Influence of fiber size on mechanical properties of strain-hardening fiber-reinforced concrete

This research deals with the influences of macro, meso and micro steel-smooth fibers on tensile and compressive properties of strain-hardening fiber-reinforced concretes (SFCs). The different sizes, indicated by length/diameter ratio, of steel-smooth fiber added in plain matrix (Pl) were as follows: 30/0.3 for the macro (Ma), 19/0.2 for the meso (Me) and 13/0.2 for the micro fiber (Mi). All SFCs were used the same fiber volume fraction of 1.5%. The compressive specimen was cylinder-shaped with diameter × height of 150 × 200 mm, the tensile specimen was bell-shaped with effective dimensions of 25 × 50 × 100 mm (thickness × width × gauge length).

Journal of Science and Technology in Civil Engineering, NUCE 2020 14 (3): 84–95 INFLUENCE OF FIBER SIZE ON MECHANICAL PROPERTIES OF STRAIN-HARDENING FIBER-REINFORCED CONCRETE Duy-Liem Nguyena,∗, Thac-Quang Nguyenb , Huynh-Tan-Tai Nguyena a Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan street, Thu Duc district, Ho Chi Minh city, Vietnam b Faculty of Civil Engineering, Campus in Ho Chi Minh City, University of Transport and Communications, No 450-451 Le Van Viet street, District 9, Ho Chi Minh city, Vietnam Article history: Received 13/07/2020, Revised 05/08/2020, Accepted 10/08/2020 Abstract This research deals with the influences of macro, meso and micro steel-smooth fibers on tensile and compressive properties of strain-hardening fiber-reinforced concretes (SFCs) The different sizes, indicated by length/diameter ratio, of steel-smooth fiber added in plain matrix (Pl) were as follows: 30/0.3 for the macro (Ma), 19/0.2 for the meso (Me) and 13/0.2 for the micro fiber (Mi) All SFCs were used the same fiber volume fraction of 1.5% The compressive specimen was cylinder-shaped with diameter × height of 150 × 200 mm, the tensile specimen was bell-shaped with effective dimensions of 25 × 50 × 100 mm (thickness × width × gauge length) Although the adding fibers in plain matrix of SFCs produced the tensile strain-hardening behaviors accompanied by multiple micro-cracks, the significances in enhancing different mechanical properties of the SFCs were different Firstly, under both tension and compression, the macro fibers produced the best performance in terms of strength, strain capacity and toughness whereas the micro produced the worst of them Secondly, the adding fibers in plain matrix produced more favorable influences on tensile properties than compressive properties Thirdly, the most sensitive parameter was observed to be the tensile toughness Finally, the correlation between tensile strength and compressive strength of the studied SFCs were also reported Keywords: aspect ratio; strain-hardening; post-cracking; ductility; fiber size https://doi.org/10.31814/stce.nuce2020-14(3)-08 c 2020 National University of Civil Engineering Introduction Under serious mechanical and environmental loadings, e.g earthquake, impact, blast load and marine environment, a civil infrastructure has revealed the hasty deterioration, and this might cause construction collapse, even damage to person Clearly, there has been a great concern in improving the robustness, energy absorption capacity, crack resistance and durability of civil infrastructure Strain-hardening fiber-reinforced concretes (SFCs) is a promising construction material because it has performed its superior mechanical properties, e.g., compressive strength possibly exceeding 80 MPa, post-cracking tensile strength exceeding MPa, strain capacity exceeding 0.3% even though the SFCs were used a low volume content of fibers, less than 2.5% [1, 2] Especially, SFCs could generate a strain-hardening behavior accompanied with multiple micro-cracks under tensile loadings [3, 4], ∗ Corresponding author E-mail address: liemnd@hcmute.edu.vn (Nguyen, D.-L.) 84 Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering this mechanism was considered a superior property high2018 mechanical and cracking reJournal of as Science and Technology in Civilresulting Engineering,inNUCE ; e-ISSN 2734 9268 with zones: linear-elastic zone, sistance of SFCs Fig shows a p-ISSN typical1859-2996 strain-hardening curves strain-hardening zone and crack opening zone [3] Tensile stress B (epc , spc ) Hardening branch Post-cracking Crack generating First-cracking (ecc , scc ) A Linear branch No Crack ecc Linear-elastic zone No Crack 66 Strain hardening Multiple microcracks C Tensile strain Crack opening Crack Localization Figure Typical strain-hardening response curve of SFCs 67 68 epc Figure Typical strain-hardening response curve of SFCs Experiment On the theand mechanical 69 other 2.1 hand, Materials preparationproperties of specimensof SFCs have been reported to be dependent much on fiber characteristics, e.g., fiber aspect ratio (length/diameter ratio), fiber size and shape, fiber vol70 Fig shows the experimental testing program while Tables and provide the ume content, fiber material [4–9] Also, in the process of making SFCs, the fiber type and fiber 71 composition of plain matrix of SFCs (Pl) and fiber features, respectively Three types content greatly the fiber probability heterogeneous fiber distribution and30/0.3 fiber for flocculation gov72 of affected steel-smooth were usedofwith their length/diameter ratios as follows: erning workability and viscosity of a concrete mixture [6] Despite the available references, the in73 the macro (Ma), 19/0.2 for the meso (Me) and 13/0.2 for the micro fiber (Mi) All fluencing74factors regarding fiber characteristics should be thoroughly clarified Two questions would SFCs were added a same fiber volume fraction of 1.5% For the compressive test, the be answered this investigation: the order in terms ofmm steel-smooth fiber size for enhanc75 in cylindrical specimen withwhether its diameter×height of 100×200 was used with gauge 76 length of 100 mm For the tensile test, to thethat bell-shaped specimen was used with ing compressive properties of SFCs was similar for enhancing tensile properties?; and, what 77 effective dimensions of 25×50×100 mm (thickness×width×gauge length) The mixing significances in enhancing tensile and compressive parameters of SFCs using different reinforcing 78 fiber detail sizes of SFC mixture could be referred previous study [7] after research The steel-smooth were? This situation led totothe motivation for All thisspecimens experimental 79 casting were placed in a laboratory room for days prior to demolding After main objectives of this research work are as follows: (i) to explore the sensitivity of macro, meso and 80 demolding, the specimens were water-cured at 25 °C for 14 days Next, the specimens micro fibers to tensile and compressive properties of SFCs, and (ii) to correlate the tensile strength 81 were removed from the water tank and dried at 70 °C in a drying oven for at least 12 to compressive strength of SFCs containing macro, meso and micro steel-smooth fibers The study 82 h All the specimens were tested at the age of 18 days result is expected to provide more useful information for enlarging the application of SFCs in both civil and military infrastructures Experiment 2.1 Materials and preparation of specimens Fig shows the experimental testing program while Tables and provide the composition of plain matrix of SFCs (Pl) and fiber features, respectively Three types of steel-smooth fiber were used with their length/diameter ratios as follows: 30/0.3 for the macro (Ma), 19/0.2 for the meso (Me) and 13/0.2 for the micro fiber (Mi) All SFCs were added a same fiber volume fraction of 1.5% 85 Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering For the compressive test, the cylindrical specimen with its diameter × height of 100 × 200 mm was used with gauge length of 100 mm For the tensile test, the bell-shaped specimen was used with effective dimensions of 25 × 50 × 100 mm (thickness × width × gauge length) The mixing detail of SFC mixture could be referred to previous study [7] All specimens after casting were placed in a laboratory room for days prior to demolding After demolding, the specimens were water-cured at 25◦C for 14 days Next, the specimens were removed from the water tank and dried at 70◦C in a Journal of Science and Technology in Civil Engineering, NUCE 2018 drying oven for at least 12 h All thep-ISSN specimens were tested at9268 the age of 18 days 1859-2996 ; e-ISSN 2734 Compression This study Plain matrix Macro fiber Meso fiber Micro fiber Previous study[3] Uniaxial tension 83 Figure testingprogram program Figure2.2.Experimental Experimental testing 84 Table compositionofofSFCs SFCs Table1.1.Plain Plainmatrix matrix composition 85 Cement (Type 0.80 Cement III) (TypeSilica III) 0.80 Notation Silica fume fume Diameter (mm) 0.3 0.2Me 0.2Mi 87 Superplas- 1.00 1.00 0.20 0.20 0.04 0.3 0.2 0.2 30 30 19 19 13 13 100 2580 95 2788 100 95 65 65 Water 0.26 0.04 Table 2 Fiber Fiber features Table features Diameter Length Aspect ratio Tensile strength (mm) (mm) (L/D) ratio (L/D) (MPa) Tensile Length (mm) Aspect Ma Ma Me Mi Silica Fly ash Fly ash Water Silica sand sand ticizer Superplasticizer 0.07 0.07 86 Notation Commented [A1]: Background ảnh dù 0.26 strength (MPa) 2580 2788 2788 2788 2.2 Experiment setup 2.2 Experiment setup 88 All specimens were tested using a universal test machine with applied 89 displacement speed of mm/min The frequency of data acquisition under All specimens were tested using a universal test machine with applied displacement speed of 90 compression tests was Hz Fig presents the experimental setup for uniaxial mm/min The frequency of data acquisition under compression tests was Hz Fig presents the 91 tension and compression Two and three linear variable differential transformers experimental setup for were uniaxial tension and compression Two and2018 three linear variable differential Journal of Science Technology Civil Engineering, NUCE 92 (LVDTs) attached toandtensile and incompressive specimens, respectively The 93 94 p-ISSN 1859-2996 ; e-ISSN 2734 9268 average values from LVDTs were used to perform the response of stress versus strain curve Tensile specimen 95 96 Compressive specimen Commented [A2]: Background ảnh dùng trắng Figure Experiment setup Figure Experiment setup 97 Experiment result and discussion 98 3.1 Tensile and compressive behaviors of SFCs 86 99 100 101 102 Fig shows the tensile stress versus strain response curves of SFCs As shown in Fig 4, the plain matrix revealed the strain-softening behavior while the SFCs added reinforcing fibers displayed the strain-hardening behaviors accompanied by multiple micro-cracks The compressive stress versus strain responses of SFCs were presented specimen specimen 95 Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering 96 Figure Experiment setup transformers (LVDTs) were attached to tensile and compressive specimens, respectively The average 97values Experiment result and discussion from LVDTs were used to perform the response of stress versus strain curve 98 3.1 Tensile and compressive behaviors of SFCs Experiment result and discussion 99 Fig shows the tensile stress versus strain response curves of SFCs As shown Tensile and behaviors of the SFCs revealed strain-softening behavior while the SFCs added 1003.1 in Fig 4, thecompressive plain matrix Fig shows the tensile stress versus strain response behaviors curves of SFCs As shownbyinmultiple Fig 4, the accompanied 101 reinforcing fibers displayed the strain-hardening matrix revealed thecompressive strain-softening behavior while the responses SFCs addedofreinforcing fibers displayed stress versus strain SFCs were presented 102plainmicro-cracks The the strain-hardening behaviors accompanied by multiple micro-cracks The compressive stress versus 103 in Fig As shown in Fig 5, there were so many different profile curves according to strain responses of SFCs were presented in Fig As shown in Fig 5, there were so many different curves almost linear from thelinear start from of loading 104profile SFC types: the profile curves according to SFC types:were the profile curves were almost the startto of their loading revealedthe thestrain-softening strain-softening behavior 105to their peaks As As shown in inFig peaks shown Fig.4,4,the theplain plain matrix matrix revealed behavior while reinforcing fibers displayed the strain-hardening responses accompanied by multiple reinforcing fibers displayed the strain-hardening responses 106the SFCs whileadded the SFCs added micro-cracks 107 accompanied by multiple micro-cracks Journal JournalofofScience Scienceand andTechnology TechnologyininCivil CivilEngineering, Engineering,NUCE NUCE2018 2018 p-ISSN p-ISSN1859-2996 1859-2996; ;e-ISSN e-ISSN2734 27349268 9268 (a) Plain Plain (a) (b) Macro (b) Macro (a) Plain (c) Meso (c) (c)Meso Meso 108 108 109 109 (d) Micro Micro (d) (d) Micro Figure 4.4.Tensile Tensile behaviors ofofSFCs Figure behaviors of SFCs Figure4 Tensile behaviors SFCs 87 Commen Commen (c) (c) Meso Meso 108 108 108 109 109 109 (d) Micro (d) Micro Figure Tensile behaviors of SFCs Figure Tensile behaviors of SFCs Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering (a) (a) Plain Plain (a) Plain (b) (b) Macro Macro (b) Macro (c) Meso (d) Micro Figure Compressive behaviors of SFCs 6 Tables and supply the average values of six investigated parameters, including tensile strength, tensile strain capacity, tensile toughness (Table 3), compressive strength, compressive strain capacity, compressive toughness (Table 4) Fig shows the comparison of mechanical properties of SFCs under tension and compression As shown in Fig 6, the addition of macro and meso fibers in plain matrix clearly enhanced all the investigated parameters, whereas there was a reduction in compressive strain capacity and compressive toughness of SFCs containing micro fibers The reinforcing fibers embedded in the SFCs helped generate a mechanism of crack bridging [1, 3], and this mechanism resulted in the enhanced strengths in both tension and compression Besides, the ineffectiveness of the micro fiber in enhancing mechanical properties of SFC would be discussed in Section 3.2 The macro fibers produced the best performance in most of the investigated parameters, under both tension and compression This phenomenon could be explained through the highest aspect ratio of the macro fibers, equaling to 100, since the higher aspect ratio would produce the higher mechanical property of the composites [5, 10, 11] In contrast, the micro fiber, having its lowest aspect ratio of 65, would produce the lowest mechanical property 88 (c) (d) (c)Meso Meso (d) Micro Micro Figure Compressive behaviors of SFCs Figure Compressive behaviors of SFCs 110 110 111 111 Series Table Table 3 Tensile Tensile parameters parameters Nguyen, D.-L., et al / Journal of Science and Technology in CivilTensile Engineering Tensile strength Tensile strain Tensile strength Tensile strain Tensile Series Series (MPa) capacity (%) toughness (MPa) Table Tensile capacity (%) toughness (MPa.%) (MPa.%) parameters Pl 2.53 0.025 0.07 Pl 2.53 0.025 0.07 Tensile strength (MPa) Ma 7.64 Ma 7.64 2.53 Me 8.05 Me 8.05 7.64 Mi 5.69 Mi 8.05 5.69 5.69 Pl Ma Me Mi 112 112 Series Series Series Pl Ma Me Mi Tensile strain 0.53 capacity (%) 0.53 0.025 0.38 0.38 0.53 0.33 0.33 0.38 0.33 Tensile toughness (MPa.%) 3.91 3.91 0.07 3.30 3.30 3.91 3.19 3.30 3.19 Table Table 4 Compressive Compressive parameters parameters Compressive Compressive strain Compressive Compressive Compressiveparameters strain Table Compressive strength capacity toughness (MPa.%) strength(MPa) (MPa) capacity (%) (%) Pl 89.01 0.165 Pl strength (MPa) 89.01 Compressive strain 0.165capacity (%) Compressive Ma 113.20 0.193 Ma 113.20 0.193 89.01 0.165 113.20 0.193 Me 103.63 0.187 Me 103.63 0.187 103.63 0.187 Mi 91.52 0.164 Mi 91.52 0.164 91.52 0.164 8.66 Compressive toughness (MPa.%) 11.45 8.66 10.65 7.53 11.45 10.65 7.53 113 113 Journal of Science and Technology in Civil Engineering, NUCE 2018 p-ISSN 1859-2996 ; e-ISSN 2734 9268 (a) (b) (a)Strength Strength (b) Strain (a) Strength (b) Strain capacity capacity 77 (c) (c) Toughness Toughness 114 Figure Comparison of mechanical properties of SFCs Figure Comparison of mechanical properties of SFCs 115 Tables and supply the average values of six investigated parameters, 116 including tensile strength, tensile strain capacity, tensile toughness (Table 3), Figs.117 and displaystrength, cracking behaviorsstrain of SFCs under tension toughness and compression, compressive compressive capacity, compressive (Table 4) respectively Under tension, the6SFCs the multiple micro-cracks withofthe presence of the embedded fibers 118 Fig showsproduced the comparison of mechanical properties SFCs under tension and 119 compression As shown in Fig 6, the addition of macro and meso fibers in plain 120 matrix clearly enhanced all the investigated 89parameters, whereas there was a reduction 121 in compressive strain capacity and compressive toughness of SFCs containing micro 122 fibers The reinforcing fibers embedded in the SFCs helped generate a mechanism of 123 crack bridging [1,3], and this mechanism resulted in the enhanced strengths in both 124 tension and compression Besides, the ineffectiveness of the micro fiber in enhancing Nguyen, D.-L., et al / Journal of Science Technology in Civilin Engineering Journal and of Science and Technology Civil Engineering, NUCE 2018 Journal of Science and Technology in Civil Engineering, NUCE 2018 p-ISSN 1859-2996 ; e-ISSN2018 2734 9268 2018 Journal of Science andTechnology Technology inCivil Civil Engineering, NUCE 2018 Journalofof Science and Technology CivilEngineering, Engineering, NUCE 2018 Journal Journal Science of and Science Technology and ininCivil in Engineering, NUCE NUCE p-ISSN 1859-2996 ; e-ISSN 2734 9268 but single crack with no fibers Under compression, the SFCs with the embedded fibers produced the p-ISSN 1859-2996 ; e-ISSN 2734 9268 9268 p-ISSN 1859-2996 ; e-ISSN 2734 9268 p-ISSN 1859-2996 p-ISSN 1859-2996 ; e-ISSN 2734 ; e-ISSN 9268 2734 local tensile cracks along the specimen height whereas there was a broken damage for the specimens without fiber (a) Plain (a) Plain (a)Plain Plain (a)Plain Plain(a) (a) Journal of Journal Scienceofand Technology in Civil Engineering, NUCE 2018 Science and Technology in Civil Engineering, NUCE 2018 p-ISSN 1859-2996 ; e-ISSN(a) 9268 Plain p-ISSN 1859-2996 ;2734 e-ISSN 2734 9268 (a) Plain (a) Plain 137 137 137 137 137 138 138 (b) Macro (b) Macro (b) Macro Macro (b) Macro Macro (b) (b) (b) Macro (c) Meso (c) Meso (d) Micro(d) Micro Figure 7.Figure Cracking behaviorsbehaviors of SFCs of under tension Cracking SFCs under tension (b) Macro (b) Macro (c) Meso(c)(c)Meso (d) Micro Meso Micro (d) Micro (c) Meso(c) Meso (d)(d)Micro (d) Micro Figure Cracking behaviors of SFCs under tension Figure Cracking behaviors of SFCs SFCs under tension tension (c) Meso(c) Meso (d)7 Micro (d) Micro behaviors Figure Cracking SFCs under tension Figure 7.Figure Cracking Cracking behaviors behaviors ofofSFCs of under tension under Figure 7.Figure Cracking behaviorsbehaviors of SFCs of under tension Cracking SFCs under tension 138 138 138 (a) Plain Plain (a) Plain(a) (b) Macro (b) Macro Macro (b) (a) Plain (a) Plain (b) Macro (b) Macro (c) Meso Meso (c) Meso(c) (d) Micro (d) Micro (d) Micro 9 Figure Cracking behaviors of SFCs under compression 3.2 Sensitivities of fiber size to the studied mechanical properties of SFCs To evaluate the sensitive significance of fiber sizes to tensile and compressive properties of SFCs, the strength, failure strain and toughness of each series were normalized by corresponding parameters (a) Plain (b) Macro (d) Micro (c) Meso(c) Meso (d) Micro (a) Plain (b)slope Macro of the plain matrix, as performed in Fig In this figure, the line with a higher revealed more (a) Plain (a) Plain (b) Macro (b) Macro 9 sensitivity Table supplies the slope values of all curves of normalized parameter versus fiber content responses presented in Fig Generally, the addition of steel-smooth fibers in plain matrix produced more favorable influences on enhancing tensile properties than compressive properties This could 90 normalized by corresponding parameters the plain matrix, as performed in Fig 43 143 normalized by corresponding parameters of theofplain matrix, as performed in Fig In In this figure, the with line with a higher revealed sensitivity supplies 44 144 this figure, the line a higher slopeslope revealed moremore sensitivity TableTable supplies the the values all curves of normalized parameter versus content responses 45 145 slopeslope values of allof curves of normalized parameter versus fiberfiber content responses presented in Fig Generally, the addition of steel-smooth in plain matrix 46 146 presented in Fig Generally, the addition of steel-smooth fibersfibers in plain matrix produced favorable influences on enhancing tensile properties compressive 47 147 produced moremore favorable influences on enhancing tensile properties than than compressive Nguyen, D.-L.,to et the al / different Journal offailure-crack Science and Technology in Civil Engineering properties be attributed the tensile 48 148 properties This This couldcould be attributed to the different failure-crack typestypes in thein tensile andbecompressive specimen although the crack bridging of the 49 149 and compressive specimen thefailure-crack crack bridging of the couldcould prevent attributed to thealthough different types infibers thefibers tensile andprevent compressive specimen although propagation in both tension and compression The failure of tensile specimen 50 150 crackcrack propagation in both tension and compression The failure of tensile specimen the crack bridging of the fibers could prevent crack propagation in both tension and compression dominated by pull-out mechanism that was influenced by the 51 151 was was dominated by fully fiberfiber pull-out mechanism that was greatly influenced by the The failure of fully tensile specimen was dominated bygreatly fully fiber pull-out mechanism that was greatly 152 interfacial bond resistance of fiber-matrix, and the failure crack in this case was 52 interfacial bond resistance of fiber-matrix, and the failure crack in this case was influenced by the interfacial bond resistance of fiber-matrix, and the failure crack in this case was perpendicular the direction of applied stress [12,13] Oncontrary, the contrary, the failure 53 153 perpendicular to thetodirection applied stress [12,13] On the the the failure of of the failure of compressive perpendicular to the ofdirection of applied stress [12, 13] On contrary, compressive specimen was controlled by shear resistance or locally tensile resistance, 54 154 compressive specimen was controlled by shear resistance or locally tensile resistance, specimen was controlled by shear resistance or of locally tensile resistance, with aNUCE failure crack not Journal of NUCE Science and Technology in Civil E Journal of Science and Technology in Civil Engineering, 2018 2018 Science and Technology Engineering, a failure not perpendicular the direction of applied stress, as described in 55 155 with with a failure crackcrack not perpendicular to thetodirection of Journal applied stress, as described in in Civil p-ISSN 1859-2996 ; e-ISSN perpendicular to the direction of applied stress, asp-ISSN described in Fig 10; e-ISSN [14] 1859-2996 ; e-ISSN 27342734 92689268 p-ISSN 1859-2996 Fig.[14] 10 [14] 56 156 Fig 10 Technology in Civil Engineering, NUCE 2018 1859-2996 ; e-ISSN 2734(a) 9268 strength (a) Tensile strength (a) Tensile Tensile strength (b) Compressive strength Compressive strength (b)Tensile Compressive strength (c) Tensile strain capacity (c)(b) strain capacity 10 y (d) 10 (e) Tensile toughness (f) (f) Compressive toughness (f)Tensile Compressive toughness toughness 157 Figure Response of paramete 157 157 Figure Response of normalized parameter versus fiberfiber content ofnormalized SFCs Figure Response of normalized parameter versus content of SFCs Figure Response of normalized parameter versus fiber content of SFCs 158versus Table Slope of normalized parameter versus fiber 158 158 TableTable Slope of normalized parameter fiber5.fiber content response curves of SFCs Slope of normalized parameter versus content response curves of SFCs Strength (MPa) Strain capacity Strength (MPa) Strain capacity (%) (%) Toughness (MPa.%) Strength (MPa) Strain capacity Toughness (MPa.%) Series Series Series Tension Compression Tension Comp Table Slope of normalized parameter versus fiberTension content response curves of SFCs Tension Compression Compression Tension Compression Tension Compression Tension Compression Tension Compression 2.01 53.350.85 14.13 Ma Ma 2.01 2.01 0.85 0.85 14.1314.13Ma 0.78 0.78 53.35 0.88 0.88 Strength (MPa) Strain capacity (%) Me Toughness (MPa.%) 2.12 40.30 0.77 10.13 Me Me 2.12 2.12 0.77 0.77 10.1310.13 0.75 0.75 40.30 0.82 0.82 1.50 0.69 8.80 -0 Tension Compression Tension Compression Tension Compression Mi Mi 1.50 1.50 0.69 0.69 8.80 8.80 Mi -0.66 -0.66 24.74 24.74 -0.58-0.58 (d) straincapacity capacity (d) Compressive Compressive strain Series strain capacity (c) Tensile strain capacity (d) (c) Compressive strain capacity (d)Tensile Compressive strain capacity Ma 2.01 159 159 0.85 Me 2.12 0.77 (f) Compressive toughness Mi 1.50 0.69 ormalized parameter versus fiber content of SFCs ameter versus fiber content response curves of SFCs Strain capacity (%) Toughness (MPa.%) Tension Compression Tension Compression 14.13 0.78 53.35 0.88 10.13 0.75 40.30 0.82 (e) Tensile toughness (e) toughness (e) Tensile Tensile toughness 14.13 10.13 8.80 91 159 0.78 0.75 −0.66 53.35 40.30 24.74 11 11 0.88 0.82 −0.58 11 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 Journal of Science and Technology in Civil Engineering, NUCE 2018 Journal of Science and Technology in Civil Engineering, NUCE 2018 p-ISSNp-ISSN 1859-2996 ; e-ISSN 2734 9268 1859-2996 ; e-ISSN 2734 9268 Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering Fiber FiberMajor bridging bridging crack Major crack Under tension tension a)(a)Under a) Under tension Shear Shear crack crack Locally Locally tensiletensile crack crack Fiber Fiber bridging bridging Fiber Fiber bridging bridging Under compression b) Under compression b)(b)Under compression Figure 10 Failure crack underdirect direct tension tension and 10 Failure crack under andcompression compression Figure Figure 10 Failure crack under direct tension and compression 160 Commented Commented [A3] As shown in Table 5, the micro fibers produced the smallest slope in most of tensile and compressive parameters Even for compressive strain and toughness, the micro fibers generated the reductions in mechanical properties, as shown in Figs 6(b) and 6(c), and/or the negative slopes in Table It could be stated that the worst favorable fiber type in enhancing tensile and compressive properties was the micro fibers The reduction in compressive strain and toughness of SFC containing micro of Science and Technology in Civil Engineering, NUCE 2018should be confirmed in fiber was really unclear Journal in comparison with plain matrix, and this tendency p-ISSN 1859-2996 ; e-ISSN 2734 9268 a further study The macro and meso fibers produced the favorable influences on tensile and compressive properties with positive slope The highest slope was for tensile toughness produced from Fiber Major the macro fibers, i.e.,bridging the most sensitive parameter was tensile toughness In general, the macro fiber crack was better than the meso with parameters revealing higher values, only was worse than the meso Locally Shear with parameter (tensile strength) revealing lower value Fig 11 shows the explanation for the worst tensile 161 crack crack in Fig 11, favorable effect in enhancing mechanical properties of the micro fibers As displayed 162 the minimum Figure 11 Minimum embedded length for developing fully bond of included fiber-matrix Fiber zones: the embedded length (Llength full bond ofbond fiber-matrix ) for developing Figure 11 Minimum embedded for developing fullyFiber of fiber-matrix bridging bridging debonded length (L ), the softening length (L ), and the bonded length (L ), the total of Ld of and L s s 163 As shown din Table 5, the micro fibers produced the smallestb slope in most As shown in Table 5, the micro fibers produced the smallest slope in most of was defined as the length of the damage zone It was required a minimum embedded length (L0 ) re164 tensile and compressive parameters Even for compressive strain and toughness, the garding fiber diameter (d f ) in orderEven to develop the bond of fiber-matrix the aspect tensile and to compressive parameters for compressive strain and [15], toughness, theratio of the 165 micro micro fibers generated the reductions in mechanical properties, as shown in Figs fibers, equaling to 65, may be not enough for producing L in pull-out mechanism, this6(b) resulted as shown in Figs 6(b) micro fibers generated the reductions in mechanical properties, a) Under tension b) Under compression 166 theand 6(c), and/or the negative slopes in Table It could be stated that the worst low mechanical properties of SFCs It was noted that the such explanation was for smooth fiber and 6(c),160 and/or the negative slopes Table 5.direct It could that the worst Figure 10 Failureincrack under tensionbe andstated compression 167 favorable fiber type in enhancing tensile and compressive properties was the micro Commented [A3]: Back favorable fiber type in enhancing tensile and compressive properties was the micro 168 fibers The reduction in compressive strain and toughness of SFC containing micro fibers The reduction in compressive strain and toughness of SFC containing micro 169 fiber was really unclear in comparison with plain matrix, and this tendency should be fiber was really unclear in comparison with plain matrix, and this tendency should be 170 confirmed in a further study The macro and meso fibers produced the favorable confirmed in a further study macro andproperties meso fibers the favorable 171 influences on tensile andThe compressive with produced positive slope The highest influences on tensile and compressive properties with positive slope The highest 172 slope was for tensile toughness produced from the macro fibers, i.e., the most slope was for tensile toughness produced from the macro fibers, i.e., the most 173 sensitive parameter was tensile toughness In general, the macro fiber was better than sensitive tensile toughness In higher general, the macro fiberworse was better thanmeso 174 theparameter meso withwas parameters revealing values, only was than the the parameters revealing higherrevealing values, only wasvalue worseFig than 11 the shows meso the 175 meso withwith 5parameter (tensile strength) lower with parameter (tensile strength) revealing value Fig 11 properties shows the 176 1explanation for the worst favorable effect inlower enhancing mechanical of the 161 explanation the worst favorable enhancing mechanical properties 177 micro fibers As ineffect Fig in 11, the minimum embedded lengthof (the 162 for Figure 11.displayed Minimum embedded length fordeveloping developing fully bond fiber-matrix Lo ) for Figure 11 Minimum embedded length for fully bond ofoffiber-matrix micro fibers As displayed in Fig 11, the minimum embedded length ( o ) for 163 As shown in Table 5, the micro fibers produced the smallest slope inLmost of 92 164 165 166 167 tensile and compressive parameters Even 12 for compressive strain and toughness, the micro fibers generated the reductions 12 in mechanical properties, as shown in Figs 6(b) and 6(c), and/or the negative slopes in Table It could be stated that the worst favorable fiber type in enhancing tensile and compressive properties was the micro Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering type, for other fiber types, e.g., twisted or hooked fiber types, it was required a furthur investigation to clarify 3.3 Correlation between the tensile strength and compressive strength of SFCs For ordinary concrete (OC), the direct tensile is often correlated with the compressive strength using a square root scale in a few standards Eq (1) presents the such correlation according to ACI 318 for OC [16] The correlation between the tensile strength and compressive strength of SFCs may different from that of OC, this was because the tensile strength of SFCs was importantly improved with the use of reinforcing fibers in the concrete mixture Some references were reported that a power relationship between the tensile strength and compressive strength of SFCs was valid [17, 18], whereas other references were still proposed a square root scale between them [19, 20], as displayed in Eq (2) The coefficient (λ) in Eq (2) would be drawn based on the data of experimental tests ft = 0.33 σ pc = λ fc (1) fSFC (2) where fc is the compressive strength of OC using a cylindrical specimen of 150 × 300 mm, ft is the tensile strength of OC, fSFC is the compressive strength of SFCs using a cylindrical specimen of 100 × 200 mm, σ pc is the post-cracking tensile strength of SFCs Table Coefficients in correlation between tensile and compressive strength of SFCs Type of fiber Tensile strength (MPa) Compressive strength (MPa) Coefficient (λ) Plain Ma Me Mi 2.53 7.64 8.05 5.69 89.01 113.20 103.63 91.52 0.27 0.72 0.79 0.59 Table supplies the drawn coefficients, λ, for various fiber types as follows: 0.27 for Pl, 0.72 for Ma, 0.79 for Me and 0.59 for Mi Comparatively, the order in term of λ was observed as follows: Pl < Mi < Ma < Me, this order was completely agreed with the order in term of tensile strength Compared with OC, the SFCs containing the embedded fibers generated a higher λ, from 1.8 to 2.4 times, although the plain matrix produced a lower λ, only 0.8 times The drawn coefficients of SFCs were spread out and significantly dependent upon the reinforcing fibers Conclusions The experimental results supplied helpful information on the sensitivity of macro, meso and micro steel-smooth fibers to tensile and compressive properties of SFCs The observations and conclusions can be listed as follows: - The adding steel-smooth fibers in plain matrix of SFC produced more favorable influences on tensile properties than compressive properties - The micro fibers and macro steel-smooth fibers generally produced the smallest and highest sensitivity, respectively, for enhancement of tensile and compressive parameters of SFCs The macro 93 Nguyen, D.-L., et al / Journal of Science and Technology in Civil Engineering steel-smooth fiber could be employed for improving performances of reinforced concrete structures using SFCs - The most sensitive parameter of SFCs, among the six parameters investigated under tension and compression, was observed to be the tensile toughness - The coefficients in correlation between tensile and compressive strength of SFCs using a square root scale was scattered and higher than that of ordinary concrete Acknowledgements This research was funded by the Vietnam 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Tension Compression Tension Comp Table Slope of normalized parameter versus fiberTension content response curves of SFCs Tension Compression Compression Tension Compression Tension Compression... Response of paramete 157 157 Figure Response of normalized parameter versus fiberfiber content ofnormalized SFCs Figure Response of normalized parameter versus content of SFCs Figure Response of. .. Correlations among mechanical properties of steel fiber reinforced concrete Construction and Building Materials, 23(12):3468–3474 [19] Thomas, J., Ramaswamy, A (2007) Mechanical properties of steel fiber- reinforced