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Author's personal copy Materials Science and Engineering A 527 (2010) 544–552

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High speed tensile behavior of sisal fiber cement composites Flávio de Andrade Silva a , Deju Zhu b , Barzin Mobasher b,∗ , Chote Soranakom b , Romildo Dias Toledo Filho c a

Institute of Construction Materials, TU Dresden, 01062 Dresden, Germany Department of Civil and Environmental Engineering, Arizona State University, Tempe, AZ 85287-8706, United States c Civil Engineering Department, COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68506, CEP 21941-972, Rio de Janeiro, RJ, Brazil b

a r t i c l e

i n f o

Article history: Received 8 July 2009 Received in revised form 6 August 2009 Accepted 7 August 2009

Keywords: Sisal fiber High strain rate Image analysis Tensile strength Strain capacity

a b s t r a c t The experimental behavior of sisal fiber reinforced cement composites subjected to high speed tension load was studied. High strain rates were achieved by using a high rate servo-hydraulic testing machine. A state-of-the-art high speed Phantom camera was also used to take images from the specimen during the test. The images were used in a digital image correlation model to determine the displacement fields and to calculate crack spacing. The effect of strain rate was investigated by comparing static and dynamic tensile tests which were performed at strain rates ranging from 5.5 × 10−6 to 24.6 s−1 , respectively. A numerical tension stiffening model based on nonlinear finite difference method was used to simulate tensile cracking behavior of sisal fiber cementitious composites. The composite presented strain rate sensitivity for ultimate tensile strength and strain capacity with a dynamic amplification factor of 1.26. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Long aligned sisal fiber reinforced cement composites are a new class of sustainable construction materials with superior tensile strength and ductility. This composite system presents a strain hardening behavior with enhanced strength and ductility that is primarily governed by the composite action that exists such that the fibers bridge the matrix cracks and transfer the loads, allowing a distributed microcrack system to develop [1]. These materials are strong enough to be used as load bearing structural members in applications such as structural panels, impact & blast resistance, repair and retrofit, earthquake remediation, strengthening of unreinforced masonry walls, and beam-column connections. Thus, the response to impulse loading, for applications in extreme loading conditions, becomes of great importance. There are very few test methods for the cement based materials subjected to high strain rates. The Society of Automotive Engineers (SAE) coordinated development of a set of standards and practice guidelines for dynamic tensile testing at medium strain rates [2,3]. The International Iron and Steel Institute (IISI) formed a consortium to develop a high strain rate tensile test standard for sheet steel [4], and European researchers have been working on an ISO standard [5]. The SAE [3] and IISI [4] projects provided details on the relations between

∗ Corresponding author. Tel.: +1 480 965 0141; fax: +1 480 965 0557. E-mail address: [email protected] (B. Mobasher). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.08.013

specimen size and wave propagation, inertia effect, strain measurement technique, loading devices, and measurement, system ringing, gripping devices, and clamping mechanism. The dynamic tensile response of any material is a difficult experiment to perform with only a few published results for cement based materials. Most of the available literature on the dynamic tensile behavior of concrete are based on investigations of plain concrete which exhibits an increase in tensile strength for increasing strain rates [6–12]. For example, Xiao et al. [6] reported that compared to the quasi-static tensile strength of concrete (strain rate of 10−5 s−1 ), the dynamic tensile strengths at strain rates of 10−4 , 10−3 and 10−2 s−1 increase by 6%, 10% and 18%, respectively. Birkimer and Lindemann [7] reported that the dynamic strength measured at a strain rate of 20 s−1 was between 17.2 and 22.1 MPa, while the static tensile strength was 3.4 MPa at the quasi-static strain rate of 0.57 × 10−6 s−1 . Dynamic tensile data on fiber reinforced concrete is even more limited. Kim et al. [13] investigated the strain rate effect on the tensile behavior of high performance fiber reinforced cement composites (HPFRCC) using two deformed high strength steel fibers, namely hooked fibers and twisted (Torex) fibers. The strain rate ranged from pseudo static (strain rate of 0.0001 s−1 ) to seismic (strain rate of 0.1 s−1 ). The results showed that the tensile behavior of HPFRCC with twisted fibers is sensitive to the strain rate, while hooked fiber reinforced specimens show no rate sensitivity. It was also observed that lower fiber volume fraction (Vf = 1%) reinforced specimens show higher sensitivity than higher volume fractions

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(Vf = 2%). Maalej et al. [14] performed dynamic tensile tests in engineered cement composites (ECC) containing 0.5% steel and 1.5% polyethylene fibers (in volume). The applied strain rate ranged from 2 × 10−6 to 2 × 10−1 s−1 . Results indicate a substantial increase in the ultimate tensile strength from 3.1 to 6 MPa with increasing strain rate. The strain capacity does not appear to be affected by the strain rate. In the present work, a new sustainable material, namely long aligned sisal fiber reinforced composite was characterized under high speed direct tension test conducted with a servo-hydraulic testing machine. The test machine can operate in closed-loop and opened-loop at a maximum speed of 14 m/s with a load capacity of 20 kN. The speed of the actuator is controlled by the level of opening of the servo-valve delivering hydraulic supply. Therefore the rate of flow of hydraulic fluid controls the actuator speed. The effect of strain rate was investigated by comparing static and dynamic tensile tests conducted at strain rates of 5.5 × 10−6 and 24.6 s−1 , respectively. A state-of-the art high speed Phantom camera was used to record specimen deformation during high speed tests. The crack pattern and failure behavior of the composites were captured at a sampling rate of 10,000 fps (frames per second). The images were used in a digital image correlation model previously developed in MATLAB code [15] to determine the displacement fields and calculate the crack spacing as a function of strain. Failure behavior and cracking pattern were also observed using the images. A numerical tension stiffening model based on nonlinear finite difference method developed by Soranakom [16] was used to simulate tensile cracking and stress–strain behavior of sisal fiber reinforced composite under dynamic and static loads. For this purpose two different interface models were used, one to simulate the dynamic and the other the static load. 2. High speed tensile test methodology 2.1. Dynamic tensile test procedure The setup of the dynamic tensile testing is presented in Fig. 1. Once the test starts, the actuator accelerates to reach the specified speed and then maintains that rate. During this range of motion, the slack adaptor engages and transfers the force to the specimen. The slack adaptor consists of a sliding bar with a conical end that travels within a hollow tube. It travels freely with the actuator at the specified velocity before making contact with the cone-shaped

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surface of the sliding bar. This eliminates the inertia effect of the lower grip and actuator during the acceleration stage. However, the sudden engagement with the upper portion of the setup generates a high amplitude stress waves, causing oscillations at the system’s natural frequency, i.e. system ringing [17]. To reduce the inertia effect, lightweight grips made of stainless steel and weighing approximately 1500 g, as shown in Fig. 2 were used. Specimens were installed between two steel wedges with serrated faces. Piezoelectric load washers are recommended for dynamic tests [18] because conventional load cell has a much lower response frequency. In this work, the load was measured by a Kistler 9041A piezoelectric force link (load washer) with a capacity of 90 kN and rigidity of 7.5 kN/␮m and a frequency response of 33 kHz. The load signal was amplified through a Kistler 5010B dual mode charge amplifier. A high speed digitizer was used to record the force from the piezoelectric force link, and the response of the LVDT of actuator which measured the deformation of the specimen. A data acquisition system operated at a maximum rate of 5 Ms/s. 2.2. Data processing Processing of dynamic data is more cumbersome than the static tests. The signals from load washer and LVDT of actuator were recorded at sampling rate of 250 kHz. The high frequency noise was filtered using a low-pass filter with cut-off frequency of 3 kHz. In addition, a Phantom v.7 high speed digital camera with sampling rate of 10,000 fps was used to capture the image of the specimen in between the grips to measure the crack spacing and failure behavior of different composites. Six specimens were tested with geometry of 152.4 mm × 25.4 mm × 12 mm (length × width × thickness) under high speed testing. A gage length of 50.8 mm was used and the strain rate was 24.6 s−1 . Parameters measured from the experimental data include the stress–strain curves, Young’s modulus, tensile strength (peak stress), ultimate strain and toughness. Toughness is evaluated using the total area under the stress–strain curve. The reported results reflected the average and standard deviation values of each tested set. Tensile stress–strain curves of specimens tested under static and dynamic conditions were compared. An example of the recorded responses generated by the servohydraulic high rate testing setup is given in Fig. 3. The figure presents the recorded force, displacement of stroke and its corre-

Fig. 1. (a) Schematic diagram of the test set-up for high speed tensile testing. (b) Detail of the grip which can fit different specimen thicknesses by changing the internal wedge grips and (c) the sample in place before the dynamic test.

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Fig. 2. Dynamic test set-up and sample before (a) and after (b) the test.

sponding velocity vs. the time history of the entire test, of cement composite reinforced with sisal fibers. The test duration was less than 20 ms within a nearly constant actuator velocity of 1180 mm/s as shown by the linear fit of the displacement–time prior to imposition of the load (Fig. 3). 3. Materials and processing To produce durable natural fiber composites, the cementitious matrix consisted of 50% Portland cement, 30% metakaolin (MK) and 20% calcined waste crushed clay brick (CWCCB) following previous works [19]. The matrix was produced using the Portland cement CPII F-32 defined by the Brazilian standard [20] as composed with filler (in mass: 85% < clinker < 91%; 3% < gypsum < 5%; 6% < filler < 10%) with a 28 days compressive strength of 32 MPa. The metakaolin (MK) was obtained from Metacaulim do Brasil Industria e Comércio LTDA, and calcined waste crushed clay brick (CWCCB) from an industry located in Itaborai—RJ, Brazil, calcined at 850 ◦ C. River sand with maximum diameter of 1.18 mm and density of 2.67 g/cm3 and a naphthalene superplasticizer Fosroc Reax Conplast SP 430 with content of solids of 44% were used. The mortar matrix used had a mix design of 1:1:0.4 (cementitious material:sand:water by weight). Wollastonite fiber (JG class,

Fig. 3. Force history, displacement history of actuator, and its corresponding velocity history curves at nominal velocity of 1180 mm/s, generated by the servohydraulic high rate testing setup.

CaSiO3), obtained from Energyarc, with an average equivalent diameter of 40 ␮m and an aspect ratio of 15 was used as a microreinforcement in the composite production (Vf = 5%). Wollastonite is a naturally occurring white, non-metallic mineral with an acicular morphology. The sisal fibers were characterized to have an irregular crosssection with mean area ranging from 0.04 to 0.05 mm2 and a mean density, elastic modulus, and tensile strength of 0.9 g/cm3 , 19 GPa and 400 MPa, respectively [21]. These fibers were extracted from a sisal farm located in the city of Valente, state of Bahia, Brazil. More information on the sisal fibers mechanical properties and its morphology can be obtained elsewhere [21,22]. The matrix was produced using a bench-mounted mechanical mixer of 20 L capacity. The cementitious materials were homogenized by dry mixing for 30 s prior to addition of sand and 5% by volume of wollastonite. The dry ingredients were mixed for an additional 30 s prior to addition of superplasticizer and water. The mixture was blended for 3 min. For the production of the laminates, the mortar mix was placed in a steel mold, one layer at a time, followed by single layers of long unidirectional aligned fibers (up to 5 layers). The samples were consolidated using a vibrating table operated at a frequency of 65 Hz, resulting in a sisal fiber volume fraction of 10%. After casting the composites were compressed at 3 MPa for 5 min. The specimens were covered in their molds for

Fig. 4. (a) Experimental tensile static stress–strain behavior of the sisal fiber cement composite (50.8 mm gage length) and (b) a tested sample showing only three cracks. Both tensile and shear cracks can be observed.

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24 h prior to moist curing for 28 days in a cure chamber with 100% RH and 23 ± 1 ◦ C. 4. Static test Direct tensile tests were performed in an electromechanical Instron universal testing machine model 4411 with a load cell of 1000 lbs (4.44 kN). The tests were controlled by the cross-head displacement at a rate of 0.016 mm/min (strain rate of 5.5 × 10−6 s−1 ). Four specimens measuring 152.4 mm × 25.4 mm × 12 mm (length × width × thickness) were tested using a gage length of 50.8 mm with fixed–hinged boundary conditions. Aluminum thin sheets were glued on both ends of the specimen at the gripping regions. A set of mechanical grips were used. The tensile load and cross-head displacement were recorded. Images were recorded during static tests using a high resolution digital camera and a frame grabber. The composite crack spacing was measured using image analysis and correlated with the applied strain under tensile response. 5. Image analysis—digital image correlation (DIC) method White light illumination was used to obtain B&W images. Random dots were marked on the surface of the composites to create a contrast in the uniform specimen face (see Fig. 1c). A procedure known as cross-correlation (also known as template matching) which relies on tracking two sequential images to estimate relative motion of surfaces imaged under different stresses was used. After obtaining the displacement vectors (u, v), results can be subjected to a gradient operation using numerical methods in order to obtain the strain field [23,24]. The above procedure developed by Mobasher et al. was implemented in a MATLAB code [15] and used in the present investigation to calculate the displacement field and strain of the composite tested under high speed tension. 6. Discussion and analysis 6.1. Static test Fig. 4 shows the static tensile behavior of the sisal fiber reinforced cement composite (gage length = 50.8 mm). The stress–strain curve can be divided in five distinct zones and labeled with roman numerals. Zone I is the linear elastic range. The modulus computed from the cross-head displacement data resulted in an average value of 0.75 GPa. This takes into account the machine and grip compliance resulting in a value that is much smaller than those obtained using strain gages. The average modulus calculated using strain gage measurements (see Fig. 5b) was 35 GPa [1]. The linear zone is terminated by initial crack formation in the matrix phase at the bending over point or BOP (reported as of BOP− from experiments) as shown in Fig. 4. After the initiation of cracks in the matrix, its load carrying capacity does not vanish as the cracks are bridged by the longitudinal fibers. The strain range within Zone II is associated with formation of matrix cracks; however, no single crack has traversed the entire specimen width. The term defined as BOP (bending over point) corresponds to a lower bound of stress level at which the linearity in stress–strain ends, and an upper bound of the first matrix crack that completely propagates across the width. As indicated in the experimental results shown in Fig. 4 the linear behavior terminates at the BOP− = 4.2–5.8 MPa. The bend over point ranges from the beginning of non-linearity at 4.8 MPa to a point where the slope decreases (BOP+ = 4.8–6.2 MPa). Zone II is therefore defined as the stable cracking range between the two stress levels of BOP− and BOP+ . The BOP values obtained for the gage length of 50.8 mm

Fig. 5. Experimental tensile static response of the sisal fiber cement composite for a gage length of 300 mm [1]. (a) Stress–strain curve and correlation of crack spacing and strain obtained from actuator LVDT, (b) stress–strain curve showing a comparison of strain gage and actuator LVDT responses, and (c) parallel tensile cracks in a total of 12 were observed.

are in the same range of those reported for a 300 mm gage length in the author’s previous work [1]. Individual values and averages are presented in Table 1. Zone III is characterized by multiple cracking formation with strain hardening. For the reduced specimen length used (50.8 mm) only 3 cracks are observed (see Fig. 4b) compared to an average of 12 cracks per specimen for the 300 mm gage length [1] (see Fig. 5c). Formation of shear cracks at ±45◦ can be seen in Fig. 4b possibly due to the reduced gage length-width ratio. Zone IV corresponds to the completion of cracking phase and initiation of debonding. As the cracking saturates, this zone is dominated by progressive interfacial damage due to crack widening, and ultimately leading to failure by fiber pullout. The average ultimate strain of the composite is 3% (measured from cross-head displacement) which shows the capacity of the sisal fibers to cause crack distribution. The average ultimate strength was 11 MPa, a value which was approximately the same for both sample lengths. An ultimate strain of 1.53% was obtained for specimens with gage length of 300 mm. The post peak strain softening behavior occurs in Zone V and is characterized by peak and total toughness values of 8.27 and 14.20 kJ/m2 , respectively. 6.2. High speed tension test A typical high speed stress–strain response of the sisal fiber reinforced composite is presented in Fig. 6. The tests were performed at a strain rate of 24.6 s−1 . The differences between the bounds of the BOP values could not be differentiated in these tests, hence only single values are reported. Using the same methodology as in the static test, the dynamic tensile curve can be divided into five zones. Zone I represents the elastic region characterized by an average dynamic modulus calculated from the actuator LVDT as 1 GPa

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Fig. 6. Experimental high speed tensile response of sisal fiber cement composite.

which is still much lower than the values measured using strain gages. Zone II is characterized by the formation of the first crack with a BOP ranging in 5.1–10.6 MPa. A higher scatter for BOP values was obtained when compared to static results. As in the static tests, Zones III and IV are marked by the formation of three cracks with a strain hardening behavior. A distinction between Zones III and IV cannot be drawn from the stress–strain curve. Nevertheless, the widening of the cracks, which occurs in Zone IV, was observed in the images. Strong strain rate dependence was noticed for ultimate strain values with an average of 10%. These results are different than the work of Yang and Li [25] who observed that in ECC, the tensile strain capacity decreased from 3% to 0.5% when the loading rate increased from quasi-static (10−5 s−1 ) to seismic strain rate (10−1 s−1 ). In contrast Maalej et al. [14] reported that the tensile strain capacity in their tests was insensitive to strain rate. Dynamic testing at high rates requires a testing system that is characterized with respect to its range of natural frequencies. System ringing is an artifact of specimen–machine interaction and has been discussed in quantitative [17] and qualitative [2,5] ways. To understand the effect of the natural frequency of the testing system in dynamic tensile testing, the vibration response of a typical tensile testing system is analyzed using a single degree of freedom spring-mass model. A tensile testing system with a slack adaptor is comparable to a dynamic system excited by an applied impulse. Consider a single-degree freedom under-damped spring-mass system, as shown and excited by impulse is given by [17] in Fig. 7. Under free vibration, the response of such an under-damped system initially at rest is x=

V

ωn



1 − 2



e−ωn t sin

1 −  2 ωn t

(1)

where V is the mass velocity at the end of impulse period, ωn = 2fn is the angular natural frequency of the system and fn is the natural frequency in Hz.  is the damping ratio of viscous c to the critical damping cc which is less than one for the under-damped system

Fig. 7. Single-degree freedom vibration model, consisting of a mass, a spring and a damper.

given by =

c cc

(2)

where, cc = 2ωn , m is the mass. If  is small and negligible, Eq. (1) can be simplified as the following which represents the response of a single-degree freedom undamped spring-mass system: x=

V sin ωn t ωn

(3)

Eq. (1) indicates that a dynamic system will oscillate at its natural frequency when excited by an impulse loading, and its amplitude is determined by the sudden change in velocity, its natural frequency and the damping ratio. Since the amplitude of the oscillation is reciprocal to the natural frequency of the dynamic system, a testing system with a higher natural frequency will produce a system ringing with lower amplitude. Modal analysis was conducted to identify the natural frequency of the testing system. The predominant frequencies are identified as 0.9, 1.4 and 1.6 kHz and damping ratio is 0.02. Quantitative calculation of the stress due to the system ringing, as it is a common issue for dynamic testing, results in the magnitude of oscillatory stress when testing different composites/materials. The theoretical response of the under-damped system with the frequency of 1.4 kHz and the actual response when testing sisal fiber reinforced composites specimen were plotted in Fig. 8a. The following method was used to extract the stress oscillation: apply a low-pass filter with a cut-off frequency of 1.6 kHz and then subtract the filtered stress values from the original values. A comparison of raw and filtered stress vs. time responses is shown in Fig. 8b. One should notice that the experimental stress oscillation caused by system ringing

Table 1 Summary of static tensile test results. Sample id

UTS (MPa)

 BOP(−) (MPa)

 BOP(+) (MPa)

Ultimate straina (mm/mm)

Max. straina (mm/mm)

Static modulusa (GPa)

Peak toughnessa (kJ/m2 )

Total toughnessa (kJ/m2 )

1s 2s 3s 4s Average (standard dev.)

10.59 9.04 13.69 10.56 11.00 (1.9)

4.43 4.66 5.79 4.19 4.96 (0.7)

6.04 5.62 6.17 5.78 5.94 (0.4)

0.026 0.020 0.033 0.027 0.03 (0.01)

0.029 0.037 0.045 0.040 0.04 (0.01)

0.77 0.72 0.81 0.69 0.75 (0.06)

7.47 3.66 12.51 9.43 8.27 (3.7)

9.08 11.76 19.57 16.40 14.20 (4.7)

a

˙ = 5.5 × 10−6 s−1 (measured from cross-head LVDT data). Strain rate (ε)

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Fig. 8. (a) Comparison of amplitude of stress oscillation between analytical model and experimental data and (b) comparison of raw and filtered stress vs. time responses.

Fig. 9. Dynamic vs. static stress–strain behavior of the sisal fiber reinforced cement composite (gage length = 50.8 mm). (a) Comparison of static and dynamic crack spacing and stress–strain and (b) fiber pullout failure mechanism under dynamic tension test.

matched model prediction with the frequency of 1.4 kHz although the magnitude of experimental stress oscillation did not decay in the same way as the model prediction. This was because the testing system vibrates with multiple frequencies and not just at 1.4 kHz. In general the presented data indicate an increase in UTS, BOP, and toughness when compared to static tests. Individual results, along with their average and standard deviation are presented in Table 2. A dynamic amplification factor (DAF), which is the ratio between dynamic response and static response (in UTS), is computed to illustrate the strain rate effect and is in the range of 1.26. A comparison of static and dynamic tension behavior is presented in Fig. 9a. The BOP levels for the dynamic tests were twice

as much as those reported for static tests. Note that in Fig. 9a the increased energy absorption capacity for the high speed tension test is mainly due to the prolonged strain softening region of the dynamic test. Both tensile and shear cracks were observed in high speed tension specimens resulting in an average of three cracks per specimen. It can be seen from the images that the composite failure is a result of crack widening leading to fiber pullout. Even at high strain levels (e.g. ε = 0.25 mm/mm) a residual strength of 2 MPa due to the interfacial fiber-matrix bond strength is observed, resulting in an enormous energy absorption capacity. Peak and total toughness values of 45.5 and 102.64 kJ/m2 are reported, respectively which are as much as 7 times higher than the static tests.

Table 2 Summary of dynamic tensile test results. Sample id

UTS (MPa)

 BOP (MPa)

Ultimate straina (mm/mm)

Max. straina (mm/mm)

Dynamic modulusa (GPa)

Peak toughnessa (kJ/m2 )

Total toughnessa (kJ/m2 )

1d 2d 3d 4d 5d 6d Average (standard dev.)

11.66 12.60 12.90 14.35 14.60 14.10 13.37 (1.2)

5.14 9.47 7.73 7.71 7.75 10.58 8.06 (1.85)

0.09 0.05 0.09 0.12 0.21 0.05 0.10 (0.06)

0.56 – 0.65 0.73 0.78 0.61 0.67 (0.09)

0.94 1.00 0.90 1.09 0.73 1.61 1.04 (0.3)

38.27 – 44.59 58.02 56.37 30.23 45.50 (11.8)

74.55 – 103.86 93.68 132.42 108.68 102.64 (21.2)

a

˙ = 24.6 s−1 (measured from actuator LVDT data). Strain rate (ε)

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Fig. 10. Comparison of individual high speed tension tests.

Fig. 10 shows a plot of all samples tested under high speed tension. It can be seen that the UTS varied from approximately 12–14 MPa and the ultimate strain (strain at UTS) ranged from 0.05 to 0.2 mm/mm. The higher data scatter in strain might be due to slippage in the grips during the high speed test. Nevertheless, the data dispersion is acceptable for dynamic tests performed on cement composites materials. 6.3. Tension stiffening model The finite difference tension stiffening model developed by Soranakom [16] was used to simulate the crack spacing and stress–strain response of the sisal fiber reinforced composites under static and dynamic loads. In this model a cracked tension specimen is idealized as a series of 1-D segments consisting of fiber, matrix, and interface elements. The matrix is treated as brittle with no strain-softening response. As the load on the composite is increased such that the cracking stress of the matrix is reached, the matrix phase cracks, and the load is solely carried by the longitudinal yarns through the interface elements. The individual pullout segments are allowed to continue carrying the load at crack locations. In nonlinear analysis, an iterative solution algorithm is used to enforce load-deformations to follow the material constitutive laws. Once the slip distributions are solved and corresponding stress and strain responses are identified, results are added to represent the overall tensile response. Two different fiber-matrix interface models were used as shown in Fig. 11. The static model has a high bond strength and low slip range while the dynamic presents elastic plastic frictional shear with a longer slip range. The material parameters were held constant for all the simulations and are described as follows: fiber modulus = 19 GPa, fiber UTS = 400 MPa, matrix modulus = 35 GPa, and young’s modulus efficiency factor of 0.6. A simulation of the dynamic test for different gage lengths was performed and the results are presented in Fig. 12. It can be seen that by reducing the gage length the ultimate strain increases but the crack spacing decreases. Therefore, the number of cracks formed during dynamic tests are the same for the different gage lengths, indicating that the frictional bond strength is not enough to transfer load from matrix to the fiber therefore there are a lower number of cracks and more pullout. The mechanism of failure is then converted to significant fiber pullout resulting in high energy

Fig. 11. Static and dynamic interface model used in the tension stiffness model.

absorption. This phenomenon is confirmed by the images obtained from the high speed camera (see Fig. 9b). Fig. 13 compares the experimental response and numerical simulation of sisal fiber reinforced composites under static and dynamic loads. The predicted crack spacing response obtained from the tension stiffness model showed a good correlation with the experimental calculation, as the model accurately predicts the final crack spacing. The predicted stress–strain response also shows a good fit with experimental values therefore validating the used model. 6.4. Image analysis The displacement field generated by the digital image correlation method is presented in Fig. 14. The arrows represent the specimen displacement field obtained from two sequential images. Fig. 14 indicates potential sample rotation at strain levels around 2.25%. Nevertheless, the rotation tends to decrease for larger strain levels. Different displacement levels were also observed after the first crack formation. Fig. 14d shows a distinct displacement level

Fig. 12. Numerical simulation showing the effect of gage length on the ultimate strain and crack spacing of sisal fiber reinforced composites.

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Fig. 13. Comparison of experimental responses and numerical simulation for sisal fiber reinforced composites under (a) dynamic and (b) static loads.

Fig. 14. Displacement fields obtained using the DIC method (a–c). The displacement level in pixels is shown by the bar graph (d) for a strain of 1.5%. This displacement values corresponds to different locations in the composite. Each row and column corresponds to a width of 10 pixels.

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for the region below and above the crack. It can be seen that as the stress concentrates on the crack that formed in the center part of the composite, crack widening takes place. 7. Conclusions The following conclusions can be drawn from the present work on the tensile behavior of sisal fiber reinforced cement composites under low and high strain rates: • There is a significant increase in UTS for the dynamic tensile test. A tensile strength DAF of 1.26 was computed. The dynamic stress–strain behavior was similar to the static case with multiple crack formation followed by strain hardening behavior. Both tensile and shear cracks were observed. • The first crack strength was found to be sensitive to strain rate. An increase of BOP+ from 5.94 to 8.06 MPa was observed between static and dynamic tests. • Strain rate sensitivity was noticed for the ultimate strain as it increased from 3% in static to 10% in dynamic tensile tests. The main failure mechanism in both cases was fiber pullout. • The tension stiffening model used was able to accurately predict the crack spacing and stress–strain behavior of the sisal fiber reinforced cement composites under dynamic and static loads. The model has shown that under dynamic load, a reduced frictional bond results in a lower capacity of fiber-matrix stress transfer leading to wider crack spacing and promoting a fiber pullout failure mechanism which increases the energy absorption capacity of the composite system. • The digital image correlation method was a powerful tool to determine the displacement field in cement composites. It was observed that during the crack formation, part of the composite may rotate due to formation of cracks resulting in different strain levels at different regions of the material.

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