Fiber Bridging Degradation Based Fatigue Analysis of ECC under Flexure

This paper proposes a fatigue analysis method of Engineered Cementitious Composite (ECC) under fatigue flexure by applying the concept of fiber bridging degradation. The mechanical degradation of materials under fatigue load is considered a major factor for fatigue crack propagation and subsequent fracture. FEM with the concept of both smeared crack and discrete crack is introduced for representing the consequences of multiple cracks and a localized crack, respectively. The bridging stress degradation law under fatigue load as well as the constitutive relation under static load is introduced as essential input material properties in the fatigue analysis. In order to verify the fatigue analysis, a flexural fatigue test program of two kinds of ECC, PVA-ECC and PE-ECC, was conducted. The fatigue characteristics of flexural beams predicted by the proposed model such as S-N relation and the evolution of midspan deflection agree well with those from the test results. It is also shown that the fatigue analysis is applicable to determine the bridging stress degradation relation of ECC by flexural fatigue tests.

In the development of the fatigue analysis method, the failure of ordinary cementitious materials , such as plain concrete or Fiber Reinforced Concrete (FRC), under fatigue flexure or fatigue tension is governed by the initiation and the propagation of a single localized crack; therefore, the fictitious crack approach is appropriate and enough for representing the crack and the failure mechanism. The fatigue analysis based on the fictitious crack concept has been successfully developed for predicting the fatigue life and fatigue characteristics of RC beams as well as reinforced FRC beams2) .
However, in the case of ECC under fatigue tension , its failure mechanism is governed not only by a single localized crack, but also by multiple cracks and their propagation3), 4). Multiple cracks are distributed in the tensile zone of the beam before a localized crack takes place. The distribution of these multiple cracks slow down the initiation of a localized crack, and it leads to the extension of fatigue life. Therefore, fictitious crack concept only is not adequate for reproducing the failure mechanisms and fatigue life. In this study , the concept of smeared crack approach is introduced for representing the effects of multiple cracking processes.
The objective of this study is to propose an analytical model considering the effects of multiple cracks as well as a localized crack in order to predict the fatigue performances of ECC under fatigue flexure. Two types of ECC with two different fibers: polyvinyl alcohol (PVA) and polyethylene (PE) were tested under fatigue flexure, and they are used for the verification of the analytical model. The S-N relation and the evolution of midspan deflection predicted by the analytical model are compared to those from experiments.

Fatigue Analysis of ECC Flexural Beams
The development of fatigue analysis of ECC flexural beams and the governing material relations are discussed in this section. In order to reproduce the failure process and predict the structural properties of ECC by an analytical approach, the failure mechanism observed from flexural fatigue experiments is considered in the modeling. The consequent initiations and propagations of both multiple fine cracks and a large localized crack are taken into account as major mechanisms in the analytical model.
For material relations, the material degradation law under fatigue loading is considered the essential cause of crack propagation. For mechanical degradation, after a crack initiates in ECC, the transferred stress across crack occurs due to fiber bridging action. When fatigue loading is applied, the transferred stress across cracks reduces according to the degradation of the fiber bridging. This mechanism is so called"Bridging Stress Degradation".

2.1
Modeling An FEM model is proposed incorporating the above described fatigue failure mechanism. It is found from the flexural fatigue experiment5),6) that the flexural fatigue failure of the ECC involves three stages: the initiation of multiple cracks, the propagation of those cracks, and the propagation of a localized crack. At a small number of fatigue loading cycles, multiple cracks initiate along the flexural span as well as into shear span of the specimen, then those cracks propagate stably and lead to a gradual increase in midspan deflection of the specimen. Finally, only one crack localizes, and it induces the final failure of the specimen.
The analytical model is proposed by combining both smeared crack and discrete crack concept. Smeared crack elements are introduced for representing the multiple cracking process, and discrete crack elements or interface elements are used for representing the localized cracking The degradation law of multiple cracks in ECC represented by smeared crack elements can be illustrated as shown by Fig. 3.The degradation law is assumed to be related to two coefficients for each material, k1 and k2 as shown in Eq.(4).The coefficients k1 and k2 of the level of dependencies on the number of cycles, N, and tensile strain, ct, respectively.
When k1 is large, the degradation of material is N-dominant relation and when k2 is large, the degradation of materials is much affected by the tensile strain level, Et. The bridging stress degradation rate is large when k1 and k2 are large.   Table1   *Water-cementitious material ratio **Sand-cementitious material ratio months so as to alleviate the effect of initial hydration development.

3.2
Apparatus and test procedure The apparatus employed in this study was a 200kN capacity feed back controlled loading machine. For static loading, the tests were carried out under displacement control condition, while fatigue tests were under load control condition.Four-point flexural tests were conducted both under static loading and fatigue loading. Specimens were simply supported on a clear span of 300 mm and were subjected to two-point load at one-third of the span.
Static flexural test were conducted before fatigue flexural tests under displacement control condition.They were performed in accordance with JCI standard for test methods of FRC(JCI-SF412)).The static flexural strengths of two ECCs were determined Rased on the average flexural strength, the maximum fatigue stress were determined for each level.In order to construct the fatigue stress-life relation(S-N relation), five levels for PVA-ECC and four levels for PE-ECC were conducted.
For flexural fatigue tests, specimens were subjected to an 8Hz sinusoidal cyclic load.The ratio between the maximum flexural stress and the minimum flexural stress was set constantly equal to 0.2for all specimens in order to avoid any impact and slip of specimens during testing. 33Data collection Linear Variable Differential Transducers(LVDTs) were introduced to measure the deflection at the midspan of specimens from both sides of specimens.They were mounted on a steel frame fixed on a specimen so that the displacement evolution produced only by the specimens can be measured.    The experiment showed that both ECCs exhibited an extended fatigue life at high fatigue stess level (Fig. 8(a) and Fig. 8(b)).The shape of S-N relation of both ECCs (4) and (5))are changed gradually for each trial.When either k1 or k2 is increased the fatigue life become shorter, and when k2is increased, the slope of S-N relation tends to become more negative with the increase of N. After several trials, the final degradation relations for both two kinds of ECC are shown below.
PVA-ECC (6) PE-ECC (7) It is noticed that the coefficient k1in the degradation law of PVA-ECC is smaller, but the paremeter k2 of PVA-ECC is larger than that of PE-ECC.This implies that PVA-ECC exhibits the bridging stress degradation, which is more dependent on the tensile strain level than that of PE-ECC.
(2) Comparison of damage evolution The comparison of damage evolution are conducted in order to verify the obtained bridging stress degradation.
The evolution of midspan deflection and displacement measured by 71gauges are used for this verification.
The evolution of midspan deflection of PVA-ECC and PE-ECC from the experiment is illustrated in Fig.   9(a)and Fig. 9(b), respectively.Only one typical specimens for each fatigue stress level is shown.It is found from experiments that the evoltion of midspan deflection depended on fatigue stress level.The midspan deflection of both types of ECC at final failure reduced with the decrease of fatigue stress level.   From the evolution of midspan deflection, it is found that PVA-ECC exhibited more fatigue stress dependent than that of PE-ECC.At a higher fatigue stress level, an initial tensile strain was larger, and it resulted in the higher rate of increase of midspan deflection because of higher rate of expansion of fractured zone.This supports that the degradation of PVA-ECC is more tensile strain dependent than that of PE-ECC.This conforms to the bridging stress degradation relation obtained from the analysis that the stress degradation of PVA-ECC is much dependent on tensile strain level than that of PE-ECC.It can be concluded that the fiber bridging characteristics governs the bridging stress degradation law of ECCs. materials that exhibit a single crack failure, such as fiber reinforced concrete or plain concrete, the uniaxial tensile fatigue test of specimen with a notch at the center was proposed for determining the bridging stress degradation13)and it was shown that the bridging stress degradation obtained from the experiment can be introduced for predicting structural properties of those materials.However, in the case of ECC, the method for determining the bridging stress degradation has not been proposed yet due to the difficulties in fatigue tension test set-up for capturing multiple cracks in a specific area. This study shows that it is able to introduce the proposed analytical model for determining the bridging stress degradation of ECC.The flexural fatigue test, which is simpler in test setting than uniaxial tension test is conducted in order to investigate flexural fatigue properties of beam.Then, the S-N curve is constructed and the evolution of midspan deflection is recorded. These results are used in curve fitting with the analytical results obtained from the assumed bridging stress degradation relation.The bridging stress degradation is adopted when the analytical results can reproduce the experiment results.

Conclusion
A fatigue analysis method of ECC under fatigue flexure has been proposed by applying the concept of fiber bridging degradation. The analysis has been developed based on the fatigue failure mechanism of ECCs that is governed by a crack propagation process. The initiation of multiple cracks and the propagation of a localized crack are simulated by smeared crack elements and interface elements, respectively.
For material relation, the bridging stress degradation law of ECC which considers fiber rupture and fiber/matrix interface bond degradation is discussed and based on this law, the simplified degradation relation which depends on only two parameters N and et, are proposed as the input of the analysis.
The fatigue flexural tests of ECCs were conducted in order to compare with the analysis results.The S-N relation from the experiment is introduced with the fatigue analysis model to determine the fatigue bridging stress degradation relation of ECC.The evolution of midspan deflection was selected for the verification.It is shown that the analytical results can reproduce the evolution characteristics that fatigue stress dependent evolution of midspan deflection.
This study supports that it is able to apply the flexural fatigue test of ECC as an alternative method to determine the bridging stress degradation relation.
For structural application, the analysis model is used for predicting fatigue performances of ECC.When the bridging stress degradation relation is known, the flexural fatigue properties of ECC beams, such as the S-N relation and the evolution of deflection are predictable.
The fiber bridging characteristics, fiber rupture and fiber pull out involves the bridging stress degradation law of ECCs.Therefore, for the further development, the uniaxial tensile fatigue test would be an interesting topic in the sense that it is essential to the development and the verification of micromechanics based bridging stress degradation law.