We added CaCO3 whiskers into polyvinyl alcohol (PVA)-steel hybrid fiber system to obtain multiscale hybrid fiber reinforced cement mortar (MHFRC). Three-point bending (3-p-b) tests were carried out on 64 notched beams to investigate fracture behavior of MHFRC. Double K Fracture Criterion (DKFC) and Work Fracture Method (WFM) were employed to obtain fracture parameters. Influence of the volume fraction of CaCO3 whiskers, content of PVA-steel hybrid fiber and water/ cement ratio (w/c) on fracture parameters are discussed. Addition of composite fibers consisting of CaCO3 whiskers and PVA-steel hybrid fibers could improve fracture behavior of MHFRC. As the content of CaCO3 whiskers increases, fracture parameters first increase and then decrease. Content of PVA-steel fibers also affect fracture behavior of the matrix. Thus, an optimum ratio between CaCO3 whiskers and PVA and steel fibers contents exist that provide the best fracture performance of cement matrix: 1 vol % of CaCO3 whiskers, 0.5 vol % of PVA fibers and 1.5 vol % of steel fibers (S15P05W10). Influence of the w/c value is also discussed. Fracture toughness (KIC) and fracture energy (GF) of S15P05W10 group decreased as w/c values increased. The synergy of fibers in S15P05W10 was evaluated quantitatively, and the results indicated positive synergy effect on unstable fracture toughness (Kun IC ) and fracture energy (GF) in cement matrix with higher w/c values.
Accepted Manuscript Fracture Behavior of Cement Mortar Reinforced by Hybrid Composite Fiber Consisting of CaCO3 Whiskers and PVA-Steel Hybrid Fibers Mingli Cao, Chaopeng Xie, Junfeng Guan PII: DOI: Reference: S1359-835X(19)30075-2 https://doi.org/10.1016/j.compositesa.2019.03.002 JCOMA 5356 To appear in: Composites: Part A Received Date: Revised Date: Accepted Date: 11 November 2018 22 February 2019 March 2019 Please cite this article as: Cao, M., Xie, C., Guan, J., Fracture Behavior of Cement Mortar Reinforced by Hybrid Composite Fiber Consisting of CaCO3 Whiskers and PVA-Steel Hybrid Fibers, Composites: Part A (2019), doi: https://doi.org/10.1016/j.compositesa.2019.03.002 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain Fracture Behavior of Cement Mortar Reinforced by Hybrid Composite Fiber Consisting of CaCO3 Whiskers and PVA-Steel Hybrid Fibers Mingli Caoa, Chaopeng Xiea,*, Junfeng Guanb,** a School of Civil Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China b School of Civil and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450045, China ABSTRACT We added CaCO3 whiskers into polyvinyl alcohol (PVA)-steel hybrid fiber system to obtain multiscale hybrid fiber reinforced cement mortar (MHFRC) Three-point bending (3-p-b) tests were carried out on 64 notched beams to investigate fracture behavior of MHFRC Double K Fracture Criterion (DKFC) and Work Fracture Method (WFM) were employed to obtain fracture parameters Influence of the volume fraction of CaCO3 whiskers, content of PVA-steel hybrid fiber and water/ cement ratio (w/c) on fracture parameters are discussed Addition of composite fibers consisting of CaCO3 whiskers and PVA-steel hybrid fibers could improve fracture behavior of MHFRC As the content of CaCO3 whiskers increases, fracture parameters first increase and then decrease Content of PVA-steel fibers also affect fracture behavior of the matrix Thus, an optimum ratio between CaCO3 whiskers and PVA and steel fibers contents exist that provide the best fracture performance of cement matrix: vol % of CaCO whiskers, 0.5 vol % of PVA fibers and 1.5 vol % of steel fibers (S15P05W10) Influence of the w/c value is also discussed Fracture toughness (KIC) and fracture energy (GF) of S15P05W10 group decreased as w/c values increased The synergy of fibers in S15P05W10 was evaluated quantitatively, and the results indicated positive synergy effect on unstable fracture toughness (KunIC ) and fracture energy (GF) in cement matrix with higher w/c values Negative synergy was observed for the initial fracture toughness (K ini IC ) Comprehensive reinforcing index (RIv) was introduced as the characteristic parameters of the hybrid fibers Fracture parameters increased first and then decreased as RIv increased Furthermore, the microscope morphologies of CaCO3 whiskers, PVA and steel fibers in the cement matrix were shown These results helped to establish microscopic reinforcing mechanism of the hybrid fibers in the cement matrix Based on the experiment results, empirical formulas, which taking into account fiber factor RIv and matrix factor w/c, were proposed to calculate fracture parameters of MHFRC KEYWORDS: CaCO3 whisker; hybrid fiber; fracture parameter; synergy; fiber reinforcing index; water/ cement ratio HIGHLIGHTS 3-p-b tests for multiscale hybrid-fiber reinforced cement mortar were performed S15P05W10 group showed higher fracture toughness and fracture energy Synergy of fibers in S15P05W10 group with different waters/cement ratio were evaluated Microscopic reinforcing mechanism of hybrid fibers was clarified Theoretical models were proposed to calculate fracture parameters Introduction Fibers can effectively improve mechanical properties of cement-based materials, such as low tensile strength, brittle failure, weak cracking resistance and poor energy absorption capability [1-3] Thus, fibers are widely used as reinforcing materials, particularly in cement-based materials [1,4] Traditionally, metallic, polymeric and natural fibers, especially steel fibers are widely implemented in cement-based materials to “arrest” the cracks [5-6] The advantages of steel fibers include restricting or delaying small cracks from developing into macro-cracks, fiber bridge the cracks in post-cracking stage, and enhancing ductility and energy absorption capability of the matrix [2,4] Recently, to improve properties of cement-based materials and to save cost, the concept of hybrid fiber was proposed, which involves, mixing fibers of various types and with different sizes into a hybrid fiber composite [7] Comparing with single fiber reinforced cement-based materials, hybrid fibers inherit advantages of the individual fibers making hybrid-fiber reinforced cement-based materials with superior performance [7] Hossain [8] used polyvinyl alcohol (PVA) and steel fibers to reinforce self-consolidating concrete (FRSCC), and studied its strength and fracture energy The result showed that the compressive/flexural/splitting tensile strength and fracture energy of FRSCC improved, and fracture energy gain was more significant than strength gain Almusallam [9] performed mode-I fracture tests on steel-Kevlar-polypropylene hybrid-fiber reinforced concrete (HFRC), and studied how these fibers affected fracture energy of HFRC The results indicated that replacing steel fiber with Kevlar or polypropylene fiber does not affect the fracture energy However, higher steel fiber content, increases the fracture energy Lawler [10] reported that microfibers could increase the mechanical properties of hybrid-fiber reinforced mortar in pre-peak, and that macro-fibers play a bridging role of macro-cracks during the post-cracking However, all these hybrid fibers were macroscopic in scale Geometrical sizes of these fibers are not compatible with the scales of cement hydration and cement pastes [11] Carbon nanotubes and nanofibers were also reported for reinforcement of cement-based materials to achieve toughening and reinforcing at the microscale [12-16] However, their complex dispersion processes and high costs restrict their wider applications CaCO3 whiskers are new type of micro-fibers able to effectively improve mechanical properties of cement-based materials [17-19] Cao et al [20-22] employed CaCO3 whiskers, PVA and steel fibers to form a new multiscale hybrid fiber system with multilevel and multiscale characteristics equal or comparable to cement-based materials A series of test demonstrated that cementitious composites reinforced with multiscale hybrid fibers could arrest cracks at multilevel and improve the flexural strength, energy absorption capacity and plastic shrinkage performance of the matrix Table shown the types and size of different fibers used in the literatures Table The types and size of different fibers used in the literatures Researchers Hossain et al [8] Almusallam et al [9] Konsta et al.[12][14] Gdoutos et al.[13] Hu et al.[15] Stynoski et al.[16] Cao et al.[17-22] Fiber types Fiber size Classify PVA fiber Diameter 0.04mm, Length 8mm Macro- reinforcers FibraFlex (FF) metallic fiber Width 1.6mm, Thickness 0.029mm, Length 20mm Width 1.0mm, Thickness 0.024mm, Length 5mm Macro- reinforcers Hook-ends steel fiber Diameter 0.75mm, Length 60mm Macro- reinforcers Kevlar fiber Diameter 0.5mm, Length 45mm Macro- reinforcers Polypropylene fiber Width 1.0mm, Thickness 0.6mm, Length 50mm Macro- reinforcers Multi-walled carbon nanotubes Diameter 20-40nm, Length 10-30μm (MWCNTs) Diameter 20-40nm, Length 10-100μm MWCNTs Diameter 20-45nm, Length ≥10μm Nano- reinforcers Carbon nanofiber Diameter 100nm, Length 50-200μm Micro- reinforcers MWCNTs-TNM3 Diameter 10-20nm, Length 10-30μm Nano- reinforcers MWCNTs-TNMC1 Diameter＜8nm, Length 10-30μm Nano- reinforcers Carbon fiber Length 6mm Macro- reinforcers MWCNTs Diameter 20-40nm, Length 0.5-40μm Nano- reinforcers CaCO3 whisker Diameter 0.5-2μm, Length 20-30μm Micro- reinforcers Nano- reinforcers Fracture behavior is a fundamental mechanical property of hardened cement-based materials that play an important role in design and safety evaluation of structures [23] Linear elastic fracture mechanics was introduced by Kaplan in 1961 to determine fracture toughness of concrete Numerous fracture tests were performed since then to measure the fracture behavior of concrete [24-25] However, as research progressed, fracture process zone (FPZ) was found at the tip of a crack in quasi-brittle materials, which causes the size effect of fracture parameters [26] Therefore, several nonlinear fracture models were developed to measure fracture toughness, such as fictitious crack model, crack band model, two-parameter fracture model, size effect model, effective crack model and double-K fracture criterion (DKFC) [24-26] These nonlinear fracture models can not only be applied to quasi-brittle materials, but can also be used in fiber-reinforced cementitious composites (FRCC) Ghasemi et al [1] obtained fracture toughness of FRSCC using the size effect model Kazemi et al [2] determined the fracture parameters of steel-fiber reinforced high strength concrete using the work of fracture method (WFM), which is based on the fictitious crack and size effect models Carpinteri et al [3] considered possible crack deflection during stable crack propagation and proposed a modified two-parameter fracture model to calculate Mode I plain-strain fracture toughness of polypropylene-fiber reinforced concrete Zhang et al [27] proposed a new crack extension resistance theory that simultaneously considers cohesive forces and bridging stresses to calculate the double-K fracture parameters of steel-fiber reinforced concrete Their results showed that unstable fracture toughness increased as the volume ratio of steel fiber increased However, initial fracture toughness did not have a similar trend Fracture behavior based on 3-p-b test of cement-based materials reinforced by CaCO3 whiskers and PVA-steel hybrid fibers did not receive a lot of attention in the literature Therefore, our goal is to study fracture behavior of CaCO3 whiskers-PVA-steel hybrid fibers reinforced cement mortar (MHFRC) CaCO3 whiskers, a new type of microfiber material, was mixed with PVA-steel hybrid fibers and then added into the cement mortar We studied how CaCO3 whisker content, change of the PVA-steel fiber content and water cement ratios (w/c) affect mechanical propertied of MHFRC Fracture toughness (KIC) and fracture energy (GF) were calculated based on DKFC and WFM, respectively The results were compared to those obtained for unmodified cement mortar The synergy between CaCO3 whiskers, PVA and steel fibers was evaluated quantitatively Moreover, relationship between the comprehensive reinforcing index (RIv), w/c and fracture parameters was developed This paper also describes crack resistance process and morphological characteristics of CaCO3 whisker, PVA and steel fibers in cement mortar and clarifies the microscopic reinforcing mechanism of the hybrid fibers Finally, empirical formulas taking into account factors associated with both fiber (RIv) and matrix (w/c) were proposed to calculate fracture parameters of MHFRC Fracture parameters 2.1 Double-K fracture criterion (DKFC) Fracture toughness (KIC) is an important parameter in fracture analysis, and different fracture models were proposed for their determination fracture parameters Xu and Reinhardt [28-30] studied crack propagation of quasi-brittle materials and proposed analytical methods to determine fracture parameters A simplified method to determine double-K fracture parameters of three-point bending (3-p-b) tests was further developed [31] Two important characteristics, initial fracture un toughness (Kini IC ) and unstable fracture toughness (K IC ), were introduced to evaluate fracture behavior and to divide the crack propagation process into the three stages: K ICini , crack initiation stage K K ICini K K ICun , stable crack propagation stage (1), K ICun , unstable crack propagation stage K where K is the stress intensity factor, which represents the crack-extension resistance under conditions of crack-tip plane strain in Mode I [32], Kini IC is the initial fracture toughness, which represent the stress intensity factor at the initial crack tip when external load reaches the initial cracking load, KunIC is the unstable fracture toughness, which is defined as a stress intensity factor at the critical effective crack tip at the external load equal to the peak load [26] According to DKFC, Kini IC can be calculated using LEFM formula: 3P0 S 2W B K ICini F1 (V0 ) (2), a0 F1 (V0 ) 1.99 V0 ( V0 )( 2.15 3.93V0 2.7V02 ) (1 (3), 2V0 )( V0 )2 where P0 is the initial cracking load, which can be obtained by strain gauge technique; S, W and B are span, height and thickness of the beams, respectively (at S/W =4), a0 is length of the initial crack and V0 represents height ratios of beams, which can be obtained as a0/W Similarly, KunIC can be calculated based on modified LEFM formula, which considers FPZ existence: 3Pmax S 2W B K ICun F1 (Vc ) 1.99 Vc ( Vc )( 2.15 3.93Vc 2.7Vc ) (5), (1 ac (4), ac F1 (Vc ) (W H )arctg 2Vc )( Vc )2 B E CMODc 32.6 Pmax 0.1135 H0 (6), where Pmax is the peak load; ac is the critical effective crack length, which corresponds to the peak load; CMODc is the critical crack mouth opening displacement, which corresponds to the peak load; Vc represents the height ratios of the beams which can be calculated as ac/W; H0 is the thickness of the knife edges used to fix extensometer, and E is the Young’s modulus, which obtained from the compressive cylinder measurements 2.2 Work fracture method (WFM) Fracture energy (GF) is another important parameter in fracture analysis The work of fracture method (WFM), which based on fictitious crack model, is the simplest and most popular method to acquire the fracture energy [2] In our work, 3-p-b test of notched beams recommend by RILEM 50-FMC was employed to determine the fracture energy [33] According to the WFM, fracture energy can be calculated from the following equations: GF =(W0 W0 (7), mg ) / Alig F( )d (8), where W0 is the work of the external load and can be calculated by the area under the load-net deflection, m is the weight of the beams, g represents acceleration due to gravity equal to 9.81m/s2, δ0 is the net deflection at the final failure of the beam, and Alig is area of the ligaments of notched beams Experimental procedure 3.1 Materials We used Type P·O 42.5R cement from Onoda Cement Factory (Dalian, China) and fly ash from Gongyi No Power Factory (Zhengzhou, China) Moreover, to ensure the repeatability of subsequent tests, their chemical compositions are shown in Table Silica sand with a fineness modulus of 1.9 and density of 2.65 g/cm3 was used as fine aggregate Superplasticizer from Sika was used to ensure workability of the fresh mixture CaCO3 whiskers were provided by Youxing Technology Co (Changde,China), and their chemical composition is also shown in Table Smooth and straight PVA fibers were acquired from Wanwei High-Tech Material Co (Chaohu, China) Steel fibers were from Bekaert OL Their properties and morphologies are presented in Table and Figure 1, respectively Defoaming agent, tributyl phosphate, was applied to eliminate the bubbles in the mixture Table Chemical compositions of cement, fly ash and CaCO3 whiskers wt.% Composition CaO SiO2 Al2O3 SO3 Fe2O3 MgO K2O TiO2 SrO ZnO P2O5 MnO CuO MoO3 Cement 58.61 22.58 6.01 4.57 4.17 1.91 1.18 0.43 0.24 0.09 0.07 0.06 0.03 0.03 Fly ash 9.80 51.49 24.36 2.14 5.49 1.20 - - - - - - - - Whisker 92.31 0.44 0.10 0.60 0.19 5.96 - - 0.73 - - - - - Table Fibers properties Fiber type Steel fiber PVA fiber CaCO3 whisker Density (g/cm3) 7.80 1.30 2.86 Length, l (mm) 13 0.02 - 0.03 Diameter, d (μm) 200 39.7 0.5 - Aspect ratio, l/d 65 151.13 10 - 60 Tensile strength, f (MPa) 2850 1529.5 3000 - 6000 (a) (b) (c) (d) Figure Morphologies of CaCO3 whiskers (optical image (a) and SEM micrograph (b)) as well as (c) PVA and (d) steel fibers 3.2 Mixing design To investigate the effect of the volume fraction of CaCO3 whiskers on the MHFRC fracture parameters, 3-p-b fracture tests were using MHFRCs with different CaCO3 whisker contents and the same PVA and steel fibers content Influence of volume fraction of PVA and steel fibers on fracture parameters were investigated as well with another four groups of MHFRCs Six additional groups of MHFRCs with different w/c ratios were also used to study fracture parameters A constant sand cement ratio (s/c =0.5) was used in all groups The mix proportion of hybrid fiber and w/c of the matrix is presented in Table Table Mix proportion of hybrid fiber and water cement ratio of matrix Fiber dosage/(kg/m3) Volume fraction/% Water cement ratio Steel PVA CaCO3 Steel PVA CaCO3 (w/c) fiber fiber whisker fiber fiber whisker Plain 0.3 0 0 0 CW10 0.3 0 0 28.6 P05 0.3 0.5 0 6.5 S15 0.3 1.5 0 117 0 S15P05W00 0.3 1.5 0.5 117 6.5 S15P05W10 0.3 1.5 0.5 117 6.5 28.6 S15P05W20 0.3 1.5 0.5 117 6.5 57.2 S15P05W30 0.3 1.5 0.5 117 6.5 85.8 S18P02W10 0.3 1.8 0.2 140.4 2.6 28.6 S12P08W10 0.3 1.2 0.8 93.6 10.4 28.6 S10P10W10 0.3 1.0 1.0 78 13 28.6 S15P05W10a 0.24 1.5 0.5 117 6.5 28.6 S15P05W10b 0.28 1.5 0.5 117 6.5 28.6 S15P05W10c 0.32 1.5 0.5 117 6.5 28.6 S15P05W10d 0.36 1.5 0.5 117 6.5 28.6 S15P05W10e 0.40 1.5 0.5 117 6.5 28.6 Group Plain: plain cement mortar; CW10: 1.0 vol % of CaCO3 whiskers; P05: 0.5 vol % of PVA fibers; S15: 1.5 vol % of steel fibers; S15P05W00: 0.5 vol % of PVA + 1.5 vol % of steel fibers; S15P05W10: 1.0 vol % of CaCO3 whiskers+ 0.5 vol % of PVA +1.5 vol % of steel fibers Other groups have similar meaning as S15P05W10 3.2 Samples preparation and experimental procedures Raw materials were blended using UJZ-15 mortar mixer To ensure uniformity, dry raw materials, such as cement, fly ash, CaCO3 whiskers and silica sand, were mixed together for 120 seconds, after which water and superplasticizer were added, and the mixture was blended for another 120 seconds Constant flowability without segregation was used to control superplasticizer amount When cement mortar showed a good workability, PVA and steel fibers were added gradually and mixed to ensure their adequate dispersion Finally, a defoaming agent was added dropwise into the fresh mixture, which was then mixed for another 30 seconds to eliminate bubbles caused by the fiber addition The fresh mixture was carefully placed into special steel molds with 1mm thin blades at the mid-span of their side panels (40 × 40 × 200 mm in size) Schematic of the mold used in this work is illustrated in Figure All samples were covered with a plastic sheet, and stored at laboratory temperature and demolded after 24 hours A precast crack was created at the mid-span of each beam during the casting process, after which these notched beams were cured for 28 days at 20 ± 2℃ and at over 95% of relative humidity according to GB/T 50081-2002 standard [34] The thin blade fixed at the mid-span of the side panel of the steel mold could potentially influence fiber distribution and orientation at the tip of the thin blade, but it could not affect the fiber flow on the other side of the thin blade at the cross section at the mid-span In addition, this molding method satisfied the side loading requirement of side loading of flexural testing which described in ASTM C1609/C1609M-12 Figure Schematic of the mold In comparison to other fracture tests, 3-p-b tests were the simplest and had the minimum requirements for specimen forming and testing instruments Therefore, to determine the fracture parameters of different groups, 3-p-b fracture tests were performed on the notched beams by DKFC and WFM Each group in Table had four same notched beams 40 × 40 × 200 mm in size Crack depth of each beam was16 mm During the testing, an extensometer was fixed on a pair of knife edges to measure the crack mouth opening displacement A linear variable displacement transducer (LVDT) was used to measure the mid-span deflections of the notched beams The electric universal testing machine (WDW-50, Sinter, Changchun, China) was employed for 3-p-b fracture testing Displacement control was selected for loading, rate for which was maintained at 0.1 mm/min [2] Testing data were collected using DH3820 high speed static strain test analysis system at 10 Hz The span length was 160 mm and the span depth ratio (S/W) was 4:1 The loading diagram of the notched beams is shown in Figure 240 210 C3 C3 200 100 180 Gain ratio of GF Gain ratio of GF 150 16 12 C2 C2 14 12 10 Gain ratio of K un IC Gain ratio of Kun IC C1 2.5 Gain ratio of Kini IC 10 CW P0 2.0 0 0 S1 5W0 5W1 5W2 5W3 0 0 P P P P 5 5 S1 S1 S1 S1 Gain ratio of Kini IC S10P10W10 S12P08W10 S15P05W10 S18P02W10 (a) (b) Gain ratio of GF 300 250 C3 n 200 150 100 18 Gain ratio of Kun IC 16 C2 i Pla 14 12 10 Gain ratio of Kini IC C1 C1 3.0 a S1 d 0c 0e 10 10 W1 W1 5W 5W 05 05 P0 P P P 5 5 S1 S1 S1 S1 b W1 05 5P W1 S1 05 5P (c) 18 Figure Gain ratio of fracture parameters for different groups 4.4 Synergy assessment Synergy assessment can help understand the hybridization effect of hybrid fibers in the matrix [38] Thus, various methods were proposed to calculate synergy by researchers [38-41] Analysis of the fracture parameters indicated that MHFRC had a better fracture behavior than that samples with single-fiber reinforced cement mortar MHFRC demonstrated even better performance than the sum of CaCO3 whiskers, PVA fiber and steel fiber Therefore, synergy among these three fillers is obvious In the study, synergy between CaCO3 whiskers, PVA fiber and steel fiber was evaluated based on the following formula [38-40]: S FPhybrid mix n (10), FPsin gle fiber -mix i where FPhybrid-mix and FPhybrid-mix are the fracture parameters of FRCC group and single-fiber reinforced cement mortar, respectively; i represent the type of fibers (i= is 1.0 vol % of CaCO3 whiskers, i= is 0.5 vol % of PVA fiber and i= is 1.5 vol % of steel fiber); S is synergy value: at S >1 the synergy is positive, at S ≤ the synergy is negative or zero Calculated S values are shown in Table All S values for KiniIC are negative Thus, CaCO3 whiskers, PVA and steel fibers had negative synergy, which can be attributed to the gradual, multi-scale failure At the crack initiation stage, already existing or produced by the applied load micro-cracks are micron-size Only the CaCO3 whiskers or some of the PVA fibers are also micron-size; steel fibers and most of the larger PVA fibers will not work at the micron-scale of tacks Thus, synergy between CaCO3 whiskers, PVA and steel fibers is weakened Moreover, synergy of KunIC and GF decreased gradually as w/c increased (see Table 7) Synergy between KunIC and GF for S15P05W10a, S15P05W10b and S15P05W10 groups was positive Positive synergy is more likely to appear in the matrix with higher w/c Thus, w/c is an important factor for synergy evaluation and cannot be ignored Figure 10 shows that the S of GF is higher than S value of KunIC Thus, contribution of synergy effect for the hybrid fibers containing all three components (CaCO3 whiskers, PVA and steel fibers) on fracture energy is greater than the effect on unstable fracture toughness Table The results of synergy evaluation Synergy Group S15P05W10a Kini IC KunIC GF -0.112 0.354 0.476 19 S15P05W10b -0.366 0.184 0.294 S15P05W10 -0.367 0.156 0.272 S15P05W10c -0.403 -0.064 -0.111 S15P05W10d -0.559 -0.077 -0.384 S15P05W10e -0.714 -0.097 -0.491 0.5 The synergy of Kun IC The synergy of GF Synergy 0.4 0.3 0.2 0.1 S15P05W10a un IC Figure 10 Comparison K S15P05W10b S15P05W10 and GF synergies for samples with higher water/ cement ratios 4.5 Relationship between fracture parameters and factors influencing them Geometrical shapes, volume fraction, mechanical properties of fibers and matrix properties are significant factors affecting the fracture behavior of FRCC Reinforcing index (RI) was used to describe characteristics of the hooked ends of the steel fibers in concrete by Ezeldin et al [42] RI was later employed to describe characteristic of PVA and synthetic polyethylene fibers in engineered cementitious composite (ECC) slabs by Said et al [43,44] Chinese standards define RI as a characteristic of fiber content, which can be calculated from the fiber content and aspect ratio [45] However, in the reports mentioned above, RI was used to describe only one fiber type and is not suitable to describe hybrid fibers Almusallam et al [9] incorporated effect of fibers on tensile strength and extended the concept of comprehensive reinforcing index (RIv) to describe characteristic of composites based on hybrid fibers Li and Cao [46] applied the concept of RIv to cementitious composites reinforced by CaCO3 whiskers-PVA-steel hybrid fibers and found a good relationship between RIv and flexural properties of the composites Thus, in this work, we also used RIv to describe hybrid fibers using the following expression: m RI v = ki v fi j li f i a ( ) di f s (11), where RIv is comprehensive reinforcing index of hybrid fibers ki is mechanical anchoring coefficient between fibers and matrix, (set as equal according to the literature [46]); vfi is the volume fraction of fiber; li and di represent lengths and equivalent diameters of fibers, respectively; fi is the tensile strengths of fibers; fs is the tensile strength of steel fiber a represents tension 20 stiffness parameter (it was set as 0.5 for PVA fibers and CaCO3 whiskers and for steel fibers [46]) The suffix j represents the type of fibers The following values of j were assigned: for CaCO3 whiskers, for PVA fibers and for steel fibers The influencing factor of hybrid fiber were integrated as RIv according to formula (11) Fitting of the fracture parameters vs RIv curves (shown in Figure 11 and Table 8) was performed using quadratic polynomial Fitting curves show that as the value of RIv increased, different fracture parameter increased but then decreased indicating existence of an optimal value of RIv corresponding to the maximum fracture parameters Optimum RIv values calculated using fitting equations, can be used to guide the mix design of CaCO3 whisker-PVA-steel hybrid fibers to achieve the desired fracture-related properties Relationship between w/c and fracture parameters were linear: as w/c values increased, fracture parameters decreased except for Δac We believe that increased values of w/c would weaken the interface between fibers and the matrix making the fibers easy to be pulled out from the matrix (see Figure 12) Increased w/c values also lead to Δac increase, which is related to cohesive force of the matrix Comparing the fitting results in Figure 12 (a) with those in Figure 12 (c), one can see that effect of w/c factor on the unstable propagation of cracks is more significant than on the initial propagation of cracks 20 1.0 0.8 0.6 Δac(mm) Kini (MPam1/2) IC 15 0.4 10 0.2 0.0 0.00 The length of FPZ The fitting curve of Δac Initial fracture toughness The fitting curve of Kini IC 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.00 0.32 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 RIv RIv (a) (b) 12 7000 6000 5000 GF (N/m) Kun (MPam1/2) IC 4000 3000 2000 1000 Unstable fracture toughness The fitting curve of Kun IC 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 Fracture energy The fitting curve of GF -1000 0.00 0.32 RIv 0.04 0.08 0.12 0.16 RIv 21 0.20 0.24 0.28 0.32 (c) (d) Figure 11 Fitting of the fracture parameters vs RIv curves Table The relationship between RIv and fracture parameters Fracture parameters Fitting results K Δac Δac = 1.728 + 135.16 × (RIv) - 315.04 × (RIv) R2 =0.773 2 Kun IC = -1.062 + 83.855 × (RIv) - 188.82 × (RIv) GF 1.4 GF = -925.49 + 54180 × (RIv) - 111731 × (RIv) 18 Initial fracture toughness The fitting curve of Kini IC 1.2 0.202 un IC K R =0.846 0.215 R2 =0.814 0.222 R =0.817 0.242 The length of FPZ The fitting curve of Δac 17 1.0 0.8 Δac(mm) Kini (MPam1/2) IC Optimum RIv KiniIC = 0.189 + 5.262 × (RIv) - 13.026 × (RIv)2 ini IC 0.6 0.4 16 15 K ICini 0.2 R2 0.0 0.22 0.24 2.207 4.570( w / c ) ΔaC 0.961 0.26 R2 0.28 0.30 0.32 0.34 0.36 0.38 0.40 14 0.22 0.42 0.24 0.26 0.28 0.30 w/c 0.34 0.36 0.38 0.40 0.42 w/c (a) 12 0.32 11.162 15.280( w / c ) 0.8091 (b) 8000 Unstable fracture toughness The fitting curve of Kun IC Fracture energy The fitting curve of GF 7000 11 Kun (MPam1/2) IC 6000 GF (N/m) 10 5000 4000 K ICun R2 0.22 17.475 25.638( w / c ) 3000 0.843 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 2000 0.22 0.42 GF 15727 R2 0.937 0.24 33684( w / c ) 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 w/c w/c (c) (d) Figure 12 Relationship between w/c and fracture parameters Mechanism analysis and models for fracture parameters calculations 5.1 Mechanism analysis MHFRC is a type of polyphase and compound material, thus, its cracking process is influenced by many factors, such initial raw materials and their initial mixing proportions, mixing 22 regime, etc Analogous to the three stages of fracture in DKFC, crack arresting stage can also be divided into three stages: crack arresting at the initiation stage, crack arresting at the stable crack propagation stage and crack arresting at the unstable crack propagation stage Figure 13 presents schematics of these different crack arresting processes Crack pre-existing in the fiber-containing composite will cause stress redistribution in MHFRC when the load is applied As the load increases, the cracking will first occur in the C-S-H and cement paste layers In the cracking resistance zone, PVA and steel fibers will not participate in cracking process because of their own scale size limitations Therefore, only micron-sized CaCO3 whiskers can effectively inhibit and delay generation, extension and connection of these micro-cracks by the effects of the whisker pull out, crack deflection, whisker bridging and whisker breakage [18] Figure 13 (a) shows schematics of micro-crack arrest by CaCO3 whiskers at the pre-crack tip during the crack initiation stage Later, once the load is applied and stress intensity factor K becomes equal to KiniIC , micro-cracks will transform into macro-cracks and expand along the pre-crack tip Cracking resistance zone is composed with CaCO3 whiskers and some PVA and steel fibers (see Figure 13 (b)) During the stable crack propagation stage, crack expansion needs to overcome the crack resistance zone at the tip of the crack and consume more energy Then, as soon as the value of K reaches KunIC value, cracking process enters unstable crack propagation stage The crack extends further and expands, and, at the same time, presence of PVA and steel fibers become noticeable The pull out or breakage of PVA-steel hybrid fibers consumes energy, thus, it will induce stress redistribution Fibers near the broken fibers will be pulled out from matrix or break Figure 13 (c) shows the area that the crack through, such as matrix cracking, fibers is pulled out or breakage and fiber bridging According to our analysis of crack arresting process (see Figure 13 (a) to (c)) can be known that as crack propagation increased, and the crack arresting ability of hybrid fibers gradually enhanced Strength of crack arresting zone is different for various samples including for samples from the same batch This difference comes from to the fiber distribution at the tip of the initial crack This is why different test results (and as a consequence, different fracture parameters) for the samples in the same batch were observed 23 (a) (b) (c) Figure 13 Crack arresting process at the (a)initiation, (b) stable crack propagation and (c) unstable crack propagation stages According to the multiscale characteristic of hybrid fiber used in this paper, macro and micro means of observation are used to observe the fiber morphology We used automatic stereo optical CARI ZEISS Germany microscope to analyze macroscopic steel and PVA fibers Scanning electron microscopy (SEM) was performed to analyze micro-morphology of the fibers and microstructure of matrix Steel fibers present in the S15P05W10 group became warped and their surface is covered with matrix material after the 3-p-b testing (see Figure 14 (a)) It indicates good bonding performance between steel fibers and the cement matrix PVA fiber surface is also covered by the matrix materials (see Figure 14 (b)) probably because surface of PVA fibers have a lot of hydroxyl groups capable of forming strong bonds with the cement matrix (a) (b) Figure 14 Optical micrograph of steel and PVA fibers in the matrix The fibers morphology in Figure 15 corresponds to the crack arresting process at initiation, stable crack propagation and unstable crack propagation stages in Figure 13 CaCO whisker fracture, pull out and crack deflection are the main mechanism providing reinforcement, micro-cracks arrest and delaying the formation of a micro-crack [18, 47-49] (see Figure 15 (a)) CaCO3 whisker morphology occurred at the whole fracture process, especially at the crack initiation stage which described in Figure 13 (a) Figure 15 (b) shows PVA fiber pulled out from the cement-matrix However, the remaining part of the PVA is still on the sliding surface across the crack Thus, PVA fibers form strong bonds with the cement-matrix, which agree with results of optical microscopy Steel fiber are pulled out (shown in Figure 15 (c)), PVA fiber contortion and bridging indicate stress transfer to matrix and energy dissipation processes [10,49] The PVA and steel fibers morphology mainly occurred at the stable crack propagation and the unstable crack propagation stages which described in Figure 13 (b) and (c) 24 Thus, hybrid fiber composed of CaCO3 whiskers as well as PVA-steel fibers can effectively improve fracture properties of MHFRC by inhibiting and delaying the generation, extension and connection of cracks Their reinforcing mechanism are fiber pull out, PVA fiber bridging, whisker breakage and crack deflection (a) (b) (c) Figure 15 Fiber morphology obtainded by SEM 5.2 Models for fracture parameter calculations We considered RIv (including fibers type, fibers content and aspect ratio) and w/c values as 25 the main factors affecting fracture behavior of MHFRC According to the fracture parameters discussed above, we analyzed fracture mechanism with the goal to establish model for fracture parameters calculations, which takes into account multiple factors obtained by the regression analysis described above These calculation models are presented by the equation below: (i) Model of initial fracture toughness calculation: KICini 27.7( RI v )2 40.2( RI v )2 ( w / c ) 15.7( RI v )( w / c ) 10.9( RI v ) 2.7( w / c ) (12), (ii) Model of unstable fracture toughness calculation: KICun 361( RI v )2 416( RI v )2 ( w / c ) 177( RI v )( w / c ) 153.7( RI v ) 1.4( w / c ) 0.9 (13), (iii) Model of fracture energy calculation: GF 297288.2( RI v )2 617011.4( RI v )2 ( w / c ) 298328.1( RI v )( w / c ) 143740.3( RI v ) +2248.1( w / c ) 1600.8 (14), (iv) Model of the length of FPZ calculation: ac 235.8( RI v )2 253.3( RI v )2 ( w / c ) 109.2( RI v )( w / c ) 101.7( RI v ) 2.2( w / c ) 1.1 (15) Relationship between theoretical fracture parameters calculated using Eq (12) - (15) and experimental results is shown in Figure 16 These points approach 1, thus, theoretical results agree well with the experimental ones Average value, standard deviation and variable coefficient of the ratio of experimental and theoretical are shown in inserts in Figure 16 Average error was 15%, with the exception of KunIC However, ranges of standard deviations and variable coefficients differ for different values probably because of fibers dispersion throughout the cement matrix However, overall, theoretical model for fracture parameters calculation reflects influence of fibers factor (RIv) and matrix factor (w/c) on fracture parameters However, they not take fiber dispersion into account Factor influencing fiber dispersion need to be studied further 26 1.5 15 K /K ini IC- theoretical Kun / Kun =1 IC- experimental IC- theoretical =1 12 Kun (MPam1/2) IC- experimental Kini (MPam1/2) IC- experimental 1.2 ini IC- experimental 0.9 0.6 Kini / Kini IC- theoretical IC- experimental 0.3 Average value Standard deviation Variable coefficient 0.961 0.196 0.204 0.0 0.0 0.3 0.6 0.9 1.2 Kun / Kun IC- theoretical IC- experimental Average value Standard deviation Variable coefficient 0.778 0.44 0.566 1.5 Kini (MPam1/2) IC- theoretical (a) 12 15 (b) 25 10000 GF- experimental /GF - theoretical = 20 ac- experimental (mm) 8000 GF- experimental (N/m2) Kun (MPam1/2) IC- theoretical 6000 4000 ac- experimental /ac - theoretical = 15 10 GF- experimential / GF - theoretical 2000 ac- experimental / ac - theoretical Average value 0.866 Standard deviation Variable coefficient 0.418 Average value 0.483 1.034 0 2000 4000 6000 8000 Standard deviation Variable coefficient 0.311 0.302 10000 GF - theoretical (N/m2) 10 15 20 25 ac - theoretical (mm) (d) (c) Figure 16 Relationship between theoretically and experimentally obtained fracture parameters Conclusion We added CaCO3 whiskers into the PVA-steel fibers with the goal to develop a multiscale hybrid fiber system for cement mortar reinforcement Fracture behavior of MHFRC was evaluated using fracture toughness and fracture energy, which were based on the DKFC and WFM, respectively Comparing to the plain cement mortar, fracture behavior of MHFRC improved significantly after it was reinforced by the hybrid fiber system because of the presence of both micro- and macro-scale fibers as well as their positive synergy The following conclusions were made: un Initial fracture toughness (Kini IC ), unstable fracture toughness (KIC ) and fracture energy (GF) improved with fiber addition, especially when 1.0 vol % of CaCO3 whiskers, 0.5 vol % of PVA fibers and 1.5 vol % of steel fibers were added Comparing to the plain group, the KiniIC and KunIC value for the S15P05W10 group increased 2.996 and 14.632 times, respectively, un while GF increased 240.096 times Kini and GF values for the S15P05W10 sample IC , KIC decreased as water/ cement ratio (w/c) increased Thus, S15P05W10a group with w/c= 0.24 exhibited the best fracture behavior 27 Synergy effect of fibers presence (judge by change and values of fracture parameters) was observed when vol % of CaCO3 whiskers, 0.5 vol % of PVA fibers and 1.5 vol % of steel fibers were added to MHFRC Synergy effect on Kini IC was negative probably because only CaCO3 whiskers can arrest the cracks on the micro scale Steel and PVA fibers not enhance fracture toughness at the micro-scale this scale at the initiation stage Moreover, w/c affects the synergy, and a positive synergy is more likely to appear in the matrix with a high w/c Quantitative evaluation of the synergy on KunIC and GF of S15P05W10a were 0.354 and 0.476, respectively Relationship between fiber reinforcing index (RIv) and fracture parameters was fitted using quadratic polynomial Values of optimum RIv can be acquired from this fit to provide guidance during mixing and preparation of hybrid fiber system consisting of CaCO3 whiskers and PVA-steel fibers to achieve best fracture properties Relationship between w/c and fracture parameters is linear: fracture parameters decreases significantly, (with the exception of Δac) as w/c increases Multiscale cracking resistance process of MHFRC can be illustrated by three stages: crack arresting at the initiation stage, crack arresting at the stable crack propagation stage and crack arresting at the unstable crack propagation stage Analysis of fiber morphology indicated that the reinforcing mechanism of the cement-based matrix by the multiscale hybrid fibers were fiber pull out, PVA fiber bridging, whisker breakage and crack deflection Several polynomial regression models of fracture parameters affected by different factors were obtained using regression analysis Comparison of the experimentally and theoretically obtained results verified that these models can be applied without taking into account the fiber dispersion Improved fracture behavior of MHFRC demonstrates feasibility of cement matrix reinforcement by hybrid fibers composed of a combination of CaCO3 whiskers, PVA and steel fibers with the goal to achieve multiscale cracking resistance of the matrix Our empirical formulas take into account factors and properties of fibers and the matrix properties and determine fracture parameters to evaluate fracture behavior of fiber reinforced cement based-materials for structural applications Acknowledgment The authors would like to acknowledge the support of this work by the Natural Science Foundation of China under Grant No.51678111, No.51478082 and No 51779095 Reference [1] Ghasemi, M., Ghasemi, M R., & Mousavi, S R (2018) Investigating the effects of maximum aggregate size on self-compacting steel fiber reinforced concrete fracture parameters Construction & Building Materials, 162, 28 674-682 [2] Kazemi, M T., Golsorkhtabar, H., Beygi, M H A., & Gholamitabar, M (2017) Fracture properties of steel fiber reinforced high strength concrete using work of fracture and size effect methods Construction & Building Materials, 142, 482-489 [3] Carpinteri, A., Fortese, G., Ronchei, C., Scorza, D., & Vantadori, S (2017) Mode i fracture toughness of fibre reinforced concrete Theoretical & Applied Fracture Mechanics, 91, 66-75 [4] Caggiano, A., Cremona, M., & Faella, C (2012) Fracture behavior of concrete beams reinforced with mixed long/short steel fibers Construction & Building Materials, 37(3), 832-840 [5] Abadel, A A (2015) Mechanical properties of hybrid fibre-reinforced concrete-analytical modelling and experimental behaviour Magazine of Concrete Research, 68(16), 823-843 [6] Güneyisi, E., Gesoglu, M., Özturan, T., & İpek, S (2015) Fracture behavior and mechanical properties of concrete with artificial lightweight aggregate and steel fiber Construction & Building Materials, 84, 156-168 [7] Shao, Y D., & Wang, W F (2012) Experimental study on fracture properties of hybrid fiber reinforced concrete Advanced Materials Research, 450-451, 518-522 [8] [8] Hossain, K M A., Lachemi, M., Sammour, M., & Sonebi, M (2013) Strength and fracture energy characteristics of self-consolidating concrete incorporating polyvinyl alcohol, steel and hybrid fibres Construction & Building Materials, 45(45), 20-29 [9] Almusallam, T., Ibrahim, S M., Al-Salloum, Y., Abadel, A., & Abbas, H (2016) Analytical and experimental investigations on the fracture behavior of hybrid fiber reinforced concrete Cement & Concrete Composites, 74, 201-217 [10] Lawler, J S., Wilhelm, T., Zampini, D., & Shah, S P (2003) Fracture processes of hybrid fiber-reinforced mortar Materials & Structures, 36(3), 197-208 [11] Rana, S., & Fangueiro, R (2013) A review on nanomaterial dispersion, microstructure, and mechanical properties of carbon nanotube and nanofiber reinforced cementitious composites Journal of Nanomaterials,2013,(2013-7-29), 2013(7), 80 [12] Konsta-Gdoutos, M S., Metaxa, Z S., & Shah, S P (2010) Highly dispersed carbon nanotube reinforced cement based materials Cement & Concrete Research, 40(7), 1052-1059 [13] Gdoutos, E E., Konsta-Gdoutos, M S., & Danoglidis, P A (2016) Portland cement mortar nanocomposites at low carbon nanotube and carbon nanofiber content: a fracture mechanics experimental study Cement & Concrete Composites, 70, 110-118 [14] Konsta-Gdoutos, M S., Metaxa, Z S., & Shah, S P (2010) Multi-scale mechanical and fracture characteristics and early-age strain capacity of high performance carbon nanotube/cement nanocomposites Cement & Concrete Composites, 32(2), 110-115 [15] Hu, Y., Luo, D., Li, P., Li, Q., & Sun, G (2014) Fracture toughness enhancement of cement paste with multi-walled carbon nanotubes Construction & Building Materials, 70, 332-338 29 [16] Stynoski, P., Mondal, P., & Marsh, C (2015) Effects of silica additives on fracture properties of carbon nanotube and carbon fiber reinforced portland cement mortar Cement & Concrete Composites, 55, 232-240 [17] Cao, M L., & Zhang, C (2012) Dispersion, microstructure and mechanical properties of ground calcium carbonate whisker-reinforced portland cement Applied Mechanics & Materials, 174-177, 1398-1401 [18] Cao, M., Zhang, C., & Wei, J (2013) Microscopic reinforcement for cement based composite materials Construction & Building Materials, 40(3), 14-25 [19] Cao, M., Zhang, C., Lv, H., & Xu, L (2014) Characterization of mechanical behavior and mechanism of calcium carbonate whisker-reinforced cement mortar Construction & Building Materials, 66(1), 89-97 [20] Cao, M., Zhang, C., & Lv, H (2014) Mechanical response and shrinkage performance of cementitious composites with a new fiber hybridization Construction & Building Materials, 57(5), 45-52 [21] Cao, M., Zhang, C., Li, Y., & Wei, J (2015) Using calcium carbonate whisker in hybrid fiber-reinforced cementitious composites Journal of Materials in Civil Engineering, 27(4), 04014139 [22] Cao, M., Li, L., & Khan, M (2018) Effect of hybrid fibers, calcium carbonate whisker and coarse sand on mechanical properties of cement-based composites Materiales de Construcción, 68(330), 156 [23] Beygi, M H A., Kazemi, M T., Nikbin, I M., & Amiri, J V (2013) The effect of water to cement ratio on fracture parameters and brittleness of self-compacting concrete Materials & Design, 50(4), 267-276 [24] Kumar, S., Pandey, S R., & Srivastava, A K L (2014) Determination of double- k, fracture parameters of concrete using peak load method Engineering Fracture Mechanics, 131, 471-484 [25] Liu, X., & Li, Z (2016) Determining double- k, fracture parameters of concrete only by the measured peak load Theoretical & Applied Fracture Mechanics, 85, 412-423 [26] Qing, L B., Nie, Y T., Wang, J., & Hu, Y (2017) A simplified extreme method for determining double‐k fracture parameters of concrete using experimental peak load Fatigue & Fracture of Engineering Materials & Structures, 40(2) [27] Zhang, J., Xue, Q., & He, J G (2016) The Double-K Fracture Criterion of Steel Fiber Reinforced Concrete International Conference on Fracture Mechanics of Concrete and Concrete Structures [28] Xu, S., & Reinhardt, H W (1999) Determination of double-determination of double- k, criterion for crack propagation in quasi-brittle fracture part i: experimental investigation of crack propagation International Journal of Fracture, 98(2), 111-149 [29] Xu, S., & Reinhardt, H W (1999) Determination of double- k, criterion for crack propagation in quasi-brittle fracture, part ii: analytical evaluating and practical measuring methods for three-point bending notched beams International Journal of Fracture, 98(2), 151-177 [30] Xu, S., & Reinhardt, H W (1999) Determination of double- k, criterion for crack propagation in quasi-brittle fracture, part iii: compact tension specimens and wedge splitting specimens International Journal of Fracture, 98(2), 179-193 [31] Xu, S., & Reinhardt, H W (2000) A simplified method for determining double-k fracture parameters for three-point bending tests International Journal of Fracture, 104(2), 181-209 30 [32] ASTM E 399e12, Standard test Method for Linear Elastic Plane-strain Fracture Toughness KIC of Metallic Materials, ASTM International 3.01, 2012 [33] RILEM Technical Committee 50-FMC (1985) Determination of the fracture energy of mortar and concrete by means of three-point bend tests of notched beams, proposed RILEM draft recommendations RILEM, Materials and Structures 18(106), 285-296 [34] GB/T 50081(2002) Standard for test method of mechanical properties on ordinary concrete, China Architecture & Building Press; Beijing, China [35] ASTM C469, Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression, ASTM International, West Conshohocken, PA, 2014 [36] GB/T 17671 (1999) Method of testing cement-determination of strength-ISO, China Architecture & Building Press; Beijing, China, 80-81 [37] Gao D., & Zhang T (2007) Fracture energy of steel fiber reinforced high strength concrete under three-point bending Journal of Hydraulic Engineering, 38 (9), 1115- 1127 (in Chinese) [38] Banthia, N., Majdzadeh, F., Wu, J., & Bindiganavile, V (2014) Fiber synergy in Hybrid Fiber Reinforced Concrete (HyFRC) in flexure and direct shear Cement and Concrete Composites, 48, 91-97 [39] Soleimani, S M., & Banthia, N (2005) Flexural response of hybrid fiber-reinforced cementitious composites Aci Materials Journal, 102(6), 382-389 [40] Tran, N T., & Kim, D J (2017) Synergistic response of blending fibers in ultra-high-performance concrete under high rate tensile loads Cement and Concrete Composites, 78, 132-145 [41] Banthia, N., & Gupta, R (2004) Hybrid fiber reinforced concrete (HyFRC): fiber synergy in high strength matrices Materials and Structures, 37(10), 707-716 [42] Ezeldin, A S., & Balaguru, P N (1992) Normal and high-strength fiber-reinforced concrete under compression Journal of Materials in Civil Engineering, 4(4), 415-429 [43] Said, S H., Razak, H A., & Othman, I (2015) Flexural behavior of engineered cementitious composite (ECC) slabs with polyvinyl alcohol fibers Construction and Building Materials, 75, 176-188 [44] Said, S H., & Razak, H A (2015) The effect of synthetic polyethylene fiber on the strain hardening behavior of engineered cementitious composite (ECC) Materials & Design, 86, 447-457 [45] CECS:38 (2004), Technical specification for fiber reinforced concrete structures, China Association for engineering construction standardization, China Architecture & Building Press; Beijing, China [46] Cao, M., & Li, L (2018) New models for predicting workability and toughness of hybrid fiber reinforced cement-based composites Construction & Building Materials, 176, 618-628 [47]Alrekabi, S., Cundy, A B., Lampropoulos, A., Whitby, R L D., & Savina, I (2017) Mechanical performance of novel cement-based composites prepared with nano-fibres, and hybrid nano-and micro-fibres Composite Structures, 178, 145-156 [48] Nelson, P K., Li, V C., & Kamada, T (2002) Fracture toughness of microfiber reinforced cement composites Journal of Materials in Civil Engineering, 14(5), 384-391 31 [49] Silva, F J., & Thaumaturgo, C (2003) Fibre reinforcement and fracture response in geopolymeric mortars Fatigue & Fracture of Engineering Materials & Structures, 26(2), 167-172 32 ... study fracture behavior of CaCO3 whiskers- PVA-steel hybrid fibers reinforced cement mortar (MHFRC) CaCO3 whiskers, a new type of microfiber material, was mixed with PVA-steel hybrid fibers and. .. whiskers, content of PVA-steel hybrid fiber and water/ cement ratio (w/c) on fracture parameters are discussed Addition of composite fibers consisting of CaCO3 whiskers and PVA-steel hybrid fibers could.. .Fracture Behavior of Cement Mortar Reinforced by Hybrid Composite Fiber Consisting of CaCO3 Whiskers and PVA-Steel Hybrid Fibers Mingli Caoa, Chaopeng Xiea,*, Junfeng Guanb,** a School of