Crack closure and flexural tensile capacity with SMA fibers randomly embedded on tensile side of mortar beams

2.1 Preparation of specimens and material properties

In this study, beam specimens with a cross section of 40 × 40 mm and a length of 160 mm were designed. Figure 1 shows the dimensions and geometry of the specimens, including a cross-sectional view. The SMA fibers with a length of 30 mm and a diameter of 0.67 mm were fabricated from NiTi and NiTiNb SMA wires with compositions of 56.8% Ni and 43.2% Ti, and 42.5% Ni, 45.3% Ti, and 12.2% Nb, respectively.

Figure 1

Geometry and cross section of a beam specimen (units: mm).

The water-to-cement and sand-to-cement ratios were 0.40 and 2.5, respectively. Superplasticizer was added at 1.0% by the cement mass. Therefore, the amounts of water, cement, and sand used in the study were 0.428, 1.07, and 2.14 kg, respectively. Cement and sand were mixed under dry conditions for approximately 3 min. After dry mixing, water was added to the mixture: two-thirds of water was first mixed for approximately 3 min, and the remaining water was mixed for 1 min. SMA fibers were then added to the mixture, and the cement composites randomly mixed with SMA fibers were prepared. The cement composites incorporated with SMA fibers were poured only in the bottom half of the beam, as shown in Figure 1. Smooth two steel wires with 2 mm in diameter were installed at 5 mm from the bottom of the beam specimen. Immediately after that, normal cement mortar was poured in the top half of the beam.

The test variable considered in this study was the volume fractions of the SMA fibers, 0.50%, 0.75%, and 1.00%. In addition, this study evaluated the effect of tensile steel bars on the flexural strength and crack-closing capacity. Table 1 lists the names and numbers of the specimens with test variables. The experimental data of the NiTi SMA specimens were taken from the previous study [36], which was designed by an author of the article.

The SME of the SMA results from a phase transformation from the martensitic to austenitic state. Austenite start and finish temperatures used in this study, A _s and A _f, were 74.2 and 100.3°C for the NiTi SMA fiber and 80.1 and 93.9°C for the NiTiNb SMA fiber. In fact, A _f was designed to prevent damage to the cementitious matrix during the heating process. In addition, the mechanical properties of the SMA fibers and steel bars – the yielding and ultimate stresses and the modulus of elasticity – were determined by conducting uniaxial tensile tests. Vision measurement and image analysis technique using targets on a wire were used to accurately obtain the stress–strain curves of the NiTi and NiTiNb SMA and the round steel wires, as shown in Figure 2. The yielding stress obtained by the 0.2% offset method was approximately 1,064 and 853 MPa for NiTi and NiTiNb SMA fibers, respectively. The ultimate stress of the NiTi and NiTiNb SMA fibers was approximately 1,467 and 1,133 MPa, respectively. The modulus of elasticity of the SMA fibers was 35.5 GPa, as presented in Figure 2. The smooth steel wire showed the yielding stress of approximately 328 MPa, ultimate strength of 422 MPa, and modulus of elasticity of 102.6 GPa.

Figure 2

Stress and strain curves of the SMA fibers and steel wires.

2.2 Experimental setup and procedure

A four-point bending test was performed for evaluating the flexural strength of the beam reinforced with SMA fibers on the tensile bottom side. The beams developed permanent flexural cracks during the bending test. Therefore, heating was applied to the beams, and the extent to which cracks were closed by the SME of the SMA fibers was evaluated.

Figure 3 shows the setup and instrumentation for the bending tests and crack-closing tests. The beam span was set to 120 mm under simply supported conditions. The load was applied under displacement control at a rate of 0.1 mm/min. The distance between the loading points on the top surface of the beam was 300 mm, which led to a constant moment in the middle of the beam. The magnitude of the load was measured using a load cell mounted on an actuator, and the vertical deflection was simultaneously measured with a linear voltage displacement transducer (LVDT) installed in the middle of the beam, as shown in Figure 3a. A preliminary test found that the first cracking occurred at a vertical deflection of around 0.2 mm, and thus, the bending test was continued up to a vertical deflection three times the first cracking deflection, which is around 0.6 mm. However, the deflection of 0.6 mm was adjusted appropriately to prevent the collapse of the beam. Subsequently, the applied load was gradually removed to measure the widths of permanent cracks formed at the bottom of the beam.

Figure 3

Experimental setup: (a) beam test and (b) crack-closing test.

To evaluate the flexural crack closing, heat was applied to activate the SME of the SMA fibers embedded in the beam. A heating plate that could be placed at the bottom of the beam was fabricated in this study, as shown in Figure 3b. The beam was heated up to 120°C by using a controller installed on the heating plate. Thermocouples were installed on the side surfaces at the middle of the beam to ensure that the temperature of all the SMA fibers in the beam approached the target temperature. After the target temperature was maintained for about 30 min, a magnifying lens was used to measure crack widths and compare the widths before and after heating. The crack width was also measured after the beam was cooled to room temperature to ensure that the closed crack width remained unchanged.

3.1 Load and deflection curves

Figure 4 shows an example of load and vertical deflection curves plotted from load cell and LVDT measurements for the control specimens and the NiTiNb SMA fiber–embedded beam specimens with fiber volume fractions (v _f) of 0.50%, 0.75%, and 1.00%. The load and vertical deflection curves of the beam specimens with NiTi SMA fibers, plotted in ref. [36], were similar. The load increases almost linearly with the deflection. The load, at which a crack was initiated on the beam, was defined as the cracking load P _cr. The control beam specimens without tensile wires showed a significant decrease in the load resistance and immediate flexural failure once a crack occurred and propagated, as shown in Figure 4a. On the other hand, the beam specimens without tensile wires but incorporated with SMA fibers on the tensile bottom side of the beam showed a load resistance after a crack occurred. The load resistance dropped immediately after a crack occurred on the beam but recovered to maintain some residual resistance until failure, as shown in Figure 4b–d. In particular, as the volume fraction of the SMA fibers increased, the post-cracking load resistance tended to increase. The beams with tensile wires showed a typical behavior resisted by wires, particularly after crack, as expected. Table 2 summarizes the critical and ultimate loads, P _cr and P _u, obtained from the beam tests.

Figure 4

Example of load and deflection curves of the beam specimens with and without tensile wires: (a) v _f = 0%, (b) v _f = 0.50%, (c) v _f = 0.75%, and (d) v _f = 1.00%.

The trends in P _cr and P _u were evaluated with changes in the fiber volume fraction and tensile wire for the NiTiNb and NiTi SMA fibers, as presented in Figure 5. The mean value of P _cr ranged from 3.85 to 5.30 kN for the NiTiNb fiber–embedded beams and from 3.85 to 4.83 kN for the NiTi SMA fiber–embedded beams with fiber volume fractions of 0 to 1.00%. The linear regression analysis showed that the increase of P _cr was approximately 1 kN when SMA fibers were incorporated in the beams. Therefore, the influence of SMA fibers on P _cr was minimal, and no significant difference was found between the control beams and the SMA fiber–embedded beams, as well as the embedment of tensile wires. P _u also tended to increase somewhat with increasing fiber volume fraction. According to the linear regression analysis, P _u increased by approximately 1.7 and 0.72 kN per a 1% increase of the NiTiNb and NiTi SMA fibers, respectively, as shown in Figure 6. The little higher P _u in the NiTi fiber–embedded beams is attributed to the higher ultimate strength of the NiTi fiber.

Figure 5

Cracking loads of the beam specimens with fiber volume fractions: (a) beam specimens without tensile wires and (b) beam specimens with tensile wires.

Figure 6

Ultimate loads of the beam specimens with fiber volume fractions.

3.2 Ultimate flexural moment

This study assessed the ultimate flexural moment of the SMA fiber–embedded beams with tensile wires. Figure 7 shows the simplified stress distribution with a linear strain distribution. Based on the simplified rectangular stress distribution in the compression and tension zones, the ultimate moment can be calculated as follows:

where A _s and f _y are the area and yielding stress of the tensile wire, respectively; b and h are the width and depth of the cross section, respectively; and f _t is the ultimate tensile stress of the SMA fiber–embedded cement composites. According to American concrete institute (ACI) 544.4R-88 [37], based on the study of Henager and Doherty [38], f _t is calculated by the following equation:

where l and d _f are the length and diameter of the fibers, respectively, and α _b is the bond efficiency factor, which was taken as 1 for straight fibers in the study. f _t can also be calculated using the following equation [39].

where σ _f is the ultimate strength of the fibers and α _o is the orientation factor, which was taken as 0.64 for the beams with fibers only incorporated in the tension zone [40]. A main difference is that equation (3) accounts for the stress of the fibers instead of the aspect ratio of geometry.

Figure 7

Strain and stress distributions of the SMA fiber–embedded beam with tensile wires at the ultimate state.

Table 3 compares the mean ultimate flexural moments obtained from the bending tests with those from equations (2) and (3). The ratio of the ultimate moment obtained using equation (2), M u ACI , to the experimental value, M u exp , was 0.58 to 0.70. This is similar to the previous discussion by Swamy and Al-Taan [40], who showed the calculated-to-test flexural moment of 0.772, indicating the underestimation of the ultimate flexural moment using the ACI model [37]. On the other hand, the ultimate flexural moment calculated using equation (3), M u [ 39 ] , was overestimated by approximately 141–191%. As a result, equation (2), which accounts for the geometry aspect ratio of the fibers, tends to underestimate the ultimate moment of the fiber-reinforced cement composite. On the contrary, equation (3) overestimates the ultimate moment because of an unclear estimation of the strength of the fibers at the ultimate state.

When calculating the ultimate flexural moment of the SMA fiber–embedded beams with tensile wires, this study suggests that the ultimate strain of the fibers was assumed to be four times the yielding strain of the tensile wire. The ultimate moment calculated using the proposed method, M u rev , was reasonably in agreement with the experimental value. The ratio of M u rev to M u exp ranged from 0.89 to 1.06.

3.3 Residual flexural tensile strength

From the load and deflection relationships obtained from the bending tests, the residual tensile strengths of the beams embedded with NiTiNb SMA fibers were investigated. The NiTi SMA fiber–embedded beams, which showed relatively large slip in the beginning of the bending tests [36], were excluded in this investigation. The flexural tensile strength is calculated by the following equation [41]:

where P is the applied load and b, d, and L are the width, depth, and span length of the beam specimen, respectively. The cracking strength, denoted by f _cr, is the strength at the first cracking load P _cr. The mean vertical deflection at P _cr was calculated to be 0.26 mm. Therefore, the residual strengths after cracking, denoted by f ₄₀₀ and f ₃₀₀, were defined at deflections of L/400 (= 0.3 mm) and L/300 (= 0.4 mm), respectively. f ₄₀₀ represents the reduction in the flexural strength immediately after cracking, and f ₃₀₀, at which cracks are propagated to the top of the cross section and the beam is close to collapse, represents the trend in the residual strength with an increase in the post-cracking deflection.

Figure 8 shows the cracking and residual strengths with fiber volume fractions from 0 to 1.00%. The dotted lines were obtained from a linear regression analysis. The cracking strength f _cr increases with the fiber volume fraction, as shown in Figure 8a, but the increase rate in f _cr is relatively small. According to the linear regression, f _cr increased by approximately 1.40 MPa for a 1.00% increase in the SMA fiber volume fraction. The residual flexural strengths f ₄₀₀ and f ₃₀₀ showed a definite increase in the SMA fiber–embedded beams with increasing fiber volume fraction, as shown in Figure 8b and c. The dotted lines for f ₄₀₀ and f ₃₀₀ show a rate of increase of approximately 7.00 and 6.49 MPa for a 1.00% increase in the fiber volume fraction, respectively. For the control specimens without SMA fibers, which proceed to collapse immediately after cracking, f ₄₀₀ and f ₃₀₀ are zero. The mean f ₄₀₀ and f ₃₀₀ ranged from 2.82 to 6.68 MPa and from 2.62 to 6.33 MPa, respectively, in the beams with the volume fraction of SMA fibers from 0.50 to 1.00%. In particular, f ₃₀₀ was approximately 87% to 95% of f ₄₀₀, indicating that the amount of the decrease in the residual flexural strength is small and that the post-cracking residual strength is maintained in the SMA fiber–embedded beams.

Figure 8

Residual flexural strengths of the beam specimens with fiber volume fractions: (a) f _cr, (b) f ₄₀₀, and (c) f ₃₀₀.

3.4 Energy absorption capacity

This study also evaluated the energy absorption capacity of the NiTiNb SMA fiber–embedded beams. The energy absorption capacity can be calculated using the load and deflection values up to a certain point, that is, the areas below the load and deflection curves. Figure 9 shows the energy absorption capacities calculated up to the cracking deflection, L/400, and L/300, which are denoted by E _cr, E ₄₀₀, and E ₃₀₀, respectively. The linear regression line, dotted line in Figure 9a, exhibits an almost constant slope in the range of fiber volume fractions of 0 to 1.00%. This indicates that the effect of SMA fibers on E _cr is negligible, which corresponds to a small increase in the cracking strength with an increase in the fiber volume fraction. On the other hand, E ₄₀₀ and E ₃₀₀ show a large increase with an increase in the fiber volume fraction from 0 to 1.00%, as shown in Figure 9b and c. As the fiber volume fraction increased from 0.50 to 1.00%, the mean E ₄₀₀ up to L/300 increased from 0.579 to 0.767 J, and E ₃₀₀ increased from 0.726 to 1.114 J. According to a linear regression analysis of the fiber volume fraction ranging from 0 to 1.00%, E ₄₀₀ and E ₃₀₀ showed an increase of 0.768 and 1.170 J, respectively.

Figure 9

Energy absorption capacities of the beam specimens with fiber volume fractions: (a) E _cr, (b) E ₄₀₀, and (c) E ₃₀₀.