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Improvement of Mechanical Properties of Wood-Plastic Composite Floors Based on the Optimum Structural Design
Acta Mechanica Solida Sinica, Vol. 29, No. 4, August, 2016 Published by AMSS Press, Wuhan, China
ISSN 0894-9166
Improvement of Mechanical Properties of Wood-Plastic Composite Floors Based on the Optimum Structural Design⋆⋆ Yun Ding
Yang Zhang1 Mingyin Jia1
1
Ping Xue1⋆ Jianchen Cai2
Xiaoming Jin1
1
( College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China) (2 College of Mechanical Engineering, Quzhou University, Quzgou 324000, China) Received 20 January 2015, revision received 5 March 2016
ABSTRACT A study is carried out on the structural design of wood-plastic composite floors. The geometric parameters of the cavities, the structure, and the means to optimize the performance of these light boards are investigated. Various structural parameters of the boards, such as size, shape, and the pattern of cavities are also studied. The optimal structure can be determined by calculation and analysis of the strength, stiffness, weight and cost of the material. A finite element model for the mechanical analysis of wood-plastic composite floors is established; and the results are used to verify the strength criteria under bending deformation, which is the most common loading condition of flooring board.
KEY WORDS wood plastic composite, cavities, flooring board, optimal structure, the finite element model
I. Introduction Wood is the only renewable, eco-friendly and recyclable material that can form a healthy, comfortable and natural part of our living environment. However, because the improvement of life quality in China has raised the demand for timber, China has been experiencing an acute shortage of forest resources. The discrepancy between timber supply and demand has long been a critical issue, which has made the search for alternatives to wood the most obvious solution to the problem. Fiber-reinforced plastic composites have come into wide use over the last decade, and have relieved the demand for timber resources to some extent. In the early 2000s, the output of natural fiber/thermoplastic composites in North America and Europe reached 68.5 million tons, including 590,000 tons of wood-plastic composites made of a range of wood fibers from different sources that accounted for 87% of the total output[1] . Wood-plastic composites are green biomass materials using plastics as matrices and fibers of wood or bamboo as reinforcements, which have gradually become an important type of functional materials with the development of science and technology. Compared with traditional wood, wood-plastic composites possess the hardness of plastics and the process ability of thermoplastics. These composites can also be reused and recycled. Furthermore, wood-plastic composites are biodegradable, highly resistant to insects and rot, and have low water absorption capacity. These characteristics make the materials more ⋆ ⋆⋆
Corresponding author. E-mail: xp [email protected] Project supported by the National 12th Five-Year Plan of Science and Technology with Grant No. 2012BAD23B0203.
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durable than natural wood[2–5] . So far many studies have been made on the mechanical properties of biomass fiber/plastic composites. To name just a few, Bengtsson et al.[6] investigated the application of a silane coupling agent in wood-plastic composites and analyzed their mechanical properties; Liu et al. and Yao et al.[7, 8] studied the effects of different types of coupling agents and their proportions on the mechanical properties of high-density polyethylene (HDPE) composites reinforced with rice straw or bamboo fiber, analyzed the influence of different coupling agents on the interfacial properties of composites, and tested their impacts and tensile strengths; Yao and Wu[9] studied the manufacturing process of the core-surface structure of wood-plastic composites, as well as the influence of surface properties on the impact strength. Flooring boards are subject to varying degrees of stress, which is particularly the case for the floors in public buildings and outdoor spaces. The mechanical strength of floorboard is closely related to its service life and safety of users. When used outdoors, ordinary wooden floorboards experience climate change and may rot, which increases the risk of damage and the cost. Several lightweight, corrosion-resistant and aesthetically pleasing wood-plastic composite flooring materials have recently become available and are widely used in outdoor gardens, hiking trails, and public parks. The design of lightweight floors is currently an important industrial issue because of the enormous demand for floorboards to comply with national standards. To reduce both the cost and the degree of effect upon the environment, besides meeting the strength requirements, the amount of flooring material used should be minimized, as should the amount of energy consumed during production. Currently the lightweight design technology has been widely applied in many fields. For example, Ying and Jian[10] used a designed tower plate for a wind generator with a unique lightweight crosssectional structure. Wang et al.[11] significantly reduced the weight of passenger train floors by using a modular floating floor with elastic sealing structure. Ringsberg et al.[12] investigated the design of lightweight structures for offshore platforms. Meschut et al.[13] designed a lightweight structure for car bodies. However, few studies have been reported on the structural design of lightweight wood-plastic composite floors. In the present study, an optimized flooring board design with cavities to reduce mass is offered. Analysis of the strength, stiffness, weight and cost of flooring boards with different types of core-cavity has been done using mechanical strength theory. A theoretical method is proposed to analyze and optimize the cross-sectional design of extruded wood-plastic composite flooring board.
II. Modeling and Simulation 2.1. Common cavity structure of wood-plastic composite floors The wood-plastic flooring boards now in common use can be either solid or hollow. The cross-sectional shape of the cavities in hollow floors can be circular, rectangular, oval, or rectangular with rounded corners, as shown in Fig.1. The cavities are usually evenly spaced across the width of the board and their number can vary significantly. Most wood-plastic composite flooring boards have cylindrical cavities. The rectangular cavities with rounded corners are also common; but the oval shaped ones are rarely used. The cross sectional shape of the cavity is determined by the required strength of the board, which can facilitate the manufacturing process. The overall performance of a rectangular cavity is close to that of one with sharp corners, because the actual radius of the rounding is quite small. However, the calculations needed for the determination of the load bearing properties are complicated and in this study the discussion will be limited to the analysis of the properties of wood-plastic composite flooring boards with cylindrical and rectangular cavities. 2.2. Assessment of the cross-sectional design of wood-plastic floors Wood-plastic floors are required to have a reliable and constant load bearing capacity and a certain degree of hardness, which depend on the service conditions. At present, the international market regulations impose few requirements with respect to these wood-plastic floors. China has only one National Standard, which stipulates the bending failure load. The related contents are quoted as follows. Table 1 shows that according to the National Standard, the requirement for wood-floor strength is based on the application of the product in public and non-public places, where different regulations apply. In this study we have confined our attention to the use of wood-plastic composite flooring boards in public places, where the strength requirement is high. Flooring of this type used in non-public places
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Fig. 1. Cross-section structure of floor holes. Table 1. Wood-plastic floor standard of China
Standard number
Test item
GBT 24508-2009
Bending failure load
Assessment standard Public places are required to use wood-plastic floors with ≥2500 N. Non-public places are required to use wood-plastic floors with ≥1800 N.
has lower strength requirement. The wood-plastic floor standard of China considers vertical load acting at a point half way between two adjacent joists. The standard stipulates that wood-plastic flooring should not break under load, but does not elucidate the amount of allowed bending. A large amount of deformation occurring in the floor during practical use can not only affect the appearance of board, but also cause an accident. Therefore, the proposed design should restrict floor deformation. A study of the strength and hardness of wood-plastic composite floors should consider two aspects: 1) wood-plastic composite floors should not suffer excessive damage from deformation under a service load; 2) this deformation should not affect the environmental appearance and the safety of users. Different types of cavity structure affect the load bearing performance of wood-plastic composite flooring with respect to the fixed condition. The cross-sectional structure of the boards should maximize the strength while keeping the amount of material used to a safe minimum and facilitating the production and processing as far as possible. 2.3. Stress analysis of the cross-sectional structure of wood-plastic composite floors 2.3.1. Strength analysis of wood-plastic composite floors The load condition of a wood-plastic composite floor placed on top of a joist is shown in Fig.2, where h denotes the member width (m), b the member thickness (m), x the distance from the center of joist A to the load point (m), L the distance from the center of joist A to joist B (m), and F the equi-spaced load (N), respectively. Both the shear deformation and bending occur under a vertical downwards force because the span ratio is small. However, the shear deformation is negligible compared with bending, and a wood-plastic composite flooring member can thus be treated as an Euler-Bernoulli beam, as seen in Fig.3. According to Euler-Bernoulli beam theory: M (1) W where σ is the bending stress (Pa), M the bending moment (N·m) and W the bending section coefficient (m3 ), respectively. σ=
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Fig. 3. Floor stress analysis equivalent to the EulerBernoulli beam.
Fig. 2. Diagram of the floor under force.
N cavities with diameter d exist in the section (see Fig.4), which can be obtained according to Eq.(1). 96F LX − X 2 , [nd + (n + 1) t = b, d < h, nd < b, X ≤ L] (2) σZ = (16bh2 − 3nπd4 /h) where σ Z is the bending stress around the z axis direction (Pa), d the diameter of a cylindrical cavity (m), t the cavity spacing (m), and n the number of cavities, respectively.
Fig. 4. Cross-section diagram of floor with circular holes.
∂σZ 96F (L − 2X) = =0 (3) ∂Z (16bh2 − 3nπd4 ) L The results show that when the values of parameters, b, h, n, F , L and d, are constant, the value of X is L/2, and σZ reaches a maximum. When the load is applied on the centerline of the member, the bending stress is at a maximum, which is σcircular max =
FL FL 4 = 2 2bh nπd 2bh 2S 2 − − 3 8h 3 nπh 2
(4)
where σ circularmax represents the maximum bending stress on a member with cylindrical cavities in the z direction (Pa), S the total cross-sectional area of the cavities (m2 ), respectively. N -rectangular cavities with a width of bk (m) and height of hk (m) are created in the section (see Fig.5). According to Eq.(1), the maximum bending stress (Pa) of a member with rectangular cavities in Z direction can be written as σrectangular max =
FL FL = 2bh2 2nbk h3k 2bh2 2Sh2k − − 3 3h 3 3h
(5)
Equations (4) and (5) show that the maximum bending stress is related to the size and number of cavities in the fixed floorboard sectional dimension, joist span and load. According to the first strength theory of the mechanics of materials, a flooring board will satisfy the strength requirement if the maximum bending stress is smaller than or equal to the allowable stress for wood-plastic composite floors:
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Fig. 5. Cross-section diagram of a floor with rectangular holes.
σmax ≤ σb where σmax is the maximum bending stress (Pa); and σb the the maximum allowable stress for woodplastic composites (Pa), respectively. By combining Eqs.(4) and (5), the following equations can be obtained: 2S 2 2bh2 nπd4 2bh2 Fcircular max = σb − = σb − (6) 3L 8hL 3L nπhL 2nbk h3k 2Sh2k 2bh2 2bh2 − = σb − (7) Frectangular max = σb 3L 3hL 3L 3hL where Fcircular max is the maximum load bearing of a member with cylindrical cavities (N), and Frectangular max the maximum load bearing of a flooring board with rectangular cavities (N), respectively. There must be at least 5 mm of material between the top surface of the wood-plastic board and the hollow space inside. The parameter is therefore as follows: d ≤ h − 10 b−5 n ≤ d+5 hk ≤ h − 10 b−5 n ≤ bk + 5 Equations (6) and (7) show that the total cross-sectional size of the cavities S can be determined, when the materials, formats, and joist spans of wood-plastic composite flooring boards are fixed to ensure the strength. In addition, two parameters can easily determine the load from the perspective of stress performance, which are the total size of cavities S and the number of cavities. The smaller the total size of cavities is, the greater the strength and the allowable load are. However, economy of production can be achieved by including larger cavities and using the least amount of material without compromising strength and durability. The best material-efficient cavity configuration that will not adversely affect the mechanical properties can be determined by adjusting the total number and dimension of the cavities. 2.3.2. Calculating and analyzing the stiffness of wood-plastic composite flooring boards Calculation of the strength of wood-plastic composite flooring board has been discussed in the previous section. However, a floor not only needs strength, but also needs to be sufficiently stiff so that it will not bend appreciably under load. Large deformation during use may spoil the aesthetics of installation, and even cause instability. Excessive bending may also cause damage, and thus should not exceed the allowable amount; Careful consideration needs to be given to stiffness at the design stage. To evaluate the bending deformation, the board is treated as an Euler-Bernoulli beam. The beam axis before deformation is the x axis; the vertical axis is y (see Fig.6); and the xy plane is the vertical plane of symmetry of the beam. In symmetrical bending of the beam, the deformed axis can be plotted as a curve of the deflection in the xy plane. The horizontal ordinate of the deflection curve is any point of x; and w represents the longitudinal coordinate, which is the displacement of the center of x coordinate in the y direction. From Euler-Bernoulli beam theory, the following equation can be deduced: FX L W =− 3L2 − 4X 2 0≤X ≤ (8) 48EIZ 2
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Fig. 6. Diagram of floor-bending deformation under force.
where W is the bending deformation (m); E the elastic modulus of the wood-plastic composite (Pa) and IZ the moment of inertia around the z axis (m4 ), respectively. bh3 nπd4 − (9) 12 64 By substituting Eq.(9) into Eq.(8), the bending displacement of a flooring board with cylindrical cavities can be obtained as follows: 4F X L 2 2 (10) Wcircular = − 3L − 4X 0≤X≤ E (16bh3 − 3nπd4 ) 2 IcircularZ =
where Wcircular denotes the bending deformation of a flooring board with cylindrical cavities (m). bh3 nbk h3k − (11) 12 12 By substituting Eq.(11) into Eq.(8), the bending displacement of a board with rectangular cavities is as follows: FX L 2 2 Wrectangular = − 3L − 4X (12) 0≤X≤ 4E (bh3 − nbk h3k ) 2 IrectangularZ =
where Wrectangular is the bending deformation of a board with rectangular cavities (m). When other parameters are fixed, Eq.(8) is a quadratic function around X. When X = L/2, W reaches the maximum value. Therefore, the maximum displacement occurs on the midline when a board bends under force, and the following is obtained: Wcircular max = −
4F L3 =− E (16bh3 − 3nπd4 )
Wrectangular max = −
F L3 3S 2 3 4E bh − nπ
F L3 F L3 = − 4E (bh3 − nbk h3k ) 4E (bh3 − Sh2k )
(13)
(14)
where Wcircular max represents the maximum bending deformation of a board with cylindrical cavities (m), and Wrectangular max the maximum bending deformation of a board with rectangular cavities (m), respectively. If the maximum bending displacement Wmax is smaller than or equal to the allowable value [W] of the wood-plastic composite material during use, the flooring board satisfies the strength requirements. Eqsuations (13) and (14) show that the maximum bending displacement can be calculated according to certain parameters such as the total size of cavities, load and joist spacing, when the material, format and joist spans are fixed. To ensure proper strength and endurance, the total size of cavities can be selected when n is fixed. From an economical point of view, the larger the total size of the cavities is, the smaller the amount of material is required.
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2.4. Design techniques for cavity cross-sectional structure optimization in wood-plastic composite floors The size of a wood-plastic composite flooring board is typically 0.6-6 m × 0.06-0.3 m, and the thickness ranges from 0.008 to 0.06 m. The wood-plastic flooring used in this study was 1.0 m long, 0.18 m wide and 0.025 m thick. The joist spacing L was 0.35 m. The elastic modulus E of the wood-plastic composite board was 3.5 GPa; the Poisson’s ratio µ was 0.3; and the maximum allowable stress σb was 25 MPa (these data were derived from the actual tests of wood-plastic composites). When analyzing and calculating the maximum amount of deformation, the applied load used was 1000 N, which is greater than the average weight of an adult. The processing of wood-plastic composite requires that the top thickness of the board (the distance between the upper surface and a cavity) should not be less than 0.005 m. Therefore, the number and size of the cavities included are restricted. Table 2 shows the parameter values for cylindrical cavities; and Table 3 shows those for rectangular cavities. Table 2. Parameter values of the circular holes
n dmax (10−3 m) Smax (10−6 m2 )
1 15 177
2 15 353
3 15 530
4 15 707
5 15 883
6 15 1060
7 15 1236
8 15 1413
9 14.4 1465
10 12.5 1227
11 10.9 1026
12 9.6 868
10 12.5 15 1875
11 10.9 15 1799
12 9.6 15 1728
13 8.5 737
Table 3. Parameter values of the rectangular holes
n bk max (10−3 m) hk max (10−3 m) Smax (10−6 m2 )
1 15 15 225
2 15 15 450
3 15 15 675
4 15 15 900
5 15 15 1125
6 15 15 1350
7 15 15 1575
8 15 15 1800
9 14.4 15 1944
13 8.5 15 1658
In Tables 2 and 3, dmax denotes the maximum allowable diameter of a cylindrical cavity (m), bk max the maximum allowable width of a rectangular cavity (m), hk max the maximum allowable height of a rectangular cavity (m), and Smax the maximum allowable total size of cavities (m2 ), respectively.
III. Results and Discussions 3.1. Effect of the total size of cavities on the mechanical properties of wood-plastic composite flooring boards When the number and size of cavities are fixed, the maximum allowable load on the flooring board and the maximum amount of bending deformation can be calculated by altering the total size S of the cavities and using Eqs.(6), (7), (13) and (14). According to Tables 2 and 3, the total size of cavities is at a maximum when there are nine cavities. Therefore, the number of cavities should be set as nine so that the largest total cavity size can possibly be achieved. The height of rectangular cavity should be set as a maximum of 15 mm to satisfy the thickness requirement of 5 mm and to still achieve the largest cavity size. The calculation and analysis results are shown in Fig.7 and 8. The total size of holes S should be selected to meet the requirements for hardness and strength. As mentioned before, the allowable load and strength of a flooring board will increase with a reduction in cavity size, but the larger the total cavity size is, the smaller the amount of material is required. Figures 7 and 8 show that with an increase in S, the maximum load-bearing capacity decreases and the bending increases. It is known from the mechanics of materials that stress and cross-sectional area have an inverse relationship in a floorboard under stress. Any increase in the total cavity size may raise the stress on the cross-section. According to the first strength theory, stresses greater than the maximum allowable one for the material can result in damage. An increase in the total area of core cavities will inevitably lead to a reduction of the maximum allowable load. 3.2. Effect of the number of cavities on the mechanical property of wood-plastic composite floors The maximum allowable load on the floor and the maximum amount of bending deformation can be calculated by changing the number of cavities and using Eqs.(7), (8), (13) and (14). According to the
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Fig. 7. Relationship between the total hole size and the maximum load.
Fig. 8. Relationship between the total hole size and the maximum bending deformation.
Fig. 9. Relationship between the amount of holes and the maximum load.
Fig. 10. Relationship between the amount of holes and the maximum bending deformation.
national standard, the maximum load on an outdoor wood-plastic composite floor should be greater than 2500 N. However, one company has decided that the maximum load should not be less than 5190 N and made the actual production comply with that. As previously mentioned, the maximum S can be 9×10−4 m2 , which accounts for 20% of the total cross-sectional area. The maximum height of a rectangular hole should be 15 mm to meet the thickness requirement of 5 mm. The calculation and analysis results are shown in Figs.9 and 10. The number of cavities n can be selected to meet the hardness and strength requirements. By analyzing the calculation results (Figs.9 and 10), the following conclusions can be drawn when the total size of cavities S is fixed. 1) If the number of cavities n of the floor with cylindrical cavities is increased, the strength and hardness of the floor increase. 2) The mechanical properties do not change with the number of cavities when the height of a rectangular cavity remains unchanged. 3) A flooring board with cylindrical cavities has better mechanical properties than one with rectangular cavities. When the total size of core cavities is fixed, and the number of cavities is increased, the cavity size needs to be smaller. This means there will be more material between the holes and the top and bottom surfaces of the board. The maximum stress from bending occurs at the bottom of the floor, which is under tension. Because there is more material here, the board will be stronger. 3.3. The finite element analysis of wood-plastic composite floor 3.3.1. The finite element model of wood-plastic composite floor According to the mechanical model of wood-plastic composite floor shown in Fig.3 and the actual situation discussed earlier, two finite element models that consider two situations have been established. The models are as follows: 1) having the same cavity number but different total cavity sizes; 2) having the same total cavity size but different cavity numbers. The cross-section of the wood-plastic composite
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board is 0.18 m wide and 0.025 m thick. The member is 1 m long and the joist span is 0.35 m. The maximum allowable stress for this wood-plastic composite is 25 MPa; the elastic modulus is 3.5 GPa; and the Poisson’s ratio is 0.3. The actual-use status is simulated for the calculation of the maximum bending displacement. The downwards load applied on the midline of the board is set as 1000 N, according to the national standard. Solid 95 is chosen as the entity unit; and the intellectual finite element mesh division from ANSYS is selected for meshing. The total number of grids is 166110. The boundary conditions are as follows: 1) Each end of the board is free to rotate. 2) One end of the board has a y-axis displacement constraint. 3) The other side of the board has a y-axis and a z-axis displacement constraints. 4) All constraints are imposed on an endpoint at the bottom of the board. 5) The maximum stress on the board must be less than the allowable stress of the material. 3.3.2. The Finite Element Analysis Table 4. Comparison between the theoretical and calculated values of the maximum load of wood-plastic composite floors with circular holes
S (10−6 m2 ) 0 225 337.5 450 562.5 675 787.5 900 1012.5 1125 1237.5 1350 1462
Theoretical value (N) 5357 5347 5334 5316 5293 5265 5232 5193 5150 5101 5047 4989 4925
Calculated value (N) 5302 5259 5251 5214 5193 5165 5146 5106 5060 5009 4965 4900 4837
Relative error (%) 1.03 1.64 1.56 1.92 1.88 1.9 1.64 1.68 1.75 1.8 1.63 1.79 1.78
Table 5. Comparison between the theoretical and calculated values of the maximum bending deformation of wood-plastic composite floors with circular holes
S (10−6 m2 ) 0 225 337.5 450 562.5 675 787.5 900 1012.5 1125 1237.5 1350 1462
Theoretical value (10−3 m) 1.089 1.091 1.094 1.097 1.102 1.108 1.115 1.123 1.133 1.144 1.156 1.169 1.184
Calculated value (10−3 m) 1.103 1.110 1.112 1.117 1.121 1.127 1.131 1.141 1.154 1.164 1.174 1.185 1.203
Relative error (%) 1.29 1.76 1.63 1.85 1.73 1.68 1.37 1.59 1.87 1.71 1.59 1.33 1.64
Tables 4 and 5 show comparisons between the theoretical and calculated maximum load and maximum bending deformation of a wood-plastic composite board with cylindrical cavities. The theoretical results are considered consistent with the finite element simulation because the relative error is less than 2% (relative error = (calculated value - theoretical value)/theoretical value). The relative error of the finite element simulation is controlled by several means: 1) There is no simplified physical model of the board, so fillet or similar problems don’t occur. 2) The uniform linear load is spread evenly over 61 nodes.
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3) The boundary restriction conditions are accurate and comprehensive. 4) Solid 95, which has high precision, is chosen for the finite element mesh generation and the relative error was well controlled. Therefore, the design theory for these wood-plastic composite flooring boards with hollow cavities has proved to be feasible and effective.
IV. Conclusions The theoretical calculation and simulation analysis show that the weight of wood-plastic composite floors can be reduced by altering the shape, number, and size of cavities without affecting the mechanical properties. The following conclusions are therefore drawn. 1. When the number of cavities is fixed, the stiffness and strength of a wood-plastic composite flooring board decrease with an increase in the total size of cavities. 2. When the total size of cavities is fixed, the stiffness and strength of the wood-plastic composite board increase with an increase in the number of cavities. 3. When both the number and the total size of cavities are fixed, the stiffness and strength of boards with cylindrical cavities are higher than those with rectangular cavities. 4. A method of exhaustion can be adopted to select the number and size of cavities to satisfy the need for strength. A design with the largest total cavity area is optimal. According to the results discussed earlier, the number of cylindrical cavities would be 11 with a cross-sectional diameter of 10.74 mm in a wood-plastic composite board which is 0.18 m wide and 0.025 m thick, presuming the maximum load to be no less than 5190 N. This design is the best and the most material-efficient, and would save up to 22% of the material. The wood-plastic flooring is now used quite extensively because it is environmentally friendly, attractive, corrosion-resistant and strong. Reducing the weight of board by making it hollow not only reduces the amount of material used in production, but also makes the transportation cheaper and facilitates construction, which are of practical significance. The type of wood-plastic composite flooring can be chosen to suit the purpose. For example, a rectangular hole structure with a high aspect ratio is recommended when high mechanical loading is envisaged and the maximum amount of cavities are desired. Even if there is no need for high strength, there is still a need for lightness, and then a board with a cylindrical hole structure is recommended. In other service environments, the design parameters can be easily calculated using the equations based on the required performance characteristics. This study has demonstrated the practical significance of optimum structural design; and the methods discussed here can be universally applied in the wood-plastic composite flooring board manufacturing industry.
References [1] Laurent,M.M., Recent research developments in wood plastic composites. Journal of Vinyl and Additive Technology, 2009, 15(3): 136-138. [2] William,L.J., Research needs in wood physics : a broad overview. Wood and Fiberence, 1988, 20(2): 277-294. [3] Jungil,S., Douglas,J.G., Shane,O.N. and Costas,M., Understanding the viscoelastic properties of extruded polypropylene wood plastic composites. Journal of Applied Polymer Science, 2003, 89(6): 1638-1644. [4] Anatole,A.K., Wood-plastic Composites. New Jersey: John Wiley & Sons Inc, 2007. [5] Robert,F.L. and Lawrence,E.N., Mechanical Properties of Polymers and Composites (2nd edition). New York: Marcel Dekker, 1993. [6] Bengtsson,M. and Oksman,K., Silane crosslinked wood plastic composites: Processing and properties. Composites Science and Technology, 2006, 66(13): 2177-2186. [7] Liu,H,Z., Yao,F., Xu,Y.J. and Wu,Q.L., A novel wood flour-filled composite based on microfibrillar highdensity polyethylene (HDPE)/Nylon-6 blends. Bioresource Technology, 2010, 101(9): 3295-3297. [8] Yao,F., Wu,Q.L., Lei,Y. and Xu,Y.J., Rice straw fiber-reinforced high-density polyethylene composite: Effect of fiber type and loading. Industrial Crops and Products, 2008, 28(1): 63-72. [9] Yao,F. and Wu,Q.L., Coextruded polyethylene and wood-flour composite: Effect of shell thickness, wood loading, and core quality. Journal of Applied Polymer Science, 2010, 118(6): 3594-3601. [10] Ying,L. and Jian,L.B., Lightweight structure design for wind energy by integrating nanostructured materials. Materials and Design, 2014, 57: 689-696. [11] Wang,Z.T., Li,B.Q. and Zhao,F.Q., The lightweight design and calculation of railway vehicle floor. China HighTech Enterprises, 2014, 1: 125-127.
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[12] Ringsberg,J.W., Saˇ glam,H., Sarder,M.A. and Ulfvarson,A., Lightweight design of offshore platform marine structures—optimisation of weight to strength utilisation of corrugated shell plating. Ships and Offshore Structures, 2014, 9(1): 38-53. [13] Meschut,G., Janzen,V. and Olfermann,T., Innovative and highly productive joining technologies for multimaterial lightweight car body structures. Journal of Materials Engineering and Performance, 2014, 23(5): 1515-1523.
ISSN 0894-9166
Improvement of Mechanical Properties of Wood-Plastic Composite Floors Based on the Optimum Structural Design⋆⋆ Yun Ding
Yang Zhang1 Mingyin Jia1
1
Ping Xue1⋆ Jianchen Cai2
Xiaoming Jin1
1
( College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China) (2 College of Mechanical Engineering, Quzhou University, Quzgou 324000, China) Received 20 January 2015, revision received 5 March 2016
ABSTRACT A study is carried out on the structural design of wood-plastic composite floors. The geometric parameters of the cavities, the structure, and the means to optimize the performance of these light boards are investigated. Various structural parameters of the boards, such as size, shape, and the pattern of cavities are also studied. The optimal structure can be determined by calculation and analysis of the strength, stiffness, weight and cost of the material. A finite element model for the mechanical analysis of wood-plastic composite floors is established; and the results are used to verify the strength criteria under bending deformation, which is the most common loading condition of flooring board.
KEY WORDS wood plastic composite, cavities, flooring board, optimal structure, the finite element model
I. Introduction Wood is the only renewable, eco-friendly and recyclable material that can form a healthy, comfortable and natural part of our living environment. However, because the improvement of life quality in China has raised the demand for timber, China has been experiencing an acute shortage of forest resources. The discrepancy between timber supply and demand has long been a critical issue, which has made the search for alternatives to wood the most obvious solution to the problem. Fiber-reinforced plastic composites have come into wide use over the last decade, and have relieved the demand for timber resources to some extent. In the early 2000s, the output of natural fiber/thermoplastic composites in North America and Europe reached 68.5 million tons, including 590,000 tons of wood-plastic composites made of a range of wood fibers from different sources that accounted for 87% of the total output[1] . Wood-plastic composites are green biomass materials using plastics as matrices and fibers of wood or bamboo as reinforcements, which have gradually become an important type of functional materials with the development of science and technology. Compared with traditional wood, wood-plastic composites possess the hardness of plastics and the process ability of thermoplastics. These composites can also be reused and recycled. Furthermore, wood-plastic composites are biodegradable, highly resistant to insects and rot, and have low water absorption capacity. These characteristics make the materials more ⋆ ⋆⋆
Corresponding author. E-mail: xp [email protected] Project supported by the National 12th Five-Year Plan of Science and Technology with Grant No. 2012BAD23B0203.
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durable than natural wood[2–5] . So far many studies have been made on the mechanical properties of biomass fiber/plastic composites. To name just a few, Bengtsson et al.[6] investigated the application of a silane coupling agent in wood-plastic composites and analyzed their mechanical properties; Liu et al. and Yao et al.[7, 8] studied the effects of different types of coupling agents and their proportions on the mechanical properties of high-density polyethylene (HDPE) composites reinforced with rice straw or bamboo fiber, analyzed the influence of different coupling agents on the interfacial properties of composites, and tested their impacts and tensile strengths; Yao and Wu[9] studied the manufacturing process of the core-surface structure of wood-plastic composites, as well as the influence of surface properties on the impact strength. Flooring boards are subject to varying degrees of stress, which is particularly the case for the floors in public buildings and outdoor spaces. The mechanical strength of floorboard is closely related to its service life and safety of users. When used outdoors, ordinary wooden floorboards experience climate change and may rot, which increases the risk of damage and the cost. Several lightweight, corrosion-resistant and aesthetically pleasing wood-plastic composite flooring materials have recently become available and are widely used in outdoor gardens, hiking trails, and public parks. The design of lightweight floors is currently an important industrial issue because of the enormous demand for floorboards to comply with national standards. To reduce both the cost and the degree of effect upon the environment, besides meeting the strength requirements, the amount of flooring material used should be minimized, as should the amount of energy consumed during production. Currently the lightweight design technology has been widely applied in many fields. For example, Ying and Jian[10] used a designed tower plate for a wind generator with a unique lightweight crosssectional structure. Wang et al.[11] significantly reduced the weight of passenger train floors by using a modular floating floor with elastic sealing structure. Ringsberg et al.[12] investigated the design of lightweight structures for offshore platforms. Meschut et al.[13] designed a lightweight structure for car bodies. However, few studies have been reported on the structural design of lightweight wood-plastic composite floors. In the present study, an optimized flooring board design with cavities to reduce mass is offered. Analysis of the strength, stiffness, weight and cost of flooring boards with different types of core-cavity has been done using mechanical strength theory. A theoretical method is proposed to analyze and optimize the cross-sectional design of extruded wood-plastic composite flooring board.
II. Modeling and Simulation 2.1. Common cavity structure of wood-plastic composite floors The wood-plastic flooring boards now in common use can be either solid or hollow. The cross-sectional shape of the cavities in hollow floors can be circular, rectangular, oval, or rectangular with rounded corners, as shown in Fig.1. The cavities are usually evenly spaced across the width of the board and their number can vary significantly. Most wood-plastic composite flooring boards have cylindrical cavities. The rectangular cavities with rounded corners are also common; but the oval shaped ones are rarely used. The cross sectional shape of the cavity is determined by the required strength of the board, which can facilitate the manufacturing process. The overall performance of a rectangular cavity is close to that of one with sharp corners, because the actual radius of the rounding is quite small. However, the calculations needed for the determination of the load bearing properties are complicated and in this study the discussion will be limited to the analysis of the properties of wood-plastic composite flooring boards with cylindrical and rectangular cavities. 2.2. Assessment of the cross-sectional design of wood-plastic floors Wood-plastic floors are required to have a reliable and constant load bearing capacity and a certain degree of hardness, which depend on the service conditions. At present, the international market regulations impose few requirements with respect to these wood-plastic floors. China has only one National Standard, which stipulates the bending failure load. The related contents are quoted as follows. Table 1 shows that according to the National Standard, the requirement for wood-floor strength is based on the application of the product in public and non-public places, where different regulations apply. In this study we have confined our attention to the use of wood-plastic composite flooring boards in public places, where the strength requirement is high. Flooring of this type used in non-public places
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Fig. 1. Cross-section structure of floor holes. Table 1. Wood-plastic floor standard of China
Standard number
Test item
GBT 24508-2009
Bending failure load
Assessment standard Public places are required to use wood-plastic floors with ≥2500 N. Non-public places are required to use wood-plastic floors with ≥1800 N.
has lower strength requirement. The wood-plastic floor standard of China considers vertical load acting at a point half way between two adjacent joists. The standard stipulates that wood-plastic flooring should not break under load, but does not elucidate the amount of allowed bending. A large amount of deformation occurring in the floor during practical use can not only affect the appearance of board, but also cause an accident. Therefore, the proposed design should restrict floor deformation. A study of the strength and hardness of wood-plastic composite floors should consider two aspects: 1) wood-plastic composite floors should not suffer excessive damage from deformation under a service load; 2) this deformation should not affect the environmental appearance and the safety of users. Different types of cavity structure affect the load bearing performance of wood-plastic composite flooring with respect to the fixed condition. The cross-sectional structure of the boards should maximize the strength while keeping the amount of material used to a safe minimum and facilitating the production and processing as far as possible. 2.3. Stress analysis of the cross-sectional structure of wood-plastic composite floors 2.3.1. Strength analysis of wood-plastic composite floors The load condition of a wood-plastic composite floor placed on top of a joist is shown in Fig.2, where h denotes the member width (m), b the member thickness (m), x the distance from the center of joist A to the load point (m), L the distance from the center of joist A to joist B (m), and F the equi-spaced load (N), respectively. Both the shear deformation and bending occur under a vertical downwards force because the span ratio is small. However, the shear deformation is negligible compared with bending, and a wood-plastic composite flooring member can thus be treated as an Euler-Bernoulli beam, as seen in Fig.3. According to Euler-Bernoulli beam theory: M (1) W where σ is the bending stress (Pa), M the bending moment (N·m) and W the bending section coefficient (m3 ), respectively. σ=
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Fig. 3. Floor stress analysis equivalent to the EulerBernoulli beam.
Fig. 2. Diagram of the floor under force.
N cavities with diameter d exist in the section (see Fig.4), which can be obtained according to Eq.(1). 96F LX − X 2 , [nd + (n + 1) t = b, d < h, nd < b, X ≤ L] (2) σZ = (16bh2 − 3nπd4 /h) where σ Z is the bending stress around the z axis direction (Pa), d the diameter of a cylindrical cavity (m), t the cavity spacing (m), and n the number of cavities, respectively.
Fig. 4. Cross-section diagram of floor with circular holes.
∂σZ 96F (L − 2X) = =0 (3) ∂Z (16bh2 − 3nπd4 ) L The results show that when the values of parameters, b, h, n, F , L and d, are constant, the value of X is L/2, and σZ reaches a maximum. When the load is applied on the centerline of the member, the bending stress is at a maximum, which is σcircular max =
FL FL 4 = 2 2bh nπd 2bh 2S 2 − − 3 8h 3 nπh 2
(4)
where σ circularmax represents the maximum bending stress on a member with cylindrical cavities in the z direction (Pa), S the total cross-sectional area of the cavities (m2 ), respectively. N -rectangular cavities with a width of bk (m) and height of hk (m) are created in the section (see Fig.5). According to Eq.(1), the maximum bending stress (Pa) of a member with rectangular cavities in Z direction can be written as σrectangular max =
FL FL = 2bh2 2nbk h3k 2bh2 2Sh2k − − 3 3h 3 3h
(5)
Equations (4) and (5) show that the maximum bending stress is related to the size and number of cavities in the fixed floorboard sectional dimension, joist span and load. According to the first strength theory of the mechanics of materials, a flooring board will satisfy the strength requirement if the maximum bending stress is smaller than or equal to the allowable stress for wood-plastic composite floors:
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Fig. 5. Cross-section diagram of a floor with rectangular holes.
σmax ≤ σb where σmax is the maximum bending stress (Pa); and σb the the maximum allowable stress for woodplastic composites (Pa), respectively. By combining Eqs.(4) and (5), the following equations can be obtained: 2S 2 2bh2 nπd4 2bh2 Fcircular max = σb − = σb − (6) 3L 8hL 3L nπhL 2nbk h3k 2Sh2k 2bh2 2bh2 − = σb − (7) Frectangular max = σb 3L 3hL 3L 3hL where Fcircular max is the maximum load bearing of a member with cylindrical cavities (N), and Frectangular max the maximum load bearing of a flooring board with rectangular cavities (N), respectively. There must be at least 5 mm of material between the top surface of the wood-plastic board and the hollow space inside. The parameter is therefore as follows: d ≤ h − 10 b−5 n ≤ d+5 hk ≤ h − 10 b−5 n ≤ bk + 5 Equations (6) and (7) show that the total cross-sectional size of the cavities S can be determined, when the materials, formats, and joist spans of wood-plastic composite flooring boards are fixed to ensure the strength. In addition, two parameters can easily determine the load from the perspective of stress performance, which are the total size of cavities S and the number of cavities. The smaller the total size of cavities is, the greater the strength and the allowable load are. However, economy of production can be achieved by including larger cavities and using the least amount of material without compromising strength and durability. The best material-efficient cavity configuration that will not adversely affect the mechanical properties can be determined by adjusting the total number and dimension of the cavities. 2.3.2. Calculating and analyzing the stiffness of wood-plastic composite flooring boards Calculation of the strength of wood-plastic composite flooring board has been discussed in the previous section. However, a floor not only needs strength, but also needs to be sufficiently stiff so that it will not bend appreciably under load. Large deformation during use may spoil the aesthetics of installation, and even cause instability. Excessive bending may also cause damage, and thus should not exceed the allowable amount; Careful consideration needs to be given to stiffness at the design stage. To evaluate the bending deformation, the board is treated as an Euler-Bernoulli beam. The beam axis before deformation is the x axis; the vertical axis is y (see Fig.6); and the xy plane is the vertical plane of symmetry of the beam. In symmetrical bending of the beam, the deformed axis can be plotted as a curve of the deflection in the xy plane. The horizontal ordinate of the deflection curve is any point of x; and w represents the longitudinal coordinate, which is the displacement of the center of x coordinate in the y direction. From Euler-Bernoulli beam theory, the following equation can be deduced: FX L W =− 3L2 − 4X 2 0≤X ≤ (8) 48EIZ 2
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Fig. 6. Diagram of floor-bending deformation under force.
where W is the bending deformation (m); E the elastic modulus of the wood-plastic composite (Pa) and IZ the moment of inertia around the z axis (m4 ), respectively. bh3 nπd4 − (9) 12 64 By substituting Eq.(9) into Eq.(8), the bending displacement of a flooring board with cylindrical cavities can be obtained as follows: 4F X L 2 2 (10) Wcircular = − 3L − 4X 0≤X≤ E (16bh3 − 3nπd4 ) 2 IcircularZ =
where Wcircular denotes the bending deformation of a flooring board with cylindrical cavities (m). bh3 nbk h3k − (11) 12 12 By substituting Eq.(11) into Eq.(8), the bending displacement of a board with rectangular cavities is as follows: FX L 2 2 Wrectangular = − 3L − 4X (12) 0≤X≤ 4E (bh3 − nbk h3k ) 2 IrectangularZ =
where Wrectangular is the bending deformation of a board with rectangular cavities (m). When other parameters are fixed, Eq.(8) is a quadratic function around X. When X = L/2, W reaches the maximum value. Therefore, the maximum displacement occurs on the midline when a board bends under force, and the following is obtained: Wcircular max = −
4F L3 =− E (16bh3 − 3nπd4 )
Wrectangular max = −
F L3 3S 2 3 4E bh − nπ
F L3 F L3 = − 4E (bh3 − nbk h3k ) 4E (bh3 − Sh2k )
(13)
(14)
where Wcircular max represents the maximum bending deformation of a board with cylindrical cavities (m), and Wrectangular max the maximum bending deformation of a board with rectangular cavities (m), respectively. If the maximum bending displacement Wmax is smaller than or equal to the allowable value [W] of the wood-plastic composite material during use, the flooring board satisfies the strength requirements. Eqsuations (13) and (14) show that the maximum bending displacement can be calculated according to certain parameters such as the total size of cavities, load and joist spacing, when the material, format and joist spans are fixed. To ensure proper strength and endurance, the total size of cavities can be selected when n is fixed. From an economical point of view, the larger the total size of the cavities is, the smaller the amount of material is required.
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2.4. Design techniques for cavity cross-sectional structure optimization in wood-plastic composite floors The size of a wood-plastic composite flooring board is typically 0.6-6 m × 0.06-0.3 m, and the thickness ranges from 0.008 to 0.06 m. The wood-plastic flooring used in this study was 1.0 m long, 0.18 m wide and 0.025 m thick. The joist spacing L was 0.35 m. The elastic modulus E of the wood-plastic composite board was 3.5 GPa; the Poisson’s ratio µ was 0.3; and the maximum allowable stress σb was 25 MPa (these data were derived from the actual tests of wood-plastic composites). When analyzing and calculating the maximum amount of deformation, the applied load used was 1000 N, which is greater than the average weight of an adult. The processing of wood-plastic composite requires that the top thickness of the board (the distance between the upper surface and a cavity) should not be less than 0.005 m. Therefore, the number and size of the cavities included are restricted. Table 2 shows the parameter values for cylindrical cavities; and Table 3 shows those for rectangular cavities. Table 2. Parameter values of the circular holes
n dmax (10−3 m) Smax (10−6 m2 )
1 15 177
2 15 353
3 15 530
4 15 707
5 15 883
6 15 1060
7 15 1236
8 15 1413
9 14.4 1465
10 12.5 1227
11 10.9 1026
12 9.6 868
10 12.5 15 1875
11 10.9 15 1799
12 9.6 15 1728
13 8.5 737
Table 3. Parameter values of the rectangular holes
n bk max (10−3 m) hk max (10−3 m) Smax (10−6 m2 )
1 15 15 225
2 15 15 450
3 15 15 675
4 15 15 900
5 15 15 1125
6 15 15 1350
7 15 15 1575
8 15 15 1800
9 14.4 15 1944
13 8.5 15 1658
In Tables 2 and 3, dmax denotes the maximum allowable diameter of a cylindrical cavity (m), bk max the maximum allowable width of a rectangular cavity (m), hk max the maximum allowable height of a rectangular cavity (m), and Smax the maximum allowable total size of cavities (m2 ), respectively.
III. Results and Discussions 3.1. Effect of the total size of cavities on the mechanical properties of wood-plastic composite flooring boards When the number and size of cavities are fixed, the maximum allowable load on the flooring board and the maximum amount of bending deformation can be calculated by altering the total size S of the cavities and using Eqs.(6), (7), (13) and (14). According to Tables 2 and 3, the total size of cavities is at a maximum when there are nine cavities. Therefore, the number of cavities should be set as nine so that the largest total cavity size can possibly be achieved. The height of rectangular cavity should be set as a maximum of 15 mm to satisfy the thickness requirement of 5 mm and to still achieve the largest cavity size. The calculation and analysis results are shown in Fig.7 and 8. The total size of holes S should be selected to meet the requirements for hardness and strength. As mentioned before, the allowable load and strength of a flooring board will increase with a reduction in cavity size, but the larger the total cavity size is, the smaller the amount of material is required. Figures 7 and 8 show that with an increase in S, the maximum load-bearing capacity decreases and the bending increases. It is known from the mechanics of materials that stress and cross-sectional area have an inverse relationship in a floorboard under stress. Any increase in the total cavity size may raise the stress on the cross-section. According to the first strength theory, stresses greater than the maximum allowable one for the material can result in damage. An increase in the total area of core cavities will inevitably lead to a reduction of the maximum allowable load. 3.2. Effect of the number of cavities on the mechanical property of wood-plastic composite floors The maximum allowable load on the floor and the maximum amount of bending deformation can be calculated by changing the number of cavities and using Eqs.(7), (8), (13) and (14). According to the
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Fig. 7. Relationship between the total hole size and the maximum load.
Fig. 8. Relationship between the total hole size and the maximum bending deformation.
Fig. 9. Relationship between the amount of holes and the maximum load.
Fig. 10. Relationship between the amount of holes and the maximum bending deformation.
national standard, the maximum load on an outdoor wood-plastic composite floor should be greater than 2500 N. However, one company has decided that the maximum load should not be less than 5190 N and made the actual production comply with that. As previously mentioned, the maximum S can be 9×10−4 m2 , which accounts for 20% of the total cross-sectional area. The maximum height of a rectangular hole should be 15 mm to meet the thickness requirement of 5 mm. The calculation and analysis results are shown in Figs.9 and 10. The number of cavities n can be selected to meet the hardness and strength requirements. By analyzing the calculation results (Figs.9 and 10), the following conclusions can be drawn when the total size of cavities S is fixed. 1) If the number of cavities n of the floor with cylindrical cavities is increased, the strength and hardness of the floor increase. 2) The mechanical properties do not change with the number of cavities when the height of a rectangular cavity remains unchanged. 3) A flooring board with cylindrical cavities has better mechanical properties than one with rectangular cavities. When the total size of core cavities is fixed, and the number of cavities is increased, the cavity size needs to be smaller. This means there will be more material between the holes and the top and bottom surfaces of the board. The maximum stress from bending occurs at the bottom of the floor, which is under tension. Because there is more material here, the board will be stronger. 3.3. The finite element analysis of wood-plastic composite floor 3.3.1. The finite element model of wood-plastic composite floor According to the mechanical model of wood-plastic composite floor shown in Fig.3 and the actual situation discussed earlier, two finite element models that consider two situations have been established. The models are as follows: 1) having the same cavity number but different total cavity sizes; 2) having the same total cavity size but different cavity numbers. The cross-section of the wood-plastic composite
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board is 0.18 m wide and 0.025 m thick. The member is 1 m long and the joist span is 0.35 m. The maximum allowable stress for this wood-plastic composite is 25 MPa; the elastic modulus is 3.5 GPa; and the Poisson’s ratio is 0.3. The actual-use status is simulated for the calculation of the maximum bending displacement. The downwards load applied on the midline of the board is set as 1000 N, according to the national standard. Solid 95 is chosen as the entity unit; and the intellectual finite element mesh division from ANSYS is selected for meshing. The total number of grids is 166110. The boundary conditions are as follows: 1) Each end of the board is free to rotate. 2) One end of the board has a y-axis displacement constraint. 3) The other side of the board has a y-axis and a z-axis displacement constraints. 4) All constraints are imposed on an endpoint at the bottom of the board. 5) The maximum stress on the board must be less than the allowable stress of the material. 3.3.2. The Finite Element Analysis Table 4. Comparison between the theoretical and calculated values of the maximum load of wood-plastic composite floors with circular holes
S (10−6 m2 ) 0 225 337.5 450 562.5 675 787.5 900 1012.5 1125 1237.5 1350 1462
Theoretical value (N) 5357 5347 5334 5316 5293 5265 5232 5193 5150 5101 5047 4989 4925
Calculated value (N) 5302 5259 5251 5214 5193 5165 5146 5106 5060 5009 4965 4900 4837
Relative error (%) 1.03 1.64 1.56 1.92 1.88 1.9 1.64 1.68 1.75 1.8 1.63 1.79 1.78
Table 5. Comparison between the theoretical and calculated values of the maximum bending deformation of wood-plastic composite floors with circular holes
S (10−6 m2 ) 0 225 337.5 450 562.5 675 787.5 900 1012.5 1125 1237.5 1350 1462
Theoretical value (10−3 m) 1.089 1.091 1.094 1.097 1.102 1.108 1.115 1.123 1.133 1.144 1.156 1.169 1.184
Calculated value (10−3 m) 1.103 1.110 1.112 1.117 1.121 1.127 1.131 1.141 1.154 1.164 1.174 1.185 1.203
Relative error (%) 1.29 1.76 1.63 1.85 1.73 1.68 1.37 1.59 1.87 1.71 1.59 1.33 1.64
Tables 4 and 5 show comparisons between the theoretical and calculated maximum load and maximum bending deformation of a wood-plastic composite board with cylindrical cavities. The theoretical results are considered consistent with the finite element simulation because the relative error is less than 2% (relative error = (calculated value - theoretical value)/theoretical value). The relative error of the finite element simulation is controlled by several means: 1) There is no simplified physical model of the board, so fillet or similar problems don’t occur. 2) The uniform linear load is spread evenly over 61 nodes.
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3) The boundary restriction conditions are accurate and comprehensive. 4) Solid 95, which has high precision, is chosen for the finite element mesh generation and the relative error was well controlled. Therefore, the design theory for these wood-plastic composite flooring boards with hollow cavities has proved to be feasible and effective.
IV. Conclusions The theoretical calculation and simulation analysis show that the weight of wood-plastic composite floors can be reduced by altering the shape, number, and size of cavities without affecting the mechanical properties. The following conclusions are therefore drawn. 1. When the number of cavities is fixed, the stiffness and strength of a wood-plastic composite flooring board decrease with an increase in the total size of cavities. 2. When the total size of cavities is fixed, the stiffness and strength of the wood-plastic composite board increase with an increase in the number of cavities. 3. When both the number and the total size of cavities are fixed, the stiffness and strength of boards with cylindrical cavities are higher than those with rectangular cavities. 4. A method of exhaustion can be adopted to select the number and size of cavities to satisfy the need for strength. A design with the largest total cavity area is optimal. According to the results discussed earlier, the number of cylindrical cavities would be 11 with a cross-sectional diameter of 10.74 mm in a wood-plastic composite board which is 0.18 m wide and 0.025 m thick, presuming the maximum load to be no less than 5190 N. This design is the best and the most material-efficient, and would save up to 22% of the material. The wood-plastic flooring is now used quite extensively because it is environmentally friendly, attractive, corrosion-resistant and strong. Reducing the weight of board by making it hollow not only reduces the amount of material used in production, but also makes the transportation cheaper and facilitates construction, which are of practical significance. The type of wood-plastic composite flooring can be chosen to suit the purpose. For example, a rectangular hole structure with a high aspect ratio is recommended when high mechanical loading is envisaged and the maximum amount of cavities are desired. Even if there is no need for high strength, there is still a need for lightness, and then a board with a cylindrical hole structure is recommended. In other service environments, the design parameters can be easily calculated using the equations based on the required performance characteristics. This study has demonstrated the practical significance of optimum structural design; and the methods discussed here can be universally applied in the wood-plastic composite flooring board manufacturing industry.
References [1] Laurent,M.M., Recent research developments in wood plastic composites. Journal of Vinyl and Additive Technology, 2009, 15(3): 136-138. [2] William,L.J., Research needs in wood physics : a broad overview. Wood and Fiberence, 1988, 20(2): 277-294. [3] Jungil,S., Douglas,J.G., Shane,O.N. and Costas,M., Understanding the viscoelastic properties of extruded polypropylene wood plastic composites. Journal of Applied Polymer Science, 2003, 89(6): 1638-1644. [4] Anatole,A.K., Wood-plastic Composites. New Jersey: John Wiley & Sons Inc, 2007. [5] Robert,F.L. and Lawrence,E.N., Mechanical Properties of Polymers and Composites (2nd edition). New York: Marcel Dekker, 1993. [6] Bengtsson,M. and Oksman,K., Silane crosslinked wood plastic composites: Processing and properties. Composites Science and Technology, 2006, 66(13): 2177-2186. [7] Liu,H,Z., Yao,F., Xu,Y.J. and Wu,Q.L., A novel wood flour-filled composite based on microfibrillar highdensity polyethylene (HDPE)/Nylon-6 blends. Bioresource Technology, 2010, 101(9): 3295-3297. [8] Yao,F., Wu,Q.L., Lei,Y. and Xu,Y.J., Rice straw fiber-reinforced high-density polyethylene composite: Effect of fiber type and loading. Industrial Crops and Products, 2008, 28(1): 63-72. [9] Yao,F. and Wu,Q.L., Coextruded polyethylene and wood-flour composite: Effect of shell thickness, wood loading, and core quality. Journal of Applied Polymer Science, 2010, 118(6): 3594-3601. [10] Ying,L. and Jian,L.B., Lightweight structure design for wind energy by integrating nanostructured materials. Materials and Design, 2014, 57: 689-696. [11] Wang,Z.T., Li,B.Q. and Zhao,F.Q., The lightweight design and calculation of railway vehicle floor. China HighTech Enterprises, 2014, 1: 125-127.
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[12] Ringsberg,J.W., Saˇ glam,H., Sarder,M.A. and Ulfvarson,A., Lightweight design of offshore platform marine structures—optimisation of weight to strength utilisation of corrugated shell plating. Ships and Offshore Structures, 2014, 9(1): 38-53. [13] Meschut,G., Janzen,V. and Olfermann,T., Innovative and highly productive joining technologies for multimaterial lightweight car body structures. Journal of Materials Engineering and Performance, 2014, 23(5): 1515-1523.