Mechanical performance of aluminum reinforced wood plastic composites under axial tension: an experimental and numerical investigation

Wood plastic composites (WPCs) are low-cost biomass composite materials with good mechanical stability and good weather resistance that are mainly used in the areas with low stress levels. Aimed at improving the mechanical properties of WPCs, this paper proposes a new WPC reinforced with aluminum. The WPC and aluminum were hot pressed to form an aluminum reinforced wood plastic composites (A-WPC). The axial tensile properties, stress–strain relationship, and failure mechanism of the composite were studied experimentally. The results show that the ultimate stress and strain, elastic modulus, and other mechanical parameters of A-WPCs are much higher than those of WPCs. The elongation at break is 10.13 times that of WPCs, which greatly improves the ductility. Based on the equivalent stiffness theory, two calculation models were proposed to predict the tensile stress–strain relationship of A-WPCs. The tensile rebound process of A-WPCs was analyzed in depth, and then the calculation formula of the residual curvature was deduced to compare with the test results. The experimental results are in good agreement with the calculation results.


Introduction
Wood plastic composites (WPCs) are green and environment-friendly biomass composites [1][2][3], which has a wide range of raw materials, low production cost, nicelooking, and good weatherability. WPCs are widely used in indoor and outdoor decorations, landscape architecture, the automobile field, packaging and transportation, and other fields that require low mechanical properties [4]. In recent years, many studies have been completed to enhance the mechanical properties of WPCs and expand the application field of WPCs. Migneault et al. [5] and Kumari et al. [6] found that the mechanical properties of WPCs produced by an injection molding process were better than those produced by hot pressing and extrusion molding. The mechanical properties of WPCs were greatly improved when p-toluenesulfonic acid (p-TsOH) was used as a compatible coupling agent by Lin et al. [7] to remove hemicellulose from wood flour to change the cross-sectional compatibility of the WPC. Rimdusitet al. [4], Petchwattana et al. [8], Tao et al. [9], Perisicet al. [10], and Panaitescu et al. [11] tested different toughening agents to improve the impact strength, tensile elongation at break, and other mechanical properties of WPCs. Many experiments have investigated improving the mechanical properties of WPCs with carbon fiber [12], glass fiber [13], basalt fiber [14], polyester fiber [15], and mineral wool. However, no reinforcement measures can significantly improve the strength, elastic modulus, and ductility at the same time. This paper proposes a new reinforced measure by exploiting the light weight, high strength, and good ductility of aluminum to improve the mechanical properties of WPCs. The WPC and aluminum are hot pressed into an aluminum reinforced wood plastic composite (A-WPC). Experimental investigation of the tension behavior of the A-WPC has been carried out. The equivalent stiffness method is used to calculate the elastic modulus of the strengthened composite. Based on this, two sets of calculation models of the uniaxial tensile stress-strain relationship of the A-WPC are proposed to predict the load carrying capacity and stress-strain relationship of the new composite, which can provide a theoretical basis for the design and calculation of a building structure composed of A-WPCs.

Materials
The raw WPC material used in this study was composed of 30% polyolefin, 50% wood flour (60 mesh), and 15% calcium carbonate. The tensile trial samples were produced by Anhui Sentai Co., Ltd, Anhui province, China. The tensile test of the WPC was carried out according to ASTM d-143 [16]. Six specimens were tested on the electronic universal testing machine. The longitudinal and transverse strains in the middle of the specimen and the homologous real-time load were collected throughout the experiment. Table 1 lists the test results, where σ tu is the ultimate stress, ε tu infers the ultimate strain, E t represents the elasticity modulus, A implies the elongation at fracture, and ν is the Poisson's ratio. As shown in Fig. 1, the stress-strain relationship exhibits a linear character, and no obvious plasticity occurs until the specimen was damaged, implying the characteristics of brittle failure.
The aluminum alloy was made by hot rolling in Sentai Co., Ltd. The test design and operation were performed according to ASTM E8-E8M [17], and the number of aluminum samples was also 6. The measured parameters were consistent with the WPC tensile test, and the results are shown in Table 1. Comparing the test results with those of the WPC, the ultimate tensile strength, elastic modulus, ultimate strain, and elongation at break of the aluminum plate are 9.5 times, 10.4 times, 6 times, and 20.9 times those of the WPC, respectively, while the Poisson's ratio of the two materials is substantially identical.
In Fig. 2, the stress-strain relationship of the aluminum tensile test is different from that of the WPC, which has an obvious specific elastic limit point. When the curve reaches the elastic-plastic stage, the increasing rate of stress decreases relative to the increasing rate of strain, forming a yield platform. Then, the strain increases, but the stress is almost unchanged in this stage, which demonstrates the good ductility of aluminum. The failure sections are obviously necking, and they are all oblique sections. In addition, the angle between the section and sample cross axis is about 30°, as shown in Fig. 2.

Sample design
A 1.5 mm thick aluminum was first pulled into the pattern die by the hauling machine, and then the 2.5 mm thick WPC was attached to the aluminum surface by the co-extrusion machine on the side of the pattern die. The aluminum reinforced wood plastic composite plate with a thickness of 4 mm is finally formed by hot pressing (the temperature is 160-200 °C and the pressure is 20 MPa). The A-WPC tensile samples were processed based on ASTM E8-E8M [17]. The sample number is 1-1-1-6, the overall length is 450 mm, the gauge length is 200 mm, and the width is 40 mm.

Test scheme
As shown in Fig. 3a, the tensile fixtures were selected to hold the grip sections of the specimen. One longitudinal and one transverse perpendicular strain gauge were arranged on the two sides of the middle part of the sample to measure the strain in the tensile direction and perpendicular to the tensile direction during the test. In Fig. 3b, the tensile experiment of the A-WPC was carried out on a 50 kN electronic universal testing machine. The applied load was recorded simultaneously. The loading mode is crossbeam stroke control, and the loading rate is 0.5 mm/min. All load and strain data were collected by the Data Logger TDS-530(Tokyo Sokki Kenkyujo Co., Ltd., Japan), and the sampling frequency was 1 Hz.

Test results
As shown in Fig. 4a, all the specimens are damaged at the effective part, that is, the part with the smallest cross section of the sample. Unlike the aluminum test results, the failure section of the A-WPC is almost parallel to the horizontal axis of the sample, and no obvious necking is observed, as shown in Fig. 4b. This indicates that the WPC can effectively prevent the aluminum from necking when bearing a uniaxial tensile load. After the failure of the specimens, they all bent towards the WPC and  Table 2. The coefficient of variation of all the parameters is less than 17%, meeting the specification requirements. Meanwhile, only the coefficient of variation of the elongation at break is more than 10%, which is 12%. The R 2 of the ultimate strength and elastic modulus are less than 5%, which shows that the A-WPC continues to exhibit the advantages of good homogeneity, stable mechanical properties, and low dispersion of the WPC. Figure 5 shows the tensile stress-strain relationship of the A-WPC, which can be divided into three stages: elastic stage, elastic-plastic stage, and ductile failure stage. At first, the relationship between the stress and strain is linear. After reaching the proportional limit, the slope of the curve becomes smaller, and the curve enters the elastic-plastic stage. In this stage, the growth rate of stress decreases relative to the growth rate of strain, and finally, it enters the ductile failure stage. At this time, the strain increases continuously, the stress increases slowly, and the sample undergoes a large deformation, which displays brilliant ductility until the sample fails.

Calculation model Equivalent elastic modulus
The Poisson's ratio of the WPC and aluminum is consistent, which possesses the basic elements of deformation coordination, and no relative slip appears in the tensile process of the A-WPC, indicating that the A-WPC has good mechanical stability. Thus, the equivalent stiffness method can be used to calculate the elastic modulus of the A-WPC, as shown in the following equation: where E W (E A ) and t W (t A ) are the elastic modulus and the thickness of the WPC (aluminum), respectively, and w is the width of the sample. By substituting the elastic modulus of the WPC and aluminum into Eq. (1), the calculated value of the elastic modulus of the A-WPC is 27.66 GPa, which is different from the experimental result by only 12.8%.

Model I-bilinear model
The elastic-plastic stage, as the transition section between the elastic and the ductile failure stage, can be decomposed into the extended section of the elastic stage and the initial stage of the ductile failure section. Then, the stress-strain relationship can be disassembled into two linear curves. The slope of the first straight line is the elastic modulus, and the slope of the curve drops sharply after reaching the inflection point strength; therefore, the bilinear model including two straight lines can be written as the following equation: where σ ey and ε ey are the inflection point strength and homologous strain of the A-WPC, respectively, which is between the proportional limit and yield strength point, and k is a constant. According to the tensile test results, by setting the inflection point strength to be 90% of the ultimate strength, the inflection point strain is the strain corresponding to the inflection point strength, and k is suggested to be 0.03. Substituting the above parameters into Eq. (2): f = 24510ε 0 < ε ≤ 0.0031 75.98 + 735(ε − 0.0031) 0.0031 < ε ≤ 0.017 .   Figure 6 shows the fitting results of the A-WPC tensile stress-strain bilinear model. The model is simple in form and easy for hand computation. The two segments can well describe the stress-strain relationship at different stages and can also predict the elastic modulus, ultimate strength, and ultimate strain of the materials accurately.

Model II-exponential model
In the light of the tensile test characteristics of the A-WPC, the exponential function model (Eq. 4) is introduced to predict the tensile stress-strain relationship: where x = ε/ε y , σ y and ε y represent the yield stress and yield strain, respectively, and b and d are constants that can be obtained from the test results. Equation (4) is derived, and x = 0 is taken into Eq. (5), where E is the elastic modulus and E sec is the secant modulus of the yield point: Substituting the test results into Eq. (5) for the calculation and setting σ y to be 95% of the ultimate strength, ε y is the strain corresponding to the yield point. After regression analysis, we suggest that b = 0.02 and d = − 1.55. Taking these parameters into Eq. (4), the expression of the tensile stress-strain relationship of the A-WPC can be obtained as Figure 7 shows that the trend of the stress-strain relationship between the exponential model and the test (6) σ = 79.91 e 6.06ε − e −469.7ε .
results of the A-WPC is almost the same, which means this model can describe the whole process of the stressstrain relationship development. When the numerical simulation and software analysis of the A-WPC are carried out, the exponential model can get more accurate results.

Analysis of tensile springback of the A-WPC
Throughout the experiment, no interface relative slip and interface delamination occurred in all specimens, which indicates that the WPC and aluminum are in a state of coordinated deformation in the whole process of the trial. The eccentric tensile load and additional bending moment can be ignored, and the tensile process can be regarded as a plane stress state. As shown in Fig. 8, the tensile springback process of the A-WPC is as follows: assuming that the original length of the sample is L, the length after the uniaxial tensile load is L + 2δ u , and the tensile strain of the sample is ε u , when unloading, the sample begins to shrink and spring back, and bending occurs. The springback is divided into the  springback shrinkage stage and the springback bending stage. Supposing that the sample only shrinks and does not bend in the springback shrinkage stage, the sample will rebound until the resultant stress of the section is 0. Then, in the springback bending stage, the sample will bend under the action of the pure bending moment, the stress of the section will redistribute, and the final bending moment of the section will be 0.
Let us assume that the constitutive relationship of the aluminum and WPC can be described by the bilinear model, which is divided into the elastic section and linear strengthening section. In this model, E a , E a ′, σ ay , ε ay , and t a are the elastic value of the aluminum elastic section, the elastic modulus of the linear strengthening section, the yield strength, the yield strain, and the thickness, respectively. The corresponding parameters of the WPC are E w , E w ′, σ wy , ε wy , and t w , where ε ay = σ ay /E a and ε wy = σ wy /E w . The thickness of the A-WPC is t = t a + t w , the actual thickness coordinate is h, the section residual strain is ε c (h), and the bending residual curvature is A = ε c (h)/h.
When the longitudinal section with a residual strain of 0 is defined as the neutral axis of the residual strain, the offset of the neutral axis from the interface is δ. When the tensile strain is defined as ε k , the stress of the aluminum is σ ak and the stress of the WPC is σ wk ; when the rebound strain is defined as ε t , the stress of the aluminum is σ at and the stress of the WPC is σ wt ; the residual stress is ε c (z).
When the tensile strain is ε k , the stresses of the WPC and aluminum could be expressed by Eqs. (7) and (8): When the springback strain is ε t , the stresses of the aluminum and WPC follows: There is no bending of the A-WPC during the springback shrinkage stage. When the resultant force of the internal force of the section is 0, there is the following relationship: t a σ at + t w σ wt = 0. Taking Eq. (9) into it leads to the following equation: The internal moment M t can be expressed as Eq. (11): Under a pure bending load, the distance between the strain neutral axis and the interface is δ, and the rotation angle of the section relative to the z-axis is θ (δ and θ can be positive or negative). Under this condition, the bending normal stress of the aluminum is σ ab and that of the WPC is σ wb . The strain distribution of the pure bending section of the A-WPC is shown in Fig. 9.
Supposing that θ is small enough, now the strain distribution function along the z-axis is The strain is replaced by tan θ (z − δ), and the bending normal stress could be expressed as The resultant force of the pure bending normal stress distribution along the section is 0, that is, the sum of the bending normal stress of the A-WPC along the z-axis is 0, as shown in the following equation: Taking Eqs. (13) into (14), δ can be determined by the following equation: When the bending moment produced by the bending normal stress on the section is M, then Eq. (14) becomes Then, taking Eq. (13) into Eq. (16), we can figure out the expression of tanθ:

Fig. 9 Section strain distribution
If M = − M t , the transformation process of the section stress is considered to be the process of the bending moment M t formed in the springback shrinkage stage and further releasing of the bending moment, i.e., the rebound bending stage. The superposition of the two stress states determined by Eqs. (9) and (13) is the residual stress state of the section after tensile springback. The residual curvature of the A-WPC can be regarded as the curvature caused by the bending moment M t . According to the definition of the residual curvature and Eq. (12), A ≈ tanθ/2 can be calculated. By substituting Eqs. (5) and (11) into A ≈ tanθ/2, the final residual curvature of the A-WPC can be expressed as Substituting the test results into Eqs. (10) and (15), the springback strain and the offset of the neutral axis relative to the interface are calculated as ε t = 0.0033 and δ = − 1.13 mm, respectively. Then, taking the above two results into Eq. (18), A = 0.28/m −1 can be calculated. The residual strain difference of the test results of the samples labelled as 1-1-1-6 is brought into the formula A = ε c (h)/h. The results are illustrated in Fig. 10, indicating that the average residual curvature of the tensile springback of the WPC aluminum composite plate is 0.31/m −1 , which is 9.7% higher than the theoretical value. This means that Eq. (18) can accurately predict the tensile springback curvature of the A-WPC. Figure 11 shows the ratio of the mechanical parameters of the tensile test of the A-WPC to the WPC, including ultimate strength, ultimate strain, elastic modulus, Poisson's ratio, and elongation at break. The ratio of the

Comparison of the mechanical properties between the A-WPC and WPC
ultimate strength, ultimate strain, elastic modulus, and elongation at break is 3.95, 3.7, 4.03, and 10.13, respectively, while the Poisson's ratio of the A-WPC is almost equal to that of the WPC.
The results show that the ultimate strength, elastic modulus, and especially the elongation at break of the WPC are mainly enhanced by the aluminum, which indicates that the stiffness, strength, and ductility of the WPC can be significantly improved by hot pressing the WPC and aluminum. This approach fixes the problem that no reinforcement measures can significantly improve the strength, elastic modulus, and ductility at the same time.

Conclusion
The Poisson's ratio of the WPC is close to that of the aluminum, making it possible for the two materials to deform cooperatively without relative slip. Only one of the coefficients of variation of the measured mechanical properties is higher than 10%, which indicates that the mechanical properties of the reinforced WPC(A-WPC) are stable and the dispersion is small.
The strength, stiffness, and the elongation at break of the WPC are significantly enhanced, which indicates that the A-WPC can overcome the issue that no reinforcement measures can improve the strength, elastic modulus, and ductility simultaneously. These results change the current situation that WPC sare only used in the field with lower requirements for the mechanical properties.
The springback process of the A-WPC can be divided into the springback shrinkage and rebound bending stage. According to the critical state, the equilibrium equation was established, and the theoretical calculation formula of the residual curvature was obtained. The  difference between the calculation results and the experimental results is within 10%.
The equivalent stiffness principle was used to calculate the elastic modulus of the A-WPC, and two calculation models were established to predict the stress-strain relationship. The appropriate model could be selected according to the actual demand.
Abbreviations WPC: Wood plastic composite; A-WPC: Aluminum reinforced wood plastic composite.