matrix were evaluated according to NBR 7215 [ 20 ] (equivalent to ASTM C39/C39M-01 [ 21 ]) and NBR 8522-1 [ 22 ] (equivalent to BS EN 12390-13 [ 23 ]), respectively. A Controls MCC8 testing machine (cap. 2000 kN) was used and a loading rate of 0.35 MPa/s was adopted. The 28-day mean compression strength and elastic modulus determined from four specimens were 47.32 ± 6.24 MPa and 27.98 ± 1.97 GPa, respectively. More details can be found in Rocha et al. [ 17 ]. 2.2. Polypropylene macro fibers In this study, three types of polypropylene fibers were considered: 1) Barchip54 (Elasto Plastic Concrete®); 2) TamFib SP54 (Normet®); and 3) Tuf-Strand-SF (Viapol®). Geometric properties of Barchip54 and TamFib SP54 fibers were similar. Tuf-Strand-SF fibers, on the other hand, were shorter, twisted along their length and had smooth surfaces. Table 2 present the fibers primary characteristics according to the manufacturers' data sheets. The following nomenclature is hereafter considered: BF for Barchip54, TF for TamFib SP54 and VF for Tuf-Strand-SF fibers. The equivalent diameter and aspect ratio of the fibers were determined by Rocha et al. [ 17 ]. Table 2 Fiber properties according to the manufacturer and some experimental analyzes [ 17 ]. Properties BF TF VF Fiber type Barchip54 TamFib SP54 Tuf-Strand-SF Manufacturer Elasto Plastic Concrete® Normet® Viapol® Fiber material a Virgin polypropylene Polyolefin Polyethylene/ Polypropylene Fiber length (mm) 54 54 51 Equivalent diameter (mm) b 0.862 ± 0.022 0.809 ± 0.043 0.797 ± 0.047 Aspect ratio (l f /d) b 62.7 ± 1.6 66.9 ± 3.4 64.2 ± 3.8 Specific gravity (g/cm³) a 0.90 0.91 0.92 Tensile strength (MPa) a 640 540 600–650 Modulus of elasticity (GPa) a 12 10.4 9.5 Cross-section Irregular Irregular Irregular Fiber shape Embossed surface Embossed surface Twisted a obtained from information provided by the manufacturer [ 24 – 26 ]; b obtained by optical microscopy and described in Rocha et al. [ 17 ]. 2.3. Preparation of pullout samples A mold was developed using a 3D printer, an updated version initially described in Rocha et al. [ 17 ]. The mold has two symmetrical parts closed transversely by two screws at their ends. A lock was inserted at half the height of the test specimen to enable the fiber to be positioned before molding it. For this updated mold, a hole with a diameter slightly greater than that of the fiber was introduced for locking and centralization of the fiber. The hole position was defined to meet the desired fiber angles (15°, 30° and 45°). The printed pattern and fibers positioned for each orientation are shown in Fig. 1 . The process of assembling and molding the printed mold can be seen in Rocha et al. [ 17 ]. The mortar corresponding to the concrete described in Section 2.1 was used, but without the gravel. The specimens were demolded 24 h later and kept in a controlled room (relative humidity of 50 ± 5% and temperature of 20 ± 1°C) until 28 days of age, when they were tested. Samples after demolding for each angle of inclination are shown in Fig. 1 . 2.4. Short-term single-fiber pullout test with inclined fibers Pullout tests were performed to determine the pullout behavior of the fibers at different angles of inclination. The tests were carried out with a single fiber embedded on both sides of the specimen with an embedded length ( \({L}_{c}\) ) of 20 mm. To ensure pullout on a critical side with a smaller interfacial area [ 27 ], an embedment length of 20 mm was adopted for the shortest side. This setup was designed so the concrete faces remained approximately parallel during the test. Samples were inserted into specially designed grips and a displacement rate of 1.5 mm/min was adopted. The following were attached to the system: a 5 kN load cell and a linear vertical displacement transducer (LVDT) positioned on a base coupled to the grip to measure deformation during load application. Five specimens were tested for each of the three fibers and four angles. The experimental setup is shown in Fig. 2 . The maximum shear stress ( \({\tau }_{max}\) ) was computed as follows: $${\tau }_{max}=\frac{{P}_{max}}{2\pi r{L}_{c}}$$ 1 where \({P}_{max}\) is the peak load and \(r\) is the equivalent fiber radius, i.e. the radius that results in the same cross-sectional area. 2.5. Single fiber pullout creep test setup with inclined fibers To evaluate the pullout behavior under sustained load, an experimental setup was developed, as described by Rocha et al. [ 17 ]. Generally, as the fiber was embedded on both sides of the sample, with the largest embedded side being 20 mm, the chosen solution was to fix the sample with a hook attached to each of its ends, where one side would be fixed to a rigid structure and therefore free from displacement, and at the other end a hook that allowed loading with suspended free weights. Care was taken to ensure alignment of the system and that both sides of the sample remained parallel, thus simulating the crack opening phenomenon. A steel plate was welded to the upper (fixed) hook, which held the sample and extended halfway to the lower (free) hook to restrict the rotation of the sample around the y-axis (indicated in Fig. 3 ). An update to this setup was the insertion of two other plates welded to the system to prevent the sample from translating around the x and z-axis (both indicated in the Fig. 3 -a). The plates and the clamp that held the sample, which were in direct contact, had their contact surfaces sanded and lubricated with oil to reduce friction. Details of the proposed experimental setup are shown in Fig. 3 . Data was acquired automatically with an HBM 1615 at a frequency of 0.02 Hz. The weights were placed gradually to avoid dynamic overload and to achieve the final load within 5 min. The tests were conducted in a controlled room (temperature of 20 ± 1°C and relative humidity of 50 ± 5%). Three samples for each selected angle were tested at 50% of the average maximum load evaluated in the short-term pullout tests (Table 3 ). The samples remained loaded for 10 days, when loads were removed. Unfortunately, this setup could not efficiently measure recovery after unloading due to instability issues (pendulum behavior). 3. Results and discussion 3. 1. Short-term single fiber pullout test with inclined fibers Figure 4 show the pullout curves for the type of fibers and angles investigated at the same specified embedment length of 20 mm. As the LVDT used had a 10 mm full range, the curves show the displacements up to this value. However, the pullout tests were performed until failure or when the fibers were fully pulled out. Each curve represents the mean response of each group, whereas the grey shade represents the envelope of results. Table 3 summarizes the mean values of the real embedment length (measured after casting one side due to small variations from the pre-established 20 mm, as explained in section 2.3), maximum load ( \({P}_{max}\) ) and bond stress ( \({\tau }_{max}\) ), along with their corresponding standard deviations. A significant variation was observed, which may be explained by small changes in the embedded lengths due to vibration and manual insertion of the fibers. The inclined fibers had embedded lengths exceeding the initially specified 20 mm. Increasing the angle of inclination (θ) of the fibers about the direction of the load significantly influences the maximum load ( \({P}_{max}\) ), slip at the peak load, and probability of fiber rupture before pullout. For BF fibers, an increase of 13.4% and 12.4% in \({P}_{max}\) was found for angles of 15° and 30°, respectively; for TF fibers, a 5.1% increase in \({P}_{max}\) was observed for the 15° angle. However, as the embedded lengths varied, a comparison in terms of the maximum shear stresses ( \({\tau }_{max}\) ) was necessary for reliability. Therefore, the values of the angle of inclination (θ) versus the maximum shear stresses ( \({\tau }_{max}\) ) for all fibers are plotted in Fig. 5 . In this case, none of the fibers experienced higher \({\tau }_{max}\) mean values than those from the results of the fibers at 0° as reported by Rocha et al. [ 17 ]. Moreover, with an increase in the angle of inclination, the efficiency of this behavior and the pullout resistance were reduced. Although different angles of inclination were tested, the shapes of the curves are similar with only minor variations. Considering the standard deviation, small differences of \({\tau }_{max}\) were observed for all the tested angles, especially for VF fiber. During the pullout test, when the bond had already been lost, the frictional resistance mechanism was mobilized, generating an upward pressure in the matrix around the exit point, increasing the friction and consequently the force necessary to pullout the fiber [ 5 , 6 ]. This additional resistance to the pullout force can compensate for the reduced efficiency when considering only the angle of inclination [ 3 , 28 ], resulting in not pronounced changes in \({\tau }_{max}\) . Table 3 Pullout test parameters. Fiber type Embedment length (mm) Slip at peak load (mm) P max (N) Ꞇ max (MPa) BF_0° a 19.3 ± 0.829 2.85 ± 2.8x10 − 5 189.4 ± 36.8 3.85 ± 0.917 BF_15° 24.3 ± 1.49 2.64 ± 0.009 214.6 ± 28.1 3.33 ± 0.528 BF_30° 23.5 ± 1.35 3.23 ± 0.009 212.6 ± 14.2 3.36 ± 0.228 BF_45° 24.8 ± 0.37 4.35 ± 0.006 171.3 ± 59.6 2.63 ± 0.719 TF_0° a 20.5 ± 1.47 3.28 ± 7.5x10 − 5 132.5 ± 11.5 2.66 ± 0.378 TF_15° 24 ± 1.43 2.83 ± 0.005 139.2 ± 20.4 2.34 ± 0.261 TF_30° 25.1 ± 1.39 3.03 ± 0.005 124.1 ± 15.6 1.96 ± 0.324 TF_45° 23.6 ± 1.86 4.48 ± 0.007 123 ± 10.1 2.13 ± 0.283 VF_0° a 21.1 ± 1.24 1.45 ± 3.6x10 − 5 22.7 ± 14.6 0.559 ± 0.132 VF_15° 28.5 ± 0.253 2.59 ± 0.009 29.2 ± 10.5 0.414 ± 0.133 VF_30° 25.6 ± 0.752 3.61 ± 0.008 27.4 ± 8.18 0.447 ± 0.11 VF_45° 22.4 ± 0.786 3.83 ± 0.009 25.7 ± 4.94 0.467 ± 0.081 a obtained and described in Rocha et al. [ 17 ]. Localized pressure (snubbing effect) when θ ≠ 0 can cause plastic deformations in fibers and matrix fragmentation depending on the properties of the matrix and fiber stiffness [ 6 , 28 ]. When the fibers were completely pulled out, as the angle increased, fibers that were originally straight ( BF and TF ) exhibited a more curved shape, whereas the twisted ( VF ) ones became straighter, as shown in the optical microscopy images of the fibers after the pullout (Fig. 4 -b, d and f). According to Robins et al . [ 29 ], provided the final tensile strength of the fiber is not reached during the test, an increase in θ will increase the tortuosity of the path along which the fiber is pulled, leading to a higher resistance to straightening and, therefore, an increase in \({\tau }_{max}\) . For VF fibers, although for all inclinations the value of \({\tau }_{max}\) was lower than that of the fiber at 0°, a progressive increase in \({\tau }_{max}\) occurred with increasing θ, reaching its maximum value at θ = 45°. Notably, the greater the value of θ, the greater the alignment of the VF fibers, which were initially twisted. At θ = 45°, the tortuosity of the pullout tunnel increased the shear stress by causing an alignment of the fibers. All these fibers were pulled out, with minimal fiber damage other than straightening. However, for straight fibers and with a corrugated surface ( BF and TF ), the angle of inclination increased fiber degradation, reducing its strength and favoring rupture, as reported by Li et al. [ 28 ] and Kanda and Li [ 30 ]. Notably, in the case of synthetic fibers, their surface abrasion during pulling is one of the phenomena responsible for the slip-hardening behavior of these fibers, promoted by the increase in shear stress as the slip occurs. Thus, the more degraded the fiber, the greater the peak load in the stress versus slip diagram [ 3 , 28 , 31 , 32 ]. Fiber rupture was observed in one of the BF _0°, BF _30°, BF _45°, and TF _0° samples, two of the BF _15° samples, three of the TF _15° and TF _30° samples, and all the TF _45° samples. The fiber failure mode initially occurred with the consecutive rupture of the fiber's monofilaments until they could not resist pulling and broke, as reported by Deng et al. [ 31 ]. The ruptures observed were generally at fiber points initially embedded and for slippage close to or greater than 10 mm, as shown Fig. 4 -c and d. The increase in fiber degradation and the probability of rupture of these fibers ( BF and TF ) can be explained by their corrugated surfaces that favor stronger matrix bond and, in the case of inclined fibers, induce higher localized stresses at the exit point than those of straight fibers. All the TF _45° fibers ( \({P}_{max}\) = 123 N; \({\tau }_{max}\) = 2.13 MPa) failed after reaching the maximum load but still exhibited a better performance in terms of bond stress than the TF _30° fibers \({P}_{max}\) = 124.1 N; \({\tau }_{max}\) = 1.96 MPa), most likely owing to the combined effect of snubbing and fiber bending, resulting in exacerbated degradation of the fiber when pulled at this angle of inclination and consequently, premature rupture. Small matrix fragmentations were observed, especially for fibers inclined at 30° and 45°. The response of the matrix to local bending stresses also influences the general efficiency of the fiber orientation, given that fragmentation will occur if the stresses exceed the tensile strength of the concrete matrix [ 10 ]. As the matrix had a compressive strength of 47 MPa and the tensile strength increased with the compressive strength, the disintegration of the exit point portion of the fiber was not as evident as it would have been in a weaker matrix or for a high modulus fiber such as steel. Regarding the slip experienced at the point of maximum load, in the BF and TF fibers with angles of 15° ( BF = 2.64 mm; TF = 2.83 mm) and 30° ( BF = 3.23 mm; TF = 3.03 mm), accelerated slip occurred compared with fibers at 0° ( BF = 2.85 mm; TF = 3.28 mm), whereas the slip was reduced at θ = 45° ( BF = 4.35 mm; TF = 4.48 mm. In VF fibers, a behavior similar from that reported for steel fibers [ 6 , 29 , 33 , 34 ], which exhibit greater slip with an increase in the inclination angle. Particularly, for BF fibers, which have slightly higher moduli of elasticity than TF fibers and demonstrate better bond to the matrix in the samples at 0°, the slope of the stress versus slip curve increased for angles of 15° and 30°, with a reduction in the slip at the peak load. According to Li et al. [ 3 ], the friction caused by both the normal force and relative movement between the fiber and matrix can be illustrated as a tensioned fiber attached to a virtual cylinder, similar to changes in direction in fibers with modified geometry, resulting in higher pullout resistance and toughness. The inclination of the fiber can increase the slopes of the load-slip curves in the ascending branch and improve the maximum pullout load and the corresponding slip [ 35 ]. As VF fibers are straight and have a weaker matrix bond, the considerable alignment experienced when pulled out may increase the slope of the curve and, consequently, reduce the slip at the maximum load point. This effect is observed by the increase in bond tension as the angle of inclination increases, although still lower than that experienced at the 0° angle. 1.1. Single fiber pullout creep test setup with inclined fibers Polymeric fibers exhibit a considerable tendency to strain over time, even under room temperature, which can be a challenge for structural applications. Plots of the slip against loading time are shown in Fig. 6 . The curves in (a) show the mean values of the three curves for each angle, whereas those in (b) show the mean values of the creep coefficient for each angle, defined as: $${\phi }_{creep }\left(t\right)=\frac{{\delta }_{creep}\left(t\right)}{{\delta }_{inst}}$$ 2 where \(t\) is the time at which \({\phi }_{creep }\left(t\right)\) is determined, and \({\delta }_{inst}\) is the instantaneous displacement. For the ages of 3, 7, and 10 days, these parameters for the three types of fiber and the standard deviation are summarized in Table 4 . Table 4 Summary of instantaneous displacements and creep coefficients at ages 3, 7 and 10 days for all samples tested at pullout under sustained load. Fiber type δ inst (mm) φ creep 3 days 7 days 10 days BF_0° a 0.127 ± 0.064 1.97 ± 0.174 2.18 ± 0.213 2.31 ± 0.191 BF_15° 0.199 ± 0.133 1.23 ± 0.176 1.26 ± 0.207 1.28 ± 0.209 BF_30° 0.252 ± 0.033 1.18 ± 0.074 1.21 ± 0.101 1.22 ± 0.106 BF_45° 0.351 ± 0.102 1.04 ± 0.02 1.04 ± 0.031 1.05 ± 0.035 TF_0° a 0.396 ± 0.139 1.49 ± 0.226 1.59 ± 0.275 1.64 ± 0.287 TF_15° 0.106 ± 0.091 2.26 ± 1.25 2.4 ± 1.35 2.53 ± 1.48 TF_30° 0.223 ± 0.031 1.52 ± 0.266 1.61 ± 0.343 1.69 ± 0.335 TF_45° 0.195 ± 0.088 1.24 ± 0.39 1.33 ± 0.541 1.36 ± 0.586 VF_0° a 0.027 ± 0.08 3.43 4.53 7.89 VF_15° 0.016 ± 0.003 2.98 ± 0.532 3.84 ± 0.515 5.19 ± 1.28 VF_30° 0.014 ± 0.016 3.38 ± 1.14 3.87 ± 1.31 5.53 ± 0.528 VF_45° 0.027 ± 0.007 2.16 ± 0.281 2.67 ± 0.856 2.92 ± 1.13 a obtained and described in Rocha et al. [ 17 ]. For inclined fibers, as shown in the Fig. 7 , the matrix wedge on the pullout surface exerts a normal force N to allow the axial force on the fiber to change its direction [ 3 ], in other words, the friction generated at the fiber exit mitigate the stress existing in the embedded part and the creep can be basically attributed to the creep of the free length. However, when these fibers are arranged at 0°, only a direct pull is applied, with no bending. Therefore, the results demonstrate that fibers arranged at 0° are more likely to be pulled out under a long-term load than inclined fibers, since a good part of the embedded fiber also suffers creep, along with the interface. This behavior was also observed by Abrishambaf et al. [ 36 ], but for steel fibers. According to the creep coefficient graphs in Fig. 6 , as the inclined angle increases, a lower creep rate is experienced due to the reduction in the creep portions relating to fiber creep in the embedded length and interface creep. When θ = 45°, for all fibers, it can be believed that the existing creep is basically the creep of the fiber itself. As the creep of the fiber is the primary deformation mechanism of composites reinforced with synthetic macro fibers under sustained load [ 9 , 10 ], available through pullout tests with straight fibers to lead to greater deformations over time. All the samples exhibited an instantaneous initial displacement ( \({\delta }_{inst}\) ) as soon as the load was applied due to the elongation of the fiber along the free length [ 9 ] and initial pullout. This initial displacement seems dependent on the type and properties of the fiber [ 9 ] in addition to the applied load. Because the applied loads are different for each angle, the most interesting comparison of \({\delta }_{inst}\) would be through the initial stiffness given by \(K=\raisebox{1ex}{${\delta }_{inst}$}\!\left/ \!\raisebox{-1ex}{$P$}\right.\) (Fig. 8 -a). For BF fibers, a pattern can be observed with \(K\) increasing with angle, possibly resulting from its greater bending stiffness. A different response was observed for TF and VF fibers, which experienced an initial reduction of stiffness with θ, followed by an increase for θ = 30° and 45°. For BF and TF fibers, the creep coefficient \({(\phi }_{creep }\left(t\right)\) ) increases over time for all the analyzed angles, although at a decreasing rate. Incidentally, BF fibers (15°, 30°, and 45°) exhibit almost no difference between the 7- and 10-day tests, appearing to have reached the slip limit. In BF and TF fibers, \({\phi }_{creep }\left(t\right)\) decreases as the angle θ increases, as show in the Fig. 8 - b. BF fibers exhibit a significant increase in slippage over time when the fibers are aligned with the direction of the load, i.e., θ = 0°. This is justified by the fact that inclined fibers basically have the creep resulting from the creep of the fiber in the free length and aligned fibers have other slip components over time, as already explained and shown in the Fig. 7 . As for TF fibers, this significant difference is only noticed when the angle is 45°. VF fibers presented a low instantaneous initial displacement for all the angles investigated, although with a significantly higher creep growth rate than those of the other fibers, indicating that the slip continues to increase over time, justified by their smooth surfaces, which offer a lower pullout resistance than those of other fibers that have a superficial corrugation. Importantly, in the 10-day test, the creep coefficient is higher than in the 7-day test, indicating that the pullout is progressing. This shows that these fibers are so easily deformable that the deflection components caused by the change of direction at small inclination angles do not offer great resistance to slipping over time, to the point that the only significant creep is attributed to creep in the fiber itself, except for angles greater than 45°. Only one of the VF _0° fiber samples remained intact during the 10-day test, with all the others ruptured in less than 48 h, as explained in Rocha et al. [ 17 ]. As the change in fiber inclination plays an important role, evaluation of viscoelastic behavior over time is performed by applying a four-parameter rheological Burgers model. The original equation correlates strain, stress and time, which will be replaced by pullout displacement, apparent bond stress and time as follows: $$\delta \left(t\right)=\frac{{\tau }_{0}}{{R}_{1}}+\frac{{\tau }_{0}}{{R}_{2}}\left(1-exp\left(\frac{-{R}_{2}t}{{\eta }_{2}}\right)\right)+\frac{{\tau }_{0}}{{\eta }_{1}}t$$ 3 where \(\delta \left(t\right)\) is the pullout displacement at a given time \(t\) , \({\tau }_{0}\) is the bond stress, \({R}_{1}\) is the instantaneous elastic stiffness of the Maxwell unit, \({R}_{2}\) is the elastic stiffness of the Kelvin–Voigt model representing the contribution of the retarded elastic region, \({\eta }_{1}\) is the dashpot of the Maxwell element that represents the residual viscosity, and \({\eta }_{2}\) is the dashpot related to Kelvin–Voigt model that represents the internal viscosity. Table 5 presents the model parameters for all angles and fiber evaluated, which were obtained through regression of the mean experimental pullout curves under sustained load. The correlation coefficient R² is also reported for each analysis in order to prove the fit to the experimental curves. A comparison of the experimental curves and models for the three types of fibers and all the inclination angles are shown in Fig. 9 . Table 5 Burgers model parameters for the three fibers and all their inclinations. Fiber type Loading level Burgers model parameters R² R 1 (MPa/mm) R 2 (MPa/mm) η 1 (MPa.s/mm) η 2 (MPa.s/mm) BF 0° a 13.1 22.5 2.37 x 10 7 8.59 x 10 5 0.99 15° 7.65 44.7 7.12 x 10 7 2.45 x 10 6 0.99 30° 6.45 53 9.18 x 10 7 2.32 x 10 6 0.99 45° 3.93 51.7 1.36 x 10 8 1.23 x 10 4 0.76 TF 0° a 3.07 11.3 1.53 x 10 7 5.96 x 10 5 0.99 15° 11.2 18.8 5.19 x 10 7 1.04 x 10 6 0.98 30° 3.99 13.6 1.59 x 10 7 7.91 x 10 5 0.99 45° 5.34 57.9 6.81 x 10 7 5.43 x 10 6 0.96 VF 0° a 8 20 2.16 x 10 6 1.35 x 10 5 0.79 15° 13.1 12.8 3.55 x 10 6 1.23 x 10 5 0.98 30° 18.3 7.31 6.47 x 10 6 2.48 x 10 5 0.87 45° 8.14 8.53 1.25 x 10 7 1.19 x 10 6 0.97 a obtained and described in Rocha et al. [ 17 ]. A correlation coefficient greater than 0.75 was obtained for all angles of inclination, demonstrating a good fit for the model. The bond stiffness, represented by the parameter R 1 , seemed to decrease as the angle increased for BF fibers (41.6% for 15°, 50.8% for 30°, and 70% for 45°) but increased for TF (259% for 15°, 30% for 30°, and 74% for 45°) and VF fibers (63.8% for 15°, 128.8% for 30°, and 1.8% for 45°). As the BF fiber has a slightly higher modulus of elasticity than the others, this reduction in stiffness may have been caused by the lateral bending of the fiber. Conversely, for VF fibers, the stiffening may have been promoted by the straightening process during the pullout. In the case of the η 1 parameter, which represents the secondary creep rate, an increase in θ generated higher values of η 1 in all fibers, indicating a reduction in slip over time. As already discussed, the alignment of the fibers can favor the progression of the pullout. The parameter η 2 regulates the speed with which the curve enters the secondary creep stage, i.e., the smaller the η 2 , the faster the curve enters the secondary stage. For BF and TF fibers, an increase in η 2 was observed from 0° to 15° and then a decrease for angles of 30° and 45°. The interspersing of VF fibers increases with reductions. Generally, longer periods of primary creep were observed for all angles compared with their fibers at 0°, except for BF fibers at 45°. Given the good fit of the curves to the Burger model, equations were proposed that represent each of its parameters ( \({\varvec{R}}_{1}\) , \({\varvec{R}}_{2}\) , \({\varvec{\eta }}_{1}\) , \({\varvec{\eta }}_{2}\) ) as a function of the angle θ for each fiber studied, as shown in Table 6 . The functions are 2nd degree polynomials (with the exception of the coefficients \({\varvec{R}}_{1}\) and \({\varvec{\eta }}_{1}\) for the TF fiber which were better adjusted to 3rd degree polynomials) and allow you to define the parameters for any inclination angle between 0° and 45°. The vast majority of equations presented an excellent fit and can be used to feed numerical models to predict the long-term behavior of these composites. Table 6 Approximating equations of the parameters of the Burgers model as a function of the angle θ (for 0 < θ < 45°, θ in degrees) and the coefficient of correlation R². Fiber type Equations R² BF \({R}_{1}\left(\theta \right)=0.003{\theta }^{2}-0.338\theta +12.8 (MPa/mm)\) 0.966 \({R}_{2}\left(\theta \right)=-0.026{\theta }^{2}+1.81\theta +22.7 (MPa/mm)\) 0.999 \({\eta }_{1}\left(\theta \right)=-3801{\theta }^{2}+3\times {10}^{6}\theta +3\times {10}^{7} (MPa.s/mm)\) 0.981 \({\eta }_{2}\left(\theta \right)=-4329.6{\theta }^{2}+177078\theta +835168 (MPa.s/mm)\) 0.997 TF \({R}_{1}\left(\theta \right)=0.001{\theta }^{3}-0.087{\theta }^{2}+1.58\theta +3.07 (MPa/mm)\) 1.0 \({R}_{2}\left(\theta \right)=0.041{\theta }^{2}-0.936\theta +14.3 (MPa/mm)\) 0.865 \({\eta }_{1}\left(\theta \right)=7941.8{\theta }^{3}-518667{\theta }^{2}+8x{10}^{6}\theta +2\times {10}^{7} (MPa.s/mm)\) 1.0 \({\eta }_{2}\left(\theta \right)=4667.1{\theta }^{2}-114934\theta + 874844 (MPa.s/mm)\) 0.904 VF \({R}_{1}\left(\theta \right)=-0.017{\theta }^{2}+0.801\theta +7.23 (MPa/mm)\) 0.833 \({R}_{2}\left(\theta \right)=0.009{\theta }^{2}-0.687\theta +20.3 (MPa/mm)\) 0.987 \({\eta }_{1}\left(\theta \right)=5182.7{\theta }^{2}-6391.8\theta +2\times {10}^{6} (MPa.s/mm)\) 0.998 \({\eta }_{2}\left(\theta \right)=1059.1{\theta }^{2}-25755\theta +168879 (MPa.s/mm)\) 0.971 4. Conclusion Short- and long-term pullout tests were performed with angles of 15°, 20°, 30°, and 45° with respect to the direction of the load to investigate the influence of macro synthetic fibers orientation on fiber–matrix interactions. The following conclusions were drawn: The embedded lengths were greater in the samples with inclined fibers. In the short-term tests, a comparison in terms of shear stress instead of the maximum pullout load revealed that in none of the fibers did the bonding stress exceed that experienced when the fibers were aligned with the direction of the load, even with minimal variation, especially for angles of approximately 30°. Significant fiber surface degradation was observed as the angle of inclination was increased. In the specific case of twisted fibers ( VF ), they were practically aligned after the pullout. The tortuosity of the path in the pulling tunnel seems to have been responsible for this alignment, in addition to the increased slope of the tension versus slip curve for these fibers, considering the substantial challenge in pulling them out, when compared with the aligned samples. Straight fibers and those with superficial corrugation ( BF and TF ) exhibited greater adherence to the matrix. Moreover, in the case of inclined samples, a greater probability of fiber rupture was observed. This behavior was attributed to their corrugated surfaces, which favored matrix bonds and induced even greater localized stresses than those due to the snubbing effect at the exit point, promoting an exacerbated degradation of the fiber and thus resulting in the rupture of some samples. This rupture was observed in all TF fibers inclined at 45°. Minimal fragmentation of the matrix was observed, possibly due to the low stiffness of the fiber compared with that of the matrix. For straight fibers ( BF and TF ) the creep coefficient was reduced with an increase in the fiber inclination angle. Furthermore, an almost zero growth rate was obtained for the 10-day test compared with the 7-day test, indicating no further slippage. However, VF fibers increasingly deformed over time, possibly owing to the lower resistance imposed by their smooth surface. The creep reduction with an increase in the fiber inclination angle could be explained by the snubbing effect that induced force components to promote axial force deviation, in addition to the reduction of fiber creep, which under inclined loading, reduced its capacity to deform. Given this, the greater the inclination angle, the lower the creep rate will be, as the portions relating to the fiber creep in the embedded length and the interface creep are severely reduced, leaving basically the fiber creep in the free length. In long-term pullout tests, fibers with surface corrugation ( BF and TF ) had their sliding almost ceased after 7 days, which suggests that this is a sliding limit. However, the VF fibers continued to slide with a significant creep growth rate, possibly justified by their smooth surface and low adhesion to the matrix. The Burgers model was applied to the experimental curves and resulted in a good fit for all the fibers and angles of inclination. Due to this good fit, approximate functions of the parameters were determined and these can be used to model fiber-scale cementitious composites. Declarations Acknowledgment All testing was conducted at the Laboratory of Structures and Materials of the Pontifical Catholic University of Rio de Janeiro. The authors would like to thank PUC-Rio and CAPES for their support. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and by Brazilian funding agencies FAPERJ and CNPq. Luís A.G. Bitencourt Jr. would also like to acknowledge the fellowship of research productivity (PQ) granted by the National Council for Scientific and Technological Development (CNPq - Proc. N: 307175/2022-7). References J. MacKay, J.F. Trottier, Post-crack creep behavior of steel and synthetic FRC under flexural loading, in: Shotcrete: More Engineering Developments, Taylor & Francis Group, London, 2004: pp. 183–192. P. Stähli, R. Custer, J.G.M. Van Mier, On flow properties, fibre distribution, fibre orientation and flexural behavior of FRC, Materials and Structures/Materiaux et Constructions 41 (2008) 189–196. https://doi.org/10.1617/s11527-007-9229-x. V.C. Li, Y. Wang, S. Backer, Effect of inclining angle, bundling and surface treatment on synthetic fibre pull-out from a cement matrix, Composites 21 (1990) 132–140. H.-C. Wu, V.C. Li, Snubbing and Bundling Effects on Multiple Crack Spacing of Discontinuous Random Fiber-Reinforced Brittle Matrix Composites, Journal of the America Ceramic Society 75 (1992) 3487–3489. P.A. Krahl, G. de Miranda Saleme Gidrão, R.B. Neto, R. Carrazedo, Effect of curing age on pullout behavior of aligned and inclined steel fibers embedded in UHPFRC, Constr Build Mater 266 (2021). https://doi.org/10.1016/j.conbuildmat.2020.121188. Y.-S. Tai, S. El-Tawil, High loading-rate pullout behavior of inclined deformed steel fibers embedded in ultra-high performance concrete, Constr Build Mater 148 (2017) 204–218. C. Ding, L. Guo, B. Chen, Orientation distribution of polyvinyl alcohol fibers and its influence on bridging capacity and mechanical performances for high ductility cementitious composites, Constr Build Mater 247 (2020). https://doi.org/10.1016/j.conbuildmat.2020.118491. N. Tošić, S. Aidarov, A. La Fuente, Systematic Review on the Creep of Fiber-Reinforced Concrete, Materials 13 (2020). https://doi.org/10.3390/ma13225098. A.J. Babafemi, A. du Plessis, W.P. Boshoff, Pull-out creep mechanism of synthetic macro fibres under a sustained load, Constr Build Mater 174 (2018) 466–473. https://doi.org/10.1016/j.conbuildmat.2018.04.148. R. Vrijdaghs, M. di Prisco, L. Vandewalle, Short-term and creep pull-out behavior of polypropylene macrofibers at varying embedded lengths and angles from a concrete matrix, Constr Build Mater 147 (2017) 858–864. https://doi.org/10.1016/j.conbuildmat.2017.05.005. A.J. Babafemi, W.P. 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ASTM C39/C39M-01, Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens, United States, 2021. ABNT (Associação Brasileira de Normas Técnicas), Concreto endurecido - Determinação dos módulos de elasticidade e de deformação - Parte 1: Módulos estáticos à compressão - NBR 8522-1, Brazil, 2021. European Standard (EN), Testing hardened concrete Determination of secant modulus of elasticity in compression - BS EN 12390 - 13, United Kingdom, 2021. Elasto Plastic Concrete®, BarChip 54 – Concrete Fibre Reinforcement. Product data sheet, 2021. Normet Construction Chemicals, TamFib SP54 – Structural Polymer Macro Fibres for Reinforcing Concrete. Technical Data sheet, 2018. Viapol, TUF Strand SF. Technical Data sheet, 2020. A. Bentur, S. Mindess, Fibre reinforced cementitious composites, Second, Taylor & Francis, Milton Park, UK, 2007. Z. Lin, V.C. Li, Crack bridging in fiber reinforced cementitious composites with slip-hardening interfaces, J. Mech. Phys. Solids 45 (1997) 763–787. P. Robins, S. Austin, P. Jones, Pull-out behavior of hooked steel fibres, Materials and Structures/Materiaux et Constructions 35 (2002) 434–442. T. Kanda, V.C. Li, Interface property and apparent strength of high-strength hydrophilic fiber in cement matrix, J. Mater. Civ. Eng 10 (1998) 5–13. F. Deng, C. Cao, L. Xu, Y. Chi, Interfacial bond characteristics of polypropylene fiber in steel/polypropylene blended fiber reinforced cementitious composite, Constr Build Mater 341 (2022) 127897. P. Di Maida, E. Radi, C. Sciancalepore, F. Bondioli, Pullout behavior of polypropylene macro-synthetic fibers treated with nano-silica, Constr Build Mater 82 (2015) 39–44. https://doi.org/10.1016/j.conbuildmat.2015.02.047. Y. Lee, S.T. Kang, J.K. Kim, Pullout behavior of inclined steel fiber in an ultra-high strength cementitious matrix, Constr Build Mater 24 (2010) 2030–2041. https://doi.org/10.1016/j.conbuildmat.2010.03.009. Y.Y.Y. Cao, Q.L. Yu, Effect of inclination angle on hooked end steel fiber pullout behavior in ultra-high performance concrete, Compos Struct 201 (2018) 151–160. https://d0i.0rg/l0.1016/j.compstruct.2018.06.029. R. Zhang, X. Yan, L. Guo, Pullout damage analysis of steel fiber with various inclination angles and interface states in UHPC through acoustic emission and microscopic observation, Journal of Building Engineering 51 (2022). https://doi.org/10.1016/jjobe.2022.104271. A. Abrishambaf, J.A.O. Barros, V.M.C.F. Cunha, C. Frazão, Time dependent behavior of fibre pull-out in self-compacting concrete, Cem Concr Compos 77 (2017) 14–28. https://doi.org/10.1016/j.cemconcomp.2016.12.004. Cite Share Download PDF Status: Published Journal Publication published 04 Sep, 2024 Read the published version in Materials and Structures → Version 1 posted Editorial decision: Major revisions 26 Jun, 2024 Reviewers agreed at journal 23 Apr, 2024 Reviewers invited by journal 21 Apr, 2024 Editor assigned by journal 16 Apr, 2024 First submitted to journal 13 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4261406","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":293781209,"identity":"ad258105-fa26-4542-ba58-6333585e4ec7","order_by":0,"name":"Thais da Silva Rocha","email":"","orcid":"","institution":"Pontifical Catholic University of Rio de Janeiro: Pontificia Universidade Catolica do Rio de Janeiro","correspondingAuthor":false,"prefix":"","firstName":"Thais","middleName":"da Silva","lastName":"Rocha","suffix":""},{"id":293781210,"identity":"bd88e427-a9f7-44ee-bd07-6522f45f905e","order_by":1,"name":"Luís A. G. Bitencourt","email":"","orcid":"","institution":"University of Sao Paulo: Universidade de Sao Paulo","correspondingAuthor":false,"prefix":"","firstName":"Luís","middleName":"A. G.","lastName":"Bitencourt","suffix":""},{"id":293781211,"identity":"ada03d4c-eacf-4c71-a84c-d3647ea26bd4","order_by":2,"name":"Daniel Cardoso","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYDCCA2CSGYQhTDYwwquFGaaFLYFkLTwGMDH8WviOnz/44eceazn59p5vj3lqGPL52BvYHlfg0SJ5JplZsudZurHBmbPbjXmOMVi28RxgNzyDR4vBDWY2Bp4DhxM3SORuk+Zt+G/AJpHAJtlAQAvjH6CW+TNyngG1MBCnhRlkS8ONHDbitAD9YiwtcwDkl2PmhnOOAbXwHGw3xKeF7/jBhx/fHACFWPOzB29qGAyAjGMP8WlBBrDoYCRWA8FIHwWjYBSMghELAFSSRmnYGeiYAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-8171-7956","institution":"Pontificia Universidade Catolica do Rio de Janeiro","correspondingAuthor":true,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Cardoso","suffix":""}],"badges":[],"createdAt":"2024-04-13 10:14:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4261406/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4261406/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1617/s11527-024-02447-2","type":"published","date":"2024-09-04T16:05:45+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":55525099,"identity":"ea709d26-ceb5-47e5-90f9-d1ecc40d6ec2","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":107688,"visible":true,"origin":"","legend":"\u003cp\u003e3D printed pullout molds with fibers inclined to (a) 15°, (b) 30°, and (c) 45°; and specimen after demolding with fibers inclined to (a) 15°, (b) 30°, and (c) 45°.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/92a89ef9b53030f8434e8b73.jpg"},{"id":55525100,"identity":"efeb58c7-dab7-48e2-9ea3-a0ce935e304e","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":64120,"visible":true,"origin":"","legend":"\u003cp\u003eDetails of the pullout test: (a) before and (b) after the test.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/8e8ed036453c424cd65a846d.jpg"},{"id":55525103,"identity":"db3f371f-b847-49f9-9db2-e2d16a14daac","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":79688,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic with the proposed creep experimental setup and real images of the details; (b) Schematic of the arrangement of the weights suspended in the claws attached to the lower end of the sample; (c) image of the actual test in progress.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/93813a5478770e082779bf34.jpg"},{"id":55525985,"identity":"49d4ed3f-b268-49a6-8615-6556b041663a","added_by":"auto","created_at":"2024-04-29 14:49:22","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":80680,"visible":true,"origin":"","legend":"\u003cp\u003eLoad \u003cem\u003eversus\u003c/em\u003e slip curve of (a) BF; (c) \u003cem\u003eTF\u003c/em\u003e and (e) VF fiber pullout test at 0°, 15°, 30°, and 45° angles; optical microscopy images of the (b) BF; (d) \u003cem\u003eTF\u003c/em\u003e and (f) VF fiber after pulling out at the different tested angles.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/03c7710eb1489d62e17fdf99.jpg"},{"id":55525101,"identity":"87c2b1a3-8c89-4813-83f4-76d66efd000f","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":32766,"visible":true,"origin":"","legend":"\u003cp\u003eFiber inclination angles \u003cem\u003eversus\u003c/em\u003e maximum shear stresses for all fibers studied.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/e397793495ca28a7cb0dfbe6.jpg"},{"id":55525106,"identity":"a0e8200c-b060-4651-8cf5-888a88fa8cda","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":71780,"visible":true,"origin":"","legend":"\u003cp\u003eSlip \u003cem\u003eversus\u003c/em\u003e time curves for different inclinations of (a) \u003cem\u003eBF\u003c/em\u003e fiber; (c) \u003cem\u003eTF\u003c/em\u003e fiber; (e) \u003cem\u003eVF\u003c/em\u003e fiber; and creep coefficient (\u003cem\u003eφ\u003c/em\u003e\u003csub\u003e\u003cem\u003ecreep\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e (t)\u003c/em\u003e) over time for all inclinations of (b) \u003cem\u003eBF\u003c/em\u003e fiber; (d) \u003cem\u003eTF\u003c/em\u003e fiber; (f) \u003cem\u003eVF\u003c/em\u003e fiber.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/3836e46fb4146692699fc2f6.jpg"},{"id":55525107,"identity":"7ce0df93-420b-4d35-adf1-47a06866bde7","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":42665,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic drawing of the inclined fiber inserted into the cementitious matrix (a) before the load is applied and (b) during pullout.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/071d83283755c0c4bd39a139.jpg"},{"id":55525986,"identity":"d9569c25-48cf-4f30-84f3-fd4bb7bd3c99","added_by":"auto","created_at":"2024-04-29 14:49:22","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":58589,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Initial stiffness \u003cem\u003eversus\u003c/em\u003e fiber inclination angle; (b) creep coefficient at 10 days \u003cem\u003eversus\u003c/em\u003e fiber inclination angle.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/1763a53b06d93e3a9f236267.jpg"},{"id":55525105,"identity":"9d347447-3bf1-49ad-b00a-6cbee1d0d388","added_by":"auto","created_at":"2024-04-29 14:41:22","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":61076,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental curves and rheological results of the Burgers model for the (a) \u003cem\u003eBF\u003c/em\u003e fiber; (b) \u003cem\u003eTF\u003c/em\u003e fiber and (c)\u003cem\u003e VF\u003c/em\u003e fiber.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/55f7bdff6cdc125b8fcb8fd0.jpg"},{"id":64186072,"identity":"f0c7b71d-f449-45da-815b-af1d43cd6cd3","added_by":"auto","created_at":"2024-09-09 16:24:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1442726,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4261406/v1/c62504c9-5d0d-4c8c-95ca-eb9b9bf6f6ce.pdf"}],"financialInterests":"","formattedTitle":"Influence of fiber orientation on the behavior of macro synthetic fiber in short- and long-term pullout tests","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSynthetic macrofibers have been widely used in cementitious matrix reinforcement applications. However, some of their characteristics and effects have yet to be elucidated. Notably, polymeric materials tend to respond to short-term loads elastically, although they present a viscous behavior with sustained loads over time, deforming indefinitely [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. As structures need to be designed for a specific working life, the creep behavior of these materials should be investigated, considering that the structural life span is limited by the time to creep failure [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003ePullout tests are commonly used to investigate fiber\u0026ndash;matrix interactions, as they can measure the force required to extract embedded fibers. The pullout and flexural strength curves of the composite, although extremely representative of the real behavior, are influenced by various fiber and matrix characteristics, such as the angle of inclination of the fiber concerning the direction of the load. In real composites, the distribution and orientation of fibers are generally random with respect to possible fracture planes, primarily influenced by factors such as the placement point and direction, element geometry, and the use of vibrators [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In addition, fibers often tend to assume angles other than 0\u0026deg; with respect to the direction of the load, affecting the overall composite strength.\u003c/p\u003e \u003cp\u003eThe angle of inclination of the fibers can influence the pullout behavior in several ways. However, these responses are primarily dependent on fiber shape and properties, mainly whether the fiber is steel or synthetic [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The pulling process, as suggested by Li et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and Wu \u0026amp; Li [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], is analogous to a cable passing over a friction pulley. A concentration of stresses occurs on the pullout surface, close to the support point, increasing the frictional resistance due to the high contact pressures (snubbing effect) [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Owing to the tensions applied to the matrix at the fiber exit point, a local fragmentation may occur as the angle increases [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The snubbing effect is more significant in polymeric fibers than in steel fibers owing to premature matrix fragmentation caused by the high stiffness and elastic resistance of steel fibers [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In addition, the fibers are obliged to slip through this fragmented region, causing plastic deformations in the fiber [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] and increasing its probability of failure [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], especially in the case of deformed fibers with superficial corrugation [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe pullout behavior under a sustained load can also depend on the angle of inclination of the fibers. Considering steel has negligible creep at ambient temperature [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], its long-term load-carrying capacity is not a concern. However, owing to their viscoelasticity, polymeric materials exhibit high deformations over time [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Therefore, some studies have extensively investigated the pullout mechanisms of polymeric macrofibers under a sustained load [\u003cspan additionalcitationids=\"CR10 CR11 CR12\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Their results show that pullout creep is caused by a combination of fiber creep and pullout creep [\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], with the shape, surface corrugation of the fiber and its modulus of elasticity [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] being the main parameters that govern the behavior under sustained load. However, none of these studies considered the effects of fiber orientation over time.\u003c/p\u003e \u003cp\u003eThe mechanical behavior of fiber-reinforced composites is significantly related to the pullout behavior of an individual fiber. If inclined fibers behave differently from aligned fibers during the pullout, the performance of these composites cannot be evaluated solely based on fiber-aligned results. As the fibers are embedded into the matrix to bridge the cracks, an inclination concerning the direction of the load can impair the overall toughness of the composite. Therefore, the snubbing and matrix fragmentation effects for inclined fibers must be considered when modeling the pullout behavior under sustained load, especially when polymeric fibers are used.\u003c/p\u003e \u003cp\u003eThis study performed pullout tests with fibers inclined at angles at 15\u0026deg;, 30\u0026deg;, and 45\u0026deg; for three different synthetic macrofibers. First, a quasi-static test was conducted. Then, using the results, a sustained load of 50% of the maximum peak load was applied for 10 days. Finally, the influence of fiber orientation on the pullout test under sustained loading with inclined fibers was investigated and correlated with the quasi-static pullout mechanisms already established in the literature. In addition, a four-parameter Burgers rheological model that correlates pullout displacement, apparent bond stress, and time is used to predict pullout behavior over time. Expressions to obtain the rheological model parameters as a function of fiber orientation are also proposed and can be applied to simulate the behavior of these composites in mesoscale models.\u003c/p\u003e"},{"header":"2. Experimental procedure","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Materials and concrete mix\u003c/h2\u003e \u003cp\u003eThe mortar mix is similar to that reported by Souza et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], who studied concrete reinforced with polyvinyl alcohol (PVA) fibers in applications on industrial concrete floors. The composition, together with the dosage, is presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The Portland cement CPV ARI PLUS (equivalent to ASTM type III cement) supplied by Lafarge Holcim and the superplasticizer additive ADVA\u0026reg; 753, by GCP Applied Technologies were used to produce the cementitious matrix. A water/cement factor of 0.42 was adopted in the mix, with 380 kg/m\u0026sup3; of cement content. Gravel with particle sizes of 12.5 mm and 19 mm were used as coarse aggregate, whereas natural quartz sand with particle size and fineness modulus of 2.40 mm and 2.58, respectively, was adopted as fine aggregate, determined according to the Brazilian standard NBR 17054 [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] (equivalent to ASTM C136-01 [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMixture proportions [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eMaterial\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eContent (kg/m\u0026sup3;)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCement (CPV ARI)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e380\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFine aggregate\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e811\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCoarse aggregate (12.5 mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCoarse aggregate (19 mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e650\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eWater\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eSuperplasticizer\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe mortar was produced following a procedure described in previous works [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. A slump of approximately 60 mm was obtained for the plain matrix, according to the Brazilian Standard NBR 16889 [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] (equivalent to ASTM C143/C143M-12 [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]).\u003c/p\u003e \u003cp\u003eThe compressive strength and the initial tangent modulus of the fiber-free matrix were evaluated according to NBR 7215 [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] (equivalent to ASTM C39/C39M-01 [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]) and NBR 8522-1 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] (equivalent to BS EN 12390-13 [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]), respectively. A Controls MCC8 testing machine (cap. 2000 kN) was used and a loading rate of 0.35 MPa/s was adopted. The 28-day mean compression strength and elastic modulus determined from four specimens were 47.32\u0026thinsp;\u0026plusmn;\u0026thinsp;6.24 MPa and 27.98\u0026thinsp;\u0026plusmn;\u0026thinsp;1.97 GPa, respectively. More details can be found in Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Polypropylene macro fibers\u003c/h2\u003e \u003cp\u003eIn this study, three types of polypropylene fibers were considered: 1) Barchip54 (Elasto Plastic Concrete\u0026reg;); 2) TamFib SP54 (Normet\u0026reg;); and 3) Tuf-Strand-SF (Viapol\u0026reg;). Geometric properties of Barchip54 and TamFib SP54 fibers were similar. Tuf-Strand-SF fibers, on the other hand, were shorter, twisted along their length and had smooth surfaces. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e present the fibers primary characteristics according to the manufacturers' data sheets. The following nomenclature is hereafter considered: BF for Barchip54, TF for TamFib SP54 and VF for Tuf-Strand-SF fibers. The equivalent diameter and aspect ratio of the fibers were determined by Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFiber properties according to the manufacturer and some experimental analyzes [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eProperties\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eBF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eTF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eVF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber type\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eBarchip54\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eTamFib SP54\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eTuf-Strand-SF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eManufacturer\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eElasto Plastic Concrete\u0026reg;\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eNormet\u0026reg;\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eViapol\u0026reg;\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber material\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eVirgin\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003epolypropylene\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ePolyolefin\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ePolyethylene/\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003ePolypropylene\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber length (mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e54\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e54\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e51\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eEquivalent diameter (mm)\u003c/em\u003e\u003csup\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.862\u0026thinsp;\u0026plusmn;\u0026thinsp;0.022\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.809\u0026thinsp;\u0026plusmn;\u0026thinsp;0.043\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.797\u0026thinsp;\u0026plusmn;\u0026thinsp;0.047\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAspect ratio (l\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/d)\u003c/em\u003e\u003csup\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e62.7\u0026thinsp;\u0026plusmn;\u0026thinsp;1.6\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e66.9\u0026thinsp;\u0026plusmn;\u0026thinsp;3.4\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e64.2\u0026thinsp;\u0026plusmn;\u0026thinsp;3.8\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eSpecific gravity (g/cm\u0026sup3;)\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.90\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.91\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.92\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTensile strength (MPa)\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e640\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e540\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e600\u0026ndash;650\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eModulus of elasticity (GPa)\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e12\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e9.5\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCross-section\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eIrregular\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eIrregular\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eIrregular\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber shape\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eEmbossed\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003esurface\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eEmbossed\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003esurface\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eTwisted\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003ea\u003c/sup\u003e \u003cem\u003eobtained from information provided by the manufacturer\u003c/em\u003e [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]; \u003csup\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sup\u003e \u003cem\u003eobtained by optical microscopy and described in Rocha et al.\u003c/em\u003e [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Preparation of pullout samples\u003c/h2\u003e \u003cp\u003eA mold was developed using a 3D printer, an updated version initially described in Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The mold has two symmetrical parts closed transversely by two screws at their ends. A lock was inserted at half the height of the test specimen to enable the fiber to be positioned before molding it. For this updated mold, a hole with a diameter slightly greater than that of the fiber was introduced for locking and centralization of the fiber. The hole position was defined to meet the desired fiber angles (15\u0026deg;, 30\u0026deg; and 45\u0026deg;). The printed pattern and fibers positioned for each orientation are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe process of assembling and molding the printed mold can be seen in Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The mortar corresponding to the concrete described in Section 2.1 was used, but without the gravel. The specimens were demolded 24 h later and kept in a controlled room (relative humidity of 50\u0026thinsp;\u0026plusmn;\u0026thinsp;5% and temperature of 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C) until 28 days of age, when they were tested. Samples after demolding for each angle of inclination are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Short-term single-fiber pullout test with inclined fibers\u003c/h2\u003e \u003cp\u003ePullout tests were performed to determine the pullout behavior of the fibers at different angles of inclination. The tests were carried out with a single fiber embedded on both sides of the specimen with an embedded length (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{c}\\)\u003c/span\u003e\u003c/span\u003e) of 20 mm. To ensure pullout on a critical side with a smaller interfacial area [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], an embedment length of 20 mm was adopted for the shortest side. This setup was designed so the concrete faces remained approximately parallel during the test.\u003c/p\u003e \u003cp\u003eSamples were inserted into specially designed grips and a displacement rate of 1.5 mm/min was adopted. The following were attached to the system: a 5 kN load cell and a linear vertical displacement transducer (LVDT) positioned on a base coupled to the grip to measure deformation during load application. Five specimens were tested for each of the three fibers and four angles. The experimental setup is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe maximum shear stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e) was computed as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\tau }_{max}=\\frac{{P}_{max}}{2\\pi r{L}_{c}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e is the peak load and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(r\\)\u003c/span\u003e\u003c/span\u003e is the equivalent fiber radius, i.e. the radius that results in the same cross-sectional area.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Single fiber pullout creep test setup with inclined fibers\u003c/h2\u003e \u003cp\u003eTo evaluate the pullout behavior under sustained load, an experimental setup was developed, as described by Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Generally, as the fiber was embedded on both sides of the sample, with the largest embedded side being 20 mm, the chosen solution was to fix the sample with a hook attached to each of its ends, where one side would be fixed to a rigid structure and therefore free from displacement, and at the other end a hook that allowed loading with suspended free weights. Care was taken to ensure alignment of the system and that both sides of the sample remained parallel, thus simulating the crack opening phenomenon. A steel plate was welded to the upper (fixed) hook, which held the sample and extended halfway to the lower (free) hook to restrict the rotation of the sample around the y-axis (indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). An update to this setup was the insertion of two other plates welded to the system to prevent the sample from translating around the x and z-axis (both indicated in the Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e-a). The plates and the clamp that held the sample, which were in direct contact, had their contact surfaces sanded and lubricated with oil to reduce friction. Details of the proposed experimental setup are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Data was acquired automatically with an HBM 1615 at a frequency of 0.02 Hz. The weights were placed gradually to avoid dynamic overload and to achieve the final load within 5 min.\u003c/p\u003e \u003cp\u003eThe tests were conducted in a controlled room (temperature of 20\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C and relative humidity of 50\u0026thinsp;\u0026plusmn;\u0026thinsp;5%). Three samples for each selected angle were tested at 50% of the average maximum load evaluated in the short-term pullout tests (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The samples remained loaded for 10 days, when loads were removed. Unfortunately, this setup could not efficiently measure recovery after unloading due to instability issues (pendulum behavior).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\n\u003ch3\u003e3. 1. Short-term single fiber pullout test with inclined fibers\u003c/h3\u003e\n\u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e show the pullout curves for the type of fibers and angles investigated at the same specified embedment length of 20 mm. As the LVDT used had a 10 mm full range, the curves show the displacements up to this value. However, the pullout tests were performed until failure or when the fibers were fully pulled out. Each curve represents the mean response of each group, whereas the grey shade represents the envelope of results. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes the mean values of the real embedment length (measured after casting one side due to small variations from the pre-established 20 mm, as explained in section 2.3), maximum load (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e) and bond stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e), along with their corresponding standard deviations. A significant variation was observed, which may be explained by small changes in the embedded lengths due to vibration and manual insertion of the fibers. The inclined fibers had embedded lengths exceeding the initially specified 20 mm.\u003c/p\u003e \u003cp\u003eIncreasing the angle of inclination (θ) of the fibers about the direction of the load significantly influences the maximum load (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e), slip at the peak load, and probability of fiber rupture before pullout. For \u003cem\u003eBF\u003c/em\u003e fibers, an increase of 13.4% and 12.4% in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e was found for angles of 15\u0026deg; and 30\u0026deg;, respectively; for \u003cem\u003eTF\u003c/em\u003e fibers, a 5.1% increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e was observed for the 15\u0026deg; angle. However, as the embedded lengths varied, a comparison in terms of the maximum shear stresses (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e) was necessary for reliability. Therefore, the values of the angle of inclination (θ) \u003cem\u003eversus\u003c/em\u003e the maximum shear stresses (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e) for all fibers are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. In this case, none of the fibers experienced higher \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003emean values than those from the results of the fibers at 0\u0026deg; as reported by Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Moreover, with an increase in the angle of inclination, the efficiency of this behavior and the pullout resistance were reduced. Although different angles of inclination were tested, the shapes of the curves are similar with only minor variations. Considering the standard deviation, small differences of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003ewere observed for all the tested angles, especially for \u003cem\u003eVF\u003c/em\u003e fiber. During the pullout test, when the bond had already been lost, the frictional resistance mechanism was mobilized, generating an upward pressure in the matrix around the exit point, increasing the friction and consequently the force necessary to pullout the fiber [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. This additional resistance to the pullout force can compensate for the reduced efficiency when considering only the angle of inclination [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], resulting in not pronounced changes in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePullout test parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber type\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eEmbedment length (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eSlip at peak load (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(N)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eꞆ\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(MPa)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e19.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.85\u0026thinsp;\u0026plusmn;\u0026thinsp;2.8x10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e189.4\u0026thinsp;\u003cem\u003e\u0026plusmn;\u0026thinsp;36.8\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e3.85\u0026thinsp;\u0026plusmn;\u0026thinsp;0.917\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.3\u0026thinsp;\u0026plusmn;\u0026thinsp;1.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e214.6\u0026thinsp;\u0026plusmn;\u0026thinsp;28.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e3.33\u0026thinsp;\u0026plusmn;\u0026thinsp;0.528\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e23.5\u0026thinsp;\u0026plusmn;\u0026thinsp;1.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.23\u0026thinsp;\u0026plusmn;\u0026thinsp;0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e212.6\u0026thinsp;\u0026plusmn;\u0026thinsp;14.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e3.36\u0026thinsp;\u0026plusmn;\u0026thinsp;0.228\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e171.3\u0026thinsp;\u0026plusmn;\u0026thinsp;59.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e2.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.719\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e20.5\u0026thinsp;\u0026plusmn;\u0026thinsp;1.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.28\u0026thinsp;\u0026plusmn;\u0026thinsp;7.5x10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e132.5\u0026thinsp;\u0026plusmn;\u0026thinsp;11.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e2.66\u0026thinsp;\u0026plusmn;\u0026thinsp;0.378\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e24\u0026thinsp;\u0026plusmn;\u0026thinsp;1.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.83\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e139.2\u0026thinsp;\u0026plusmn;\u0026thinsp;20.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e2.34\u0026thinsp;\u0026plusmn;\u0026thinsp;0.261\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e25.1\u0026thinsp;\u0026plusmn;\u0026thinsp;1.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e124.1\u0026thinsp;\u0026plusmn;\u0026thinsp;15.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e1.96\u0026thinsp;\u0026plusmn;\u0026thinsp;0.324\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e23.6\u0026thinsp;\u0026plusmn;\u0026thinsp;1.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.48\u0026thinsp;\u0026plusmn;\u0026thinsp;0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e123\u0026thinsp;\u0026plusmn;\u0026thinsp;10.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e2.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.283\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e21.1\u0026thinsp;\u0026plusmn;\u0026thinsp;1.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.45\u0026thinsp;\u0026plusmn;\u0026thinsp;3.6x10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e22.7\u0026thinsp;\u0026plusmn;\u0026thinsp;14.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.559\u0026thinsp;\u0026plusmn;\u0026thinsp;0.132\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e28.5\u0026thinsp;\u0026plusmn;\u0026thinsp;0.253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.59\u0026thinsp;\u0026plusmn;\u0026thinsp;0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e29.2\u0026thinsp;\u0026plusmn;\u0026thinsp;10.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.414\u0026thinsp;\u0026plusmn;\u0026thinsp;0.133\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e25.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.752\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e27.4\u0026thinsp;\u0026plusmn;\u0026thinsp;8.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.447\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e22.4\u0026thinsp;\u0026plusmn;\u0026thinsp;0.786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.83\u0026thinsp;\u0026plusmn;\u0026thinsp;0.009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e25.7\u0026thinsp;\u0026plusmn;\u0026thinsp;4.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e \u003cp\u003e0.467\u0026thinsp;\u0026plusmn;\u0026thinsp;0.081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ea\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eobtained and described in Rocha et al.\u003c/em\u003e [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLocalized pressure (snubbing effect) when θ\u0026thinsp;\u0026ne;\u0026thinsp;0 can cause plastic deformations in fibers and matrix fragmentation depending on the properties of the matrix and fiber stiffness [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. When the fibers were completely pulled out, as the angle increased, fibers that were originally straight (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e) exhibited a more curved shape, whereas the twisted (\u003cem\u003eVF\u003c/em\u003e) ones became straighter, as shown in the optical microscopy images of the fibers after the pullout (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e-b, d and f). According to Robins \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], provided the final tensile strength of the fiber is not reached during the test, an increase in θ will increase the tortuosity of the path along which the fiber is pulled, leading to a higher resistance to straightening and, therefore, an increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e. For \u003cem\u003eVF\u003c/em\u003e fibers, although for all inclinations the value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e was lower than that of the fiber at 0\u0026deg;, a progressive increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e occurred with increasing θ, reaching its maximum value at θ\u0026thinsp;=\u0026thinsp;45\u0026deg;. Notably, the greater the value of θ, the greater the alignment of the \u003cem\u003eVF\u003c/em\u003e fibers, which were initially twisted. At θ\u0026thinsp;=\u0026thinsp;45\u0026deg;, the tortuosity of the pullout tunnel increased the shear stress by causing an alignment of the fibers. All these fibers were pulled out, with minimal fiber damage other than straightening. However, for straight fibers and with a corrugated surface (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e), the angle of inclination increased fiber degradation, reducing its strength and favoring rupture, as reported by Li et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] and Kanda and Li [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Notably, in the case of synthetic fibers, their surface abrasion during pulling is one of the phenomena responsible for the slip-hardening behavior of these fibers, promoted by the increase in shear stress as the slip occurs. Thus, the more degraded the fiber, the greater the peak load in the stress versus slip diagram [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFiber rupture was observed in one of the \u003cem\u003eBF\u003c/em\u003e_0\u0026deg;, \u003cem\u003eBF\u003c/em\u003e_30\u0026deg;, \u003cem\u003eBF\u003c/em\u003e_45\u0026deg;, and \u003cem\u003eTF\u003c/em\u003e_0\u0026deg; samples, two of the \u003cem\u003eBF\u003c/em\u003e_15\u0026deg; samples, three of the \u003cem\u003eTF\u003c/em\u003e_15\u0026deg; and \u003cem\u003eTF\u003c/em\u003e_30\u0026deg; samples, and all the \u003cem\u003eTF\u003c/em\u003e_45\u0026deg; samples. The fiber failure mode initially occurred with the consecutive rupture of the fiber's monofilaments until they could not resist pulling and broke, as reported by Deng et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The ruptures observed were generally at fiber points initially embedded and for slippage close to or greater than 10 mm, as shown Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e-c and d. The increase in fiber degradation and the probability of rupture of these fibers (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e) can be explained by their corrugated surfaces that favor stronger matrix bond and, in the case of inclined fibers, induce higher localized stresses at the exit point than those of straight fibers. All the \u003cem\u003eTF\u003c/em\u003e_45\u0026deg; fibers (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e= 123 N; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e= 2.13 MPa) failed after reaching the maximum load but still exhibited a better performance in terms of bond stress than the \u003cem\u003eTF\u003c/em\u003e_30\u0026deg; fibers \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{max}\\)\u003c/span\u003e\u003c/span\u003e= 124.1 N; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{max}\\)\u003c/span\u003e\u003c/span\u003e= 1.96 MPa), most likely owing to the combined effect of snubbing and fiber bending, resulting in exacerbated degradation of the fiber when pulled at this angle of inclination and consequently, premature rupture.\u003c/p\u003e \u003cp\u003eSmall matrix fragmentations were observed, especially for fibers inclined at 30\u0026deg; and 45\u0026deg;. The response of the matrix to local bending stresses also influences the general efficiency of the fiber orientation, given that fragmentation will occur if the stresses exceed the tensile strength of the concrete matrix [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. As the matrix had a compressive strength of 47 MPa and the tensile strength increased with the compressive strength, the disintegration of the exit point portion of the fiber was not as evident as it would have been in a weaker matrix or for a high modulus fiber such as steel.\u003c/p\u003e \u003cp\u003eRegarding the slip experienced at the point of maximum load, in the \u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e fibers with angles of 15\u0026deg; (\u003cem\u003eBF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.64 mm; \u003cem\u003eTF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.83 mm) and 30\u0026deg; (\u003cem\u003eBF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.23 mm; \u003cem\u003eTF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.03 mm), accelerated slip occurred compared with fibers at 0\u0026deg; (\u003cem\u003eBF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.85 mm; \u003cem\u003eTF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.28 mm), whereas the slip was reduced at θ\u0026thinsp;=\u0026thinsp;45\u0026deg; (\u003cem\u003eBF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.35 mm; \u003cem\u003eTF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.48 mm. In \u003cem\u003eVF\u003c/em\u003e fibers, a behavior similar from that reported for steel fibers [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], which exhibit greater slip with an increase in the inclination angle. Particularly, for \u003cem\u003eBF\u003c/em\u003e fibers, which have slightly higher moduli of elasticity than \u003cem\u003eTF\u003c/em\u003e fibers and demonstrate better bond to the matrix in the samples at 0\u0026deg;, the slope of the stress versus slip curve increased for angles of 15\u0026deg; and 30\u0026deg;, with a reduction in the slip at the peak load. According to Li et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], the friction caused by both the normal force and relative movement between the fiber and matrix can be illustrated as a tensioned fiber attached to a virtual cylinder, similar to changes in direction in fibers with modified geometry, resulting in higher pullout resistance and toughness. The inclination of the fiber can increase the slopes of the load-slip curves in the ascending branch and improve the maximum pullout load and the corresponding slip [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. As \u003cem\u003eVF\u003c/em\u003e fibers are straight and have a weaker matrix bond, the considerable alignment experienced when pulled out may increase the slope of the curve and, consequently, reduce the slip at the maximum load point. This effect is observed by the increase in bond tension as the angle of inclination increases, although still lower than that experienced at the 0\u0026deg; angle.\u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e1.1. Single fiber pullout creep test setup with inclined fibers\u003c/h2\u003e \u003cp\u003ePolymeric fibers exhibit a considerable tendency to strain over time, even under room temperature, which can be a challenge for structural applications. Plots of the slip against loading time are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The curves in (a) show the mean values of the three curves for each angle, whereas those in (b) show the mean values of the creep coefficient for each angle, defined as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\phi }_{creep }\\left(t\\right)=\\frac{{\\delta }_{creep}\\left(t\\right)}{{\\delta }_{inst}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e is the time at which \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\phi }_{creep }\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e is determined, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }_{inst}\\)\u003c/span\u003e\u003c/span\u003e is the instantaneous displacement. For the ages of 3, 7, and 10 days, these parameters for the three types of fiber and the standard deviation are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of instantaneous displacements and creep coefficients at ages 3, 7 and 10 days for all samples tested at pullout under sustained load.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eFiber type\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003einst\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003eφ\u003c/em\u003e\u003csub\u003e\u003cem\u003ecreep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e3 days\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e7 days\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e10 days\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.127\u0026thinsp;\u0026plusmn;\u0026thinsp;0.064\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.97\u0026thinsp;\u0026plusmn;\u0026thinsp;0.174\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e2.18\u0026thinsp;\u0026plusmn;\u0026thinsp;0.213\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e2.31\u0026thinsp;\u0026plusmn;\u0026thinsp;0.191\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.199\u0026thinsp;\u0026plusmn;\u0026thinsp;0.133\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.23\u0026thinsp;\u0026plusmn;\u0026thinsp;0.176\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.26\u0026thinsp;\u0026plusmn;\u0026thinsp;0.207\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.209\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.252\u0026thinsp;\u0026plusmn;\u0026thinsp;0.033\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.18\u0026thinsp;\u0026plusmn;\u0026thinsp;0.074\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.21\u0026thinsp;\u0026plusmn;\u0026thinsp;0.101\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.22\u0026thinsp;\u0026plusmn;\u0026thinsp;0.106\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eBF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.351\u0026thinsp;\u0026plusmn;\u0026thinsp;0.102\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.031\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.05\u0026thinsp;\u0026plusmn;\u0026thinsp;0.035\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.396\u0026thinsp;\u0026plusmn;\u0026thinsp;0.139\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.49\u0026thinsp;\u0026plusmn;\u0026thinsp;0.226\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.59\u0026thinsp;\u0026plusmn;\u0026thinsp;0.275\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.287\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.106\u0026thinsp;\u0026plusmn;\u0026thinsp;0.091\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2.26\u0026thinsp;\u0026plusmn;\u0026thinsp;1.25\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e2.4\u0026thinsp;\u0026plusmn;\u0026thinsp;1.35\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e2.53\u0026thinsp;\u0026plusmn;\u0026thinsp;1.48\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.223\u0026thinsp;\u0026plusmn;\u0026thinsp;0.031\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.266\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.343\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.69\u0026thinsp;\u0026plusmn;\u0026thinsp;0.335\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eTF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.195\u0026thinsp;\u0026plusmn;\u0026thinsp;0.088\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.24\u0026thinsp;\u0026plusmn;\u0026thinsp;0.39\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.33\u0026thinsp;\u0026plusmn;\u0026thinsp;0.541\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1.36\u0026thinsp;\u0026plusmn;\u0026thinsp;0.586\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_0\u0026deg;\u003c/em\u003e \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.027\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e3.43\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_15\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.016\u0026thinsp;\u0026plusmn;\u0026thinsp;0.003\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2.98\u0026thinsp;\u0026plusmn;\u0026thinsp;0.532\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e3.84\u0026thinsp;\u0026plusmn;\u0026thinsp;0.515\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e5.19\u0026thinsp;\u0026plusmn;\u0026thinsp;1.28\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_30\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.014\u0026thinsp;\u0026plusmn;\u0026thinsp;0.016\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e3.38\u0026thinsp;\u0026plusmn;\u0026thinsp;1.14\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e3.87\u0026thinsp;\u0026plusmn;\u0026thinsp;1.31\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e5.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.528\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVF_45\u0026deg;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.027\u0026thinsp;\u0026plusmn;\u0026thinsp;0.007\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2.16\u0026thinsp;\u0026plusmn;\u0026thinsp;0.281\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e2.67\u0026thinsp;\u0026plusmn;\u0026thinsp;0.856\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e2.92\u0026thinsp;\u0026plusmn;\u0026thinsp;1.13\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ea\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eobtained and described in Rocha et al.\u003c/em\u003e [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor inclined fibers, as shown in the Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the matrix wedge on the pullout surface exerts a normal force N to allow the axial force on the fiber to change its direction [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], in other words, the friction generated at the fiber exit mitigate the stress existing in the embedded part and the creep can be basically attributed to the creep of the free length. However, when these fibers are arranged at 0\u0026deg;, only a direct pull is applied, with no bending. Therefore, the results demonstrate that fibers arranged at 0\u0026deg; are more likely to be pulled out under a long-term load than inclined fibers, since a good part of the embedded fiber also suffers creep, along with the interface. This behavior was also observed by Abrishambaf et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], but for steel fibers. According to the creep coefficient graphs in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, as the inclined angle increases, a lower creep rate is experienced due to the reduction in the creep portions relating to fiber creep in the embedded length and interface creep. When θ\u0026thinsp;=\u0026thinsp;45\u0026deg;, for all fibers, it can be believed that the existing creep is basically the creep of the fiber itself. As the creep of the fiber is the primary deformation mechanism of composites reinforced with synthetic macro fibers under sustained load [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], available through pullout tests with straight fibers to lead to greater deformations over time.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAll the samples exhibited an instantaneous initial displacement (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }_{inst}\\)\u003c/span\u003e\u003c/span\u003e) as soon as the load was applied due to the elongation of the fiber along the free length [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] and initial pullout. This initial displacement seems dependent on the type and properties of the fiber [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] in addition to the applied load. Because the applied loads are different for each angle, the most interesting comparison of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\delta }_{inst}\\)\u003c/span\u003e\u003c/span\u003e would be through the initial stiffness given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(K=\\raisebox{1ex}{${\\delta }_{inst}$}\\!\\left/ \\!\\raisebox{-1ex}{$P$}\\right.\\)\u003c/span\u003e\u003c/span\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e-a). For \u003cem\u003eBF\u003c/em\u003e fibers, a pattern can be observed with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(K\\)\u003c/span\u003e\u003c/span\u003e increasing with angle, possibly resulting from its greater bending stiffness. A different response was observed for \u003cem\u003eTF\u003c/em\u003e and \u003cem\u003eVF\u003c/em\u003e fibers, which experienced an initial reduction of stiffness with θ, followed by an increase for θ\u0026thinsp;=\u0026thinsp;30\u0026deg; and 45\u0026deg;.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor \u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e fibers, the creep coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(\\phi }_{creep }\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e) increases over time for all the analyzed angles, although at a decreasing rate. Incidentally, \u003cem\u003eBF\u003c/em\u003e fibers (15\u0026deg;, 30\u0026deg;, and 45\u0026deg;) exhibit almost no difference between the 7- and 10-day tests, appearing to have reached the slip limit. In \u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e fibers, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\phi }_{creep }\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e decreases as the angle θ increases, as show in the Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e - b. \u003cem\u003eBF\u003c/em\u003e fibers exhibit a significant increase in slippage over time when the fibers are aligned with the direction of the load, i.e., θ\u0026thinsp;=\u0026thinsp;0\u0026deg;. This is justified by the fact that inclined fibers basically have the creep resulting from the creep of the fiber in the free length and aligned fibers have other slip components over time, as already explained and shown in the Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. As for \u003cem\u003eTF\u003c/em\u003e fibers, this significant difference is only noticed when the angle is 45\u0026deg;.\u003c/p\u003e \u003cp\u003e \u003cem\u003eVF\u003c/em\u003e fibers presented a low instantaneous initial displacement for all the angles investigated, although with a significantly higher creep growth rate than those of the other fibers, indicating that the slip continues to increase over time, justified by their smooth surfaces, which offer a lower pullout resistance than those of other fibers that have a superficial corrugation. Importantly, in the 10-day test, the creep coefficient is higher than in the 7-day test, indicating that the pullout is progressing. This shows that these fibers are so easily deformable that the deflection components caused by the change of direction at small inclination angles do not offer great resistance to slipping over time, to the point that the only significant creep is attributed to creep in the fiber itself, except for angles greater than 45\u0026deg;. Only one of the \u003cem\u003eVF\u003c/em\u003e_0\u0026deg; fiber samples remained intact during the 10-day test, with all the others ruptured in less than 48 h, as explained in Rocha et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs the change in fiber inclination plays an important role, evaluation of viscoelastic behavior over time is performed by applying a four-parameter rheological Burgers model. The original equation correlates strain, stress and time, which will be replaced by pullout displacement, apparent bond stress and time as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\delta \\left(t\\right)=\\frac{{\\tau }_{0}}{{R}_{1}}+\\frac{{\\tau }_{0}}{{R}_{2}}\\left(1-exp\\left(\\frac{-{R}_{2}t}{{\\eta }_{2}}\\right)\\right)+\\frac{{\\tau }_{0}}{{\\eta }_{1}}t$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta \\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e is the pullout displacement at a given time \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\tau }_{0}\\)\u003c/span\u003e\u003c/span\u003e is the bond stress, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{1}\\)\u003c/span\u003e\u003c/span\u003e is the instantaneous elastic stiffness of the Maxwell unit, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{2}\\)\u003c/span\u003e\u003c/span\u003e is the elastic stiffness of the Kelvin\u0026ndash;Voigt model representing the contribution of the retarded elastic region, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{1}\\)\u003c/span\u003e\u003c/span\u003e is the dashpot of the Maxwell element that represents the residual viscosity, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{2}\\)\u003c/span\u003e\u003c/span\u003e is the dashpot related to Kelvin\u0026ndash;Voigt model that represents the internal viscosity.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the model parameters for all angles and fiber evaluated, which were obtained through regression of the mean experimental pullout curves under sustained load. The correlation coefficient R\u0026sup2; is also reported for each analysis in order to prove the fit to the experimental curves. A comparison of the experimental curves and models for the three types of fibers and all the inclination angles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBurgers model parameters for the three fibers and all their inclinations.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eFiber type\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eLoading level\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003eBurgers model parameters\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eR\u0026sup2;\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(MPa/mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(MPa/mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(MPa.s/mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e(MPa.s/mm)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eBF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u0026deg; \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.37 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.59 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.12 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.45 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.18 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.32 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.36 x 10\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23 x 10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eTF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u0026deg; \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.53 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.96 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e11.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e18.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.19 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.04 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.59 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.91 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e57.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.81 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.43 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eVF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u0026deg; \u003csup\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.16 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.35 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.55 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.47 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.48 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.25 x 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.19 x 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003csup\u003e \u003cem\u003ea\u003c/em\u003e \u003c/sup\u003e \u003cem\u003eobtained and described in Rocha et al.\u003c/em\u003e [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA correlation coefficient greater than 0.75 was obtained for all angles of inclination, demonstrating a good fit for the model. The bond stiffness, represented by the parameter R\u003csub\u003e1\u003c/sub\u003e, seemed to decrease as the angle increased for \u003cem\u003eBF\u003c/em\u003e fibers (41.6% for 15\u0026deg;, 50.8% for 30\u0026deg;, and 70% for 45\u0026deg;) but increased for \u003cem\u003eTF\u003c/em\u003e (259% for 15\u0026deg;, 30% for 30\u0026deg;, and 74% for 45\u0026deg;) and \u003cem\u003eVF\u003c/em\u003e fibers (63.8% for 15\u0026deg;, 128.8% for 30\u0026deg;, and 1.8% for 45\u0026deg;). As the \u003cem\u003eBF\u003c/em\u003e fiber has a slightly higher modulus of elasticity than the others, this reduction in stiffness may have been caused by the lateral bending of the fiber. Conversely, for \u003cem\u003eVF\u003c/em\u003e fibers, the stiffening may have been promoted by the straightening process during the pullout.\u003c/p\u003e \u003cp\u003eIn the case of the \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e parameter, which represents the secondary creep rate, an increase in θ generated higher values of \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e in all fibers, indicating a reduction in slip over time. As already discussed, the alignment of the fibers can favor the progression of the pullout.\u003c/p\u003e \u003cp\u003eThe parameter \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e regulates the speed with which the curve enters the secondary creep stage, i.e., the smaller the \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, the faster the curve enters the secondary stage. For \u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e fibers, an increase in \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e was observed from 0\u0026deg; to 15\u0026deg; and then a decrease for angles of 30\u0026deg; and 45\u0026deg;. The interspersing of \u003cem\u003eVF\u003c/em\u003e fibers increases with reductions. Generally, longer periods of primary creep were observed for all angles compared with their fibers at 0\u0026deg;, except for \u003cem\u003eBF\u003c/em\u003e fibers at 45\u0026deg;.\u003c/p\u003e \u003cp\u003eGiven the good fit of the curves to the Burger model, equations were proposed that represent each of its parameters (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\eta }}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\eta }}_{2}\\)\u003c/span\u003e\u003c/span\u003e) as a function of the angle θ for each fiber studied, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The functions are 2nd degree polynomials (with the exception of the coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\eta }}_{1}\\)\u003c/span\u003e\u003c/span\u003e for the \u003cem\u003eTF\u003c/em\u003e fiber which were better adjusted to 3rd degree polynomials) and allow you to define the parameters for any inclination angle between 0\u0026deg; and 45\u0026deg;. The vast majority of equations presented an excellent fit and can be used to feed numerical models to predict the long-term behavior of these composites.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eApproximating equations of the parameters of the Burgers model as a function of the angle θ (for 0\u0026thinsp;\u0026lt;\u0026thinsp;θ\u0026thinsp;\u0026lt;\u0026thinsp;45\u0026deg;, θ in degrees) and the coefficient of correlation R\u0026sup2;.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eFiber type\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eEquations\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eR\u0026sup2;\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eBF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{1}\\left(\\theta \\right)=0.003{\\theta }^{2}-0.338\\theta +12.8 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.966\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{2}\\left(\\theta \\right)=-0.026{\\theta }^{2}+1.81\\theta +22.7 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{1}\\left(\\theta \\right)=-3801{\\theta }^{2}+3\\times {10}^{6}\\theta +3\\times {10}^{7} (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.981\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{2}\\left(\\theta \\right)=-4329.6{\\theta }^{2}+177078\\theta +835168 (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eTF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{1}\\left(\\theta \\right)=0.001{\\theta }^{3}-0.087{\\theta }^{2}+1.58\\theta +3.07 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{2}\\left(\\theta \\right)=0.041{\\theta }^{2}-0.936\\theta +14.3 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.865\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{1}\\left(\\theta \\right)=7941.8{\\theta }^{3}-518667{\\theta }^{2}+8x{10}^{6}\\theta +2\\times {10}^{7} (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{2}\\left(\\theta \\right)=4667.1{\\theta }^{2}-114934\\theta + 874844 (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.904\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eVF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{1}\\left(\\theta \\right)=-0.017{\\theta }^{2}+0.801\\theta +7.23 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.833\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{2}\\left(\\theta \\right)=0.009{\\theta }^{2}-0.687\\theta +20.3 (MPa/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.987\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{1}\\left(\\theta \\right)=5182.7{\\theta }^{2}-6391.8\\theta +2\\times {10}^{6} (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.998\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{2}\\left(\\theta \\right)=1059.1{\\theta }^{2}-25755\\theta +168879 (MPa.s/mm)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.971\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eShort- and long-term pullout tests were performed with angles of 15\u0026deg;, 20\u0026deg;, 30\u0026deg;, and 45\u0026deg; with respect to the direction of the load to investigate the influence of macro synthetic fibers orientation on fiber\u0026ndash;matrix interactions. The following conclusions were drawn:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe embedded lengths were greater in the samples with inclined fibers. In the short-term tests, a comparison in terms of shear stress instead of the maximum pullout load revealed that in none of the fibers did the bonding stress exceed that experienced when the fibers were aligned with the direction of the load, even with minimal variation, especially for angles of approximately 30\u0026deg;.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSignificant fiber surface degradation was observed as the angle of inclination was increased. In the specific case of twisted fibers (\u003cem\u003eVF\u003c/em\u003e), they were practically aligned after the pullout. The tortuosity of the path in the pulling tunnel seems to have been responsible for this alignment, in addition to the increased slope of the tension versus slip curve for these fibers, considering the substantial challenge in pulling them out, when compared with the aligned samples.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eStraight fibers and those with superficial corrugation (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e) exhibited greater adherence to the matrix. Moreover, in the case of inclined samples, a greater probability of fiber rupture was observed. This behavior was attributed to their corrugated surfaces, which favored matrix bonds and induced even greater localized stresses than those due to the snubbing effect at the exit point, promoting an exacerbated degradation of the fiber and thus resulting in the rupture of some samples. This rupture was observed in all \u003cem\u003eTF\u003c/em\u003e fibers inclined at 45\u0026deg;. Minimal fragmentation of the matrix was observed, possibly due to the low stiffness of the fiber compared with that of the matrix.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFor straight fibers (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e) the creep coefficient was reduced with an increase in the fiber inclination angle. Furthermore, an almost zero growth rate was obtained for the 10-day test compared with the 7-day test, indicating no further slippage. However, \u003cem\u003eVF\u003c/em\u003e fibers increasingly deformed over time, possibly owing to the lower resistance imposed by their smooth surface.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe creep reduction with an increase in the fiber inclination angle could be explained by the snubbing effect that induced force components to promote axial force deviation, in addition to the reduction of fiber creep, which under inclined loading, reduced its capacity to deform. Given this, the greater the inclination angle, the lower the creep rate will be, as the portions relating to the fiber creep in the embedded length and the interface creep are severely reduced, leaving basically the fiber creep in the free length.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIn long-term pullout tests, fibers with surface corrugation (\u003cem\u003eBF\u003c/em\u003e and \u003cem\u003eTF\u003c/em\u003e) had their sliding almost ceased after 7 days, which suggests that this is a sliding limit. However, the \u003cem\u003eVF\u003c/em\u003e fibers continued to slide with a significant creep growth rate, possibly justified by their smooth surface and low adhesion to the matrix.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe Burgers model was applied to the experimental curves and resulted in a good fit for all the fibers and angles of inclination. Due to this good fit, approximate functions of the parameters were determined and these can be used to model fiber-scale cementitious composites.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgment\u003c/h2\u003e \u003cp\u003eAll testing was conducted at the Laboratory of Structures and Materials of the Pontifical Catholic University of Rio de Janeiro. The authors would like to thank PUC-Rio and CAPES for their support. This study was financed in part by the \u003cem\u003eCoordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior - Brasil\u003c/em\u003e (CAPES) - Finance Code 001 and by Brazilian funding agencies FAPERJ and CNPq. Lu\u0026iacute;s A.G. Bitencourt Jr. would also like to acknowledge the fellowship of research productivity (PQ) granted by the National Council for Scientific and Technological Development (CNPq - Proc. N: 307175/2022-7).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJ. MacKay, J.F. Trottier, Post-crack creep behavior of steel and synthetic FRC under flexural loading, in: Shotcrete: More Engineering Developments, Taylor \u0026amp; Francis Group, London, 2004: pp. 183\u0026ndash;192.\u003c/li\u003e\n\u003cli\u003eP. St\u0026auml;hli, R. Custer, J.G.M. Van Mier, On flow properties, fibre distribution, fibre orientation and flexural behavior of FRC, Materials and Structures/Materiaux et Constructions 41 (2008) 189\u0026ndash;196. https://doi.org/10.1617/s11527-007-9229-x.\u003c/li\u003e\n\u003cli\u003eV.C. Li, Y. Wang, S. Backer, Effect of inclining angle, bundling and surface treatment on synthetic fibre pull-out from a cement matrix, Composites 21 (1990) 132\u0026ndash;140.\u003c/li\u003e\n\u003cli\u003eH.-C. Wu, V.C. Li, Snubbing and Bundling Effects on Multiple Crack Spacing of Discontinuous Random Fiber-Reinforced Brittle Matrix Composites, Journal of the America Ceramic Society 75 (1992) 3487\u0026ndash;3489.\u003c/li\u003e\n\u003cli\u003eP.A. Krahl, G. de Miranda Saleme Gidr\u0026atilde;o, R.B. Neto, R. Carrazedo, Effect of curing age on pullout behavior of aligned and inclined steel fibers embedded in UHPFRC, Constr Build Mater 266 (2021). https://doi.org/10.1016/j.conbuildmat.2020.121188.\u003c/li\u003e\n\u003cli\u003eY.-S. Tai, S. El-Tawil, High loading-rate pullout behavior of inclined deformed steel fibers embedded in ultra-high performance concrete, Constr Build Mater 148 (2017) 204\u0026ndash;218.\u003c/li\u003e\n\u003cli\u003eC. Ding, L. Guo, B. Chen, Orientation distribution of polyvinyl alcohol fibers and its influence on bridging capacity and mechanical performances for high ductility cementitious composites, Constr Build Mater 247 (2020). https://doi.org/10.1016/j.conbuildmat.2020.118491.\u003c/li\u003e\n\u003cli\u003eN. To\u0026scaron;ić, S. Aidarov, A. La Fuente, Systematic Review on the Creep of Fiber-Reinforced Concrete, Materials 13 (2020). https://doi.org/10.3390/ma13225098.\u003c/li\u003e\n\u003cli\u003eA.J. Babafemi, A. du Plessis, W.P. Boshoff, Pull-out creep mechanism of synthetic macro fibres under a sustained load, Constr Build Mater 174 (2018) 466\u0026ndash;473. https://doi.org/10.1016/j.conbuildmat.2018.04.148.\u003c/li\u003e\n\u003cli\u003eR. Vrijdaghs, M. di Prisco, L. 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Silva, Creep Mechanisms in Precracked Polypropylene and Steel Fiber\u0026ndash;Reinforced Concrete, Journal of Materials in Civil Engineering 33 (2021). https://doi.org/10.1061/(asce)mt.1943-5533.0003775.\u003c/li\u003e\n\u003cli\u003eF.R. Souza, V.N. Lima, D.C.T. Cardoso, F.A. Silva, Experimental Study of Polyvinyl Alcohol (PVA) Fiber Reinforced Concrete under Cyclic Loading, in: CILAMCE-PANACM-2021 Proceedings of the XLII Ibero-Latin-American Congress on Computational Methods in Engineering and III Pan-American Congress on Computational Mechanics, ABMEC-IACM, 2021.\u003c/li\u003e\n\u003cli\u003eABNT (Associa\u0026ccedil;\u0026atilde;o de Normas T\u0026eacute;cnicas), Agregados - Determina\u0026ccedil;\u0026atilde;o da composi\u0026ccedil;\u0026atilde;o granulom\u0026eacute;trica - M\u0026eacute;todo de ensaio. NBR 17054, Brazil, 2022.\u003c/li\u003e\n\u003cli\u003eASTM C136-01, Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates 1, West Conshohocken, PA: ASTM., 2017. www.astm.org,.\u003c/li\u003e\n\u003cli\u003eT. da S. Rocha, D.C.T. Cardoso, L.A.G. Bitencourt, Macro synthetic fiber pullout behavior in short- and long-term tests, Constr Build Mater 384 (2023). https://doi.org/10.1016/j.conbuildmat.2023.131491.\u003c/li\u003e\n\u003cli\u003eABNT (Associa\u0026ccedil;\u0026atilde;o Brasileira de Normas T\u0026eacute;cnicas), Concreto - Determina\u0026ccedil;\u0026atilde;o da consist\u0026ecirc;ncia pelo abatimento do tronco de cone - NBR 16889, S\u0026atilde;o Paulo, SP, 2020.\u003c/li\u003e\n\u003cli\u003eASTM C143/C143M-12, Standard Test Method for Slump of Hydraulic-Cement Concrete, West Conshohocken, PA, 2015.\u003c/li\u003e\n\u003cli\u003eABNT (Associa\u0026ccedil;\u0026atilde;o Brasileira de Normas T\u0026eacute;cnicas), Cimento Portland - Determina\u0026ccedil;\u0026atilde;o da resist\u0026ecirc;ncia \u0026agrave; compress\u0026atilde;o de corpos de prova cil\u0026iacute;ndricos - NBR 7215, Brazil, 2019.\u003c/li\u003e\n\u003cli\u003eASTM C39/C39M-01, Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens, United States, 2021.\u003c/li\u003e\n\u003cli\u003eABNT (Associa\u0026ccedil;\u0026atilde;o Brasileira de Normas T\u0026eacute;cnicas), Concreto endurecido - Determina\u0026ccedil;\u0026atilde;o dos m\u0026oacute;dulos de elasticidade e de deforma\u0026ccedil;\u0026atilde;o - Parte 1: M\u0026oacute;dulos est\u0026aacute;ticos \u0026agrave; compress\u0026atilde;o - NBR 8522-1, Brazil, 2021.\u003c/li\u003e\n\u003cli\u003eEuropean Standard (EN), Testing hardened concrete Determination of secant modulus of elasticity in compression - BS EN 12390 - 13, United Kingdom, 2021.\u003c/li\u003e\n\u003cli\u003eElasto Plastic Concrete\u0026reg;, BarChip 54 \u0026ndash; Concrete Fibre Reinforcement. Product data sheet, 2021.\u003c/li\u003e\n\u003cli\u003eNormet Construction Chemicals, TamFib SP54 \u0026ndash; Structural Polymer Macro Fibres for Reinforcing Concrete. Technical Data sheet, 2018.\u003c/li\u003e\n\u003cli\u003eViapol, TUF Strand SF. Technical Data sheet, 2020.\u003c/li\u003e\n\u003cli\u003eA. Bentur, S. Mindess, Fibre reinforced cementitious composites, Second, Taylor \u0026amp; Francis, Milton Park, UK, 2007.\u003c/li\u003e\n\u003cli\u003eZ. Lin, V.C. Li, Crack bridging in fiber reinforced cementitious composites with slip-hardening interfaces, J. Mech. Phys. Solids 45 (1997) 763\u0026ndash;787.\u003c/li\u003e\n\u003cli\u003eP. Robins, S. Austin, P. Jones, Pull-out behavior of hooked steel fibres, Materials and Structures/Materiaux et Constructions 35 (2002) 434\u0026ndash;442.\u003c/li\u003e\n\u003cli\u003eT. Kanda, V.C. Li, Interface property and apparent strength of high-strength hydrophilic fiber in cement matrix, J. Mater. Civ. Eng 10 (1998) 5\u0026ndash;13.\u003c/li\u003e\n\u003cli\u003eF. Deng, C. Cao, L. Xu, Y. Chi, Interfacial bond characteristics of polypropylene fiber in steel/polypropylene blended fiber reinforced cementitious composite, Constr Build Mater 341 (2022) 127897.\u003c/li\u003e\n\u003cli\u003eP. Di Maida, E. Radi, C. Sciancalepore, F. Bondioli, Pullout behavior of polypropylene macro-synthetic fibers treated with nano-silica, Constr Build Mater 82 (2015) 39\u0026ndash;44. https://doi.org/10.1016/j.conbuildmat.2015.02.047.\u003c/li\u003e\n\u003cli\u003eY. Lee, S.T. Kang, J.K. Kim, Pullout behavior of inclined steel fiber in an ultra-high strength cementitious matrix, Constr Build Mater 24 (2010) 2030\u0026ndash;2041. https://doi.org/10.1016/j.conbuildmat.2010.03.009.\u003c/li\u003e\n\u003cli\u003eY.Y.Y. Cao, Q.L. Yu, Effect of inclination angle on hooked end steel fiber pullout behavior in ultra-high performance concrete, Compos Struct 201 (2018) 151\u0026ndash;160. https://d0i.0rg/l0.1016/j.compstruct.2018.06.029.\u003c/li\u003e\n\u003cli\u003eR. Zhang, X. Yan, L. Guo, Pullout damage analysis of steel fiber with various inclination angles and interface states in UHPC through acoustic emission and microscopic observation, Journal of Building Engineering 51 (2022). https://doi.org/10.1016/jjobe.2022.104271.\u003c/li\u003e\n\u003cli\u003eA. Abrishambaf, J.A.O. Barros, V.M.C.F. Cunha, C. Fraz\u0026atilde;o, Time dependent behavior of fibre pull-out in self-compacting concrete, Cem Concr Compos 77 (2017) 14\u0026ndash;28. https://doi.org/10.1016/j.cemconcomp.2016.12.004.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"materials-and-structures","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"maas","sideBox":"Learn more about [Materials and Structures](http://link.springer.com/journal/11527)","snPcode":"11527","submissionUrl":"https://www.editorialmanager.com/maas/default2.aspx","title":"Materials and Structures","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"fiber orientation, cement composites, macro synthetic fiber, pullout, creep","lastPublishedDoi":"10.21203/rs.3.rs-4261406/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4261406/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSynthetic fibers deforming over time can be a concern in structural design, particularly in serviceability limit states. Short-term pullout tests are commonly used to predict fiber\u0026ndash;matrix interactions, but even in this case, an individualized evaluation of the pullout behavior of single fibers oriented parallel to the load direction may not be sufficient to predict the efficiency of the composite. In the present work, short- and long-term pullout tests were performed with fibers oriented at angles of 15\u0026deg;, 30\u0026deg;, and 45\u0026deg; with respect to the direction of the load to investigate the influence of macro synthetic fibers orientation on fiber\u0026ndash;matrix interactions. In short-term tests, optical microscopy images were obtained on the pulled-out fibers to correlate the surface degradation of the fibers with the stress versus strain curves. In quasi-static pullout (short-term), small reductions in pullout strength were observed for all fibers and angles, in addition to an intensive degradation of their surfaces owing to the significant snubbing effect of this type of fiber. In contrast, for the long-term tests, a creep reduction was observed with increasing fiber inclination angle caused by the creep reduction of the fiber due to non-axial loading and additional force components produced by the deviation of the axial force. The parameters of Burgers rheological model were written as a function of the fiber orientation angle, with excellent adjustment to the experimental data.\u003c/p\u003e","manuscriptTitle":"Influence of fiber orientation on the behavior of macro synthetic fiber in short- and long-term pullout tests","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-29 14:41:17","doi":"10.21203/rs.3.rs-4261406/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revisions","date":"2024-06-26T17:57:08+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-04-23T06:03:55+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-21T22:27:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-16T18:41:37+00:00","index":"","fulltext":""},{"type":"submitted","content":"Materials and Structures","date":"2024-04-13T06:14:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"materials-and-structures","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"maas","sideBox":"Learn more about [Materials and Structures](http://link.springer.com/journal/11527)","snPcode":"11527","submissionUrl":"https://www.editorialmanager.com/maas/default2.aspx","title":"Materials and Structures","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f486b88d-da34-47f1-8a30-148dac91bd40","owner":[],"postedDate":"April 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-09-09T16:15:00+00:00","versionOfRecord":{"articleIdentity":"rs-4261406","link":"https://doi.org/10.1617/s11527-024-02447-2","journal":{"identity":"materials-and-structures","isVorOnly":false,"title":"Materials and Structures"},"publishedOn":"2024-09-04 16:05:45","publishedOnDateReadable":"September 4th, 2024"},"versionCreatedAt":"2024-04-29 14:41:17","video":"","vorDoi":"10.1617/s11527-024-02447-2","vorDoiUrl":"https://doi.org/10.1617/s11527-024-02447-2","workflowStages":[]},"version":"v1","identity":"rs-4261406","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4261406","identity":"rs-4261406","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}