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Experimental study on crack bridging in engineered cementitious composites under fatigue tensile loading
Construction and Building Materials 154 (2017) 167–175
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Experimental study on crack bridging in engineered cementitious composites under fatigue tensile loading Ting Huang a, Y.X. Zhang a,b,⇑, S.R. Lo a, C.K. Lee a a b
School of Engineering and Information Technology, The University of New South Wales, Canberra, Australian Defence Force Academy, ACT 2600, Australia State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, China
h i g h l i g h t s Experimental study of cyclic crack bridging behaviour of PVA-ECC. Establish of the relationship between crack bridging stress and the number of loading cycles. Study of the crack bridging degradation behaviours of PVA-ECC.
a r t i c l e
i n f o
Article history: Received 8 September 2016 Received in revised form 10 July 2017 Accepted 26 July 2017
Keywords: Crack bridging degradation Engineered Cementitious Composite (ECC) Polyvinyl alcohol (PVA) fibre Uniaxial fatigue tension test
a b s t r a c t The crack bridging behaviour of Engineered Cementitious Composites (ECCs) under fatigue tensile loading is investigated experimentally in this paper. Uniaxial fatigue tension tests were conducted on precracked specimens under deformation control with constant crack opening displacement amplitude. The crack bridging stress at the maximum crack opening displacement was obtained against the number of loading cycles. Eight maximum crack opening displacement levels were tested in total. The crack bridging stress was found to decrease with the increase of loading cycles. The crack bridging stress degradation is generally more significant in ECCs than in steel fibre reinforced concrete. In addition, the crack bridging stress degradation behaviour of ECCs reinforced with polymeric fibres was found to be distinct from that of steel fibre reinforced concrete with presence of accelerated stress degradation. The experiment demonstrates that it is important to take the fibre fatigue rupture into account in the analysis of mechanical behaviour degradation of ECCs and that the crack opening affects the crack bridging degradation behaviour. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The advances in material design theory and fibre technology in recent decades have greatly boosted the development of High Performance Fibre Reinforced Cementitious Composites (HPFRCCs), a class of fibre reinforced cement-based materials characterised by the pseudo strain-hardening behaviour in tension [1]. Engineered Cementitious Composites (ECCs), known for their enhanced tensile strain-hardening capacity and superior tensile ductility with less fibre reinforcement [2], belong to a relatively new and unique class of HPFRCCs. ECCs are usually reinforced with short discrete polymeric fibres, such as polyethylene (PE) [3], polyvinyl alcohol (PVA) [4] and polypropylene (PP) [5]. ECCs reinforced with no more ⇑ Corresponding author at: School of Engineering and Information Technology, The University of New South Wales, Canberra, Australian Defence Force Academy, ACT 2600, Australia. E-mail address: [email protected] (Y.X. Zhang). http://dx.doi.org/10.1016/j.conbuildmat.2017.07.193 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
than 2% by volume fraction of PE fibres or PVA fibres can attain a tensile strain capacity up to 3–6% [3,4]. In addition, the tensile strain-hardening process in ECCs is accompanied by multiple microcrackings. The high tensile ductility and microcracking are of great value in elevating the load carrying capacity, deformation capacity and energy absorption capacity as well as promoting the structural integrity of the structure. Moreover, the high tensile strain capacity and multiple microcracking characteristics offered by ECCs were found to be very promising in improving the structural fatigue performance especially at high stress levels [6]. Therefore, ECCs are regarded as very attractive construction and building materials for a broad range of applications. Especially, ECCs are highly suitable for situations where large deformation and/or cyclic/fatigue loading conditions are expected, such as earthquake-resistant structural members [7], link slabs for jointless bridging decks [8,9] and overlays for deteriorated pavement [10,11].
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The progressive formation of multiple microcracks is the key factor contributing to the high tensile ductility of ECCs. By using fracture mechanics and micromechanics theories to create certain fibre-matrix interaction within ECCs [12], the crackbridging fibres are able to sustain increasing load without catastrophic failure. This gives rise to a strain-hardening response after first cracking with initiation of multiple cracks. As a result, both the strain-hardening behaviour and the multiple-cracking behaviour of ECCs rely on the crack bridging behaviour of the fibres. The crack bridging capacity of the fibres generally will degrade under fatigue loading conditions [13–15] and such degradation behaviour needs to be taken into account when ECCs are employed in structures subjected to long-term fatigue loading. However, up-to-date investigations on the fatigue performance and mechanical behaviour degradation of ECCs are limited. Instead of conducting constant stress amplitude fatigue testing, Matsumoto et al. [13] studied the overall crack bridging capacity of multiple cracks under fatigue tension by conducting cyclic tension tests on PVA-ECC under constant strain amplitude. Tensile stress at the maximum strain level was found to continuously decrease with the increase of loading cycles, indicating the decrease of the fibre bridging stress across those cracks. The bridging stress degradation gradually decelerated for up to 103 cycles, and it then sharply accelerated between 103 and 105 cycles before the bridging stress eventually got stabilised at around 105 cycles. The underlying causes of such bridging stress degradation are associated with reduction of bond strength and/or loss of bridging fibres due to fibre fatigue rupture. In Lee et al.’s study [16], cyclic single-fibre pull-out tests on PVA fibres were conducted under displacement control with a constant amplitude. With fibre rupture deliberately avoided, the degradation of the fibre pull-out load can only be attributed to the deterioration of fibre-matrix interface properties due to continuous interface damage under cyclic load. However, the decrease in the fibre pull-out load decelerated constantly towards ceasing, showing no sign of abrupt acceleration compared to the bridging stress degradation behaviour of the composite. It is believed that the bridging stress degradation behaviour is affected by the combined actions of the different degradation mechanisms. However, this cannot be confirmed experimentally by just investigating the behaviour of a single fibre or the overall behaviour of multiple cracks. Zhang et al. studied the individual crack behaviour for steel fibre reinforced concrete under fatigue loading [17]. In steel fibre reinforced concrete, fibre fatigue rupture is unlikely to occur due to its high fibre tensile strength. Instead, the steel fibres tend to slip out of the matrix due to gradual reduction of interface bonding. As a result, after a rapid decrease at the initial stage, the crack bridging stress in steel fibre reinforced concrete was found to become stabilised gradually with the degradation rate decelerating continuously. While fibre fatigue rupture is believed to occur in cementitious composites reinforced with low-strength and low-hardness polymeric fibres such as most ECCs [6], no such experimental studies on the cyclic crack bridging behaviour of polymeric fibre reinforced cementitious composites have been reported yet. In order to gain an insightful understanding on the degradation behaviour of the mechanical properties of ECCs under fatigue loading, the individual crack bridging behaviour in a PVAECC under fatigue tensile loading is studied experimentally in this work. Fatigue tension tests were conducted with precracked specimens subjected to deformation-controlled cyclic loading. The effect of the maximum crack opening displacement on the crack bridging stress degradation behaviour is also investigated.
2. Experimental programme 2.1. Material Despite that ECCs reinforced with a wide variety of fibres have been successfully designed, special attention has been paid to the PVA-ECC due to the competitive price-performance ratio of PVA fibre [18]. In this work, the fatigue test was carried out on a PVA-ECC, which was developed in an earlier study by Huang and Zhang [19] with demonstrated tensile strain-hardening and multiple-cracking behaviour. The matrix of the PVA-ECC was composed of cement, fly ash, fine sand and water. ASTM Type I ordinary portland cement (OPC) and a low-calcium Class F fly ash were used. The fine sand had a maximum particle size of 300 mm and a mean particle size of 200 mm. Viscosity agent, i.e. high-range water-reducing admixture (HRWRA), was added in order to achieve adequate workability. Short discrete PVA fibre (trade-named KURALON K-II REC15), which was manufactured by Japan Kuraray Co., Ltd., was employed at a volume fraction of 2.2%. The chemical and physical properties of the OPC and fly ash are shown in Table 1. The properties of the PVA fibre and mix proportions of the PVA-ECC are shown in Tables 2 and 3, respectively. It should be noted that the size of the ingredients and mix proportions may affect the material properties of the ECC material significantly. The ingredients used and the corresponding mix proportions are normally tailored to meet the requirements for the tensile strain-hardening characteristics. The mix proportions of PVA-ECC used in this work were determined in such a way as to accommodate the use of local ingredients yet resulting in optimum tensile and compressive properties [19]. The basic mechanical properties of the PVA-ECC at the age of 28 days were tested and the results are summarised in Table 4. The Young’s modulus was determined using cylinder specimens of 100 mm in diameter and 200 mm in height. The compressive strength was determined using 50 50 50 mm cubic specimens. The tensile properties were measured by direct tension tests with dog-bone shaped coupon specimens. The dog-bone specimen has an effective testing zone of 80 35 20 mm and the loading rate is 0.20 mm/min [19].
2.2. Specimen According to the authors’ investigation, although a number of direct tension tests on the ECCs have been reported [13,14,18,20,21], no universal standard has been established to specify the specimen shape, dimensions and test method for the static and fatigue tension test of ECCs so far. However, the dog-bone shaped prismatic specimen with a reduced section as shown in Fig. 1(a) has been most often used in the fatigue tension test of ECCs [13,14]. The tensile specimen has been designed especially to eliminate the overall failure of a specimen at or near the grip and to control the initiation of cracks in a specific area. Within this area, multiple cracks are intended to initiate randomly and grow. In order to study and measure the relationship between the crack bridging stress and the crack opening of a single crack, tensile specimen with a notch introduced at the middle was proposed to control the crack location [17,22,23]. In the present work, uniaxial fatigue tension tests were conducted on pre-notched specimens for the study of the cyclic crack bridging behaviour of the PVA-ECC. The specimen geometry and dimensions are shown in Fig. 1(b). A 5 mm wide notch was
Table 1 Chemical and physical properties of the OPC and Class F fly ash. Property Chemical properties SiO2 (%) Fe2O3 (%) Al2O3 (%) CaO (%) MgO (%) SO3 (%) Na2O (%) K2O (%) P2O5 (%) TiO2 (%) MnO (%) Mn2O3 (%) Loss on ignition (%) Soluble residue (%) pH Physical properties Fineness (m2/kg) Bulk density (kN/m3) Moisture (%)
OPC
Fly Ash
20.5 3.2 4.1 64.8 1 3.2 0.23 0.68
59.6 3.3 29.1 3.2 0.4 0.2 0.28 0.48 0.7 1.1
1.3 0.38 12.4 353 3.1 0.19
<0.1 1.5 11.5 647 2.21 <0.1
T. Huang et al. / Construction and Building Materials 154 (2017) 167–175 Table 2 Basic properties of the PVA fibre. Nominal tensile strength (MPa)
Young’s modulus (GPa)
Diameter (mm)
Length (mm)
1600
41
39
12
Table 3 Composition and mix proportion of the PVA-ECC.
*
Cement
Fly ash
Sand
Water
HRWRA
PVA fibre*
1.0
1.2
0.8
0.65
0.01
2.2
PVA fibre is by volume fraction, and all others are by weight.
Table 4 Mechanical properties of the PVA-ECC at 28 days. Young’s modulus (GPa)
Compressive strength (MPa)
Ultimate tensile strength (MPa)
Tensile strain capacity (%)
20.3
56
5.26
1.01
introduced circumferentially in the middle of the specimen with deep notches of 12 mm in depth on the front and back surfaces for crack initiation and shallow notches of 7 mm in depth on the two laterals to guide crack propagation. A mixer with a rotating blade was used to produce the PVA-ECC mixture. At first all solid ingredients except fibres were dry mixed for a couple of minutes. During this time, all HRWRA was added in the water to form a liquid solution. After the dry ingredients were thoroughly mixed, the HRWRA solution was added and all ingredients were mixed for another couple of minutes. Once the liquefied fresh mortar mixture had reached a consistent and uniform state, the fibres were gradually added in small amounts while the mixer kept mixing until all the fibres were completely added. The mixture was further mixed for a couple of minutes to make sure all fibres could disperse evenly in the mortar matrix without clumping before being cast into the moulds of the dog-bone shaped prismatic specimen. The specimens were demoulded after 24 h, and then cured at 100% relative humidity and 23 °C until the day of testing. The notches were produced before the testing using a diamond saw. The specimens were tested at an age of at least 28 days.
2.3. Test set-up and loading procedures The set-up for the uniaxial fatigue tension test is shown in Fig. 2. All tests were conducted using a 250 kN load capacity InstronÒ actuator equipped for closed-loop testing. The specimen was held at each end by clamping using four tightening bolts.
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Sand meshes were employed in between the clamp-specimen interfaces to enhance the friction contact. The clamping force should be large enough to make a reliable specimen fixture, yet will not damage the specimen. In order to determine the most optimal clamping force, different tightening torques were tried and their abilities to produces a reliable clamping system were examined until the optimal tightening torque was found. Nevertheless, the silicon carbide particles on the sand mesh could be crushed/triturated or the specimen gradually creeped during the fatigue testing, which would form a gap between the clamp-specimen interface and result in the loss of clamping force. So each tightening bolt was used with a stack of Belleville spring washers. The spring washer stack had been configured to obtain a deflection of 2 mm under the set clamping force and would make up for any gap of up to 2 mm. It was expected that the spring washer stack would recover its deflection to restore the clamping system in case the tightening bolt was relaxed. Two LVDTs with a 15 mm gauge length were used to measure the crack opening displacement, which were attached to the specimen across the notches as shown in Fig. 2. Once a crack is formed at the notch, the displacement across the notch is lumped at the crack opening displacement. Due to such a small gauge length used, the deformation outside the notch is negligible and the crack opening displacement is taken to be equal to the displacement measured. In uniaxial tension tests especially for cementitious materials, special attention needs to be paid to avoid unintended bending effects, which may arise from the misalignment of the specimen and can affect the test results severely. In order to ensure the specimen remains correctly aligned during the direct tension test, the specimen should be first perfectly aligned in the loading direction before the test starts and allowed to rotate freely in the test so that it can be automatically adjusted during the testing. As a result, the pin-pin boundary condition has been generally employed for the static tensile testing of ECCs in previous studies. Such a boundary condition could be enforced by installing at both ends a universal joint between the specimen and the loading rig [20,24]. For static testing, such set-up will allow the applied axial load to be transferred from the loading rig to the specimen without causing any bending effects, and multiple cracks will successively occur under an increasing load. However, when it comes to the single crack behaviour under cyclic loading, the effect of secondary bending moment occurred at the crack will become significant under rotatable boundaries and make a great impact. Such secondary bending moment originates in the nonuniform stiffness distribution throughout the crack plane caused by nonuniform distribution of bridging fibres. Since this study focused on the cyclic crack bridging behaviour of an individual crack in the PVA-ECC, special attention was dedicated to initiate a uniform crack throughout the cross section. The universal joints were also utilised in this study, but only for the instalment of specimen for a perfect alignment at the beginning of the test. They were locked after the test started in order to suppress the free rotation of the specimen and the occurrence of the secondary moment. In order to determine the degradation of the crack bridging capacity, the uniaxial fatigue tension test was conducted under deformation control with a constant amplitude between the maximum crack opening displacement dmax and the minimum crack opening displacement dmin . A total of eight series of fatigue tension tests with different maximum crack opening displacement levels were carried out. The eight selected maximum crack opening displacement levels were 0.050, 0.080, 0.110, 0.130, 0.150, 0.170, 0.200 and 0.230 mm, respectively. In order to obtain three valid results for each case, extra specimens were prepared and at least three
Fig. 1. (a) Geometry of the commonly used tensile specimen for fatigue tension test of ECCs; (b) Pre-notched specimen for the assessment of cyclic crack bridging.
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Fig. 2. Test set-up of measuring crack bridging in uniaxial fatigue tension.
10.00 9.00 8.00
Load , kN
7.00 6.00 5.00
1 10 100 1,000 10,000 100,000 200,000 300,000
max
=0.150 mm,
min
=0.120 mm
4.00 3.00 2.00 1.00 0.00 0.120
0.130
0.140
0.150
Crack opening displacement , mm Fig. 4. Typical load-crack opening displacement curve from the fatigue tension test. Fig. 3. Loading procedure for conducting cyclic crack bridging test under deformation control.
3. Results and discussion specimens were tested for each displacement level. The minimum crack opening displacement corresponding to a specific maximum crack opening displacement was determined by a loading-unloading tension test in the first load application for each specimen. The specimen was first loaded at a rate of 0.0003 mm/s to induce a crack until reaching the assigned maximum crack opening displacement. It was then unloaded at a rate of 0.05 kN/s to almost zero load (e.g. 0.5 kN). The residual crack opening displacement at this point was then chosen as the minimum crack opening displacement that corresponded to this assigned maximum crack opening displacement for this specimen. Finally, the cyclic load was applied with a sine waveform between the maximum and minimum crack opening displacement at a frequency of 2 Hz for at least 200,000 cycles. It was stopped when either the maximum load ceased to decline or the number of cycles reached 500,000 cycles. A typical loading procedure is shown in Fig. 3. The testing system worked in conjunction with MTS TestSuiteTM Multipurpose Elite software for loading control and data collection. During the fatigue tension tests, the load and crack opening displacement data were recorded with a data acquisition speed of 80 Hz.
Fig. 4 shows the typical load-crack opening displacement curves obtained from the fatigue tension test when the number of load cycles N ¼ 1, 10, 102, 103, 104, 105, 2 105 and 3 105. As can be seen, the secant stiffness of the reloading branches reduced with the increase of cycles, and thus the load at the maximum crack opening displacement decreased gradually. The diagrams of the crack bridging stress at the maximum crack opening displacement versus the number of loading cycles under the different maximum crack opening displacement levels are shown in Fig. 5(a)–(h). In Fig. 5, while the results in the range of 1–10,000 cycles are displayed in Fig. 5(ai)–(hi), those in the range of 1–500,000 cycles are displayed in Fig. 5(aii)–(hii). Note that in these figures only the average result of the individual tests for each case is displayed, and the crack bridging stress at the maximum crack opening
T. Huang et al. / Construction and Building Materials 154 (2017) 167–175
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Fig. 5. Relation of normalised bridging stress and number of fatigue cycles.
displacement rN has been normalised by its value at the first cycle r1 , i.e. rN =r1 . Fig. 5 clearly shows that the crack bridging stress at the maximum crack opening displacement decreases with the increase of loading cycles. Furthermore, as can be seen from Fig. 5, two major degradation behaviour of the crack bridging stress in the PVA-ECC can be iden-
tified. While the degradation of the crack bridging stress can be divided into three stages for the cases with the maximum crack opening displacement of 0.050 mm and 0.230 mm, it should be described using four stages when the maximum crack opening displacement is between 0.080 mm and 0.170 mm. The behaviour characteristics during each stage are illustrated in Fig. 6
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Fig. 5 (continued)
(a) and (b). In both situations, the crack bridging stress decreased very rapidly at the initial stage before the degradation decelerated sharply at the beginning of the second stage. This is defined as Stage Ⅰ. In the three-stage behaviour, the degradation rate would continuously decelerate with the increase of loading cycles and eventually the crack bridging stress was stabilised at the end of
the second stage. This is defined as Stage Ⅱ. Beyond this, the crack bridging stress was hardly affected by further loading cycles and remained nearly constant in the third stage defined as Stage III. However, another stage (referred to as Stage Ⅳ) with an accelerated rate of the stress degradation could be found in some situations. This stage occurred within the second stage and it
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173
Fig. 6. Different degradation behaviour of the crack bridging stress.
Normalised crack bridging stress
1.0 0.9 0.8 0.7 0.6
0.050 0.080 0.110 0.130 0.150 0.170 0.200 0.230
0.5 0.4 0.3 0.2 0.1 0.0 1
10
100
1000
10000
100000
Accumulated crack opening displacement , mm Logarithm scale Fig. 7. Crack bridging degradation with different maximum crack openings.
interrupted the decelerated bridging stress degradation. The start and terminus of this stage are indicated by the two inflection points on the curve. The initial stage generally lasted no more than 1000 cycles. But the crack bridging stress could reduce as much as 15–30% from their original values by the end of 1000 cycles. After the initial fast dropping stage, the gradually decelerated stress degradation could continue up to 1 105 to 5 105 cycles before the crack bridging stress started to level off. For the maximum crack opening displacement of 0.050 mm and 0.230 mm, the crack bridging stress was found to undergo a further 30% and 35% reduction in this stage and get stabilised at 55% and 35% of their original values, respectively. The three-stage degradation behaviour of the crack bridging stress of the PVA-ECC is quite similar to that of the steel fibre reinforced concrete [17]. However, the PVA-ECC exhibited more significant bridging stress degradation than the steel fibre reinforced concrete. While the PVA fibre showed the fast bridging stress degradation in 600–1000 cycles, the steel fibre showed this behaviour within the first 10–15 cycles [17]. When it comes to the residual bridging stress, for a comparison, the steel fibre was found to be able to retain about 70% of the original values for a maximum crack opening displacement of 0.050 mm [17]. The peculiar stage with an accelerated rate of stress degradation started to arise from the maximum crack opening displacement of 0.080 mm. It was found to occur at around 1 105, 7 104, 3 104, 2 104, 1.5 103 and 1 103 cycles for the maximum crack opening displacement of 0.080, 0.110, 0.130, 0.150, 0.170 and 0.200 mm, respectively. This stage had appeared earlier as the maximum crack opening displacement increased. Besides, the
duration of the accelerated stress degradation was found to reduce with the increase of the maximum crack opening displacement. This behaviour lasted for about 125,000 cycles for the maximum crack opening displacement of 0.080 mm, but only lasted for about 3000 cycles when the maximum crack opening displacement rose to 0.200 mm. The reduction in the crack bridging stress caused by this degradation behaviour was significant, ranging from 22% to 40%. The crack bridging stress reduced 22.5%, 27.5%, 31%, 35%, 40% and 25% for the maximum crack opening displacements of 0.080, 0.110, 0.130, 0.150, 0.170 and 0.200 mm respectively within this stage. The largest stress degradation was found to occur at the maximum crack opening displacement of 0.170 mm. Before this peak, the larger the maximum crack opening displacement, the more the stress decay. After that, it was the opposite. It indicates that the degradation behaviour of the crack bridging stress is affected by the maximum crack opening displacement, which is consistent with the tendency of fibre rupture behaviour as explained in the following. As the loading conditions of each series of the fatigue tension tests are different, the crack bridging stress degradation under different maximum crack opening displacements are plotted in Fig. 7 using the normalised crack bridging stress and accumulated crack opening displacement change. The accumulated crack opening displacement change was demonstrated to be an effective parameter to quantify the fibre-matrix interface damage [16]. The accumulated crack opening displacement change dAC is calculated by
dAC ¼ 2Nðdmax dmin Þ
ð1Þ
Two kinds of distinct degradation behaviour are identified in Fig. 7. In general, when the maximum crack opening displacement is small, such as the 0.050 mm in this study, the degradation process of the crack bridging stress is characterised by a few stable stages. Each of these stages has an almost constant rate of degradation with the increase of the accumulated crack opening displacement change. This kind of crack bridging stress degradation behaviour is believed to be attributed to the gradual weakening of the fibre-matrix interface [16]. The fibre bridging stress increases as the maximum crack opening displacement increases and may reach the residual fibre tensile strength. As a result, fibre fatigue rupture may start to take place once the maximum crack opening displacement increases to a certain value, such as the 0.100 mm in this study. The fibre rupture generally can cause a significant reduction of the crack bridging stress [25,26], and thus a stage with an accelerated rate of degradation is observed to arise in the process. This behaviour tends to occur earlier as the maximum crack opening displacement increases from 0.100 mm to 0.170 mm and this is also accompanied by more profound stress degradation. However, if the maximum crack opening displacement continues to increase from 0.170 mm to 0.200 mm, the effect of the fibre fatigue rupture on the stress degradation is found to decline, and it disappears at the maximum crack opening
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displacement of 0.230 mm and above. The degradation process of the crack bridging stress turns back to stable stages with an almost constant degradation rate separately. It is expected that most of the suspected fibres have ruptured under first few loading cycles due to the large crack opening displacement before they may break under the successive fatigue loading. Based on the discussions, the accelerated crack bridging degradation is thought to be related to the fibre fatigue rupture. The occurrence of the fibre fatigue rupture is thought to be typical for polymeric fibre reinforced cementitious composites [6]. This is because the polymeric fibres, due to their relatively low hardness, tend to suffer from severe surface abrasion when they slip against the hard surrounding matrix repeatedly. The fibre fatigue rupture was not found in the steel fibre reinforced concrete [17]. For the steel fibre reinforced concrete with a maximum crack opening displacement of 0.100 mm under cyclic fatigue tensile loading, the crack bridging stress reduced about 50% of its origin value after 105 cycles [17]. For the PVA-ECC studied here with a similar maximum crack opening displacement of 0.110 mm, a 40% reduction in the initial crack bridging stress was observed at 7 104 cycles just before the fibre fatigue rupture occurred. However, subsequently, reduction in the initial crack bridging stress reached about 78% after 105 cycles due to the fibre fatigue rupture. Hence, the effect of the fibre fatigue rupture on the crack bridging degradation of ECCs could be very significant.
4. Summary and conclusions In this paper, the individual crack behaviour of PVA-ECC under fatigue tensile loading was investigated experimentally. The uniaxial fatigue tension tests were conducted under deformation control with a constant crack opening displacement amplitude. The relation between the crack bridging stress at the maximum crack opening displacement and the number of load cycles was obtained. Eight maximum crack opening displacement levels were tested. It is found that the crack bridging stress decreases with the increase of load cycles. The crack bridging stress decreases rapidly within the first 600–1000 load cycles. Then it decelerates continuously with the increase of load cycles unless being interrupted by the occurrence of fibre fatigue rupture, which can induce accelerated stress degradation. The influence of the fibre fatigue rupture on the crack bridging stress degradation is related to the maximum crack opening displacement. The fibre fatigue rupture may not be observed when the maximum crack opening displacement is either too small or too large. Within a certain range, the fibre fatigue rupture is meant to show up, and the greater the maximum crack opening displacement, the earlier it will occur. The reduction of the crack bridging stress caused by the fibre fatigue rupture is found to be up to 40% of the original value. The effect of potential fibre fatigue rupture on the bridging stress degradation behaviour of ECCs can be very important and should be taken into account when applying ECCs in fatigue intensive structures. The relation between the crack bridging stress and the accumulated crack opening displacement change was also studied. Two distinct crack bridging stress degradation behaviours are identified for different maximum crack opening displacement levels. One is characterised by a steady stress degradation with the increase of the accumulated crack opening displacement change, the other is recognised by the presence of extra accelerated stress degradation related with the fibre fatigue rupture. This shows that the fibre fatigue rupture does occur in ECCs reinforced with polymeric fibres. It is of great importance to take into account the synergistic effect of both degradation mechanisms, i.e. the interface degradation and fibre fatigue rupture, in the analysis of mechanical degradation of ECCs. Finally, bridged cracks with smaller crack openings
generally show less significant stress degradation. Thus an enhanced multiple-cracking behaviour with formation of a large number of small cracks rather than a few large cracks can be very advantageous to the fatigue performance of ECCs.
Acknowledgements The scholarship support to the first author from UNSW Canberra and Chinese Scholarship Council is greatly acknowledged. Financial support from the Stake Key Laboratory of Subtropical Building Science awarded to the second author is also acknowledged.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on crack bridging in engineered cementitious composites under fatigue tensile loading Ting Huang a, Y.X. Zhang a,b,⇑, S.R. Lo a, C.K. Lee a a b
School of Engineering and Information Technology, The University of New South Wales, Canberra, Australian Defence Force Academy, ACT 2600, Australia State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, China
h i g h l i g h t s Experimental study of cyclic crack bridging behaviour of PVA-ECC. Establish of the relationship between crack bridging stress and the number of loading cycles. Study of the crack bridging degradation behaviours of PVA-ECC.
a r t i c l e
i n f o
Article history: Received 8 September 2016 Received in revised form 10 July 2017 Accepted 26 July 2017
Keywords: Crack bridging degradation Engineered Cementitious Composite (ECC) Polyvinyl alcohol (PVA) fibre Uniaxial fatigue tension test
a b s t r a c t The crack bridging behaviour of Engineered Cementitious Composites (ECCs) under fatigue tensile loading is investigated experimentally in this paper. Uniaxial fatigue tension tests were conducted on precracked specimens under deformation control with constant crack opening displacement amplitude. The crack bridging stress at the maximum crack opening displacement was obtained against the number of loading cycles. Eight maximum crack opening displacement levels were tested in total. The crack bridging stress was found to decrease with the increase of loading cycles. The crack bridging stress degradation is generally more significant in ECCs than in steel fibre reinforced concrete. In addition, the crack bridging stress degradation behaviour of ECCs reinforced with polymeric fibres was found to be distinct from that of steel fibre reinforced concrete with presence of accelerated stress degradation. The experiment demonstrates that it is important to take the fibre fatigue rupture into account in the analysis of mechanical behaviour degradation of ECCs and that the crack opening affects the crack bridging degradation behaviour. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The advances in material design theory and fibre technology in recent decades have greatly boosted the development of High Performance Fibre Reinforced Cementitious Composites (HPFRCCs), a class of fibre reinforced cement-based materials characterised by the pseudo strain-hardening behaviour in tension [1]. Engineered Cementitious Composites (ECCs), known for their enhanced tensile strain-hardening capacity and superior tensile ductility with less fibre reinforcement [2], belong to a relatively new and unique class of HPFRCCs. ECCs are usually reinforced with short discrete polymeric fibres, such as polyethylene (PE) [3], polyvinyl alcohol (PVA) [4] and polypropylene (PP) [5]. ECCs reinforced with no more ⇑ Corresponding author at: School of Engineering and Information Technology, The University of New South Wales, Canberra, Australian Defence Force Academy, ACT 2600, Australia. E-mail address: [email protected] (Y.X. Zhang). http://dx.doi.org/10.1016/j.conbuildmat.2017.07.193 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
than 2% by volume fraction of PE fibres or PVA fibres can attain a tensile strain capacity up to 3–6% [3,4]. In addition, the tensile strain-hardening process in ECCs is accompanied by multiple microcrackings. The high tensile ductility and microcracking are of great value in elevating the load carrying capacity, deformation capacity and energy absorption capacity as well as promoting the structural integrity of the structure. Moreover, the high tensile strain capacity and multiple microcracking characteristics offered by ECCs were found to be very promising in improving the structural fatigue performance especially at high stress levels [6]. Therefore, ECCs are regarded as very attractive construction and building materials for a broad range of applications. Especially, ECCs are highly suitable for situations where large deformation and/or cyclic/fatigue loading conditions are expected, such as earthquake-resistant structural members [7], link slabs for jointless bridging decks [8,9] and overlays for deteriorated pavement [10,11].
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The progressive formation of multiple microcracks is the key factor contributing to the high tensile ductility of ECCs. By using fracture mechanics and micromechanics theories to create certain fibre-matrix interaction within ECCs [12], the crackbridging fibres are able to sustain increasing load without catastrophic failure. This gives rise to a strain-hardening response after first cracking with initiation of multiple cracks. As a result, both the strain-hardening behaviour and the multiple-cracking behaviour of ECCs rely on the crack bridging behaviour of the fibres. The crack bridging capacity of the fibres generally will degrade under fatigue loading conditions [13–15] and such degradation behaviour needs to be taken into account when ECCs are employed in structures subjected to long-term fatigue loading. However, up-to-date investigations on the fatigue performance and mechanical behaviour degradation of ECCs are limited. Instead of conducting constant stress amplitude fatigue testing, Matsumoto et al. [13] studied the overall crack bridging capacity of multiple cracks under fatigue tension by conducting cyclic tension tests on PVA-ECC under constant strain amplitude. Tensile stress at the maximum strain level was found to continuously decrease with the increase of loading cycles, indicating the decrease of the fibre bridging stress across those cracks. The bridging stress degradation gradually decelerated for up to 103 cycles, and it then sharply accelerated between 103 and 105 cycles before the bridging stress eventually got stabilised at around 105 cycles. The underlying causes of such bridging stress degradation are associated with reduction of bond strength and/or loss of bridging fibres due to fibre fatigue rupture. In Lee et al.’s study [16], cyclic single-fibre pull-out tests on PVA fibres were conducted under displacement control with a constant amplitude. With fibre rupture deliberately avoided, the degradation of the fibre pull-out load can only be attributed to the deterioration of fibre-matrix interface properties due to continuous interface damage under cyclic load. However, the decrease in the fibre pull-out load decelerated constantly towards ceasing, showing no sign of abrupt acceleration compared to the bridging stress degradation behaviour of the composite. It is believed that the bridging stress degradation behaviour is affected by the combined actions of the different degradation mechanisms. However, this cannot be confirmed experimentally by just investigating the behaviour of a single fibre or the overall behaviour of multiple cracks. Zhang et al. studied the individual crack behaviour for steel fibre reinforced concrete under fatigue loading [17]. In steel fibre reinforced concrete, fibre fatigue rupture is unlikely to occur due to its high fibre tensile strength. Instead, the steel fibres tend to slip out of the matrix due to gradual reduction of interface bonding. As a result, after a rapid decrease at the initial stage, the crack bridging stress in steel fibre reinforced concrete was found to become stabilised gradually with the degradation rate decelerating continuously. While fibre fatigue rupture is believed to occur in cementitious composites reinforced with low-strength and low-hardness polymeric fibres such as most ECCs [6], no such experimental studies on the cyclic crack bridging behaviour of polymeric fibre reinforced cementitious composites have been reported yet. In order to gain an insightful understanding on the degradation behaviour of the mechanical properties of ECCs under fatigue loading, the individual crack bridging behaviour in a PVAECC under fatigue tensile loading is studied experimentally in this work. Fatigue tension tests were conducted with precracked specimens subjected to deformation-controlled cyclic loading. The effect of the maximum crack opening displacement on the crack bridging stress degradation behaviour is also investigated.
2. Experimental programme 2.1. Material Despite that ECCs reinforced with a wide variety of fibres have been successfully designed, special attention has been paid to the PVA-ECC due to the competitive price-performance ratio of PVA fibre [18]. In this work, the fatigue test was carried out on a PVA-ECC, which was developed in an earlier study by Huang and Zhang [19] with demonstrated tensile strain-hardening and multiple-cracking behaviour. The matrix of the PVA-ECC was composed of cement, fly ash, fine sand and water. ASTM Type I ordinary portland cement (OPC) and a low-calcium Class F fly ash were used. The fine sand had a maximum particle size of 300 mm and a mean particle size of 200 mm. Viscosity agent, i.e. high-range water-reducing admixture (HRWRA), was added in order to achieve adequate workability. Short discrete PVA fibre (trade-named KURALON K-II REC15), which was manufactured by Japan Kuraray Co., Ltd., was employed at a volume fraction of 2.2%. The chemical and physical properties of the OPC and fly ash are shown in Table 1. The properties of the PVA fibre and mix proportions of the PVA-ECC are shown in Tables 2 and 3, respectively. It should be noted that the size of the ingredients and mix proportions may affect the material properties of the ECC material significantly. The ingredients used and the corresponding mix proportions are normally tailored to meet the requirements for the tensile strain-hardening characteristics. The mix proportions of PVA-ECC used in this work were determined in such a way as to accommodate the use of local ingredients yet resulting in optimum tensile and compressive properties [19]. The basic mechanical properties of the PVA-ECC at the age of 28 days were tested and the results are summarised in Table 4. The Young’s modulus was determined using cylinder specimens of 100 mm in diameter and 200 mm in height. The compressive strength was determined using 50 50 50 mm cubic specimens. The tensile properties were measured by direct tension tests with dog-bone shaped coupon specimens. The dog-bone specimen has an effective testing zone of 80 35 20 mm and the loading rate is 0.20 mm/min [19].
2.2. Specimen According to the authors’ investigation, although a number of direct tension tests on the ECCs have been reported [13,14,18,20,21], no universal standard has been established to specify the specimen shape, dimensions and test method for the static and fatigue tension test of ECCs so far. However, the dog-bone shaped prismatic specimen with a reduced section as shown in Fig. 1(a) has been most often used in the fatigue tension test of ECCs [13,14]. The tensile specimen has been designed especially to eliminate the overall failure of a specimen at or near the grip and to control the initiation of cracks in a specific area. Within this area, multiple cracks are intended to initiate randomly and grow. In order to study and measure the relationship between the crack bridging stress and the crack opening of a single crack, tensile specimen with a notch introduced at the middle was proposed to control the crack location [17,22,23]. In the present work, uniaxial fatigue tension tests were conducted on pre-notched specimens for the study of the cyclic crack bridging behaviour of the PVA-ECC. The specimen geometry and dimensions are shown in Fig. 1(b). A 5 mm wide notch was
Table 1 Chemical and physical properties of the OPC and Class F fly ash. Property Chemical properties SiO2 (%) Fe2O3 (%) Al2O3 (%) CaO (%) MgO (%) SO3 (%) Na2O (%) K2O (%) P2O5 (%) TiO2 (%) MnO (%) Mn2O3 (%) Loss on ignition (%) Soluble residue (%) pH Physical properties Fineness (m2/kg) Bulk density (kN/m3) Moisture (%)
OPC
Fly Ash
20.5 3.2 4.1 64.8 1 3.2 0.23 0.68
59.6 3.3 29.1 3.2 0.4 0.2 0.28 0.48 0.7 1.1
1.3 0.38 12.4 353 3.1 0.19
<0.1 1.5 11.5 647 2.21 <0.1
T. Huang et al. / Construction and Building Materials 154 (2017) 167–175 Table 2 Basic properties of the PVA fibre. Nominal tensile strength (MPa)
Young’s modulus (GPa)
Diameter (mm)
Length (mm)
1600
41
39
12
Table 3 Composition and mix proportion of the PVA-ECC.
*
Cement
Fly ash
Sand
Water
HRWRA
PVA fibre*
1.0
1.2
0.8
0.65
0.01
2.2
PVA fibre is by volume fraction, and all others are by weight.
Table 4 Mechanical properties of the PVA-ECC at 28 days. Young’s modulus (GPa)
Compressive strength (MPa)
Ultimate tensile strength (MPa)
Tensile strain capacity (%)
20.3
56
5.26
1.01
introduced circumferentially in the middle of the specimen with deep notches of 12 mm in depth on the front and back surfaces for crack initiation and shallow notches of 7 mm in depth on the two laterals to guide crack propagation. A mixer with a rotating blade was used to produce the PVA-ECC mixture. At first all solid ingredients except fibres were dry mixed for a couple of minutes. During this time, all HRWRA was added in the water to form a liquid solution. After the dry ingredients were thoroughly mixed, the HRWRA solution was added and all ingredients were mixed for another couple of minutes. Once the liquefied fresh mortar mixture had reached a consistent and uniform state, the fibres were gradually added in small amounts while the mixer kept mixing until all the fibres were completely added. The mixture was further mixed for a couple of minutes to make sure all fibres could disperse evenly in the mortar matrix without clumping before being cast into the moulds of the dog-bone shaped prismatic specimen. The specimens were demoulded after 24 h, and then cured at 100% relative humidity and 23 °C until the day of testing. The notches were produced before the testing using a diamond saw. The specimens were tested at an age of at least 28 days.
2.3. Test set-up and loading procedures The set-up for the uniaxial fatigue tension test is shown in Fig. 2. All tests were conducted using a 250 kN load capacity InstronÒ actuator equipped for closed-loop testing. The specimen was held at each end by clamping using four tightening bolts.
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Sand meshes were employed in between the clamp-specimen interfaces to enhance the friction contact. The clamping force should be large enough to make a reliable specimen fixture, yet will not damage the specimen. In order to determine the most optimal clamping force, different tightening torques were tried and their abilities to produces a reliable clamping system were examined until the optimal tightening torque was found. Nevertheless, the silicon carbide particles on the sand mesh could be crushed/triturated or the specimen gradually creeped during the fatigue testing, which would form a gap between the clamp-specimen interface and result in the loss of clamping force. So each tightening bolt was used with a stack of Belleville spring washers. The spring washer stack had been configured to obtain a deflection of 2 mm under the set clamping force and would make up for any gap of up to 2 mm. It was expected that the spring washer stack would recover its deflection to restore the clamping system in case the tightening bolt was relaxed. Two LVDTs with a 15 mm gauge length were used to measure the crack opening displacement, which were attached to the specimen across the notches as shown in Fig. 2. Once a crack is formed at the notch, the displacement across the notch is lumped at the crack opening displacement. Due to such a small gauge length used, the deformation outside the notch is negligible and the crack opening displacement is taken to be equal to the displacement measured. In uniaxial tension tests especially for cementitious materials, special attention needs to be paid to avoid unintended bending effects, which may arise from the misalignment of the specimen and can affect the test results severely. In order to ensure the specimen remains correctly aligned during the direct tension test, the specimen should be first perfectly aligned in the loading direction before the test starts and allowed to rotate freely in the test so that it can be automatically adjusted during the testing. As a result, the pin-pin boundary condition has been generally employed for the static tensile testing of ECCs in previous studies. Such a boundary condition could be enforced by installing at both ends a universal joint between the specimen and the loading rig [20,24]. For static testing, such set-up will allow the applied axial load to be transferred from the loading rig to the specimen without causing any bending effects, and multiple cracks will successively occur under an increasing load. However, when it comes to the single crack behaviour under cyclic loading, the effect of secondary bending moment occurred at the crack will become significant under rotatable boundaries and make a great impact. Such secondary bending moment originates in the nonuniform stiffness distribution throughout the crack plane caused by nonuniform distribution of bridging fibres. Since this study focused on the cyclic crack bridging behaviour of an individual crack in the PVA-ECC, special attention was dedicated to initiate a uniform crack throughout the cross section. The universal joints were also utilised in this study, but only for the instalment of specimen for a perfect alignment at the beginning of the test. They were locked after the test started in order to suppress the free rotation of the specimen and the occurrence of the secondary moment. In order to determine the degradation of the crack bridging capacity, the uniaxial fatigue tension test was conducted under deformation control with a constant amplitude between the maximum crack opening displacement dmax and the minimum crack opening displacement dmin . A total of eight series of fatigue tension tests with different maximum crack opening displacement levels were carried out. The eight selected maximum crack opening displacement levels were 0.050, 0.080, 0.110, 0.130, 0.150, 0.170, 0.200 and 0.230 mm, respectively. In order to obtain three valid results for each case, extra specimens were prepared and at least three
Fig. 1. (a) Geometry of the commonly used tensile specimen for fatigue tension test of ECCs; (b) Pre-notched specimen for the assessment of cyclic crack bridging.
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Fig. 2. Test set-up of measuring crack bridging in uniaxial fatigue tension.
10.00 9.00 8.00
Load , kN
7.00 6.00 5.00
1 10 100 1,000 10,000 100,000 200,000 300,000
max
=0.150 mm,
min
=0.120 mm
4.00 3.00 2.00 1.00 0.00 0.120
0.130
0.140
0.150
Crack opening displacement , mm Fig. 4. Typical load-crack opening displacement curve from the fatigue tension test. Fig. 3. Loading procedure for conducting cyclic crack bridging test under deformation control.
3. Results and discussion specimens were tested for each displacement level. The minimum crack opening displacement corresponding to a specific maximum crack opening displacement was determined by a loading-unloading tension test in the first load application for each specimen. The specimen was first loaded at a rate of 0.0003 mm/s to induce a crack until reaching the assigned maximum crack opening displacement. It was then unloaded at a rate of 0.05 kN/s to almost zero load (e.g. 0.5 kN). The residual crack opening displacement at this point was then chosen as the minimum crack opening displacement that corresponded to this assigned maximum crack opening displacement for this specimen. Finally, the cyclic load was applied with a sine waveform between the maximum and minimum crack opening displacement at a frequency of 2 Hz for at least 200,000 cycles. It was stopped when either the maximum load ceased to decline or the number of cycles reached 500,000 cycles. A typical loading procedure is shown in Fig. 3. The testing system worked in conjunction with MTS TestSuiteTM Multipurpose Elite software for loading control and data collection. During the fatigue tension tests, the load and crack opening displacement data were recorded with a data acquisition speed of 80 Hz.
Fig. 4 shows the typical load-crack opening displacement curves obtained from the fatigue tension test when the number of load cycles N ¼ 1, 10, 102, 103, 104, 105, 2 105 and 3 105. As can be seen, the secant stiffness of the reloading branches reduced with the increase of cycles, and thus the load at the maximum crack opening displacement decreased gradually. The diagrams of the crack bridging stress at the maximum crack opening displacement versus the number of loading cycles under the different maximum crack opening displacement levels are shown in Fig. 5(a)–(h). In Fig. 5, while the results in the range of 1–10,000 cycles are displayed in Fig. 5(ai)–(hi), those in the range of 1–500,000 cycles are displayed in Fig. 5(aii)–(hii). Note that in these figures only the average result of the individual tests for each case is displayed, and the crack bridging stress at the maximum crack opening
T. Huang et al. / Construction and Building Materials 154 (2017) 167–175
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Fig. 5. Relation of normalised bridging stress and number of fatigue cycles.
displacement rN has been normalised by its value at the first cycle r1 , i.e. rN =r1 . Fig. 5 clearly shows that the crack bridging stress at the maximum crack opening displacement decreases with the increase of loading cycles. Furthermore, as can be seen from Fig. 5, two major degradation behaviour of the crack bridging stress in the PVA-ECC can be iden-
tified. While the degradation of the crack bridging stress can be divided into three stages for the cases with the maximum crack opening displacement of 0.050 mm and 0.230 mm, it should be described using four stages when the maximum crack opening displacement is between 0.080 mm and 0.170 mm. The behaviour characteristics during each stage are illustrated in Fig. 6
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Fig. 5 (continued)
(a) and (b). In both situations, the crack bridging stress decreased very rapidly at the initial stage before the degradation decelerated sharply at the beginning of the second stage. This is defined as Stage Ⅰ. In the three-stage behaviour, the degradation rate would continuously decelerate with the increase of loading cycles and eventually the crack bridging stress was stabilised at the end of
the second stage. This is defined as Stage Ⅱ. Beyond this, the crack bridging stress was hardly affected by further loading cycles and remained nearly constant in the third stage defined as Stage III. However, another stage (referred to as Stage Ⅳ) with an accelerated rate of the stress degradation could be found in some situations. This stage occurred within the second stage and it
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173
Fig. 6. Different degradation behaviour of the crack bridging stress.
Normalised crack bridging stress
1.0 0.9 0.8 0.7 0.6
0.050 0.080 0.110 0.130 0.150 0.170 0.200 0.230
0.5 0.4 0.3 0.2 0.1 0.0 1
10
100
1000
10000
100000
Accumulated crack opening displacement , mm Logarithm scale Fig. 7. Crack bridging degradation with different maximum crack openings.
interrupted the decelerated bridging stress degradation. The start and terminus of this stage are indicated by the two inflection points on the curve. The initial stage generally lasted no more than 1000 cycles. But the crack bridging stress could reduce as much as 15–30% from their original values by the end of 1000 cycles. After the initial fast dropping stage, the gradually decelerated stress degradation could continue up to 1 105 to 5 105 cycles before the crack bridging stress started to level off. For the maximum crack opening displacement of 0.050 mm and 0.230 mm, the crack bridging stress was found to undergo a further 30% and 35% reduction in this stage and get stabilised at 55% and 35% of their original values, respectively. The three-stage degradation behaviour of the crack bridging stress of the PVA-ECC is quite similar to that of the steel fibre reinforced concrete [17]. However, the PVA-ECC exhibited more significant bridging stress degradation than the steel fibre reinforced concrete. While the PVA fibre showed the fast bridging stress degradation in 600–1000 cycles, the steel fibre showed this behaviour within the first 10–15 cycles [17]. When it comes to the residual bridging stress, for a comparison, the steel fibre was found to be able to retain about 70% of the original values for a maximum crack opening displacement of 0.050 mm [17]. The peculiar stage with an accelerated rate of stress degradation started to arise from the maximum crack opening displacement of 0.080 mm. It was found to occur at around 1 105, 7 104, 3 104, 2 104, 1.5 103 and 1 103 cycles for the maximum crack opening displacement of 0.080, 0.110, 0.130, 0.150, 0.170 and 0.200 mm, respectively. This stage had appeared earlier as the maximum crack opening displacement increased. Besides, the
duration of the accelerated stress degradation was found to reduce with the increase of the maximum crack opening displacement. This behaviour lasted for about 125,000 cycles for the maximum crack opening displacement of 0.080 mm, but only lasted for about 3000 cycles when the maximum crack opening displacement rose to 0.200 mm. The reduction in the crack bridging stress caused by this degradation behaviour was significant, ranging from 22% to 40%. The crack bridging stress reduced 22.5%, 27.5%, 31%, 35%, 40% and 25% for the maximum crack opening displacements of 0.080, 0.110, 0.130, 0.150, 0.170 and 0.200 mm respectively within this stage. The largest stress degradation was found to occur at the maximum crack opening displacement of 0.170 mm. Before this peak, the larger the maximum crack opening displacement, the more the stress decay. After that, it was the opposite. It indicates that the degradation behaviour of the crack bridging stress is affected by the maximum crack opening displacement, which is consistent with the tendency of fibre rupture behaviour as explained in the following. As the loading conditions of each series of the fatigue tension tests are different, the crack bridging stress degradation under different maximum crack opening displacements are plotted in Fig. 7 using the normalised crack bridging stress and accumulated crack opening displacement change. The accumulated crack opening displacement change was demonstrated to be an effective parameter to quantify the fibre-matrix interface damage [16]. The accumulated crack opening displacement change dAC is calculated by
dAC ¼ 2Nðdmax dmin Þ
ð1Þ
Two kinds of distinct degradation behaviour are identified in Fig. 7. In general, when the maximum crack opening displacement is small, such as the 0.050 mm in this study, the degradation process of the crack bridging stress is characterised by a few stable stages. Each of these stages has an almost constant rate of degradation with the increase of the accumulated crack opening displacement change. This kind of crack bridging stress degradation behaviour is believed to be attributed to the gradual weakening of the fibre-matrix interface [16]. The fibre bridging stress increases as the maximum crack opening displacement increases and may reach the residual fibre tensile strength. As a result, fibre fatigue rupture may start to take place once the maximum crack opening displacement increases to a certain value, such as the 0.100 mm in this study. The fibre rupture generally can cause a significant reduction of the crack bridging stress [25,26], and thus a stage with an accelerated rate of degradation is observed to arise in the process. This behaviour tends to occur earlier as the maximum crack opening displacement increases from 0.100 mm to 0.170 mm and this is also accompanied by more profound stress degradation. However, if the maximum crack opening displacement continues to increase from 0.170 mm to 0.200 mm, the effect of the fibre fatigue rupture on the stress degradation is found to decline, and it disappears at the maximum crack opening
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displacement of 0.230 mm and above. The degradation process of the crack bridging stress turns back to stable stages with an almost constant degradation rate separately. It is expected that most of the suspected fibres have ruptured under first few loading cycles due to the large crack opening displacement before they may break under the successive fatigue loading. Based on the discussions, the accelerated crack bridging degradation is thought to be related to the fibre fatigue rupture. The occurrence of the fibre fatigue rupture is thought to be typical for polymeric fibre reinforced cementitious composites [6]. This is because the polymeric fibres, due to their relatively low hardness, tend to suffer from severe surface abrasion when they slip against the hard surrounding matrix repeatedly. The fibre fatigue rupture was not found in the steel fibre reinforced concrete [17]. For the steel fibre reinforced concrete with a maximum crack opening displacement of 0.100 mm under cyclic fatigue tensile loading, the crack bridging stress reduced about 50% of its origin value after 105 cycles [17]. For the PVA-ECC studied here with a similar maximum crack opening displacement of 0.110 mm, a 40% reduction in the initial crack bridging stress was observed at 7 104 cycles just before the fibre fatigue rupture occurred. However, subsequently, reduction in the initial crack bridging stress reached about 78% after 105 cycles due to the fibre fatigue rupture. Hence, the effect of the fibre fatigue rupture on the crack bridging degradation of ECCs could be very significant.
4. Summary and conclusions In this paper, the individual crack behaviour of PVA-ECC under fatigue tensile loading was investigated experimentally. The uniaxial fatigue tension tests were conducted under deformation control with a constant crack opening displacement amplitude. The relation between the crack bridging stress at the maximum crack opening displacement and the number of load cycles was obtained. Eight maximum crack opening displacement levels were tested. It is found that the crack bridging stress decreases with the increase of load cycles. The crack bridging stress decreases rapidly within the first 600–1000 load cycles. Then it decelerates continuously with the increase of load cycles unless being interrupted by the occurrence of fibre fatigue rupture, which can induce accelerated stress degradation. The influence of the fibre fatigue rupture on the crack bridging stress degradation is related to the maximum crack opening displacement. The fibre fatigue rupture may not be observed when the maximum crack opening displacement is either too small or too large. Within a certain range, the fibre fatigue rupture is meant to show up, and the greater the maximum crack opening displacement, the earlier it will occur. The reduction of the crack bridging stress caused by the fibre fatigue rupture is found to be up to 40% of the original value. The effect of potential fibre fatigue rupture on the bridging stress degradation behaviour of ECCs can be very important and should be taken into account when applying ECCs in fatigue intensive structures. The relation between the crack bridging stress and the accumulated crack opening displacement change was also studied. Two distinct crack bridging stress degradation behaviours are identified for different maximum crack opening displacement levels. One is characterised by a steady stress degradation with the increase of the accumulated crack opening displacement change, the other is recognised by the presence of extra accelerated stress degradation related with the fibre fatigue rupture. This shows that the fibre fatigue rupture does occur in ECCs reinforced with polymeric fibres. It is of great importance to take into account the synergistic effect of both degradation mechanisms, i.e. the interface degradation and fibre fatigue rupture, in the analysis of mechanical degradation of ECCs. Finally, bridged cracks with smaller crack openings
generally show less significant stress degradation. Thus an enhanced multiple-cracking behaviour with formation of a large number of small cracks rather than a few large cracks can be very advantageous to the fatigue performance of ECCs.
Acknowledgements The scholarship support to the first author from UNSW Canberra and Chinese Scholarship Council is greatly acknowledged. Financial support from the Stake Key Laboratory of Subtropical Building Science awarded to the second author is also acknowledged.
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