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Experimental Research on the Mechanical Properties of Tailing Microcrystalline Foam Glass Jinliang Bian 1 , Wanlin Cao 1, *, Lin Yang 1 and Cunqiang Xiong 2 1 2

*

The College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; [email protected] (J.B.); [email protected] (L.Y.) Beijing North Glass Sinest Technology Co., LTD, Beijing 100125, China; [email protected] Correspondence: [email protected]

Received: 19 August 2018; Accepted: 16 October 2018; Published: 20 October 2018







Abstract: Tailing microcrystalline foam glass (TMFG) is a building material that not only has the characteristics of light weight, fire resistance, and thermal insulation, but also has decorative applications. TMFG has a broad application prospect, but there has been little research on the macroscale mechanical properties of this material. In order to analyze TMFG basic mechanical properties, a series of experimental studies were carried out by performing the four-point flexural, shear, uniaxial compression, and splitting tensile strength tests. The research showed that the foaming agent (SiC) had a great influence on the mechanical properties of the material. With the reduction of the amount of SiC, the strength of the material and brittle failure increased. The microcrystalline decoration surface improved the flexural strength and compression strength of the tailing microcrystalline foam glass. The modulus of elasticity and the Poisson’s ratio are discussed, and a formula for the modulus of elasticity is proposed. Based on the analysis of the stress and strain curves, a constitutive model is proposed for the application of tailing microcrystalline foam glass and future research on this material. Keywords: tailing microcrystalline foam glass; mechanical properties; constitutive model; experimental research

1. Introduction Foam glass (FG) is a porous glass material composed of waste glass and various mineral waste materials. Generally, the production process of foam glass is as follows: Firstly, a uniform mixture is formed by adding appropriate amounts of the foaming agent, cosolvent, and various modified additives, and, then, the uniform mixture is put into a specific mold and subjected to preheating, melting, foaming, cooling, and other processes [1–3]. In 1935, the French company St. Gubain successfully developed foam glass using glass powder as the raw material and CaCO3 as the foaming agent; this mixture was heated in a refractory mold, to obtain a light material. St. Gubain developed a variety of silicate foam glass systems. Subsequently, the United States, Germany, Japan, the United Kingdom, and other countries also began the study of foam glass and issued a number of related patents and research reports. Foam glass has the advantages of low density, low thermal expansion coefficient, low thermal conductivity, and corrosion resistance. It enables heat insulation and sound absorption and is a lightweight, moisture-proof, and fire-proof building heat insulation material and decorative material. The development and application of foam glass will play a positive role in the recovery and utilization of glass wastes and in environmental protection [4–7]. However, foam glass has a low mechanical strength, so it is rarely used as a wall material. Microcrystalline foam glass (MFG) produced by the micro-crystallization of foam glass is a lightweight, high-strength material. A large number of small bubbles and needle-like crystals are evenly distributed in the main phase of the glass. MFG has several advantages, such as being a fire-proof, non-toxic, Materials 2018, 11, 2048; doi:10.3390/ma11102048

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evenly distributed in the main phase of the glass. MFG has several advantages, such as being a firenon-radioactive, corrosion-resistant, and machinableand material. Usingmaterial. MFG asUsing a wallMFG material can proof, non-toxic, non-radioactive, corrosion-resistant, machinable as a wall greatly reduce the weight of a building. Nowadays, tailing can produce not only MFG but also an MFG material can greatly reduce the weight of a building. Nowadays, tailing can produce not only MFG with a microcrystalline decorative surface by specific process, as shown in Figure 1. The material but also an MFG with a microcrystalline decorative surface by specific process, as shown in Figure 1. properties of foam glass, microcrystalline foam glass, and tailing microcrystalline foam glass (TMFG) The material properties of foam glass, microcrystalline foam glass, and tailing microcrystalline foam are compared in Table 1 [8,9].inThe compression of TMFG can reach 12.5 MPa, and 12.5 its lowest glass (TMFG) are compared Table 1 [8,9]. Thestrength compression strength of TMFG can reach MPa, thermal conductivity can reach 0.075 W/(m ·K). 0.075 The decorative is dense surface glass–ceramic, that can and its lowest thermal conductivity can reach W/(m·K). surface The decorative is dense glass– not only play a decorative role, but also greatly improve the mechanical strength of the material. TMFG ceramic, that can not only play a decorative role, but also greatly improve the mechanical strength of can be used not onlycan as abethermal insulation but also tomaterial construct multi-functional exterior the material. TMFG used not only as amaterial thermal insulation but also to construct multiwalls with integrated environmental protection, thermal insulation, fire protection, and decoration functional exterior walls with integrated environmental protection, thermal insulation, fire properties. TMFG has a broad application prospect protection, Therefore, and decoration properties. Therefore, TMFG has a [10–15]. broad application prospect [10–15].

(a)

(b)

1. Tailing Tailing microcrystalline microcrystalline foam foam glass glass (TMFG). (TMFG). (a) (a) TMFG TMFG with with aa microcrystalline microcrystalline decoration decoration Figure 1. surface; (b) (b) TMFG TMFG slab. slab. Table 1. Flexural strength (MPa). FG: foam glass; MFG: microcrystalline foam glass; TMFG: Tailing Table 1. Flexural strength (MPa). FG: foam glass; MFG: microcrystalline foam glass; TMFG: Tailing microcrystalline foam glass. microcrystalline foam glass. Material Material FG FG MFG MFG TMFG

TMFG

BulkDensity Density Water WaterAbsorption Absorption Rate Bulk Rate (kg/m33 ) (vol %) (kg/m ) (vol %) 200–400 0.8–11.0 200–400 0.8–11.0 933–1070 5.0–11.0 933–1070 5.0–11.0 300–600 1.8–2.4 300–600 1.8–2.4

Thermal Conductivity Thermal Conductivity (W/(m·K)) (W/(m·K)) 0.10–0.13 0.10–0.13 0.27–0.30 0.27–0.30 0.075–0.38 0.075–0.38

Compression Strength Compression Strength (MPa) (MPa) 1.5–3.0 1.5–3.0 5–11 5–11 4.0–12.5 4.0–12.5

Fernandes H.R. H.R. [15] [15]used usedrecycled recycledraw raw material as the main components to produce material as the main components to produce MFG,MFG, such such as sheet glass cullet and fly ashes. He used SiC as the foaming agent and found that SiC as sheet glass cullet and fly ashes. He used SiC as the foaming agent and found that SiC ledled to −3 and 0.9–1.8 MPa, to apparent density andcompressive compressivestrength strengthvalues valuesof of about about 0.18–0.35 gg· ·cm−3 apparent density and and 0.9–1.8 respectively. found thatthat the compressive strength of MFG affected not only not by apparent respectively.This Thisresearch research found the compressive strength of isMFG is affected only by density values, butvalues, also by but the internal and thickness thethickness struts andofthe phase apparent density also by porosity the internal porosity of and thecrystalline struts and the composition. Chen B. [16] used a high content of fly (50–70%) ash to produce foam at afoam low crystalline phase composition. Chen B. [16] used(50–70%) a high content of fly ash to glass produce ◦ C). The foam glass exhibited great properties, such as low density and high porosity temperature (800 glass at a low temperature (800 °C). The foam glass exhibited great properties, such as low density and mechanical strength (3.95 MPa).strength In past (3.95 studies on FG, MFG,studies and TMFG, high porosity and mechanical MPa). In past on FG,researchers MFG, andfocused TMFG, on the raw materials conditions [12–21],conditions but there has beenbut little research on researchers focused onand thethe rawpreparation materials and the preparation [12–21], there has been the mechanical properties of TMFG. Since theofmacroscale mechanical properties are very littlemacroscale research on the macroscale mechanical properties TMFG. Since the macroscale mechanical important application TMFG, a series ofof basic mechanical on the TMFG were properties for arethe very importantof for the application TMFG, a series tests of basic mechanical testscarried on the out in this study: four-point flexural, shear, uniaxial compression, and splitting tensile strength tests. TMFG were carried out in this study: four-point flexural, shear, uniaxial compression, and splitting The basic mechanical properties and relatedproperties constitutive TMFG weremodels thus determined. tensile strength tests. The basic mechanical andmodels relatedofconstitutive of TMFG were thus determined.

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Materials 2018, 11, 2048 2. Materials

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2.1. Batch Composition 2. Materials The tailing microcrystalline foam glass (TMFG) used in the following tests was composed of 2.1. Batch Composition quartz sand, waste stone residue, and glass. The batch composition was measured in terms of the weight percentage. The foaming rate wasglass controlled byused adding foaming agent to adjust the strength The tailing microcrystalline foam (TMFG) in athe following tests was composed of and density the TMFG. The mainand rawglass. materials all composition specimens were same andinwere divided quartz sand,ofwaste stone residue, The for batch wasthe measured terms of the into three batch compositions. Therate specimens with microcrystalline decorative surfaces were on weight percentage. The foaming was controlled by adding a foaming agent to adjust thebased strength the rawofmaterials with the addition of naturalfor gravel. The specific batch compositions listed andmain density the TMFG. The main raw materials all specimens were the same and wereare divided in Table 2.batch compositions. The specimens with microcrystalline decorative surfaces were based on into three the main raw materials with the addition of natural gravel. The specific batch compositions are listed Table in Table 2. 2. Batch composition. Group A: Specimens without microcrystalline decoration surface; Group AD: Specimens with microcrystalline decoration surface; Numbers 1–3: Three different batch Table 2. Batch composition. Group A: Specimens without microcrystalline decoration surface; compositions of the main raw materials. Group AD: Specimens with microcrystalline decoration surface; Numbers 1–3: Three different batch Main Raw Materials (%) Foaming Agent (%) Material of Decorative Surfaces (%) compositions of the main raw materials.

Group Group

A1 A2

A1 A3 A2 AD1 A3 AD1 AD2 AD2 AD3 AD3

Quartz 75 Quartz 80

75 8080 8075 7580 80 80 80

Waste Stone

Waste

Glass Main Residue Raw Materials (%) 10 Residue Waste Stone 10

10 10 10 10 10 10 10 10 10 10

15 Glass Waste 10 15 10 10 15 10 10 15 10 10 10

SiC

Foaming Agent (%)

1.6 SiC 1.5 1.6 1.3 1.5 1.6 1.3 1.6 1.5 1.5 1.3

Natural Gravel Natural Gravel (Fine) of Decorative Surfaces (Coarse) Material (%)

Natural Gravel (Fine)

1.3

8 88 8 8 8

Natural Gravel (Coarse)

2 22 22 2

2.2. 2.2. Production Production Process Process The Figure 2. 2. Firstly, The entire entire production production process process of of TMFG TMFG is is shown shown in in Figure Firstly, the the batch batch material material was was melted, and water was quenched using a tank furnace to obtain a basic glass raw material melted, and water was quenched using a tank furnace to obtain a basic glass raw material conforming conforming to to the the requirements requirements of of crystallization. crystallization. Then, Then, the the prepared prepared material material was was placed placed into into aa mold mold and and fired fired through a kiln. Finally, the product formed through polishing and cutting. through a kiln. Finally, the product formed through polishing and cutting.

Figure 2. Production process of TMFG.

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In Figure 2, the red, purple, and green dotted frames indicate the glass melting, sintering, and product processing processes, respectively. Thus, TMFG formed through three kinds of production processes. 2.3. Physical Properties of the Specimens The bulk density, porosity, and water absorption of Group A specimens were tested. The test methods were adopted in GB/T 3810.3-2016 standard [22]. The size of the specimens was 100 mm × 100 mm × 100 mm (width × height × length). In each of the different tests, ten specimens per group were tested, and the results were averaged. The specimens were placed in a drying box. The temperature was slowly raised to 110 ± 5 ◦ C to dry the specimens to a constant mass, and then the specimens were moved to the dryer and cooled to room temperature. According to the criterion of constant mass, the quality of the specimen is weighed two times in 24 h at constant temperature, and the mass change rate is less than 0.1%. The dry weight (m1 ) of the specimens was determined. A water tank made of inert material and a wooden grille with a section of about 50 mm × 50 mm were made. The size of the water tank should allow to immerse ten specimens. The specimens were placed on the wooden grille at the bottom of the water tank so that they were not in contact. Water was added to the water tank, and a 50 mm-thick layer of water was maintained above and below the specimens. The water was heated to boiling in 2 h, then the specimens were cooled in water to room temperature. Room temperature was maintained for 4 h. The treated specimens were placed gently in the hanging basket of an electronic balance and immersed in water to weigh their buoyant weight (m2 ). The specimens were removed from the water, and the excess moisture was wiped off with a wet towel. The liquid in the air hole of the specimens was not sucked out. The saturated weight (m3 ) was immediately determined in air. The bulk density, porosity, and water absorption of the specimens was calculated as follows: m1 m3 − m2

(1)

P=

m3 − m1 × 100% m3 − m2

(2)

A=

m3 − m1 × 100% m1

(3)

d=

where d denotes the bulk density (kg/m3 ), P denotes the porosity (%), A denotes the water absorption (%), m1 denotes the dry weight (kg), m2 denotes the buoyant weight (kg), and m3 denotes the saturated weight (kg). The bulk density, porosity, and water absorption of groups A1, A2, and A3 are shown in Table 3. As can be seen from Table 3, the porosity and water absorption decreased with the increase of the bulk density. Table 3. Bulk density and porosity of TMFG. Group A: Specimens without microcrystalline decoration surface; Numbers 1–3: Three different batch compositions of the main raw materials. Group

Bulk Density (kg/m3 )

Porosity (%)

Water Absorption (%)

A1 A2 A3

340 400 560

87.46 85.20 79.37

2.41 1.93 1.83

3. Test Setup and Instruments There has been little research on the macroscale mechanical properties of TMFG, so a reasonable experimental design is very important. The adopted test methods were as for GB/T 5486-2008 standard [23] and concrete [24]. A compression section size of 100 mm × 100 mm was adopted in

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3. Test Setup and Instruments Materials 2018, 11, x FOR PEER REVIEW There been little research on the macroscale mechanical properties of TMFG, so Materials 2018,has 11, 2048

5 of 19 a reasonable 5 of 19 experimental design is very important. The adopted test methods were as for GB/T 5486-2008 3. Test Setup and Instruments standard [23] and concrete [24]. A compression section size of 100 mm × 100 mm was adopted in GB/T 5486-2008 standard [23].The Thefour-point flexural tests and compression tests were performed There has standard been little[23]. research onfour-point the macroscale mechanical properties of TMFG, so aperformed reasonable GB/T 5486-2008 flexural tests and compression tests were on on specimens with six different batch compositions. The influences of the foaming agent SiC and the experimental design is very important. The adopted test methods were as for GB/T 5486-2008 specimens with six different batch compositions. The influences of the foaming agent SiC and the standard surface [23] andon concrete [24]. A compression section size of 100 mm ×When 100 mm wasAD adopted in decoration the of were investigated. group specimens decoration surface on the properties properties of the the materials materials were investigated. When group AD specimens GB/T 5486-2008 standard [23]. The four-point flexural tests and compression tests were performed on (those with a decoration surface) were tested, we found that a bending occurred during the compression (those with a decoration surface) were tested, we found that a bending occurred during the specimens with six different batch The influences of the foaming SiC and the test due to the different of compositions. thestrengths microcrystalline decoration surface and agent the microcrystalline compression test due tostrengths the different of the microcrystalline decoration surface and the decoration surface on the properties of the materials were investigated. When group AD specimens foam glass parentfoam material. to produce a decorative surface inside andsurface outside of a wall microcrystalline glass Furthermore, parent material. Furthermore, to produce a decorative inside and (those with a decoration surface) were tested, we foundTherefore, that a bending occurred during the in practical engineering, it is necessary to bond the material. the cross section of two bonded outside of a wall in practical engineering, it is necessary to bond the material. Therefore, the cross compression testspecimens due to thewas different strengths of The the microcrystalline decoration surface and the 100 mm of × 50 mm used group AD. thickness of group the adhesive surface was 1–2 section two bonded 100 mm × 50 in mm specimens was used in AD. The thickness ofmm. the microcrystalline foam glass parent material. Furthermore, to produce a decorative surface inside and The total size of the cross section of group ADof was the same as that of group A was in the same type of test. adhesive surface was 1–2 mm. The total size the cross section of group AD the same as that of outside of a wall in practical engineering, it is necessary to bond the material. Therefore, the cross This section, shown in Figure 3, could ensureshown that noinbending would occur during the compression group A in the same type of test. This section, Figure 3, could ensure that no bending would section of two bonded 100 mm × 50 mm specimens was used in group AD. The thickness of the test. The influence of the decorative surface wasofnot in the shear andconsidered splitting tensile occur during the compression theconsidered decorative surface adhesive surface was 1–2 mm.test. The The totalinfluence size of the cross section of group ADwas wasnot the same as thatinofthe tests; therefore, only group A specimens were subjected to these tests. In each of the tests, shear and tensile tests; only group A specimens subjected todifferent thesewould tests. In group A splitting in the same type of test.therefore, This section, shown in Figure 3, couldwere ensure that no bending three specimens in each group were tested, and the results were averaged. each of the different tests, three specimens in each group were tested, and the results were averaged. occur during the compression test. The influence of the decorative surface was not considered in the shear and splitting tensile tests; therefore, only group A specimens were subjected to these tests. In each of the different tests, three specimens in each group were tested, and the results were averaged.

(a)

(b)

(a) (b) (b) Figure 3. 3. Specimen Specimen preparation preparation for the the compression compression test. test. (a) (a) Cubic Cubic specimen; specimen; (b) Prism Prism specimens. specimens. Figure for Figure 3. Specimen preparation for the compression test. (a) Cubic specimen; (b) Prism specimens.

3.1. 3.1. Four-Point Four-Point Flexural Flexural Tests Tests

3.1.The Four-Point Flexural Tests forfor size of ofthe thespecimens specimens four-point flexural wasmm 100×mm × 100 mmmm × 400 mm× The size thethe four-point flexural teststests was 100 100 mm × 400 (width

(width ×length). height ×the length). total of 36 specimens wasloading tested. The device is400 shown Figure height ×The total of 36Aspecimens was tested. The device is shown in Figure 4. Wein measured size ofA specimens for the four-point flexural tests was 100loading mm × 100 mm × mm (width × 4. We measured the influence of the microcrystalline decoration surface. Two different conditions were theheight influence of theAmicrocrystalline decoration surface. Two different were considered, i.e. the × length). total of 36 specimens was tested. The loading device isconditions shown in Figure 4. We measured considered, i.e.,ofthe decoration surface either onthe theside top (ADs), (ADt) or the side (ADs),5.as decoration surface was placed either onwas the placed topsurface. (ADt) or to as to shown in Figure the influence the microcrystalline decoration Two different conditions were considered, i.e.shown the in decoration Figure 5. surface was placed either on the top (ADt) or to the side (ADs), as shown in Figure 5.

(a)

(a)

Figure 4. Cont.

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(b) (b)

(c)

(c)

(d)(d) Figure Four-point flexural tests; (b) (b) Splitting tensile strength test; test; (c) Uniaxial Figure 4.4. Test setups.(a)(a) (a) Four-point flexural tests; (b) Splitting (c) Uniaxial Testsetups. Four-point flexural tests; Splitting tensile strength compression test; (d) Shear Test. compression test; (d) Shear Test. Test.

(a)

(a)

(b)

(b)

Figure 5. Two ways of placing the group AD specimens. (a) Decoration surface on the top (ADt); (b) Figure 5. Two Two ways ofplacing placing thegroup groupAD ADspecimens. specimens. Decoration surface on the (ADt); ways the (a)(a) Decoration surface on the top top (ADt); (b) Decoration surface on of the side (ADs). (b) Decoration surface on the (ADs). Decoration surface on the sideside (ADs).

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3.2. Splitting Tensile Strength Test Materials 2018, 11, x FOR PEER REVIEW

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The size of the specimens for the splitting tensile strength test was 100 mm × 100 mm × 100 mm. The3.2. specimens were TMFG the microcrystalline decoration surface. Nine specimens were Splitting Tensile Strengthwithout Test tested, and the loading device is shown in Figure 4. The diameter of the steel padding was 75 mm. The size of the specimens for the splitting tensile strength test was 100 mm × 100 mm × 100 mm. A plywood cushion wasTMFG placedwithout betweenthe themicrocrystalline steel padding and the specimen. of the were cushion The specimens were decoration surface. The Ninewidth specimens should be 15–20 mm, the thickness should be 3–4 mm, the length should not be shorter than the tested, and the loading device is shown in Figure 4. The diameter of the steel padding was 75 mm. Aside length of thecushion specimen, thebetween plywood cushion shouldand notthe be specimen. reused. The width of the cushion plywood wasand placed the steel padding The splitting strength canshould be calculated as follows: should be 15–20tensile mm, the thickness be 3–4 mm, the length should not be shorter than the side length of the specimen, and the plywood cushion should not be reused. 2Fmax The splitting tensile strength can be calculated f st = as follows:

(4)

πA

f st =

2 Fmax

(4)

A where f st denotes the splitting tensile strength (MPa), Fmax denotes the maximum test load (N), 2 ). and A denotes the splitting area (mm f F

where

st

denotes the splitting tensile strength (MPa),

max

denotes the maximum test load (N), and

A denotes the splitting area (mm2). 3.3. Compression Test

The size of theTest specimens for the cubic compression test was designed to be 100 mm × 100 mm 3.3. Compression × 100 mm, while that for the prism compression test was 100 mm × 100 mm × 300 mm (width × The size of the specimens for the cubic compression test was designed to be 100 mm × 100 mm height × length). A total of 36 specimens were tested. The surface of TMFG has many pores, therefore, × 100 mm, while that for the prism compression test was 100 mm × 100 mm × 300 mm (width × height plaster was used to level the upper were and lower of the specimens, as shown Figure 3. The test × length). A total of 36 specimens tested.surfaces The surface of TMFG has many pores, in therefore, plaster device is shown in Figure 4. was used to level the upper and lower surfaces of the specimens, as shown in Figure 3. The test device is shown in Figure 4.

3.4. Shear Test

3.4. Shear Test the fragility of TMFG, the Z-shaped specimen method [24] was adopted for the Considering

shear test, with somethe improvements. Using and specimen building method reinforcement the non-shear Considering fragility of TMFG, thegauze Z-shaped [24] wasresin, adopted for the shear test, with some improvements. Using gauze and building resin, the parts were strengthened, and a shear-vulnerable surface was setreinforcement up in the shear part tonon-shear ensure pure parts were To strengthened, and a shear-vulnerable surfacethe wastest, set up the shearwas partmade to ensure shear failure. ensure no bending would occur during thein specimen frompure TMFG shear failure. To ensure no bending would occur during the test, the specimen was made from TMFG with a microcrystal decorative surface, and the cross section was formed by bonding two blocks sized with×a 150 microcrystal decorative and by device bonding blocks sized 4, 50 mm mm × 450 mm andsurface, 100 mm ×the 150cross mmsection × 450 was mm.formed The test istwo shown in Figure 50 mm × 150 mm × 450 mm and 100 mm × 150 mm × 450 mm. The test device is shown in Figure 4, and the section size of the specimen is shown in Figure 6. and the section size of the specimen is shown in Figure 6.

Figure of shear sheartest testspecimen. specimen. Figure6.6.Cross Crosssection section size size of

TheThe shear strength can bebecalculated shear strength can calculatedas asfollows: follows: s= f s f=

Fmax F max bh bh

(5) (5)

f s denotes Fmaxdenotes where the shear strength (MPa), denotesthe themaximum maximumtest testload load (N), (N), bb denotes denotes the where f s denotes the shear strength (MPa), Fmax the width of the pure shear surface (mm), and denotes the height of the pure shear surface (mm). h width of the pure shear surface (mm), and h denotes the height of the pure shear surface (mm).

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4. Test Results The result of the four-point flexural strength, compressive strength, splitting tensile strength, and shear strength tests were analyzed, and constitutive equations of TMFG are proposed in this 8paper. Materials 2018, 11, x FOR PEER REVIEW of 19 4.1. Four-Points Flexural Test 4. Test Results The from group A and group ADs produced sounds,splitting indicating broken internal Theflexure result specimens of the four-point flexural strength, compressive strength, tensile strength, pores during the loading process, and vertical penetrating cracks in the middle part of the specimens and shear strength tests were analyzed, and constitutive equations of TMFG are proposed in this were found. The destruction process without obvious signs was rapid, resulting in brittle failure. paper. There were two forms of damage to the specimens in the group ADt. One was the shear slanting cracks that the largest 4.1. appeared Four-PointsinFlexural Test shearing area. First, the microcrystalline foam glass parent metal was damaged, and, then, the microcrystalline decoration surface was destroyed in the largest shearing area. The flexure specimens from group A and group ADs produced sounds, indicating broken The damage process was rapid. The specimens ADt1 and ADt2 mainly exhibited this failure mode. internal pores during the loading process, and vertical penetrating cracks in the middle part of the The other form of destruction consisted of vertical cracks appearing in the largest moment area in the specimens were found. The destruction process without obvious signs was rapid, resulting in brittle middle part of the specimen. The parent material was damaged first, and, then, the microcrystalline failure. There were two forms of damage to the specimens in the group ADt. One was the shear decoration surface was destroyed. This type of damage occurred in ADt3, as shown in Figure 7. slanting cracks that appeared in the largest shearing area. First, the microcrystalline foam glass parent The flexural strengths were calculated with Formula (6) and are compared in Table 4. metal was damaged, and, then, the microcrystalline decoration surface was destroyed in the largest shearing area. The damage process was rapid. TheFmax specimens ADt1 and ADt2 mainly exhibited this L f p consisted = (6) 2 failure mode. The other form of destruction of vertical cracks appearing in the largest bh moment area in the middle part of the specimen. The parent material was damaged first, and, then, where f p denotes the decoration flexural strength the specimens Fmaxofdenotes maximum test load the microcrystalline surfaceofwas destroyed. (MPa), This type damagethe occurred in ADt3, as (N), L denotes the distances between the supports (mm), b denotes the specimen width (mm), and shown in Figure 7. The flexural strengths were calculated with Formula (6) and are compared in Tableh denotes the specimen height (mm). 4.

(a)

(b)

(c)

(d)

Figure7.7. Destruction Destruction types flexural test. (a) (a) Group A; (b) Ads;Ads; (c) Figure types in inthe thespecimen specimenduring duringthe the flexural test. Group A; Group (b) Group Group ADt1 and ADt2; (d) Group ADt3. (c) Group ADt1 and ADt2; (d) Group ADt3.

Table decorationsurface; surface;Numbers Numbers Table4.4.Flexural Flexuralstrength. strength.Group GroupA: A:Specimens Specimens without without microcrystalline microcrystalline decoration 1–3: Three different batch compositions of the main raw materials; ADt: Decoration surface on thetop; top; 1–3: Three different batch compositions of the main raw materials; ADt: Decoration surface on the ADs: ADs:Decoration Decorationsurface surface on on the the side. side. Group Group A A ADt ADt ADs ADs

11 1.47 MPa 1.47 3.04 MPa 3.04 MPa 1.80 MPa 1.80 MPa

Ratio Ratio 11 2.06 2.06 1.22 1.22

22 1.83 MPa 1.83 5.68 MPa MPa 5.68 3.32 MPa 3.32 MPa

Ratio Ratio 11 3.10 3.10 1.81 1.81

fp =

Ratio Mean MeanRatio Ratio 33 Ratio 3.77 MPa 3.77 11 11 6.66 MPa MPa 1.77 1.77 2.31 6.66 2.31 4.37 MPa 1.16 1.40 4.37 MPa 1.16 1.40

Fmax L bh 2

Placing way Way Placing Top Top Top Top Side Side

(6)

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where f p denotes the flexural strength of the specimens (MPa),

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Fmax denotes the maximum test 9 of 19

load (N), L denotes the distances between the supports (mm), b denotes the specimen width (mm),and h denotes the specimen height (mm). As shown shown in inTable Table4,4,the theflexural flexuralstrength strength increased with decrease of amount the amount of The SiC. increased with thethe decrease of the of SiC. The microcrystalline decoration surface also improved the flexural strength of TMFG; the flexural microcrystalline decoration surface also improved the flexural strength of TMFG; the strengths of and 1.41.4 times greater than that of of group group ADt ADtand andADs ADsspecimens specimenswere, were,respectively, respectively,2.31 2.31 and times greater than that group A specimens. TheThe orientation of the microcrystalline decoration surface greatly influenced the of group A specimens. orientation of the microcrystalline decoration surface greatly influenced flexural strength; the flexural strength of group ADt specimens was approximately 1.64 times of the flexural strength; the flexural strength of group ADt specimens was approximately 1.64that times ADs specimens. that of ADs specimens.

4.2. Compressive, Shear 4.2. Compressive, Shear and and Splitting Splitting Tensile Tensile Strength Strength Figure specimens’ failure modes. The results of the of compressive strength,strength, shear strength, Figure 88shows showsthe the specimens’ failure modes. The results the compressive shear splitting tensile strength, and flexural strength tests, compared with those for other mechanical strength, splitting tensile strength, and flexural strength tests, compared with those for other properties, presented Table 5; the unit of measure all parameters was MPa.was TheMPa. strength mechanical are properties, areinpresented in Table 5; the unit offor measure for all parameters The changes for the different groups are shown in Figure 9. strength changes for the different groups are shown in Figure 9.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8. 8. Failure (b) Specimen Specimen Figure Failure types types of of the the specimens. specimens. (a) (a) Specimen Specimen of of group group A A under under cubic cubic strength; strength; (b) of group AD under under cubic cubic strength; (c) Splitting Splitting tensile tensile failure failure for for the the group group A A specimen; specimen; (d) (d) specimen specimen of group AD strength; (c) of group group A A under under prism prism strength; strength; (e) (e) Specimen Specimen of of group group AD AD under under prism prism strength; strength; (f) (f) Specimen Specimen with with of shear failure. shear failure. Table 5. Compressive, shear, Table 5. Compressive, shear, and and splitting splitting tensile tensile tests tests results. results. Groups

Groups A1 A2 A3 A1 AD1 AD2 A2 AD3

Cubic Strength Cubic fcc

Prism Strength Prism fcp

Splitting Tensile Strength Splitting Tensile fst

Shear Strength Shear fs

4.50 5.43 cc 10.30 4.50 11.1 13.8 5.43 25.1

4.39 5.26 cp 9.80 4.39 10.74 13.1 5.26 24.2

0.66 0.82 st 1.59 0.66 0.82 -

0.93 1.18s 2.36 0.93 1.18 -

Strength

f

Strength

f

Strength

f

Strength

f

Flexural Strength Flexural fp

Strength 1.47 1.83p 3.77 1.47 1.83 -

f

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A3 10.30 A3 10.30 AD1 11.1 AD1 11.1 Materials 2018, 11, 2048 AD2 13.8 AD2 13.8 AD3 25.1 AD3 25.1

9.80 9.80 10.74 10.74 13.1 13.1 24.2 24.2

10of of 19 19 10

1.59 1.59 ----

2.36 2.36 ----

(a) (a)

(b) (b)

(c)(c)

(d)(d)

3.77 3.77 --- 10 of 19 --

Figure 9. 9. Variation Variation in in the the strengths strengths in in groups groups A A and Variation in cubic Figure and AD. AD. (a) (a) Variation Variation in cubic compressive compressive strengths; strengths; (b) Variation in prism compressive strengths; (c) Variation in shear strengths; (d) Variation in splitting (b) (b) Variation Variation in in prism prism compressive compressive strengths; strengths; (c) Variation Variation in in shear strengths; (d) Variation Variation in splitting tensile strengths. tensile strengths. strengths.

As shown shown Figure and Table 5, compressive strength, splitting tensile strength, shear shown in inFigure Figure99 9and and Table 5, the compressive strength, splitting strength, As in Table 5, the the compressive strength, splitting tensiletensile strength, shear strength, and flexural flexural strengthstrength all increased increased with the the with decrease of the the amount amount ofamount SiC, due dueof toSiC, reduction shear strength, and flexural all increased the decrease of theof due to strength, and strength all with decrease of SiC, to aa reduction ofreduction the foaming rate. The comparison of the cubic compressive strength, splitting tensile strength, aof of the foaming rate. The comparison of the cubic compressive strength, splitting tensile the foaming rate. The comparison of the cubic compressive strength, splitting tensile strength, shear strength, and flexural strength of the specimens in group A is shown in Figure 10. With the strength, shear strength, andstrength flexural of strength of the specimens in is group A is 10. shear strength, and flexural the specimens in group A shown in shown Figure in 10.Figure With the reduction in the amount of SiC, the improvement of the various mechanical properties was similar. With the reduction in the amount of SiC, the improvement of the various mechanical properties reduction in the amount of SiC, the improvement of the various mechanical properties was similar.

was similar.

Figure 10. Strength of group A compared to that of A1.

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Figure 10. Strength of group A compared to that of A1. Materials 2018, 11, 2048

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The various mechanical properties of A2 were about 1.22 times greater than those of A1, such as the compressive strength of A2 was 1.21 times that of A1, the splitting tensile strength of A2 was 1.24 The various mechanical properties of A2 were about 1.22 times greater than those of A1, such as times that of A1, the shear strength of A2 was 1.18 times that of A1, and the flexural strength of A2 was the compressive strength of A2 was 1.21 times that of A1, the splitting tensile strength of A2 was 1.24 times that of A1. 1.24 times that of A1, the shear strength of A2 was 1.18 times that of A1, and the flexural strength of A2 The various mechanical properties of A3 were about 2.45 times greater than those of A1, such as was 1.24 times that of A1. the compressive strength of A3 was 2.29 times that of A1, the splitting tensile strength of A3 was 2.41 The various mechanical properties of A3 were about 2.45 times greater than those of A1, such as times that of A1, the shear strength of A3 was 2.54 times that of A1, and the flexural strength of A3 was the compressive strength of A3 was 2.29 times that of A1, the splitting tensile strength of A3 was 2.56 times that of A1. 2.41 times that of A1, the shear strength of A3 was 2.54 times that of A1, and the flexural strength of The cubic compressive strength of TMFG without the microcrystalline decoration surface was A3 was 2.56 times that of A1. close to the prism compressive strength: the cubic compressive strength was about 1.04 times greater The cubic compressive strength of TMFG without the microcrystalline decoration surface was close than the prism compressive strength. Further, the cubic compressive strength was about 4.7 times to the prism compressive strength: the cubic compressive strength was about 1.04 times greater than greater than the shear strength, about 6.64 times greater than the splitting tensile strength, and 2.92 the prism compressive strength. Further, the cubic compressive strength was about 4.7 times greater times greater than the flexural strength. than the shear strength, about 6.64 times greater than the splitting tensile strength, and 2.92 times The conversion relations are as follows: greater than the flexural strength. The conversion relations are as follows: fcp  0.97 fcc (7)

f cp 0.97fccf cc fs =0.21

(8)(7)

ffsst = 0.21ffcccc  0.15

(9)(8)

ffst =0.34 0.15f f cc

(9) (10) f p = 0.34 f cc (10) The compression strength of the specimens with the microcrystalline decoration surface was The compression of the specimens with it. theThe microcrystalline surface was significantly higher thanstrength that of the specimens without cubic strengthdecoration of group AD was 2.48 significantly higher thatprism of the specimens without it. The of group AD was times that of group A,than and the strength of group AD was 2.47 cubic times strength that of group A. Therefore, 2.48microcrystalline times that of group A, and the prismimproved strength of group AD was times thatstrength of groupof A.TMFG. Therefore, the decorative surface the flexural and 2.47 compressive the microcrystalline decorative surface improved the flexural and compressive strength of TMFG. 4.3. Stress–Strain Constitutive Relations 4.3. Stress–Strain Constitutive Relations Figure 11 shows the representative compressive stress–strain and shear load–deflection curves. Figure 11 showsofthe representative compressive stress–strain and shear The loading process TMFG was divided into two stages: a pre-peak stage load–deflection and a post-peakcurves. stage The loading process of TMFG was divided into two stages: a pre-peak stage and a post-peak stage (Figure 11). f cpmax , 0.5 fcp max ,  fcpmax , and  0.5 fcp max in compression and Fs max , 0.5Fs max ,  F smax , (Figure 11). f cpmax , 0.5 f cpmax , ε f cpmax , and ε 0.5 f cpmax in compression and Fsmax , 0.5Fsmax , ε Fsmax , ε0.5 areare key parameters in the loading process. TMFG is brittle, and inthe theshear shearload loadapplication application key parameters in the loading process. TMFG is brittle, F s max in 0.5Fsmax p

cc

andlater the later ofloading the loading process resulted in abrupt failure; therefore, the curveininthe thepost-peak post-peak the stagestage of the process resulted in abrupt failure; therefore, the curve stagewas wasshallower. shallower. stage

(a)

(b)

Figure Figure 11. 11. Representative Representativecurves curvesfor forcompressive compressivestress stress and and shear. shear. (a) (a)Representative Representativecurve curvefor for compressive compressivestress; stress;(b) (b)Representative Representativecurve curvefor forshear shearload. load.

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Materials 11, 2048 the Figure 2018, 12 shows

12 of shear load–deflection curve for three different batch compositions of19group A. It Materials can be 2018, seen11,that thePEER reduction x FOR REVIEW in the amount of SiC increased the shear strength of the specimens. 12 of 19 However,Figure the slope in the post-peak stage decreased, and the brittleness became more obvious. 12 shows the shear load–deflection curve for three different batch compositions of group

Figure 12 shows the shear load–deflection curve for three different batch compositions of group A. It can be seen that the reduction in the amount of SiC increased the shear strength of the specimens. A. It can be seen that the reduction in the amount of SiC increased the shear strength of the specimens. However, the slope in the post-peak stage decreased, and the brittleness became more obvious. However, the slope in the post-peak stage decreased, and the brittleness became more obvious.

Figure 12. Shear load–deflection curves. Figure 12. 12. Shear Shear load–deflection load–deflection curves. curves. Figure

The The compressive stress–strain groupare areshown shown Figure 13. The compressive compressive stress–straincurves curves of of each each group in in Figure 13. The compressive The compressive stress–strain curves of each group are shown in Figure 13. The compressive strength of the increased with thethe reduction of the amount of of SiC, but thethe slope ofof thethe curves strength ofspecimen the specimen increased with reduction of the amount SiC, but slope strength of the specimen increased with the reduction of the amount of SiC, but the slope of the curves in the post-peak stage decreased, and the brittleness became more obvious (Figure 13a–b). curves in the post-peak stage decreased, and the brittleness became more obvious (Figure 13a–b). The in the post-peak stage decreased, and the brittleness became more obvious (Figure 13a–b). The microcrystalline decoration surface improved thethe compressive strengthofofthethe specimens, but the The microcrystalline decoration surface improved compressive strength specimens, but the microcrystalline decoration surface improved the compressive strength of the specimens, but the damage more abrupt (Figure13c–f). 13c–f). damage waswas more abrupt (Figure damage was more abrupt (Figure 13c–f).

(a)

(b)

(a)

(b)

(c)

(d)

(c)

(d) Figure 13. Cont.

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(e)

(f)

Figure 13. Compressive(e) stress–strain curves. (a) Compressive stress–strain (f) curves of Group A; (b) Compressive stress–strain curves of Group AD; (c) Compressive stress–strain curves of all specimens; Figure 13. Compressive stress–strain curves.(a)(a) Compressive stress–strainofcurves curves of A; Figure Compressive stress–strain curves. Compressive stress–strain of Group Group A; (b) (d)13. Comparison of stress–strain curves between A1 and AD1; (e)Comparison stress–strain curves (b) Compressive stress–strain curves of Group AD; (c) Compressive stress–strain curves of all specimens; Compressive stress–strain curves of Group AD; (c) Compressive stress–strain curves of all specimens; between A2 and AD2; (f) Comparison of stress–strain curves between A3 and AD3. (d) Comparison of stress–straincurves curvesbetween between A1 of stress–strain curves (d) Comparison of stress–strain A1 and andAD1; AD1;(e)Comparison (e)Comparison of stress–strain curves between A2 and AD2; (f) Comparison of stress–strain curves between A3 and AD3. In the dimensionless analysis of the compressive stress–strain curves, the ordinate is represented

between A2 and AD2; (f) Comparison of stress–strain curves between A3 and AD3.  c ),compressive  /  c (where by In/ the the peakanalysis stress is and the abscissa is represented by ordinate the peak c (where dimensionless of the stress–strain curves, the is represented

In the dimensionless analysis the compressive stress–strain curves, the ordinate is strain represented  c ). The by σ/σis thedata peak stress isof σc ), and abscissa is represented by ε/ε c (where the peak is strain were processed as the shown in Figure 14. c (where ). cThe data were as shown Figure by ε/c (where the processed peak stress is  c ),inand the14. abscissa is represented by  /  c (where the peak strain is

 c ). The data were processed as shown in Figure 14.

Figure 14. The dimensionless stress–strain curve and fitted curves. Figure 14. The dimensionless stress–strain curve and fitted curves.

There were initial microcracks inside the TMFG specimens. Because of the development of There were initial application, microcracksthe inside the TMFG specimens. of the development of microcracks after stress pre-peak stage curve would Because indicate stiffness changes in the microcracks after stressthe application, pre-peak would indicate stiffness in the initial stage; therefore, 2-fold linethe formula wasstage usedcurve to fit the pre-peak stage curve.changes The curve in initial stage; therefore, the 2-fold line formula was used to fit the pre-peak stage curve. The curve in the post-peak stage refers to the Hognestad concrete constitutive curve [25], and the residual stress Figure 14. The dimensionless stress–strain curve and fitted curves. the post-peak stage refers to the Hognestad concrete constitutive curve [25], and the residual stress was taken as 0.1 f cpmax . The 3-fold line Equation (11) was used to fit the loading process data for TMFG, was the taken as 0.1f Theindicated 3-fold line Equation (11) was used to14. fit the loading process data for TMFG, and fitting results by the solid in Figure cpmax . are There were initial microcracks inside the line TMFG specimens. Because of the development of and the fitting resultsapplication, are indicated by the solid line in Figure  the microcracks after stress pre-peak stage curve14. would indicate stiffness changes in the 1.33x 0 ≤ x < 0.15    initial stage; therefore, the 2-fold line was used 0to fit 1.33x x  the 0.15pre-peak stage curve. The curve in  formula y =  0.2 + 0.94( x − 0.15) 0.15 ≤ x < 1 (11)  the post-peak stage refers to the Hognestad x − 1 constitutive  0.15) 0.15  x  1 curve [25], and the residual stress 0.2  0.94( xconcrete   ) x≥1 y   1 − 0.9a( (11) xu −was 1 used to fit the loading process data for TMFG, x  1(11) was taken as 0.1f cpmax . The 3-fold line 1Equation  0.9（ a ） x 1  xu  1 The fitting curve in goodagreement with theinstress–strain and the fitting results arewas indicated by the solid line Figure 14.curve, following the application of the segment adjustment parameter a = 0.75 in Figure 14. The fitting curve was in good agreement with the stress–strain curve, following the application



1.33x

0  x  0.15

of the segment adjustment parameter a=0.75 in Figure 14. 

0.2  0.94( x  0.15) y x 1 4.4. Modulus of Elasticity and Poisson’s 1  0.9Ratio （ a ）  xu  1

0.15  x  1 x 1

(11)

The fitting curve was in good agreement with the stress–strain curve, following the application

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4.4. Modulus of Elasticity and Poisson’s Ratio The modulus of elasticity and Poisson’s ratio are important indexes of a material. The slope of the pre-peak stage curve between 0.3 f c and 0.85 f c on the stress–strain curve was taken as the modulus of elasticity of the specimens, and shown in Table 6: Table 6. Modulus of elasticity of TMFG. Groups

1

Ratio

2

Ratio

3

Ratio

A AD

4056.83 10,244.00

1.00 2.53

4707.10 15,071.50

1.00 3.20

6752.50 16,291.67

1.00 2.40

Table 6 shows that the modulus of elasticity increased with the reduction in the amount of SiC, and that the modulus of elasticity of the specimens with the microcrystalline decoration surface was higher than that of the specimen without the microcrystalline decoration surface. The modulus of elasticity of group AD was 2.71 times higher than that of group A. Poisson’s ratio is an important index of a material’s lateral deformation. TMFG without the microcrystalline decoration surface is an isotropic material; therefore, the displacement meter was arranged on one of the symmetrical surfaces, and the transverse deformation of the specimen was recorded. For the specimens with the microcrystalline decoration surface, there was a small deformation in the direction of the decorative surface compared to the nondecorative surface; therefore, the displacement meter was arranged in the direction of the nondecorative surface. The data were processed using Formula (12) to obtain the Poisson’s ratio for each specimen, as shown in Table 7. v = ε0 /ε

(12)

where v denotes the Poisson’s ratio of the specimen, ε0 denotes the transverse strain of the specimen, and ε denotes the longitudinal strain of the specimen. Table 7. Poisson’s ratio of TMFG. Group

1

2

3

A AD

1.41 1.00

0.88 0.77

0.44 0.40

The Poisson’s ratio tended to decrease with the increase in the compressive strength of TMFG, as shown in Table 7. Under the same conditions, because of the restraining effect of the decorative surface, the Poisson’s ratio of the specimens with the microcrystalline decoration surface was slightly smaller than that of the specimens without the microcrystalline decoration surface. 5. Discussion 5.1. Influence of the Physical Properties on the Mechanical Properties On the basis of the data of the physical properties in Section 2 and the results of the mechanical test in Section 4, the influence of the physical properties on the mechanical properties are discussed. The porosity and prism strength, splitting tensile strength, shear strength, and flexural strength of group A1, A2, and A3 were compared, as shown in Figure 15.

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(a)

(b)

(c)

(d)

Figure 15. Comparison Comparison of of the the porosity porosity and andmechanical mechanical properties properties of of group group A1, A1, A2, A2,and andA3 A3specimens. specimens. (a) Comparison Comparisonofofporosity porosity and prism strength ; (b) Comparison of porosity and splitting tensile and prism strength; (b) Comparison of porosity and splitting tensile strength; strength ; (c) Comparison porosity and shear (d) Comparison of porosity and flexural (c) Comparison of porosity of and shear strength; (d)strength; Comparison of porosity and flexural strength. strength.

With the increasing of the amount of the foaming agent (SiC), the porosity increased. As the porosity compressive strength,agent splitting strength, shear strength, Withwas the reduced, increasingthe of prism the amount of the foaming (SiC),tensile the porosity increased. As the and flexural that TMFGstrength, acquiredsplitting better mechanical properties. results porosity wasstrength reduced,increased, the prismso compressive tensile strength, shearSimilar strength, and were also found by F. Mear [2]. flexural strength increased, so that TMFG acquired better mechanical properties. Similar results were also found by F. Mear [2]. 5.2. Evaluation of the Elastic Modulus 5.2. Evaluation the scarcity Elastic Modulus Because ofofthe of research on the macroscopic mechanical properties of microcrystalline

foamed glass,of relevant studies the modulus elasticity ofmechanical concrete areproperties here considered. Researchers Because the scarcity of on research on the of macroscopic of microcrystalline have carried many experimental studies on the and their foamed glass,out relevant studies on the modulus of modulus elasticity of of elasticity concrete of areconcrete, here considered. results have also been adopted to formulate various standards, such as the Chinese standard Researchers have carried out many experimental studies on the modulus of elasticity of concrete, and (GB50010-2010) [26] and the American standard (ACI318-08) [27]. Some researchers have derived their results have also been adopted to formulate various standards, such as the Chinese standard relatively simple[26] calculation as those by Dhir [28][27]. andSome Mellmann [29]. The modulus of (GB50010-2010) and theformulas, Americansuch standard (ACI318-08) researchers have derived elasticity was calculated by using these Formulas (13)–(16) and compared with the experimental data, relatively simple calculation formulas, such as those by Dhir [28] and Mellmann [29]. The modulus as elasticity shown in was Figure 16. of calculated by using these Formulas (13)–(16) and compared with the experimental Code for the design of concrete structures (GB50010-2010) data, as shown in Figure 16. Code for the design of concrete structures (GB50010-2010) EC = 105 /(2.2 + 34.7/ f cc )

EC  10 / (2.2  34.7 / fcc ) 5

Building code requirements for structural concrete (ACI318M-05) Building code requirements for structural concrete (ACI318M-05) EC = 4789( f cc )1/2 1/2

EC  4789( fcc )

(13) (13)

(14) (14)

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Calculation formula formula of of Dhir Dhir Calculation

EC = 13,100 + 370 f cc

(15) (15)

EC  13 100+370 fcc

Calculation formula of Dhir Mellmann Calculation formula of Dhir Mellmann ECE=8242 + 378 ffcc 8242+378 C

(16) (16)

cc

(a)

(b)

Figure 16. Modulus of of elasticity from the test from each (a) Group(a) A; Group (b) Group Figure Modulus elasticity from the and test results and results fromformula. each formula. A; AD. (b) Group AD.

Figure Figure 16 16 shows shows that that most most of of the the results results from from the the theoretical theoretical formulas formulas are are different different from from and and larger experimental results. As for without the microcrystalline decoration surface, largerthan thanthe the experimental results. As the forTMFG the TMFG without the microcrystalline decoration the trendthe of the curve is regular. The resultsThe of Group and the calculation were compared as surface, trend of the curve is regular. resultsA of Group A and theresults calculation results were shown in Table 8. compared as shown in Table 8. Table Table 8. 8. Comparison Comparison of of the the test test results results and andthe theresults resultscalculated calculatedfrom fromeach eachformula. formula. Group Group A1 A1 A2 A2 A3 A3 Ratio

Ratio

Test Test 4056.83 4056.83 4707.10 4707.10 6752.50 6752.50 1.00

1.00

GB50010 GB50010 10,089.69 10,089.69 11,640.87 11,640.87 17,956.76 17,956.76 2.54 2.54

ACI318 ACI318 10,159.00 10,159.00 11,159.50 11,159.50 15,369.63 15,369.63 2.38 2.38

Dhir Dhir 14,765.00 14,765.00 15,109.10 15,109.10 16,911.00 16,911.00 3.12 3.12

Mellmann Mellmann 9943.00 9943.00 10,294.54 10,294.54 12,135.40 12,135.40 2.15 2.15

As be seen seenfrom fromTable Table8,8,most most calculation results relatively large, the maximum As can can be calculation results areare relatively large, and and the maximum ratio ratio between the experimental and the calculated results reached 3.12. Therefore, the existing design between the experimental and the calculated results reached 3.12. Therefore, the existing design formula formula was was not not suitable suitable for for evaluating evaluating the the elastic elastic modulus modulus of of the the TMFG. TMFG. Based Based on on the the test test results, results, Formula (17) was proposed to estimate the modulus of elasticity of Group A. The calculation results of Formula (17) was proposed to estimate the modulus of elasticity of Group A. The calculation results Formula (17) were compared with the experimental results, as shown in Figure 17. Figure 17 shows of Formula (17) were compared with the experimental results, as shown in Figure 17. Figure 17 shows that that the the calculation calculation results results of of the the proposed proposed formula formula are are in in good good agreement agreement with with the the elastic elastic modulus modulus determined by the test, so Formula (17) could be used to estimate the modulus of elasticity of determined by the test, so Formula (17) could be used to estimate the modulus of elasticity of TMFG. TMFG.

2012( fcu))1/2 ECE= ( f cu C 2012 1/ 2

(17) (17)

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Figure 17. The elastic modulus calculated by the test and the calculation results obtained with the Figure 17.formula. The elastic modulus calculated by the test and the calculation results obtained with the proposed proposed formula.

6. Conclusions 6. Conclusions (1) With the reduction of the amount of SiC, the porosity decreased, so that the mechanical properties (1) improved. With the reduction of the amount SiC, the porosity properties decreased, was so that the mechanical The improvement in theofvarious mechanical similar. The cubic compressive strength The of TMFG without in microcrystalline decoration surfaces was close to The the properties improved. improvement the various mechanical properties similar. cubic compressive TMFG without microcrystalline decoration surfaces to prism compressivestrength strength.ofThe cubic compressive strength was about 1.04 timeswas theclose prism the prism compressive strength. cubic compressive strength was prism compressive strength. The cubicThe compressive strength was about 4.7about times1.04 the times shear the strength, compressive strength. The cubic compressive strength was about 4.7 times the shear strength, about 6.64 times the splitting tensile strength, and 2.92 times the flexural strength. about 6.64 times the splitting tensile strength, and 2.92 the flexural (2) The microcrystalline decorative surface improved thetimes compressive andstrength. flexural strengths of (2) TMFG. The microcrystalline decorative improved compressive flexural strengths of The compression strengthsurface of group AD wasthe about twice that and of group A. The flexural TMFG. The strength group AD was about twice of group Thethose flexural strengths of compression groups ADt and ADs of were, respectively, 2.31 and 1.4that times greaterA.than of strengths of groups ADt andofADs were, respectively, 2.31influenced and 1.4 times greaterstrength than those of group A, and the orientation the specimens significantly the flexural of the group A, and of the decoration specimens surface. significantly influenced the flexural strength of specimens withthe theorientation microcrystalline The flexural strength of group ADt was the specimens with the microcrystalline decoration surface. The strength group ADt approximately 1.64 times that of ADs. The stress–strain curve offlexural TMFG could be of expressed by was3-fold approximately 1.64 times that of ADs. The stress–strain curve of TMFG could be expressed the line equation. by thethe 3-fold line equation. (3) With reduction of the amount of SiC, the modulus of elasticity of TMFG increased. (3) The Withmodulus the reduction of the of amount SiC,lower the modulus elasticityvalue of TMFG increased. of elasticity TMFGofwas than the of calculated obtained using The the modulus of elasticity of TMFG than thebetween calculated obtained and using thecalculated concreteconcrete-specific formulas, andwas the lower highest ratio thevalue experimental the specificwas formulas, and the highest is ratio between experimental and the calculatedofresults results 3.12 times. A formula proposed to the estimate the modulus of elasticity TMFG.was 3.12 times. A formula proposed to estimate the modulus of elasticity of TMFG. (4) With the increase inisthe compressive strength of TMFG, the Poisson’s ratio decreased. (4) The WithPoisson’s the increase in the compressive strength of TMFG, the Poisson’s ratio decreased. The ratio of the specimens with the microcrystalline decoration surface was slightly Poisson’s ratio of the specimens with the microcrystalline decoration surface was slightly smaller smaller than that of the specimens without the microcrystalline decoration surface. than that of the specimens without the microcrystalline decoration surface. Author JinliangBian Bianperformed performed experiments analyzed the and data wrote and wrote the Author Contributions: Contributions: Jinliang thethe experiments andand analyzed the data the paper. paper. Wanlin Cao proposed the topic of this study. Lin Yang and Cunqiang Xiong participated in the Wanlin Cao proposed the topic of this study. Lin Yang and Cunqiang Xiong participated in the manuscript manuscript preparation. preparation. Funding: This research was funded by The National Natural Science Foundation of China grant number Funding: This research was funded by The National Natural Science Foundation of China grant number [51878015]. [51878015]. Acknowledgments: The authors gratefully acknowledge the financial supports for this research by The National Natural Science Foundation of China under grant number 51878015. Additionally, Professor Cao, Acknowledgments: The authors gratefully acknowledge the financial supports for this research byWan-lin The National the teachers and students of the research group, and the Beijing North Glass Sinest Technology Co., LTD., Natural Science Foundation of China under grant number 51878015. Additionally, Professor Wan-lin Cao, the are greatly appreciated for their valuable help and advice concerning this study. teachers and students of the research group, and the Beijing North Glass Sinest Technology Co., LTD., are greatly Conflicts of Interest: authors declare no conflict of interest. appreciated for their The valuable help and advice concerning this study.

Conflicts of Interest: The authors declare no conflict of interest.

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