Study of Flexural and Crack Propagation Behavior of Layered Fiber-Reinforced Cementitious Mortar Using the Digital Image Correlation (DIC) Technique

materials

Article Study of Flexural and Crack Propagation Behavior of Layered Fiber-Reinforced Cementitious Mortar Using the Digital Image Correlation (DIC) Technique

Shaoqiang Meng 1, Jiaming Li 1, Zhihao Liu 1, Wenwei Wang 1, Yanfei Niu 2,* and Xiaowei Ouyang 1,*

1 Research Center for Wind Engineering and Engineering Vibration, Guangzhou University, Guangzhou 510006, China; [email protected] (S.M.); [email protected] (J.L.); [email protected] (Z.L.); [email protected] (W.W.) 2 School of Civil Engineering, Guangzhou University, Guangzhou 510006, China * Correspondence: [email protected] (Y.N.); [email protected] (X.O.)

Abstract: By optimizing the distribution of steel fibers in fiber-reinforced cementitious mortar (FRCM) through the layered structure, the role of fibers can be fully utilized, thus improving the flexural behavior. In this study, the flexural behavior of layered FRCM at different thicknesses (25 mm, 50 mm, 75 mm, 100 mm) of the steel fiber layer was investigated. The evolution of the crack propagation behavior was analyzed using the digital image correlation (DIC) technique. The results showed that the steel fiber layer thickness of 75 mm has the best flexural behavior. Moreover, the crack propagation path is more tortuous. The maximum value of crack opening displacement (COM) increases with the increase in fiber thickness. In addition, increasing the bottom layer thickness can increase the height of the tensile zone, but the interface inhibits the increase of the tensile zone.

Citation: Meng, S.; Li, J.; Liu, Z.; Keywords: layered concrete; FRCM; crack propagation behavior; DIC; interface Wang, W.; Niu, Y.; Ouyang, X. Study of Flexural and Crack Propagation Behavior of Layered Fiber-Reinforced Cementitious Mortar Using the 1. Introduction Digital Image Correlation (DIC) Technique. Materials 2021, 14, 4700. Fiber-reinforced cementitious mortar (FRCM) has attracted increasing attention due to https://doi.org/10.3390/ma14164700 its high strength, excellent flexural behavior, and crack control ability [1–3]. However, the high cost of raw materials for FRCM limits its widespread use in the engineering field [4,5]. Academic Editor: Marcos G. Alberti To expand the application of FRCM, reducing its raw material cost has become an important research subject in this field. Using low-cost fillers and aggregates to prepare a FRCM Received: 9 July 2021 matrix can reduce its raw material costs. The preparation of cementitious materials using Accepted: 16 August 2021 waste fillers has been proven to be feasible [6–9]. Many scholars [10–12] have reported that Published: 20 August 2021 the use of low-cost aggregates to prepare FRCM can reduce the cost without a significant loss of strength. Likewise, the high cost of steel fibers is a factor that cannot be ignored. Publisher’s Note: MDPI stays neutral Steel fibers account for 30–50% of the raw material cost of FRCM [13]. The cost of FRCM with regard to jurisdictional claims in can be greatly reduced by increasing the efficiency of steel fiber reinforcement. published maps and institutional affil- Under bending load, the region near the loading is mainly subjected to compressive iations. stress, and the bottom bending region is mainly subjected to tensile stress. Steel fibers can significantly increase the tensile strength in the tensile region, but the contribution of steel fibers to the compressive strength is not significant compared to the tensile strength. The reinforcement efficiency of the steel fibers can be improved by optimizing the distribution Copyright: © 2021 by the authors. of steel fibers in FRCM through a layered design. This design can reduce the cost of FRCM Licensee MDPI, Basel, Switzerland. while improving flexural behavior [14]. This article is an open access article Flexural behavior is a key indicator to evaluate the behavior of FRCM [15,16]. How- distributed under the terms and ever, most studies have mainly focused on single-layer FRCM, while research on multilayer conditions of the Creative Commons FRCM has rarely been reported. Lopez et al. [17] believe layered reinforced concrete has a Attribution (CC BY) license (https:// similar damage pattern to ordinary reinforced concrete. Yue et al. [18] believe the flexural creativecommons.org/licenses/by/ behavior of the designed double-layered beams is related to the thickness of the SHCC layer. 4.0/).

Materials 2021, 14, 4700. https://doi.org/10.3390/ma14164700 https://www.mdpi.com/journal/materials Materials 2021, 14, 4700 2 of 12

Lai et al. [19] prepared a three-layer functionally graded cementitious composite (FGCC) and indicate that FGCC can improve flexural behavior and control the development of damage. Besides, the flexural behavior of FRCM is closely related to the crack propagation behavior. The crack propagation is influenced by fiber bridging and strain distribution in the fracture process zone [20–22]. To further evaluate the flexural behavior of layered FRCM, the crack propagation behavior needs to be investigated. The usual methods to observe the crack propagation behavior are acoustic emission, swept surface electron microscopy, and cloud pattern method. Paul et al. [23] used acoustic emission and ARAMIS to accurately detect the fracture behavior of matrix and fibers in FRC. However, these methods require high testing environment and are difficult to perform full-field measurements in ordinary laboratories. The digital image correlation (DIC) technique has the advantages of full-field non-contact measurement and high accuracy, thus is widely used to observe crack propagation behavior [24–26]. For example, Ghafoori et al. [27] accurately quantified the crack propagation behavior of FRCM by the DIC technique. Therefore, the DIC technique is introduced to study the crack propagation behavior of FRCM. In this study, the FRCM beams are designed as two layers of different thicknesses. Steel fiber-doped FRCM and FRCM matrix are the bottom layer and top layer, respectively. The flexural behavior is studied by the three-point bending test. Then, the crack propagation behavior is analyzed by the DIC technique. The crack propagation behavior of layered FRCM beams with different thicknesses is investigated. Finally, the research value of layered FRCM was evaluated in terms of its manufacturing process and mechanical properties. 2. Experimental Program 2.1. Materials and Mix Design The mix design of the FRCM is listed in Table1. P.II 52.5R Portland cement, quartz powder, and silica fume were used as cementitious materials. The chemical composition of cementitious materials is summarized in Table2. Two particle sizes of quartz sand (0.212–0.425 mm and 0.425–0.710 mm) were used. The water-binder ratio (W/B) was 0.19. A superplasticizer was used to improve the workability of FRCM with a solids content of 33%. Steel fibers were incorporated to reinforce the flexural behavior of FRCM. The length of steel fiber is 13 mm and the diameter is 0.2 mm. The fiber doping is 2% (volume fraction). Its characteristic information is shown in Table3.

Table 1. Mix proportions of FRCM (kg/m3).

Cementitious Materials QS Materials W SP Fiber CEM QP SF 0.212–0.405 mm 0.425–0.710 mm Quantity 998.52 302.15 129.75 250.58 751.75 257.52 18.47 2% [Note]: CEM = portland cement, SF = silica fume, QP = quartz powder, QS = quartz sand, W = water, SP = superplasticizer.

Table 2. The chemical compositions of cementitious materials (%).

Compound CaO SiO2 Al2O3 Fe2O3 SO3 Other CEM 62.22 21.17 6.43 3.67 3.04 3.105 SF 0.431 96.94 6.43 − 0.124 1.567 QP 0.0117 97.8 1.67 0.0271 0.0044 0.3339

Table 3. Steel ﬁber properties.

Diameter Length Aspect Ratio Density Tensile Strength Elastic Modulus 3 df (mm) lf (mm) (lf/df) (g/cm ) (MPa) (GPa) 0.2 13.0 65.0 7.8 2500 200 Materials 2021, 14, x FOR PEER REVIEW 3 of 12

Table 3. Steel fiber properties.

Diameter Length Aspect Ratio Density Tensile Strength Elastic Modulus df (mm) lf (mm) (lf/df) (g/cm3) (MPa) (GPa) 0.2 13.0 65.0 7.8 2500 200

The manufacturing process of FRCM is as follows: First, cement, quartz powder, and silica powder were dry mixed for 2 min. Then, the two-grain sizes of quartz sand were Materials 2021added, 14, 4700 to the dry mix, and low-speed stirred for 2 min to obtain a uniform mixture. Third,3 of 12 water and superplasticizer were mixed into a new liquid. Fourth, half of the liquid was poured into the mixture and low-speed stirred for 1 min, and the remaining liquid was The manufacturing process of FRCM is as follows: First, cement, quartz powder, and poured into the mixturesilica powder and high were-speed dry mixed stirred for 2 for min. 5 Then,min. theOnce two-grain the mortar sizes ofpresented quartz sand suf- were ficient fluidity, theadded steel to fibers the dry were mix, carefully and low-speed dispersed stirred for into 2 min the to fresh obtain mortar. a uniform High mixture.-speed Third, stirring was conductedwater andfor superplasticizerabout 5 min until were it mixed appeared into a well new liquid.distributed Fourth, (based half of theon liquidvisual was appearance). poured into the mixture and low-speed stirred for 1 min, and the remaining liquid was The specimenpoured was divided into the mixture into two and layers, high-speed the stirredbottom for layer 5 min. was Once FRCM the mortar containing presented sufficient fluidity, the steel fibers were carefully dispersed into the fresh mortar. High- fibers and the topspeed layer stirring was FRCM was conducted matrix. for Figure about 1 5 minpresents until it the appeared models well of distributed the five speci- (based on mens considered,visual as suggested appearance). by Paulino et al. [28]. For instance, F0.25U is a double- layered FRCM, of whichThe specimenthe bottom was thickness divided into is two25 mm layers, and the the bottom top layer layer was thickness FRCM containing is 75 mm. The FRCM containingfibers and the fibers top layerwere was poured FRCM into matrix. the bottom Figure1 presents of the plastic the models mold of from the five specimens considered, as suggested by Paulino et al. [28]. For instance, F0.25U is a double- one end of the specimenlayered FRCM, to the of other which using the bottom a wide thickness scoop. is 25Then, mm andthe theFRCM top layermatrix thickness was is poured into the top75 of mm. the The plastic FRCM mold containing in the fiberssame were way. poured Compared into the to bottom extrusion, of the this plastic cast- mold ing process resultsfrom in one a end stronger of the specimen interfacial to the bond other between using a wide the scoop. two Then, layers, the such FRCM that matrix debonding does notwas occur poured under into the load. top of In the addition, plastic mold the in interface the same way.create Compareds micro to-cracks extrusion, un- this der load, consumingcasting more process energy results during in a stronger the crack interfacial expansion bond between process. the Considering two layers, such the that debonding does not occur under load. In addition, the interface creates micro-cracks under effect of surface waterload, consuming evaporation more on energy the duringbonding the crackstrength expansion of the process. interface, Considering the casting the effect time interval wasof 10 surface min [29] water. Specimens evaporation were on the covered bonding strengthwith plasti of thec sheeting interface, theto castingprevent time the evaporation ofinterval surface was water. 10 min The [29 ].specimen Specimens was were placed covered in with a room plastic with sheeting a temperature to prevent the of 20 ± 5 °C for 24evaporation h and cured of surfacein a water water. tank The for specimen 28 days was after placed demolding. in a room with a temperature of 20 ± 5 ◦C for 24 h and cured in a water tank for 28 days after demolding.

Figure 1. The specimen model. Figure 1. The specimen model.

2.2. Testing Methods 2.2. Testing Methods 2.2.1. Compressive Test 2.2.1. Compressive TestThe compressive strength test was conducted on a universal testing machine (UTM) The compressive(Shisheng strength heng Machinerytest was conducted Manufacturing on Co.,a universal LTD, Shanghai, testing China) machine with a(UTM) maximum load capacity of 3000 KN. Loading direction is perpendicular to the interface. The size of (Shisheng heng Machinery Manufacturing Co., LTD, Shanghai, China) with a maximum the specimen used was 100 mm × 100 mm × 100 mm. The test temperature was 20 ± 5 ◦C. load capacity of 3000A loading KN. Loading rate of 0.8 direction MPa/s was is used perpendicular according to theto the ASTM interface standards. The C 39 size [30 ].of The the specimen usedrecorded was 100 value mm is the× 100 average mm of× 100 three mm. specimens. The test temperature was 20 ± 5 °C . A loading rate of2.2.2. 0.8 MPa/s Flexural was Testing used according to the ASTM standards C 39 [30]. The recorded value is the averageA three-point of three bending specimens. test was conducted on a material testing system (MTS) using a servo-controlled electro-hydraulic machine (Shisheng heng Machinery Manufacturing 2.2.2. Flexural TestingCo., LTD, Shanghai, China). The loading setup is shown in Figure2. A specimen with dimensions of 100 mm × 100 mm × 400 mm and a span of 300 mm was selected, as in A three-point bending test was conducted on a material testing system (MTS) using the previous work [24,25]. Loading direction is perpendicular to the interface. The test a servo-controlledtemperature electro-hydraulic is 20 ± 5 ◦ C.machine Two steel (Shisheng frames were heng placed Machinery at 1/2 of each Manufacturing side of the specimen, Co., LTD, Shanghai,and aChina). linear variable The loading differential setup transformer is shown (LVDT) in Figure was attached 2. A specimen to each frame. with The dimensions of 100deﬂection mm × 100 will mm be accurately × 400 mm recorded and througha span twoof 300 LVTDs. mm The was displacement selected, controlas in the under a rate of 0.2 mm/min was used following the ASTM standards C1609. The roughness of the specimen surface and the bending of the specimen under load can have an impact on the

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previous work [24,25]. Loading direction is perpendicular to the interface. The test temperature is 20 ± 5 °C . Two steel frames were placed at 1/2 of each side of the specimen, and aprevious linear variable work [24,25] differential. Loading transformer direction is(LVDT) perpendicular was attached to the tointerface each frame.. The t Theest tem- deflec- perature is 20 ± 5 °C . Two steel frames were placed at 1/2 of each side of the specimen, and Materials 2021, 14, 4700 tion will be accurately recorded through two LVTDs. The displacement control under4 of 12a a linear variable differential transformer (LVDT) was attached to each frame. The deflec- rate of 0.2 mm/min was used following the ASTM standards C1609. The roughness of the tion will be accurately recorded through two LVTDs. The displacement control under a specimen surface and the bending of the specimen under load can have an impact on the rate of 0.2 mm/min was used following the ASTM standards C1609. The roughness of the test results. Therefore, a steel frame was installed on the specimen to ensure the accuracy testspecimen results. surface Therefore, and the a steelbending frame of the was specimen installed under on the load specimen can have to an ensure impact the on accuracy the of the test data. The bending equivalent stresses are expressed according to Equation (1): oftest the results. test data. Therefore, The bending a steel frame equivalent was installed stresses on are the expressed specimen according to ensure tothe Equation accuracy (1): of the test data. The bending equivalent stresses are퐿 expressed according to Equation (1): 푓 = 푃 × L 2 (1) = × 퐿bh f P 2 (1) 푓 = 푃 × bh2 (1) where L is the span of the beam, b the heightbh of the beam, and h the width of the beam.wherewhere L is the L is span the span of the of beam, the beam, b the b height the height of the of beam, the beam, and hand the h width the width of the of beam. the beam.

(a) Physical image (b) Schematic image (a) Physical image (b) Schematic image Figure 2. Three-point bending set-up. FigureFigure 2. ThreeThree-point-point bending bending set set-up.-up. 2.2.3. Digital Image Correlation 2.2.3.2.2.3. Digital Digital ImageImage Correlation DICDIC isis aa methodmethod to to calculatecalculate calculate the the the displacement displacement displacement of of ofpoints points points in ina in specifica a specific specific region region region [29]. [29]. [29 As]. As As shownshownshown in in FigureFigure 33,, two high high-resolutionhigh--resolutionresolution cameras cameras (Dantec (Dantec(Dantec LTD LTD LTD,, Kässbohrerstr,, Kässbohrerstr,Kässbohrerstr, Germany) Germany)Germany) withwith a a focal focal length length of of 50 50 mm mm (1024 (1024 × 1024× 1024 pixels) pixels) were were used used to test to the test sample the sample surface surface with with a focal length of 50 mm (1024 × 1024 pixels) were used◦ to test the sample surface with scatterwithscatter scatter patterns.patterns. patterns. The lens The shootingshooting lens shooting angle angle is angleis 45°. 45°. To isTo 45eliminate eliminate. To eliminate the the influence influence the influence of otherof other light of otherlight sourceslightsources sources onon thethe on testtest the results, test results,twotwo blueblue two lights lights blue were were lights used. used. were The The measured used. measured The area measuredarea was was 100 100 mm area mm × was × 200100200 mm. mmmm. × TheThe200 loadingloading mm. The direction loading isis directionperpendicularperpendicular is perpendicular to to the the interface interface to theof ofthe interface the specimen. specimen. of the The specimen. The test t est ◦ temperatureThetemperature test temperature isis 2020 ± 5 is°C 20.. First,First,± 5 C.thethe First, scatter scatter the pattern scatterpattern before pattern before and beforeand after after and the the afterdeformation deformation the deformation of aof a specificofspecific a specific regionregion region duringduring during the flexuralflexural the flexural loading loading loading was was acquired. acquired. was acquired. Then, Then, a Then, grayscalea grayscale a grayscale analysis analysis analysiswas was performedwasperformed performed inin combinationcombination in combination withwith awitha specific specific a specific algorithm, algorithm, algorithm, which which whichobtains obtains obtains the the strain s thetrain field strain field of fieldthe of the of region.theregion. region. The The images Theimages images were wereacquiredacquired acquired in in 1 1 s/frame. s/frame. in 1 s/frame. Detailed Detailed Detailedinformation information information about about the the DIC about DIC system thesystem DIC cansystemcan be be found found can be inin found thethe literature in the literature [30].[30]. [30].

FigureFigure 3. Test configuration conﬁguration of of the the DIC DIC technique. technique. Figure 3. Test configuration of the DIC technique. 3. Results and Discussion 3.1. Compressive Strength The compressive strength of layered FRCM with different thicknesses is shown in Figure4. The recorded value is the average of three specimens. The compressive strength of the specimen increases with the increase in the thickness of the bottom layer until 75 mm. The compressive strength reaches the maximum at the thickness of 75 mm, which is 121.0 MPa. The compressive strength of F0U is 94.3 MPa, the compressive strengths of F0.25U, F0.5U, F0.75U, and F1U increased by 2.1%, 9.6%, 28.3%, and 23.5%, respectively. Materials 2021, 14, x FOR PEER REVIEW 5 of 12

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3. Results and Discussion3. Results and Discussion 3.1. Compressive Strength3.1. Compressive Strength The compressive strengthThe compressive of layered FRCM strength with different of layered thicknesses FRCM is shown with in different thicknesses is shown in Figure 4. The recorded value is the average of three specimens. The compressive strength of the specimen increasesFigure with 4. The the increaserecorded in thevalue thickness is the of average the bottom of layer three until specimens. 75 The compressive strength mm. The compressiveof the strength specimen reaches theincreases maximum with at the the thickness increase of 75 in mm, the which thickness is of the bottom layer until 75 121.0 MPa. The compressivemm. The strength compressive of F0U isstrength 94.3 MPa, reaches the compressive the maximum strengths ofat the thickness of 75 mm, which is F0.25U, F0.5U, F0.75U, and F1U increased by 2.1%, 9.6%, 28.3%, and 23.5%, respectively. 121.0 MPa. The compressive strength of F0U is 94.3 MPa, the compressive strengths of Materials 2021, 14, 4700 F0.25U, F0.5U, F0.75U, and F1U increased by5 of 122.1%, 9.6%, 28.3%, and 23.5%, respectively.

Figure 4. The compressive strength of various bottom layer thicknesses.

3.2. Flexural Behavior 3.2.1. Load–deflection Curve

The load–deflection curves are shown in Figure 5a. Each curve is an average from Figure 4. The compressive strength of various bottom layer thicknesses. three parallel samples.Figure In the 4. Theinitial compressive stage, the load strength increases of linearly various with bottom the increase layer thicknesses.in 3.2. Flexural Behavior deflection. When the3.2.1. deflection Load-Deflection increases Curve to a certain value, the first crack appears. During loading, the limit of proportionThe load-deflectionality curves (LOP) are shown is defined in Figure 5asa. Eachthe curveinitial is an crack average strength, from and the three3.2. parallel Flexural samples. InBehavior the initial stage, the load increases linearly with the increase in modulus of rupturedeflection. (MOR) When is the defined deflection increases as flexural to a certain strength value, the first [31,32]. crack appears. Figure During 5b shows the equivalent flexuralloading,3.2.1. strength the Load limit of of specimens proportionality–deflection. T (LOP)he valueCurve is defined of as PLOP the initialis about crack strength,11.9 MPa and . The equiv- the modulus of rupture (MOR) is defined as flexural strength [31,32]. Figure5b shows alent flexural strength (PMOR) of F0.25U, F0.5U, F0.75U, and F1U are 9.987 MPa, 10.508 the equivalentThe flexural load strength–deflection of specimens. The curves value of PLOP areis about shown 11.9 MPa. Thein Figure 5a. Each curve is an average from MPa, 17.576 MPa,equivalent and 12.5217 flexural MPa strength, respectively. (PMOR) of F0.25U, F0.5U, F0.75U, and F1U are 9.987 MPa, 10.508three MPa, parallel 17.576 MPa, and samples. 12.5217 MPa, respectively. In the initial stage, the load increases linearly with the increase in deflection. When the deflection increases to a certain value, the first crack appears. During loading, the limit of proportionality (LOP) is defined as the initial crack strength, and the modulus of rupture (MOR) is defined as flexural strength [31,32]. Figure 5b shows the equivalent flexural strength of specimens. The value of PLOP is about 11.9 MPa. The equivalent flexural strength (PMOR) of F0.25U, F0.5U, F0.75U, and F1U are 9.987 MPa, 10.508 MPa, 17.576 MPa, and 12.5217 MPa, respectively.

(a) (b) Figure 5. LoadFigure–deflection 5. Load-deﬂection curves curves (a ()a )and and equivalent equivalent ﬂexural flexural strength (b )strength of specimens. (b) of specimens.

The initial crack strength of F0U and F0.25U is greater than that of the flexural strength (PLOP > PMOR), which is a deflection softening behavior. The flexural strength at the initial crack strength of F0.75U, F1U is greater than that of the flexural strength (PLOP < PMOR), which is a deflection hardening behavior. In other words, the bottom thickness is less than 50 mm for deflection softening behavior and more than 50 mm for deflection hardening behavior. This is due to the thin bottom fiber layer (<50 mm), which results in a weak bridging effect provided by the fibers. The flexural strength is mainly provided by

(a) (b)

Figure 5. Load–deflection curves (a) and equivalent flexural strength (b) of specimens.

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the bridging effect of the aggregates. As the thickness of the bottom layer increases (>50 mm), the bridging effect of the fibers can effectively inhibit crack propagation, leading to Materialsan2021 increase, 14, 4700 in flexural strength. 6 of 12

3.2.2. Deflection Capacity and Toughness The initial crack strength of F0U and F0.25U is greater than that of the flexural strength The deflection (PcapacityLOP > PMOR of), whichlayered is a deflectionFRCM with softening different behavior. thicknesses The flexural strength is shown at the in initial Fig- ure 6a. The value ofcrack δLOP strength is about of F0.75U, 0.107 F1U mm. is greater The than toughness that of the can flexural be strengthcalculated (PLOP from< PMOR the), which is a deflection hardening behavior. In other words, the bottom thickness is less than area enclosed by the50 mm deflection for deflection curve. softening The behavior toughness and more of than layered 50 mm FRCM for deflection with hardening different thicknesses is shownbehavior. as Fig Thisure is6b. due The to the average thin bottom value fiber of layer Toughness (<50 mm),LOP which is 0.641 results MPa in a weak·mm. This is due to the flexuralbridging behavior effect provided before by the cracking fibers. The being flexural provided strength is by mainly the providedFRCM matrix, by the bridging effect of the aggregates. As the thickness of the bottom layer increases (>50 mm), independent of the thefiber bridging [27,33,34]. effect of The the toughness fibers can effectively of F0U, inhibit F0.25U, crack F0.5U, propagation, F0.75U, leading and to F1U an are 0.366 MPa·mm,increase 3.395 inMPa flexural·mm, strength. 2.349 MPa·mm, 9.809 MPa·mm, and 3.718 MPa·mm, respectively. 3.2.2. Deflection Capacity and Toughness By studying the relationshipThe deflection between capacity of flexural layered FRCM strength with differentand toughness thicknesses (Fig is shownure 7), in it was found that a quadraticFigure6a . The polynomial value of δLOP can is about accurately 0.107 mm. represent The toughness this canrelationship, be calculated as shown in Equation from(2). The the area R2 is enclosed 98.3%. by the deflection curve. The toughness of layered FRCM with different thicknesses is shown as Figure6b. The average value of Toughness LOP is 0.641 MPa·mm. This is due to the2 flexural behavior before cracking being provided by the FRCM matrix, independenty = −2.76 of푥 the+ fiber0.133 [27푥,33+,3417].. The26 toughness of F0U, F0.25U, F0.5U,(2) · · · · where x is the flexuralF0.75U, strength and F1U and are 0.366 y is MPathe mm,toughness. 3.395 MPa mm, 2.349 MPa mm, 9.809 MPa mm, and 3.718 MPa·mm, respectively.

(a) (b)

Figure 6. Deflection capacityFigure 6. Deﬂection (a) and capacitytoughness (a) and (b toughness) of specimens. (b) of specimens.

By studying the relationship between ﬂexural strength and toughness (Figure7), it was found that a quadratic polynomial can accurately represent this relationship, as shown in Equation (2). The R2 is 98.3%.

y = −2.76x2 + 0.133x + 17.26 (2)

where x is the ﬂexural strength and y is the toughness.

Figure 7. The relationship between flexural strength and toughness.

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3.2.2. Deflection Capacity and Toughness The deflection capacity of layered FRCM with different thicknesses is shown in Fig- ure 6a. The value of δLOP is about 0.107 mm. The toughness can be calculated from the area enclosed by the deflection curve. The toughness of layered FRCM with different thicknesses is shown as Figure 6b. The average value of ToughnessLOP is 0.641 MPa·mm. This is due to the flexural behavior before cracking being provided by the FRCM matrix, independent of the fiber [27,33,34]. The toughness of F0U, F0.25U, F0.5U, F0.75U, and F1U are 0.366 MPa·mm, 3.395 MPa·mm, 2.349 MPa·mm, 9.809 MPa·mm, and 3.718 MPa·mm, respectively. By studying the relationship between flexural strength and toughness (Figure 7), it was found that a quadratic polynomial can accurately represent this relationship, as shown in Equation (2). The R2 is 98.3%. y = −2.76푥2 + 0.133푥 + 17.26 (2) where x is the flexural strength and y is the toughness.

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3.3. Analysis of Crack Propagation Behavior

Materials 2021, 14, 4700 3.3.1. Quantification of the Strain Fields 7 of 12 (a) (b) DIC analysis was performed for layered FRCM under different loading stages. Since F0UFigure is a brittle6. Deflection failure, capacity it is difficult (a) and for toughness the DIC ( btechnique) of specimens. to capture its crack propagation behavior. Therefore, the detailed discussion of this study is limited to the strain fields in the specimens reinforced by fiber layers. Crack patterns and strain distribution of layered FRCM under different loading stages is shown in Figure 8. At the LOP point, the first cracks of F0.25U and F0.5U appear at the top, and these cracks are mainly concentrated near the loading point. However, the first cracks of F0.75U and F1U appear at the bottom. It was also found that F1U has a longer strain region than F075U. At the MOR point, the main crack in F0.25U changes to develop from the bottom. The crack at the top of F0.5U continues to develop down to about 50 mm. The crack in F0.75U continues to develop upward to about 75 mm. The length of the cracks in F1U exceeds 75 mm. At the 40% MOR point (post-flexural strength stage), the crack width of F0.25U increases while the cracks develop further upward. Cracks developed from the bottom appear in F0.5U, and these cracks converge with the cracks generated from the top at 50 mm. Cracks in F0.75U continue to develop upward, but the increase in length is not significant. Meanwhile, the top concrete reaches the ultimate compressive strain and cracks appear. Figure 7. The relationship between flexural flexural strength and toughness. Cracks in F1U develop upward in a jagged pattern. In conclusion, when the thickness of the bottom steel fiber layer is less than 50 mm, 3.3. Analysis of Crack Propagation Behavior the3.3.1. first Quantification cracks appear ofat thethe Straintop layer. Fields This is due to the low compressive strength caused by the thicker top layer, and thus the top layer undergoes compression damage. Long DIC analysis was performed for layered FRCM under different loading stages. Since cracks developed from the bottom early in F0.25U due to the small fiber layer at the bot- F0U is a brittle failure, it is difficult for the DIC technique to capture its crack propagation tom. Crack development at 50 mm laterally in F0.5U may be related to the interface be- behavior. Therefore, the detailed discussion of this study is limited to the strain fields in tween the upper and lower layers. When the thickness of the bottom steel fiber layer is the specimens reinforced by fiber layers. more than 50 mm, the strain distribution is wider and multiple crack branches are ob- Crack patterns and strain distribution of layered FRCM under different loading stages served. F0.75U has the more complex strain and crack paths compared to F1U. The cracks is shown in Figure8. At the LOP point, the first cracks of F0.25U and F0.5U appear at the in F0.75U finally extended to about 75 mm. This may be due to the interface between the top, and these cracks are mainly concentrated near the loading point. However, the first bottom and top layers preventing the transfer of strain. Of course, this remains to be fur- cracks of F0.75U and F1U appear at the bottom. It was also found that F1U has a longer ther analyzed. strain region than F075U.

FigureFigure 8. 8. CrackCrack patterns patterns and and strain strain distribution distribution of ofspecimens specimens under under different different loads. loads.

At the MOR point, the main crack in F0.25U changes to develop from the bottom. The crack at the top of F0.5U continues to develop down to about 50 mm. The crack in F0.75U continues to develop upward to about 75 mm. The length of the cracks in F1U exceeds 75 mm. At the 40% MOR point (post-ﬂexural strength stage), the crack width of F0.25U increases while the cracks develop further upward. Cracks developed from the bottom appear in F0.5U, and these cracks converge with the cracks generated from the top at 50 mm. Cracks in F0.75U continue to develop upward, but the increase in length is not signiﬁcant. Meanwhile, the top concrete reaches the ultimate compressive strain and cracks appear. Cracks in F1U develop upward in a jagged pattern. Materials 2021, 14, 4700 8 of 12

Materials 2021, 14, x FOR PEER REVIEW 8 of 12 In conclusion, when the thickness of the bottom steel fiber layer is less than 50 mm, the first cracks appear at the top layer. This is due to the low compressive strength caused by the thicker top layer, and thus the top layer undergoes compression damage. Long cracks developed from the bottom early in F0.25U due to the small fiber layer at the bottom. 3.3.2. Quantification of COD Evolution Crack development at 50 mm laterally in F0.5U may be related to the interface between the To evaluateupper the and toughness lower layers. of Whenlayered the FRCM thickness with of the different bottom steel thicknesses, fiber layer is the more crack than opening displacement50 mm, the (COD) strain distributionevolution of is widerthe specimens and multiple is crack analyzed. branches The are COD observed. are F0.75Uquan- tified by the displacementhas the more complex field under strain anddifferent crack paths loading compared stages. to F1U. Figure The cracks9 shows in F0.75U the evolu- finally extended to about 75 mm. This may be due to the interface between the bottom and top tion of COD underlayers different preventing loading the transfer stages. of strain. It can Of course, be seen this remainsthat the to height be further is analyzed.linear as a function of COD in F0.25U (Figure 9a), F0.5U (Figure 9b), and F1U (Figure 9d). The COD 3.3.2. Quantification of COD Evolution is not linear as a function of height in F0.75U (Figure 9c). This indicates that F0.75U con- To evaluate the toughness of layered FRCM with different thicknesses, the crack open- sumes more energying displacement under bending (COD) evolutionload. of the specimens is analyzed. The COD are quantified The maximumby the value displacement of COD field for under F0.25, different F0.5U, loading F0.75U, stages. and Figure F1U 9is shows 2.87 mm, the evolution 2.95 mm, of 4.36 mm, and 3.56COD mm under, respectively. different loading It stages.is further It can shown be seen thatthat the increasing height is linear the asthickness a function of of the steel fiber layerCOD can in F0.25U effectively (Figure 9imprinta), F0.5U the (Figure propagation9b), and F1U behavior (Figure9d). of The FRCM COD.is This not linearresult as a function of height in F0.75U (Figure9c). This indicates that F0.75U consumes more is matched with the results of LVDT. energy under bending load.

(a) (b)

Figure 9.FigureCOD evolution 9. COD in evolution fracture tests in withfracture perpendicular tests with orientation perpendicular in F0.25U (orientationa), F0.5U (b), F0.75Uin F0.25U (c), and (a) F1U, F0.5U (d). (b), F0.75U (c), and F1U (d). The maximum value of COD for F0.25, F0.5U, F0.75U, and F1U is 2.87 mm, 2.95 mm, 4.36 mm, and 3.56 mm, respectively. It is further shown that increasing the thickness of the 3.3.3. Quantificationsteel ﬁber of Strain layer can Distribution effectively imprint the propagation behavior of FRCM. This result is To analyzematched the role with of the results interface of LVDT. between the bottom and top layers of the layered FRCM under loading stages, the distribution of the longitudinal strain zones will be discussed in this section. The positive value of strain indicates the tensile zone, and the negative value indicates the compressive zone, as shown in Figure 10. Figure 11 presents the distribution of the longitudinal strain zones of layered FRCM with different thicknesses under various loads. The distribution of the longitudinal strain zones of layered FRCM at the LOP point is shown in Figure 11a. The tensile zones of F0.25U and F0.5U are similar at 66.2 mm. The tensile zone of F0.75U is 38.2 mm, which is the smallest. The height of the tensile zone of F1U is 55.9 mm, which is greater than F0.75U.

Materials 2021, 14, 4700 9 of 12

3.3.3. Quantiﬁcation of Strain Distribution To analyze the role of the interface between the bottom and top layers of the layered FRCM under loading stages, the distribution of the longitudinal strain zones will be discussed in this section. The positive value of strain indicates the tensile zone, and the negative value indicates the compressive zone, as shown in Figure 10. Figure 11 presents the distribution of the longitudinal strain zones of layered FRCM with different thicknesses Materials 2021, 14, x FOR PEER REVIEWunder various loads. The distribution of the longitudinal strain zones of layered FRCM9 at of 12

Materials 2021, 14, x FOR PEER REVIEWthe LOP point is shown in Figure 11a. The tensile zones of F0.25U and F0.5U are similar9 of at12 66.2 mm. The tensile zone of F0.75U is 38.2 mm, which is the smallest. The height of the tensile zone of F1U is 55.9 mm, which is greater than F0.75U.

FigureFigureFigure 10. 10. SchematicSchematic diagramdiagram of ofof thethe the compressioncompression compression andand and tensiontension tension zones.zones. zones.

(a) LOP point (b) MOR point (a) LOP point (b) MOR point

(c) 40% MOR point Figure 11. Compressive and tensile (zonesc) 40% at MORLOP point point ( a), MOR point (b), and 40%MOR point (c).

FigureFigure 11. CCompressiveompressive andand tensile tensile zones zones at at LOP LOP point point (a ),(a MOR), MOR point point (b), (b and), and 40%MOR 40%MOR point point (c). (c). Figure 11b demonstrates the distribution of the longitudinal strain zones of layered FRCMFigure at the 11 MORb demonstrates point. The tensile the distribution zone of F0.25U of the is 84.5longitudinal mm. Although strain the zones first of cracks layered FRCMin F0.25U at the started MOR from point. the Thetop layer,tensile the zone cracks of F0.25U quickly is developed 84.5 mm. from Although the bottom the first due cracks to inthe F0.25U small startedthickness from of thethe bottomtop layer, layer. the Su cracksbsequently, quickly the developed cracks developed from the rapidlybottom up-due to theward, small leading thickness to the of high the tensile bottom zone. layer. The Subsequently, crack continues the downward cracks developed from the toprapidl layery upward,in F0.5U. leading The strainto the transferhigh tensile reaches zone. the The inte crackrface (aboutcontinues 50 mm) downward and then from the transferthe top layeris restricted. The F0.75U crack develops from the bottom and the bottom fibers transfer the in F0.5U. The strain transfer reaches the interface (about 50 mm) and then the transfer is strain upward to the interface (about 75 mm). It is indicated that the influence of the in- restricted. The F0.75U crack develops from the bottom and the bottom fibers transfer the terface prevents strain from further development. Strain in the F1U is rapidly transferred strain upward to the interface (about 75 mm). It is indicated that the influence of the in- upward from the bottom, resulting in a high stretch zone (90.2 mm). terfaceThe prevents distribution strain of from the longitudinalfurther development. strain zones Strain of layered in the FRCMF1U is atrapidly the 40% transferred MOR upwardpoint is shownfrom the in bottom,Figure 11c. resulting At this intime, a high the cracksstretch in zone F0.25U, (90.2 F0.75U, mm). and F1U develop The distribution of the longitudinal strain zones of layered FRCM at the 40% MOR point is shown in Figure 11c. At this time, the cracks in F0.25U, F0.75U, and F1U develop

Materials 2021, 14, 4700 10 of 12

Figure 11b demonstrates the distribution of the longitudinal strain zones of layered FRCM at the MOR point. The tensile zone of F0.25U is 84.5 mm. Although the first cracks in F0.25U started from the top layer, the cracks quickly developed from the bottom due to the small thickness of the bottom layer. Subsequently, the cracks developed rapidly upward, leading to the high tensile zone. The crack continues downward from the top layer in F0.5U. The strain transfer reaches the interface (about 50 mm) and then the transfer is restricted. The F0.75U crack develops from the bottom and the bottom fibers transfer the strain upward to the interface (about 75 mm). It is indicated that the influence of the interface prevents strain from further development. Strain in the F1U is rapidly transferred upward from the bottom, resulting in a high stretch zone (90.2 mm). The distribution of the longitudinal strain zones of layered FRCM at the 40% MOR point is shown in Figure 11c. At this time, the cracks in F0.25U, F0.75U, and F1U develop further. The tensile zone further increases to 90.2 mm, 88.6 mm, and 97.1 mm, respectively. The continuous increase in load leads to cracking of the top layer of concrete by reaching ultimate compressive strain, which converges with the cracks generated by tensile strain at the interface (about 50 mm). It is worth noting that the height of the tensile zone of F0.5U and F0.75U is approximately the height of their interface. In short, for bottom fiber layer thickness less than 50 mm, the flexural behavior is mainly contributed by the bridging effect of the aggregate, resulting in the high height of the tensile zone at the LOP point. After reaching the MOR point, the height of the tensile zone of F0.25U continues to increase. However, F0.5U maintains the height of the tensile zone at 50 mm due to the presence of the interface that hinders the transfer of strain. When the thickness of the bottom fiber layer is greater than 50 mm, the bending load transitions to be mainly carried by the fibers, causing the tensile zone to be smaller. Similarly, the tensile zone of F0.75U is finally kept at about 75 mm after reaching the MOR point. Since F1U has no interface, the transfer of strain is faster, leading to a higher tensile zone than F0.75U. In other words, the strain distribution of layered FRCM is mainly controlled by two factors: the thickness of the bottom fiber layer and the interface between the two layers. When the bottom fiber layer is 25 mm and 100 mm, the thickness of the bottom fiber layer is the dominant factor affecting the strain distribution. When the bottom fiber layer is 50 mm and 75 mm, the strain distribution is controlled by the combined effect of the bottom fiber layer thickness and the interface.

4. Conclusions In this study, FRCM beams are designed in layers with different thicknesses. The flexural behavior was investigated by a three-point bending test. Then, the crack propagation behavior was analyzed using the DIC technique. The effect of bottom layer thickness on the crack propagation behavior was discussed in terms of crack and strain paths, COD, and distribution of local strain fields. Based on the obtained results, we may conclude the following: (1) Increasing the thickness of the steel fiber layer can increase the equivalent flexural strength and toughness until 75 mm. The bottom steel fiber layer is less than 50 mm for flexural softening behavior and more than 50 mm for flexural hardening behavior. (2) The increase of the thickness of the steel fiber layer makes the crack development path more curved. The phenomenon of multiple crack branches appears when the thickness of the bottom layer is 75 mm. The expansion of cracks into the interface will be limited by the interface. (3) The height of the tensile zone is related to the thickness of the bottom fiber layer and the interface. For F0.25U and F1U, the thickness of the bottom fiber layer is the dominant factor affecting the strain distribution. For F0.5U and F0.75U, the strain distribution is controlled by the combined effect of the bottom fiber layer thickness and the interface. In this study, a detailed analysis of the crack expansion behavior of layered FRCM was conducted to confirm the advantages of layered FRCM. The design of layered FRCM can provide a new way to study reducing the cost of FRCM and improving its flexural Materials 2021, 14, 4700 11 of 12

behavior. However, the sample fabrication method in this study is labor-intensive and difﬁcult to apply in practical engineering. Therefore, The extrusion process may be a better choice for engineering applications. The strain ﬁeld at the interface using extruded layered FRCM will be further studied.

Author Contributions: Conceptualization, X.O.; data curation, Y.N.; formal analysis, S.M. and Y.N.; funding acquisition, X.O.; investigation, S.M., J.L., W.W. and Z.L.; methodology, Y.N.; supervision, X.O.; writing—review and editing, S.M., Y.N. and X.O. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Nature Science Foundation of China (Grant No. 52008119), the Natural Science Foundation of Guangdong Province (Grant No. 2019A1515110799 and 2021A1515012624), and the 111 project (Grant No. D21021). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The associated data in this study are available from the corresponding author. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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