Effect of Low-Stress Fatigue on the Off-Crack-Plane Fracture Energy in Engineered Cementitious Composites

-is paper presented an experimental study on the flexural properties of engineered cementitious composites (ECCs). -e bending fatigue damage, residual deformation, and damage characteristics were investigated after a certain number of low stress levels in fatigue load. -e composite fracture energy and fiber-bridging fracture energy were calculated by the J integral. It is observed that the number of cracks increased with the increment of stress levels, and most of the cracks were formed during the earlier stage of the dynamic test.-e deformation capability decreased with the increment of stress levels while the reduction of the ultimate load was minor after the dynamic load. Furthermore, the strain-hardening phenomenon of the specimen enhanced initially and then weakened with the increment of stress levels. -e residual equivalent yield strength became smaller with the increase of stress levels. Meanwhile, the trend was mild at low stress levels and then became steep at high stress levels.


Introduction
e engineered cementitious composites (ECCs), as a common composite, have been used for many important parts of the structure.
ere are lots of methods to model the fracture failure behavior in the ECC since its service life time and function depend on the stress levels to a large extent.By virtue of the three-point bending tests, Elices et al. [1] calculated the fracture energy (G F ), which is used as a parameter to present the performance of many composite materials.Li and Hashida [2] obtained the total fracture energy which is 34 kJ/m 2 of the ECC with 4% of the fiber volume fraction by making a finite element analysis about the fracture through the J integral.Zhang et al. [3,4] established the bending model and found the relationship of the flexural resistance and the specimen thickness.Zhang and Stang [5] investigated the relationship of the crack length and fatigue cycles in the ECC fatigue fracture test.
e strain and crack width brought about by the increase of the fatigue cycles cause the interfacial degradation in fiber composite materials, but the crack width is no more 100 μm before the main crack localizes.us, the effect of crack width on fracture properties of specimens is ignored in this paper [1,[6][7][8][9].
e fatigue test under the high stress level is done, and the relationship between the stress level and the fatigue life has been proven to be linear in logarithm [8][9][10].rough the linear logarithmic equation, we can estimate the fatigue life under low stress levels, but the fatigue test under low stress levels has been seldom attempted [10].e common ECC specimens are normally difficult to achieve fatigue damage when they are under low stress levels, let alone the ECC specimens with the characteristics of metal fatigue.
Owing to the difficulty of achieving fatigue damage, the crack length, crack mouth opening displacement (CMOD), and ultimate load were measured during static damage after the certain cycles of fatigue under the stress levels of 0.23, 0.26, 0.34, 0.55, 0.59, and 0.65.In this paper, a series of experiments regarding the three-point bending fatigue fracture under low stress were conducted to investigate the residual fracture energy and the residual equivalent yield strength.

Determination of Fracture Parameters of the Three-Point Bending Test of ECC
2.1.Specimen Dimensions and Materials.e three-point bending test specimens were cast in wood former with dimensions of 700 mm × 150 mm × 80 mm (Figure 1).e prefabricated crack was embedded with a 3 mm thick steel plate, and the height of the crack was 60 mm [11].After the casting was completed, the specimens were remolded until they had been sealed for curing for 24 hours.en, they were maintained for 100 days at the laboratory temperature (at about 20 °C).
e cement adopted was P.O42.5 silicate cement.As quartz sand, it was hard and good artificial sand, in which the fineness modulus was less than 2.65 and the percent of mud was not more than 1.5%.With the increment of fiber volume fraction, the compressive strength, the tensile strength, and the fracture toughness of the ECC increase.In contrast, its mechanical performance enhances slightly when the fiber volume fraction increases to 2% [12][13][14][15].Under this situation, the ECC with 2% of the fiber volume fraction shows good performance.Hence, the same fiber volume fraction was applied in the test.Table 1 shows the corresponding properties of the polyvinyl alcohol (PVA) fiber.Grade I composite fly ash was used.e compressive strength of the specimen was 36.6 MPa at 28 days [16].

Test Equipment and Test Procedure.
e whole loading procedure was completed by means of the servohydraulic system made in Beijing Foli System Company, China.A dynamic sampling system produced by Donghua Testing Technology Co. Ltd. was adopted to collect data. 1 illustrates the setup for the static test, where a vertical, linear load was applied onto the middle of the beam's top surface, using a compression test device.

Static Test. Figure
With the specimens resting on two line supports with a span length of 600 mm, the load (P) was continuously recorded by the sampling system, and the middle displacement was measured by the displacement gauge.e opening of the crack mouth opening displacement (CMOD) was measured by the clip gauge.e loading method was controlled by the middle displacement with the loading rate of 0.05 mm/min [3][4][5]17].

Dynamic Test.
e dynamic tests were conducted by the load control mode with the frequency of 1 Hz.e load shape was a sine wave shown in Figure 2 [2,12,18,19].In the test process, the maximum load (P max ) based on the ultimate load of specimens in the static test, the average load (P m ), the load range, the load amplitude (P a ), and the minimum load (P min ) can be calculated by ( 1)-( 4).e length and width of the crack with corresponding time and fatigue cycles were recorded by observation every ten minutes [8,9,13,20,21].
where P max , P min , P m , P a , and ΔP are shown in Figure 2. R is the characteristic value of the load.

Calculation Methods.
e J integral value for the three-point bending specimens is calculated by the curve of load-displacement according to the provisions of the ASTM E-24 [22].J represents the fracture energy dissipation during the cracking process.e fracture energy, the J integral value [23], is then calculated according to the following equation: where t and h represent the specimen width and height, respectively.e initial crack depth is denoted by a 0 , while A denotes the area of the curve of load-displacement [24][25][26][27].As the midspan deflection has a good linear relationship with the CMOD for the tested specimens, in this paper, A is calculated by the P-CMOD curves [13].

Advances in Civil Engineering
Following the double-K fracture criterion of concrete [28], Liu et al. [13] proposed the J IC , the starting point of the ductile stage, and the J IF , the starting point of the failure stage.
e rst crack appeared when J > J IC , the localized failure crack developed when J > J IF , and the material was in a safe state when J ≤ J IF [13].So, the threshold of fracture and failure can be applied to estimate the fracture toughness of the ECC material.Furthermore, J C , the total fracture energy, which includes all the loading processes can also be calculated by (5).

P-CMOD Curves.
e P-CMOD curves of static load specimens, the average curves for the ECC and matrix acquired by calculating the mean force at xed CMOD values, are displayed in Figures 3 and 4. e fracture surface magni ed 200 times is shown in Figure 5.A summary of the initial cracking load (P ini ), peak load (P max ), and the corresponding CMOD values is also provided in Table 2.It can be seen that the initial cracking load increased with adding PVA bers in the specimens [14].e bers increased the initial cracking load and delayed the cracking time compared to the matrix.
e corresponding CMOD values of the initial cracking load of the ECC increased much greater than those of the matrix, which demonstrated that the load was transmitted across the PVA bers as well [29]. 2 shows the results of the fracture parameters calculated by (5).P ini is measured by strain gauges pasted on the surface of specimens, that is, the cracking load of the ECC [13].P max is the maximum load during the loading process; meanwhile, the CMOD C value happens.It is clear that the beams made from the matrix had small cracking resistance since they generated the lowest values for J IC and J IF (Table 2) [13].Figure 5(a) shows that some bers were pulled out or cut from mortar, meaning that the bers were pulled out when the specimens could absorb energy.According to the frictional resistance between the bers and mortar, some other bers (Figure 5(b)), however, are ruptured when they consume more energy [6,30,31].e average initial cracking energy of the ECC is 3 times that of the matrix.e average failure fracture energy of the ECC is 7.77 kJ/m 2 , which is approximately 740 times that of the matrix.e ultimate load can be determined as 7 kN according to the average value of ultimate load of three specimens [16].Advances in Civil Engineering 3

Dynamic Test Results
. As shown in Table 3, specimens under di erent stress levels with the same number of cycles are tested in dynamic load.TPB is used as an abbreviation to the three-point bending specimen.

P-CMOD Curves.
As shown in Figure 6, the maximum CMOD values of each fatigue cycle increase with the increment of the fatigue cycles.e CMOD values increase directly until the fatigue cycles reach approximately 1000, and the growth rate reduces under the stress levels of 0.55, 0.59, and 0.65.
Nevertheless, the CMOD values increase directly under the stress levels of 0.23, 0.26, and 0.34 during the dynamic test.
Figure 7 shows the P-CMOD curves under static load after the fatigue cycles of 10,000.e di erence of the ultimate load between the minimum stress level S 0.23 and the maximum stress level S 0.65 is just 0.42 kN, which is only 5.96% of the ultimate load under the static load. is illustrates that the ultimate load of specimens under 6 types of stress levels reduced smaller compared to the average load of failure specimens under the static load.Meanwhile, with the increment of     4 Advances in Civil Engineering stress levels, the strain-hardening capacity increased at first and then decreased.is demonstrates that more and more fibers participated in the fiber bridging during the dynamic test.Simultaneously, they were pulled out or broken in fatigue load with the decrease of the flexural capacity [10,32,33].

Cracking Mode and Transformation.
As seen in Figure 8(a), the matrix specimen just has one tiny crack when it loses its bearing capacity.With adding PVA fibers into the matrix (Figure 8(b)), a large number of microcracks distribute around the initial crack edge in addition to the main crack, that is, multiple cracks under static load [31,34,35].Figures 8(c)-8(h) illustrate the difference in cracking mode and length under different stress levels.e number of cracks of the specimens reduced with the decrease of the stress level.Meanwhile, the direction of propagation of the cracks was horizontal which reduced the stress concentration at the main crack edge [36].Table 4 verified that the crack number reduces with the decreasing fatigue stress levels [14].From the crack number and smooth degree in the either side of the main crack among Figures 8(b)-8(h), it can be observed that the specimens have the tendency of developing into brittle failure, still keeping the ductile failure.Advances in Civil Engineering

Fracture Toughness.
e values of J IF and J C calculated by (5) with the experimental curves of P-CMOD are shown in Figure 9 [13].From this diagram, it is clearly seen that the J IF , the J integral value at the failure crack localizing point, and the total energy J C decrease with the increase of stress levels.When S 0.817 was calculated from the tting formula, the J IF value decreased to 0. is implies that the localized failure crack immediately developed under this stress level.e variation coe cients of 0.84 and 0.794 show that the formulas are still reliable.e contribution from this  6 Advances in Civil Engineering formula might identify the ECC structures safe or not according to the stress levels.

J R Resistance
Curve. e J R resistance curve stands for the relation between the crack extension and J integral value.During the test, it is observed that multicracks generate in the shapes of irregular curves.Hence, the single crack extension is not appropriate for ECC specimens.In this paper, the total crack length, a, is used to describe the crack extension of ECC specimens.During the experiment, the crack width observed is less than 60 μm before the main crack appears. is means that the ECC specimen starts to lose its bearing capacity when the crack width exceeds 60 μm.
erefore, the crack width can be neglected before the main crack appears, and only the total crack length is considered as the parameter.
e J integral values calculated by ( 5) with the experimental curves of P-CMOD are shown in Figure 7. Figure 10 shows the relationship between the increment of the total crack length Δa and the J integral values.Only one specimen is selected for each stress level.ere were three linear relationships with two cuto points of the crack development.In the rst stage, very few cracks had been formed during the dynamic test, and the crack length Δa had appeared while J integral was kept zero.In the second stage, lots of cracks produced, and the crack length Δa increased with the increment of J integral values.In the third stage, the cracks developed quickly after localizing.J IF can be calculated by ( 5) with P-CMOD curves shown in Figure 7.Moreover, the J IF value can also be obtained by J-Δa curves.So, there are two methods to the J IF value.
e results shown in Figure 11 illustrate that the two methods were almost equal.erefore, the J R curve can be applied to judge the fracture state of the ECC under low stress levels of fatigue.
Figure 10 illustrates the three linear relationships of the J R resistance curve.In the second stage, J integral values increased with the increment of the crack length Δa.Equation (6) shows the relationship of J and Δa when the localized failure crack developed [13].
where a ′ represents the crack length generated in the dynamic test.σ y is the residual equivalent yield stress.
According to the J R curves and (6), the results of σ y obtained are shown in Figure 12.As seen, σ y shows a decreasing trend, and the rates increase with higher stress levels [37].

Conclusion
is paper investigates the e ect of low stress levels (0.23, 0.26, 0.34, 0.55, 0.59, and 0.65) on the mechanical and fracture properties of the ECC with 2% volume fraction of the PVA ber.e following conclusions were drawn: (1) e fracture mode of the matrix was similar to that of the ECC.e di erence between the initial cracking load and the ultimate load in the ECC was greater than that of the matrix.is shows that the bers had the e ect of bending resistance and of absorbing energy.e double J integral criterion testi ed the e ect of bers in the ECC.(2) e capacity of strain hardening of the ECC increased at rst and then decreased with the increment of stress levels.In contrast, the deformation ability of the ECC always decreased.(3) e total crack length Δa was suitable to describe the fracture state of the ECC.e J R curve of the ECC had three stages and two dividing points of fatigue cracking and crack localizing.Furthermore, the  Advances in Civil Engineering linear relation of J integral and Δa in the stable stage indicated that the crack length developed regularly with the increase of fracture energy.(4) e residual equivalent yield strength σ y was applied to express the relationship between J integral and Δa in the second stage of J R curves.e residual equivalent yield strength of the ECC decreased, and the rates increased with the increment of stress levels.

Figure 6 :
Figure 6: Evolution of CMOD during the dynamic test.

Figure 7 :
Figure 7: Evolution of CMOD curves after the dynamic test.

Figure 9 :
Figure 9: Relationship of the stress level and J integral.

Figure 10 :
Figure 10: Relations between J integral and increment of the total crack length.

Figure 11 :Figure 12 :
Figure 11: Comparison of J IF results obtained from J R resistance curves and experimental P-CMOD curves.

Table 1 :
Properties of the PVA fiber.
ΔPFigure 2: Relation among load parameters for the fatigue test.

Table 2 :
Fracture parameters from three-point bending beams.

Table 3 :
Fatigue loads and corresponding stress levels.

Table 4 :
e test results during the dynamic test.