# Mechanical Properties of Fast-Growing Poplar Reinforced with Carbon Fiber

Authors: Ying Gao; Liwei Guo; Xiao Zhang; Yuzhuo Wang; Xiuying Yang; ChuanGuo Fu; Ziqing Liu
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

This paper presents mechanical properties of fast-growing poplar specimens reinforced with carbon fibers. A total of 90 specimens including 10 contrast specimens were tested to investigate the influence from the following parameters: (a) different carbon fiber ratios (0.167%, 0.251%, 0.334%, 0.401%, and 0.501%) and (b) different fiber locations. The failure mode, compressive strength, elastic modulus, and axial deformation of specimens were analyzed. The test results indicate the following: (1) The compressive strength, elastic modulus, and axial deformation of specimens reinforced with carbon fiber were significantly improved compared with that of fast-growing poplar specimens. The compressive strength, elastic modulus, and axial deformation increased by 54.1–76.03%, 11.58–22.89%, and 24.86–60.06%, respectively. (2) There was little effect on the compressive strength of the specimen with the increase of carbon fiber ratio. With the increase of carbon fiber ratio, the elastic modulus of specimens slightly decreased and the axial deformation increased. The elastic modulus decreased by 1.39–18.69%, and the axial deformation increased by 10%–48%. (3) The different locations of the carbon fiber distribution resulted in a large difference in the compressive strength of the specimens, while the effects on the modulus of elasticity and axial deformation were not significant. Finally, the compressive strength calculation formula was proposed.


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## Body

## 1. Introduction

Timber structure is a popular structural form in various regions of the world for its seismic resistance and heat preservation [1]. The wood materials are in short supply because of policies of closing mountains for afforestation and no cutting. Fast-growing poplar is widely planted for its high survival rate and short growth period [2–4]. However, the application of fast-growing poplar is limited in the field of building for the loose texture and low strength. Improving the mechanical properties of rapid growth materials has become the focus of attention. The method of gluing fast-growing poplar reinforced with carbon fiber was used in this paper.In recent years, the scholars have done a lot of work on the mechanical properties of fast-growing poplar, it is mainly focusing on chemical modification, glued wood, and glued fast-growing poplar reinforced with carbon fiber [5–24]. The main research results in chemical modification are as follows: Yue et al. [5, 6] studied the influence of boric acid phenolic formaldehyde resin (BPF) impregnation on the mechanical and combustion properties of fast-growing poplar timber specimens. The results showed that the strength of modified poplar timber specimens increased by 11.2–45.8% with the increase of BPF impregnation concentration. Pure lactic acid oligomers (OLA) and phenolic methylol urea were also commonly used in chemical impregnation [7–9]. The internal reactive deposition of CaCl2 and NaCO3 was used in modification studies [10], and some studies even combined heat treatment, chemical impregnation, and other methods to improve the performance of poplar [11, 12]. Liu et al. [13] conducted bending tests on 31 laminated timber beam specimens, and the test results showed that the combination mode and size of laminates have significant influence on the mechanical properties of specimens.With the deepening of the research on the modification of fast-growing poplar, it has been widely used that pasting or winding carbon fiber to improve mechanical properties [14–23]. Zuo et al. [14] studied the flexural performance of modified flax fiber reinforced glued laminated timber beams. The results showed that the flexural load capacity and flexural stiffness of glued laminated timber beam increased with the number of FFRP layers applied at the bottom. He et al. [15, 16] studied the mechanical properties of modified reconstituted wood structures and revealed that the improvement of the strength, modulus of elasticity, and strength-to-weight ratio of the reconstituted wood material, which effectively strengthened the interaction between the reconstituted wood beam, the reconstituted wood column, the bolts, and the steel infill plate, and the nodal force performance was significantly improved. Juliano Fiorelli et al. [17] studied the method used to produce glulam beams led to a higher efficiency of the structural elements. Zheng [18] used carbon fiber to wind the whole specimens, in order to improve its compressive bearing capacity. The compressive bearing capacity increased by 21.4% after first layer had been wound, and 83.1% after third layer had been wound. José Sena-Cruz [24] studied the bonding behavior between integrated material and GFRP by pull-out test. The stress-slip relationship for the local bonding was obtained by test data. A significant increase in flexural load capacity was found for reinforced, prestressed, and prestressed reinforced beams [25]. In addition, Wei et al. [26–29] conducted experimental research and simulation analysis on the mechanical properties of bamboo. It was found that the residual plastic strain ratio of bamboo scrimber was far lower than that of concrete, and new composite materials such as recombinant bamboo and steel-reinforced bamboo scrimber were proposed. This literature provides important insights into the study of mechanical properties of fast-growing poplar reinforced with carbon fiber.The previous research on improvement methods of fast-growing poplar mainly focuses on chemical impregnation, physical compaction, or carbon fiber reinforcement. The chemical impregnation and physical compaction methods can improve the mechanical properties of fast-growing poplar; however, this method has little improvement. The carbon fiber was added between timber boards in this paper to form a new composite material, which can be better applied in the building field. Considering the influence of different carbon fiber ratio and different fiber location, the fast-growing poplar reinforced with carbon fiber was tested and the influence rule of mechanical properties of fast-growing poplar reinforced with carbon fiber was obtained.


## 2. Experimental Program

### 2.1. Design of Specimens

A total of 90 fast-growing poplar specimens were designed and tested, as shown in Table1 and Figures 1–3. These included 10 comparison specimens and 80 specimens reinforced with carbon fiber, which are 100 mm × 100 mm × 100 mm cubes. Ten pieces of 10 mm × 100 mm × 100 mm timber boards were spliced together to form one specimen using structural adhesive. All the specimens were made in accordance with the code for design of timber structure [30].Table 1
Design parameters of the specimens.
SpecimenCarbon fiber positionCarbon fiber ratioR (%)ComparisonY1----X1----Carbon fiber ratioA12-3, 5-6, 8-90.167A22-3, 5-6, 8-90.251A32-3, 5-6, 8-90.334A42-3, 5-6, 8-90.401A52-3, 5-6, 8-90.501Carbon fiber positionB11-2, 5-6, 9-100.501B21-2, 2-3, 5-6, 8-9, 9-100.501Note.R=VcarbonfibreVspecimen×100%, R is the carbon fiber ratio, which is the ratio of the volume of the carbon fiber to the volume of the reinforced specimen; Vc is the volume of the carbon fiber; Vs is the volume of the specimen.Figure 1
Layout of the specimens: (a)Y1, (b) X1, and (c) A1-5 and B1-2.
(a)(b)(c)Figure 2
Different carbon fiber ratios: (a)A1, (b) A2, (c) A3, (d) A4, and (e) A5.
(a)(b)(c)(d)(e)In the production process, the fast-growing poplar lumber was cut, dried, cleaned, polished, and flattened to form the fast-growing poplar laminate. Carbon fiber cloth was cut into 100 mm × 100 mm size. All materials were bonded together by evenly brushing structural adhesive, as shown in Figure1. The structural adhesive was made by mixing epoxy resin and curing agent in the ratio of 2:1. The finished specimens were cured and maintained under 0.4 MPa pressure for 48 hours.Figure 3
Different carbon fiber positions: (a)A5, (b) B1, and (c) B2.
(a)(b)(c)


### 2.2. Materials

The specimens were made of No. 108 artificially cultivated fast-growing poplar (diameter at a breast height of about 20 cm, tree height of about 9 m, no insect pests and other tree quality defects, and straight trunk), which is mainly produced in Jinan city, Shandong Province, China. The 0.167 mm thick (300 g) carbon fiber was used in the test. The main components of the structural adhesive were epoxy resin and curing agent (mainly phenol-4-sulfonic acid) at the ratio of 2:1, the density of structural adhesive is 2000 kg/m3, and the structural adhesive between layers is 2000 g/m2.


### 2.3. Moisture Content

The moisture content has a significant impact on the compression strength of the composite material. Ten cubic test blocks of 20 mm × 20 mm × 20 mm were made and measured according to Method for Determination of the Moisture Content of Timber GB/T 1931–2009 [31]. The average moisture content of the fast-growing poplar was 12.39%, which met the requirements of code GB/T 50708–2012 [32], as can be seen in Table 2.Table 2
Moisture content test data.
Number12345Average %Moisture content %11.5611.9612.2712.5313.1412.39Number678910Moisture content %12.7312.1312.4012.7212.43


## 2.1. Design of Specimens

A total of 90 fast-growing poplar specimens were designed and tested, as shown in Table1 and Figures 1–3. These included 10 comparison specimens and 80 specimens reinforced with carbon fiber, which are 100 mm × 100 mm × 100 mm cubes. Ten pieces of 10 mm × 100 mm × 100 mm timber boards were spliced together to form one specimen using structural adhesive. All the specimens were made in accordance with the code for design of timber structure [30].Table 1
Design parameters of the specimens.
SpecimenCarbon fiber positionCarbon fiber ratioR (%)ComparisonY1----X1----Carbon fiber ratioA12-3, 5-6, 8-90.167A22-3, 5-6, 8-90.251A32-3, 5-6, 8-90.334A42-3, 5-6, 8-90.401A52-3, 5-6, 8-90.501Carbon fiber positionB11-2, 5-6, 9-100.501B21-2, 2-3, 5-6, 8-9, 9-100.501Note.R=VcarbonfibreVspecimen×100%, R is the carbon fiber ratio, which is the ratio of the volume of the carbon fiber to the volume of the reinforced specimen; Vc is the volume of the carbon fiber; Vs is the volume of the specimen.Figure 1
Layout of the specimens: (a)Y1, (b) X1, and (c) A1-5 and B1-2.
(a)(b)(c)Figure 2
Different carbon fiber ratios: (a)A1, (b) A2, (c) A3, (d) A4, and (e) A5.
(a)(b)(c)(d)(e)In the production process, the fast-growing poplar lumber was cut, dried, cleaned, polished, and flattened to form the fast-growing poplar laminate. Carbon fiber cloth was cut into 100 mm × 100 mm size. All materials were bonded together by evenly brushing structural adhesive, as shown in Figure1. The structural adhesive was made by mixing epoxy resin and curing agent in the ratio of 2:1. The finished specimens were cured and maintained under 0.4 MPa pressure for 48 hours.Figure 3
Different carbon fiber positions: (a)A5, (b) B1, and (c) B2.
(a)(b)(c)


## 2.2. Materials

The specimens were made of No. 108 artificially cultivated fast-growing poplar (diameter at a breast height of about 20 cm, tree height of about 9 m, no insect pests and other tree quality defects, and straight trunk), which is mainly produced in Jinan city, Shandong Province, China. The 0.167 mm thick (300 g) carbon fiber was used in the test. The main components of the structural adhesive were epoxy resin and curing agent (mainly phenol-4-sulfonic acid) at the ratio of 2:1, the density of structural adhesive is 2000 kg/m3, and the structural adhesive between layers is 2000 g/m2.


## 2.3. Moisture Content

The moisture content has a significant impact on the compression strength of the composite material. Ten cubic test blocks of 20 mm × 20 mm × 20 mm were made and measured according to Method for Determination of the Moisture Content of Timber GB/T 1931–2009 [31]. The average moisture content of the fast-growing poplar was 12.39%, which met the requirements of code GB/T 50708–2012 [32], as can be seen in Table 2.Table 2
Moisture content test data.
Number12345Average %Moisture content %11.5611.9612.2712.5313.1412.39Number678910Moisture content %12.7312.1312.4012.7212.43


## 3. Experimental Process

The test was carried out using a WAW-1000C universal testing machine (maximum test force 1000 KN) for loading in the vertical axis. The specimens reinforced with carbon fiber were placed in the testing machine, and geometric axis alignment was performed according to the standard for test method of timber structures. The test was loaded at a rate of 2 mm/min until the specimen cannot withstand the load and the test was terminated [33].


## 4. Experimental Results and Discussion

### 4.1. Failure Mode

The failure mode ofY1 was that all specimens had horizontal cracks, and some specimens had vertical cracks. From the observation of the failure specimens, it can be seen that the wood fiber was severely squeezed, and the specimen showed obvious compression deformation. The specific phenomenon is shown in Figure 4.Figure 4
Failure mode of the specimenY1.The failure modes of specimens reinforced with carbon fiber are similar to that of fast-growing poplar specimens, as shown in Figure5. Most specimens only appeared horizontal cracks, and some specimens simultaneously appeared horizontal cracks and a few vertical cracks. Compared with specimen Y1, horizontal cracks of specimens A1 to A5 were randomly distributed and had no continuity. The vertical cracks were mostly distributed in the adhesive location. With the carbon fiber ratio increases, the deformation of the specimen becomes greater and its damage reaches earlier. The outermost laminates of specimens A4 and A5 separated from the specimens, forming isolated laminates, and the continued loading of the test caused the outer laminates to buckle, and the test was ended.Figure 5
Failure mode of the specimensX1 and A1-5: (a) X1, (b) A1, (c) A2, (d) A3, (e) A4, and (f) A5.
(a)(b)(c)(d)(e)(f)According to the experimental phenomena, the carbon fiber positions of specimensA5, B1, and B2 were different, but their failure modes were similar, as shown in Figure 6. At the early stage of loading, specimens A5, B1, and B2 produced a slight wood extrusion sound. With the increase of load, the specimens showed obvious bending deformation and cracked seriously between some boards. The bond force was lost, some boards were separated from each other, and the outer boards of some specimens were even broken, and the test was ended.Figure 6
Failure mode of the specimens (a)A5, (b) B1, and (c) B2.
(a)(b)(c)


### 4.2. Compressive Strength

The following data are taken from the data collection of the test machine, and the average of the 10 specimens is taken as the selected value, wherefa is average compressive strength of 10 specimens, S is standard deviation, fk is standard value of compressive strength, and α3 is the improvement coefficient. Ea is the average of elastic modulus of 10 specimens, and Δa is the average axial deformation of 10 specimens. Where fk was collated according to GB 50005–2017 [30] and Ea and Δa were collated according to GB/T 50329–2012 [33], we have the results in Table 3 and Figures 7, 8, and 9.Table 3
Mechanical parameters of specimens with different carbon fiber ratios.
Specimenfa (MPa)S (standard deviation)fk (MPa)α3Ea (MPa)Δa (mm)Y122.842.59317.38—13203.58X127.741.50924.56115864.24A135.693.2728.811.173015644.47A235.312.23930.601.245916224.61A334.422.76728.601.164515084.80A433.243.06826.781.090414735.05A531.592.1527.071.102212915.73Figure 7
Compressive strength of specimens with different carbon fiber ratios.Table3 and Figure 7 show that the compressive strength of specimens A1 to A5 is significantly improved in comparison with that of specimens Y1 and X1. Compared with that of specimen Y1, the compressive strength of the specimens increased by 54.1–76.03%. Compared with that of specimen X1, the compressive strength of the specimens increased by 9.04–24.56%. The reason is that carbon fiber is a high strength and high modulus fiber, which increases the resistance of the specimen to bending deformation and therefore increases the compressive strength of the specimen. In addition, with the carbon fiber ratio increases, the effect on the compressive strength of the specimens is not significant. According to the above test data, the compressive strength formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in the following equation:(1)y=−0.4992x+1.798f0,where y is the measured compressive strength of carbon fiber specimen, x is the carbon fiber ratio, and f0 is the compressive strength of fast-growing poplar specimen.As shown in Table3, the compressive strength of specimens A1 to A5 with different fiber proportion increased by 17.3%, 24.6%, 16.4%, 9.0%, and 10.2%, respectively, compared with that of X1. Through data fitting, the calculation formula of α3 was obtained, as shown in the following equation:(2)α3=−0.3532ρc+1.2721.


### 4.3. Elastic Modulus

It can be seen from Table3 and Figure 8 that the elastic modulus of specimens A1 to A5 is improved in comparison with that of specimens Y1. Compared with that of specimen Y1, the elastic modulus of the specimens increased by 11.58–22.89%. Compared with that of specimen X1, the elastic modulus of the specimens decreased by 1.39–18.57%. The elastic modulus of specimens decreased in the range of 3.56–21.11% with the increase of carbon fiber ratio. As can be seen from the above research, when the ratio of carbon fibers increases, the area of the carbon fibers increases. The bond between the carbon fibers and the structural adhesive is less than the bond between the wood and the structural adhesive. The load-bearing capacity of the specimen depends on the adhesion between carbon fiber and structural adhesive. It leads to a reduction in the modulus of elasticity of the specimen. According to the above test data, the elastic modulus formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in the following equation:(3)y=−0.673x+1.413E0,where y is the measured elastic modulus of carbon fiber specimen, x is the carbon fiber ratio, and E0 is the elastic modulus of fast-growing poplar specimen.Figure 8
Elastic modulus of specimens with different carbon fiber ratios.


### 4.4. Axial Deformation

Table3 and Figure 9 show that the axial deformation of specimens A1 to A5 is significantly improved in comparison with that of specimens Y1 and X1. Compared with that of specimen Y1, the axial deformation of the specimens increased by 24.86–60.06%. Compared with that of specimen X1, the axial deformation of the specimens increased by 5.42–35.14%. When the carbon fiber ratio increased, the axial deformation increased, with a maximum increase of 48%. According to the above test data, the axial deformation formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in(4)y=3.05x2−1.02x+1.34Δ0,where y is the axial deformation of carbon fiber specimen, x is the carbon fiber ratio, and Δ0 is the axial deformation of fast-growing poplar specimen.Figure 9
Axial deformation of specimens with different carbon fiber ratios.


### 4.5. Compressive Strength, Elastic Modulus, and Axial Deformation of Carbon Fiber Position

It can be seen from Table4 and Figure 10 that the changing position of the carbon fibers has an effect on the compressive strength, but it has little effect on the modulus of elasticity and axial deformation. The maximum difference of compressive strength, elastic modulus, and axial deformation between specimens B1 and B2 and the comparison specimen A5 was 24.7%, 10.60%, and 9.1%, respectively.Table 4
Mechanical parameters of specimens with different fiber position.
Specimenfa (MPa)S (standard deviation)fk (MPa)Ea (MPa)Δa (mm)A531.592.1527.0712915.73B130.464.7920.3813515.58B231.621.6228.2114286.25Figure 10
(a) Compressive strength, (b) elastic modulus, and (c) axial deformation of specimens with different carbon fiber positions.
(a)(b)(c)


## 4.1. Failure Mode

The failure mode ofY1 was that all specimens had horizontal cracks, and some specimens had vertical cracks. From the observation of the failure specimens, it can be seen that the wood fiber was severely squeezed, and the specimen showed obvious compression deformation. The specific phenomenon is shown in Figure 4.Figure 4
Failure mode of the specimenY1.The failure modes of specimens reinforced with carbon fiber are similar to that of fast-growing poplar specimens, as shown in Figure5. Most specimens only appeared horizontal cracks, and some specimens simultaneously appeared horizontal cracks and a few vertical cracks. Compared with specimen Y1, horizontal cracks of specimens A1 to A5 were randomly distributed and had no continuity. The vertical cracks were mostly distributed in the adhesive location. With the carbon fiber ratio increases, the deformation of the specimen becomes greater and its damage reaches earlier. The outermost laminates of specimens A4 and A5 separated from the specimens, forming isolated laminates, and the continued loading of the test caused the outer laminates to buckle, and the test was ended.Figure 5
Failure mode of the specimensX1 and A1-5: (a) X1, (b) A1, (c) A2, (d) A3, (e) A4, and (f) A5.
(a)(b)(c)(d)(e)(f)According to the experimental phenomena, the carbon fiber positions of specimensA5, B1, and B2 were different, but their failure modes were similar, as shown in Figure 6. At the early stage of loading, specimens A5, B1, and B2 produced a slight wood extrusion sound. With the increase of load, the specimens showed obvious bending deformation and cracked seriously between some boards. The bond force was lost, some boards were separated from each other, and the outer boards of some specimens were even broken, and the test was ended.Figure 6
Failure mode of the specimens (a)A5, (b) B1, and (c) B2.
(a)(b)(c)


## 4.2. Compressive Strength

The following data are taken from the data collection of the test machine, and the average of the 10 specimens is taken as the selected value, wherefa is average compressive strength of 10 specimens, S is standard deviation, fk is standard value of compressive strength, and α3 is the improvement coefficient. Ea is the average of elastic modulus of 10 specimens, and Δa is the average axial deformation of 10 specimens. Where fk was collated according to GB 50005–2017 [30] and Ea and Δa were collated according to GB/T 50329–2012 [33], we have the results in Table 3 and Figures 7, 8, and 9.Table 3
Mechanical parameters of specimens with different carbon fiber ratios.
Specimenfa (MPa)S (standard deviation)fk (MPa)α3Ea (MPa)Δa (mm)Y122.842.59317.38—13203.58X127.741.50924.56115864.24A135.693.2728.811.173015644.47A235.312.23930.601.245916224.61A334.422.76728.601.164515084.80A433.243.06826.781.090414735.05A531.592.1527.071.102212915.73Figure 7
Compressive strength of specimens with different carbon fiber ratios.Table3 and Figure 7 show that the compressive strength of specimens A1 to A5 is significantly improved in comparison with that of specimens Y1 and X1. Compared with that of specimen Y1, the compressive strength of the specimens increased by 54.1–76.03%. Compared with that of specimen X1, the compressive strength of the specimens increased by 9.04–24.56%. The reason is that carbon fiber is a high strength and high modulus fiber, which increases the resistance of the specimen to bending deformation and therefore increases the compressive strength of the specimen. In addition, with the carbon fiber ratio increases, the effect on the compressive strength of the specimens is not significant. According to the above test data, the compressive strength formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in the following equation:(1)y=−0.4992x+1.798f0,where y is the measured compressive strength of carbon fiber specimen, x is the carbon fiber ratio, and f0 is the compressive strength of fast-growing poplar specimen.As shown in Table3, the compressive strength of specimens A1 to A5 with different fiber proportion increased by 17.3%, 24.6%, 16.4%, 9.0%, and 10.2%, respectively, compared with that of X1. Through data fitting, the calculation formula of α3 was obtained, as shown in the following equation:(2)α3=−0.3532ρc+1.2721.


## 4.3. Elastic Modulus

It can be seen from Table3 and Figure 8 that the elastic modulus of specimens A1 to A5 is improved in comparison with that of specimens Y1. Compared with that of specimen Y1, the elastic modulus of the specimens increased by 11.58–22.89%. Compared with that of specimen X1, the elastic modulus of the specimens decreased by 1.39–18.57%. The elastic modulus of specimens decreased in the range of 3.56–21.11% with the increase of carbon fiber ratio. As can be seen from the above research, when the ratio of carbon fibers increases, the area of the carbon fibers increases. The bond between the carbon fibers and the structural adhesive is less than the bond between the wood and the structural adhesive. The load-bearing capacity of the specimen depends on the adhesion between carbon fiber and structural adhesive. It leads to a reduction in the modulus of elasticity of the specimen. According to the above test data, the elastic modulus formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in the following equation:(3)y=−0.673x+1.413E0,where y is the measured elastic modulus of carbon fiber specimen, x is the carbon fiber ratio, and E0 is the elastic modulus of fast-growing poplar specimen.Figure 8
Elastic modulus of specimens with different carbon fiber ratios.


## 4.4. Axial Deformation

Table3 and Figure 9 show that the axial deformation of specimens A1 to A5 is significantly improved in comparison with that of specimens Y1 and X1. Compared with that of specimen Y1, the axial deformation of the specimens increased by 24.86–60.06%. Compared with that of specimen X1, the axial deformation of the specimens increased by 5.42–35.14%. When the carbon fiber ratio increased, the axial deformation increased, with a maximum increase of 48%. According to the above test data, the axial deformation formula of specimens with different carbon fiber ratio was obtained by fitting, as shown in(4)y=3.05x2−1.02x+1.34Δ0,where y is the axial deformation of carbon fiber specimen, x is the carbon fiber ratio, and Δ0 is the axial deformation of fast-growing poplar specimen.Figure 9
Axial deformation of specimens with different carbon fiber ratios.


## 4.5. Compressive Strength, Elastic Modulus, and Axial Deformation of Carbon Fiber Position

It can be seen from Table4 and Figure 10 that the changing position of the carbon fibers has an effect on the compressive strength, but it has little effect on the modulus of elasticity and axial deformation. The maximum difference of compressive strength, elastic modulus, and axial deformation between specimens B1 and B2 and the comparison specimen A5 was 24.7%, 10.60%, and 9.1%, respectively.Table 4
Mechanical parameters of specimens with different fiber position.
Specimenfa (MPa)S (standard deviation)fk (MPa)Ea (MPa)Δa (mm)A531.592.1527.0712915.73B130.464.7920.3813515.58B231.621.6228.2114286.25Figure 10
(a) Compressive strength, (b) elastic modulus, and (c) axial deformation of specimens with different carbon fiber positions.
(a)(b)(c)


## 5. Calculation of Compressive Strength

Although the specimens reinforced with carbon fiber were made of poplar timber, structural adhesive, and carbon fiber, the compressive strength was mainly provided by adhesive and timber. Carbon fiber itself has not compressive strength, but it can improve the ability of specimen to resist bending deformation, thus affecting the compressive strength of specimen. Therefore, the influence of carbon fiber on the strength of reinforced specimens was expressed by the improvement coefficient; that is, the compressive strength formula of fast-growing poplar specimens reinforced with carbon fiber could be expressed by the following equation:(5)fc=α3α1ρwfw+α2ρafa,where fc is the compressive strength of carbon fiber reinforced fast-growing poplar, fw is the compressive strength of timber, fa is the compressive strength of adhesive, ρw is the timber content ρw=100×tw/99×tw+100, ρais the adhesive content ρa=100−tw/99×tw+100, tw is the thickness of the timber, α1 is the combination coefficient of timber compressive strength, and α2 is the combination coefficient of structural adhesive strength.In Eq (5), specimen X1 did not consider the effect of carbon fibers on the compressive strength, so the coefficient α3 is taken as 1 (α3 = 1). The compressive strength of the reinforced fast-growing poplar with the thickness of 5 mm, 10 mm (X1), 15 mm, and 20 mm were obtained from [34]. The test result of compressive strength was substituted into equation (5) to give equation (6). The values of α1 and α2 could be obtained by solving any pair of equations selected from equation (6). The average values of α1 and α2 were 0.675 and 1.276, respectively, as shown in Table 5.(6)α1×0.8403×22.84+α2×0.1597×87.6=31.66,α1×0.9174×22.84+α2×0.0826×87.6=24.56,α1×0.9434×22.84+α2×0.0566×87.6=19.82,α1×0.9615×22.84+α2×0.0385×87.6=20.01.Table 5
Value ofα1 and α2.
(5) + (6)(5) + (7)(5) + (8)(6) + (7)(6) + (8)(7) + (8)Averageα10.7420.5830.7140.4160.7020.8940.675α21.2451.4631.2832.1901.3610.1131.276Equation (2) was substituted into equation (5) to give equation (7) for calculating the compressive strength of specimens reinforced with carbon fiber.Here,ρc is the carbon fiber ratio.(7)fc=α3α1ρ0f0+α2ρafa=−0.3532ρc+1.27210.675ρwfw+1.276ρafa.


## 6. Conclusion

This paper experimentally and analytically investigated mechanical properties of fast-growing poplar reinforced with carbon fiber. The following conclusions can be drawn:(1)
The compressive strength, elastic modulus, and axial deformation of specimens reinforced with carbon fiber are significantly improved compared with those of fast-growing poplar specimens. The compressive strength, elastic modulus, and axial deformation increase by 54.1–76.03%, 11.58–22.89%, and 24.86–60.06%, respectively.(2)
With the increase of carbon fiber ratio, the range of variation in compressive strength is insignificant, the elastic modulus of specimens slightly decreases, and the axial deformation increases. The elastic modulus decreases by 1.39–18.69%, and the axial deformation increases by 10%–48%.(3)
The different locations of the carbon fiber distribution resulted in a large difference in the compressive strength of the specimens, and the maximum difference of compressive strength is 8 MPa, while the effects on the modulus of elasticity and axial deformation are not significant.(4)
The compressive strength calculation formula of specimens reinforced with carbon fiber is established.



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