Analysis of Elastic Properties According to the Aspect Ratio of UHMWPE Fibers Added to PP/UHMWPE Composites

Abstract

This study comparatively analyzed the behavior of elastic properties by aspect ratio of the ultra-high molecular weight polyethylene (UHMWPE) fibers that are added when creating a composite material of polypropylene and UHMWPE. The volume fraction (VF) of UHMWPE fibers added to polypropylene was fixed at 5%. The elastic properties were lumped for analysis according to the aspect ratio of the UHMWPE fibers oriented on the polypropylene matrix; they were analyzed using the Halpin–Tsai model, which involves a theoretical approach and finite element analysis based on the homogenization method. Finite element analysis was performed for fiber aspect ratios of 0.2 to 30 UHMWPE via the homogenization technique using the ANSYS Material Designer. For theoretical comparison, UHMWPE fiber aspect ratios of 0.2 to 100 were comparatively analyzed using the Halpin–Tsai model. When the aspect ratio of UHMWPE fiber was 0.2, it was calculated as 1518 MPa, and when the aspect ratio was 30, it was 2365 MPa, and it increased by 55.8%. As the aspect ratio increased, E22 and G12 converged to a constant value (1550 MPa). In the future, when the volume fraction of UHMWPE changes from 0 to 50%, a study must be conducted to analyze the predicted behavior of the elastic properties when the aspect ratio of the UHMWPE fiber changes.

1. Introduction

The phrase “composite material” implies that two or more materials with different properties have been macroscopically mixed to become a useful material. These composites have different properties than those of the individual components of the mixture. In a composite material, each component retains its original properties in a mixed state; therefore, the properties are generally present in a non-uniform state from a microscopic perspective. These composite materials can generally be divided into five categories: fiber, particulate, laminar, flake, and skeletal composites. Among them, fiber composites are the most widely used and developed materials. The most recently used fiber-reinforcing agent is carbon fiber (CF), which is mixed with various matrix materials [1,2,3,4,5,6,7,8]. However, these carbon fibers are expensive and have disadvantages. Harmful substances can be generated in the process of mixing these fibers to make a composite material [9,10,11]. To overcome these shortcomings, various alternative fibers have recently been used, such as glass fibers [12,13,14,15,16,17,18]. Glass-fiber-reinforced plastic (FRP) is a composite material made of glass fibers that has been reinforced with synthetic resin as a matrix material. Glass-fiber-reinforced composite materials have a low modulus of elasticity and fewer disadvantages than carbon fiber in terms of strength. Various materials have been developed and used as fibers in order to overcome the disadvantages of fiber-reinforcing agents. Among the most recently used materials, ultra-high molecular weight polyethylene (UHMWPE) is significant. UHMWPE is a type of polyethylene (PE) and is also called high modulus PE (HMPE). PE polymers combine in a long chain with a high molecular weight structure. According to these long polymer properties, UHMWPE does not break even when an external force is applied, and it has the ability to disperse the external force in the direction of the chain. In addition, it has excellent wear and corrosion resistance. Therefore, many studies are being conducted to replace it with composite materials in which steel is used as an additive [19,20,21,22,23]. Since its invention in the 1950s, UHMWPE has been widely used in ships (ropes and sails for yachts), automobile parts, and medical materials (artificial joints); fabrics made from UHMWPE are also used as materials for military and police body armor, outdoor backpacks, and bags. However, UHMWPE has low heat resistance. In general, UHMWPE deforms at approximately 80–100 °C and melts at approximately 130 °C. To overcome these shortcomings, an appropriate matrix must be used to compose and utilize a composite material. Polypropylene (PP) is the most commonly used matrix that compensates for the shortcomings of UHMWPE. PP is formed by bonding methyl groups (CH₃) to the carbon atoms of a PE molecular chain. Generally, PP films are more transparent and slightly harder than PE films. Consequently, PP is the most commonly used substance for automobile parts as well as interior and exterior materials. It has a low specific gravity among plastics of 0.9, hence it is widely used to manufacture lightweight vehicular parts. A composite material that is manufactured and processed by mixing PP and UHMWPE is lightweight and high-strength. In addition, owing to the nature of the composite material, the bonding force at the surface where the two different materials are bonded is important. The creation of composite materials by mixing materials of the same polymer series is expected to exhibit excellent effects. Composite materials produced through this fiber reinforcement mechanism can be classified by fiber length into short-, long-, and continuous-fiber composites. As long-fiber-reinforced composites can be molded using a simple thermoforming process, they have advantages in terms of their productivity and the formability of complex shapes compared to traditional continuous-fiber-reinforced composites. In contrast, short-fiber-reinforced composites are advantageous for mass production because their structures can be easily formed by the conventional injection method; however, the mechanical properties of the structures are significantly lower than those of structural metals. Therefore, research on long-fiber-reinforced composites is being actively conducted to improve the shortcomings of existing continuous-fiber-reinforced composites in terms of low mechanical properties and mass production of short-fiber-reinforced composites [24,25]. Therefore, the properties of the composite materials must be compared and analyzed by considering the effect of the fiber length. To develop a fiber-reinforced composite material of PP-based UHMWPE, the change in the elastic properties must be compared and analyzed according to the length of the added UHMWPE. However, most existing composite material studies have focused on the fiber volume fraction or on changes to the type of fiber. To overcome these research limitations, it is necessary to study both the fiber volume fractions and aspect ratios. Existing studies have been conducted by adjusting the aspect ratio of the CF in carbon fiber/geopolymer-based composites [26,27,28], and by examining the mechanical strength inside glass fiber and vinyl ester resin polymers [29,30]. According to these research results, the higher the aspect ratio of the fiber, the higher the mechanical strength. However, the research results on the volume fraction of the fiber are not mentioned. In addition, the types of reinforced fibers were the same, but the matrix used was different, making it difficult to apply the research results. In order to evaluate the PP/UHMWPE fiber composite material, we considered the volume fraction and aspect ratio of the added fiber at the same time. This type of research is difficult for a number of reasons. First, when constructing a composite material, it is difficult to change two variables simultaneously: the volume fraction and aspect ratio of the fiber. When the aspect ratio of the fiber inside the composite material changes, the volume fraction changes concurrently. Since these characteristics are difficult to approach experimentally, it is necessary to conduct preliminary theoretical research using finite element analysis. Therefore, in this study, to develop a PP/UHMWPE composite material, the aspect ratio of the UHMWPE fiber added by fixing the volume fraction of UHMWPE fiber added to the composite material to 5 VF% through finite element analysis was performed. Finite element analysis was performed while sequentially increasing the aspect ratio of the UHMWPE fibers from a minimum of 0.2 to a maximum of 30. In addition, a numerical analysis model was analyzed and compared using the Halpin–Tsai model. Based on the study results, the effect of the aspect ratio of the UHMWPE fibers when manufacturing UHMWPE/PP composite materials was analyzed.

2. Materials and Methods

Figure 1 shows the tensor notation used in this study. The fibers were evenly oriented in the matrix; they form a composite material. The elastic modulus in the longitudinal direction of the matrix is denoted by E. The x-, y-, and z-axes are numbered 1, 2 and 3, respectively. The shear modulus on each side of the composite material is denoted by G. According to this tensor notation, G₁₂ implies that the shear stress occurs in the y-axis direction from the x-axis plane. This tensor notation can be applied equally to the fiber. The aspect ratio is defined as the length-to-diameter ratio of the fiber. In addition, considering the redundancy of the tensor representation, the superscript ‘m’ is used for the tensor notation of the PP matrix, and the superscript ‘f’ is used for the tensor notation of the UHMWPE fiber.

Various micromechanical models have been developed to numerically predict the elastic behavior of composite materials. Micromechanics is an analytical technique used to determine the number of individual components that make up a composite or heterogeneous material. Representatively, various analysis techniques exist, such as the rule of mixture (ROM), Chamis model, and Mori–Tanaka model. Among them, the Halpin–Tsai model has a reinforcing factor that can represent the aspect ratio; therefore, it can predict the behavior of the composite material according to the aspect ratio of the fiber. Halpin and Tsai (1969) developed a semi-empirical method for predicting composite properties. The method sensibly interpolates between the upper and lower bounds of composite properties. The Halpin–Tsai model is a mathematical model that predicts the elasticity of composites based on the shape and direction of the filler and the elastic properties of the filler and matrix [31,32,33,34]. In addition, as shown in Equations (1)–(9), this model uses the experimentally-derived reinforcing factor (ξ) and correction coefficient ($\eta$) to improve the existing ROM. The reinforcement factor depends on the shape of the fibers, their arrangement, and load conditions.

$$E_{11}=E_m\frac{\left(1+{\xi }_{11}{\eta }_{11}{V}_f\right)}{\left(1-{\eta }_{11}{V}_f\right)}$$

(1)

$$E_{22}=E_m\frac{\left(1+{\xi }_{22}{\eta }_{22}{V}_f\right)}{\left(1-{\eta }_{22}{V}_f\right)}$$

(2)

$$G_{12}=G_m\frac{\left(1+{\xi }_{12}{\eta }_{12}{V}_f\right)}{\left(1-{\eta }_{12}{V}_f\right)}$$

(3)

$${\xi }_{11}=2\left(l\times t\right)+40{(V_f)}^{10}$$

(4)

$${\xi }_{22}=2\left(w\times t\right)+40{(V_f)}^{10}$$

(5)

$${\xi }_{11}={\left(w\times t\right)}^{1.73}+40{(V_f)}^{10}$$

(6)

$${\eta }_{11}=\frac{\left(\frac{E_f}{E_m}-1\right)}{\left(\frac{E_f}{E_m}+{\xi }_{11}\right)}$$

(7)

$${\eta }_{22}=\frac{\left(\frac{E_f}{E_m}-1\right)}{\left(\frac{E_f}{E_m}+{\xi }_{22}\right)}$$

(8)

$${\eta }_{11}=\frac{\left(\frac{G_f}{G_m}-1\right)}{\left(\frac{G_f}{G_m}+{\xi }_{12}\right)}$$

(9)

Furthermore, in this study, a finite element analysis was performed through the homogenization technique using ANSYS Material Designer. ANSYS Material Designer is a module that enables material design and analysis by modeling composite materials or micromaterials per unit square. Through this module, a finite element analysis was performed by modeling the composite material. This was accomplished by setting the volume fraction of fibers per unit volume to 5 VF% using the homogenization technique. Homogenization techniques have received increasing attention over the past decades for predicting the mechanical properties of composite materials. This is because homogenization techniques can efficiently quantify the interplay between microscopic and macroscopic properties [35,36,37,38,39,40,41]. In this study, the UHMWPE fiber was assumed to be a cylinder to predict the elastic properties of the composite material. It was modeled such that the UHMWPE fiber could be randomly arranged inside the Representative Volume Element (RVE) according to the aspect ratio. Owing to the finite element analysis setup using this homogenization technique, the diameter and RVE size of the modeled PP matrix and UHMWPE fiber may differ depending on the volume fraction. In addition, the orientation of the fibers was set in the x-axis direction (longitudinal) so that they could be oriented inside the PP matrix. The modeling shape is illustrated in Figure 2. The elastic behavior of the UHMWPE fibers was compared and analyzed based on the elastic properties calculated from the RVE according to the change in the aspect ratio. The physical properties of each material used in the finite element analysis are listed in

Table 1. Properties of PP and UHMWPE.

	Polypropylene (PP)	UHMWPE
Modulus of elasticity (MPa)	1325	25,000
Shear modulus (MPa)	432.29	10,417
Poisson’s ratio	0.43	0.20
Bulk modulus of elasticity (MPa)	3154.8	13,889.0
Density (kg/m)	904	950

. The properties used are those of a linear isotropic material, but these isotropic properties can be applied to an anisotropic material in the shape of the cylindrical UHMWPE fiber, which was modeled in ANSYS Material Designer. In terms of the physical properties, the PP was obtained by quoting PolyMirae Company’s Adstif EA5074, and the UHMWPE assumed the physical properties of Mitsui Chemicals’ MIPELON product. Although the densities of PP and UHMWPE are similar, the elastic and shear moduli are large, because of the chain structure characteristics of UHMWPE. However, UHMWPE is vulnerable to deformation owing to its low Poisson’s ratio. Therefore, if the two materials are effectively combined to form a composite, a good synergistic effect can be achieved.

3. Results and Discussion

In this study, changes in the elastic properties attributed to the aspect ratio of PP/UHMWPE fibers were analyzed using finite element analysis and the Halpin–Tsai model. Numerical analysis using finite element and Halpin–Tsai analyses were performed at a 5% volume fraction of UHMWPE fibers. The higher the volume fraction of the fiber, the better the elastic properties. Due to the complexity and convergence of the finite element analysis, it was performed by setting a different aspect ratio at 5% of the UHMWPE volume fraction. Finite element analysis was performed for aspect ratios of 0.2 to 30; numerical analysis using the Halpin–Tsai model was performed for aspect ratios of 0.2 to 100 to examine the theoretical results. Therefore, from the influence of UHMWPE short fibers on the PP-based matrix, the elastic property behavior when continuous fibers were used was predicted and comparatively analyzed. As the structure of the fiber is oriented in its longitudinal direction, it presents as an anisotropic material. According to the comparative analysis in the E₁₁ direction shown in Figure 3, when the aspect ratio of the UHMWPE fiber was 0.2, the modulus of elasticity was calculated to be 1518 MPa, and when the aspect ratio was 30, it was found to be 2365 MPa. Theoretical numerical analysis indicated that the modulus of elasticity was 2415 MPa when the aspect ratio was 100. The finite element analysis and Halpin–Tsai model converged with similar results up to an aspect ratio 9 for the UHMWPE fiber. However, for aspect ratios of 9 or higher, the longitudinal elastic modulus value according to the finite element analysis result was larger than that of the numerical analysis result using the Halpin–Tsai model; this trend was the same until the aspect ratio was 30. The larger value of the longitudinal elastic modulus according to the finite element analysis can be explained by the shape modeled by the analysis. In the analysis model, as the volume fraction of 5% was set as a fixed variable, the UHMWPE fibers were modeled as if they were evenly distributed in the cross-section at a low aspect ratio. This is shown in Figure 4a; the influence of anisotropy is small. However, if the aspect ratio is increased at a fixed volume fraction of 5%, the cross-sectional arrangement density of the UHMWPE fiber decreases, as shown in Figure 4b. Therefore, the anisotropy increases, and the elastic modulus in the longitudinal direction can be large. By contrast, in the numerical analysis using the Halpin–Tsai model, this effect does not appear because it is a theoretical result value without a modeling shape. Hence, it may differ from the finite element analysis result. As such, the influence of the cross-section is increased from an aspect ratio of 9 or higher. In addition, according to the numerical analysis results using the Halpin–Tsai model, the increase rate of the elastic properties decreased from an aspect ratio of 40 or higher and converged to 2400 MPa. According to the results of this study, it is effective to assume continuous fibers at aspect ratios of 40 and higher.

E₂₂ is at a right angle to the orientation direction of the fiber; it can be calculated using the Halpin–Tsai equation. Figure 5 shows the elastic modulus in the E₂₂ direction calculated via finite element analysis. Since the result calculated using the Halpin–Tsai model is the value calculated through ξ₂₂ of the UHMWPE fiber, theoretically, it is not affected by the aspect ratio of the fiber. As ξ₂₂ is affected by the height and width of the fiber, the shape of the UHMWPE used in this study is circular. Therefore, the height and width of the fiber are the same, indicating that it has a constant value irrespective of the aspect ratio. However, the finite element analysis results differed from those of the Halpin–Tsai numerical analysis model according to the modeled UHMWPE fiber orientation within the PP matrix. As mentioned previously, the UHMWPE volume fraction was maintained at 5%, and according to the modeling results, the lower the aspect ratio, the more the UHMWPE fibers were chopped and dispersed over a large area. According to these results, the circular disk-shaped fibers were oriented. This appears as shown in y-axis section of Figure 6. Since the aspect ratio of the fiber was low, the length in the longitudinal direction (the height of the fiber) was greater than the length of the fiber. Hence, the longitudinal direction of the fiber changed in that same direction. Therefore, when the aspect ratio was less than one, the elastic modulus in the E₂₂ direction was high. The tendency of E₂₂ to be high decreased until the aspect ratio of the UHMWPE fiber became 1, and then converged from an aspect ratio of 15 to 1550 MPa. According to the numerical analysis using the Halpin–Tsai model, convergence was observed at 1502 Mpa. Since the elastic modulus in the E₂₂ direction is generally related to the cross-sectional shape of the fiber, it converged to a constant value in the circularly simulated UHMWPE fiber.

The shear modulus calculated in this study is shown in Figure 7. In the case of the shear modulus, the cross-section of the UHMWPE fiber is located on the cross-section of the PP matrix, and it is determined according to its influence. Therefore, if a fixed volume fraction of 5% is maintained in the finite element analysis, the shear modulus is temporarily calculated because the cross-sectional density of UHMWPE fibers is high in areas with low aspect ratios. However, the number of fibers decreases as the aspect ratio increases so convergence to 510 MPa can be confirmed. The Halpin–Tsai model converges at 470 MPa. In this study, the results of the predicted composite material elastic properties using the Halpin–Tsai model and finite element analysis showed that the properties were generally higher through the finite element analysis. However, most of the results were within a range of 10%, which is quite similar. This difference can be attributed to a deep relationship with the finite element analysis model. Since the theoretical Halpin–Tsai model has only a reinforcing factor (ξ) that can experimentally substitute for the effect of the aspect ratio, no factor exists that can represent other effects such as the cross-sectional shape of the UHMWPE fiber. However, in the case of the finite element analysis, the direction and other factors according to the shape of the UHMWPE were reflected, and the results were derived, showing a different trend from that of the theoretical model. As a result of predicting the elastic properties of the composite material considering the aspect ratio, the elastic modulus in the longitudinal direction increased as the aspect ratio increased; however, no significant effect was observed for aspect ratios of 40 or higher. As the aspect ratio of UHMWPE fibers exceeded 40, results similar to those of the continuous-fiber mechanism were obtained. In the future, finite element analysis must be performed considering the volume fraction and aspect ratio of UHMWPE fibers in composite materials. In addition, a precise finite element analysis model must be developed to predict the physical properties by developing actual composite materials and comparing experiments and analyses.

4. Conclusions

In this study, the tendency according to the aspect ratio of UHMWPE fibers was comparatively analyzed to develop a composite material in which these fibers were used as reinforcing materials with a PP-based matrix. The composite materials were analyzed using finite element analysis and micromechanical models. Finite element analysis was performed sequentially from an aspect ratio of 0.2 to 30. In the finite element analysis, an aspect ratio of 30 or more was modeled in the form of continuous fibers. Therefore, the limit of convergence occurred, and a finite element analysis was performed up to an aspect ratio of 30. Theoretical numerical analysis was performed using the Halpin–Tsai model to analyze and compare aspect ratios from 0.2 to 100. In the finite element analysis, the basic model included PP used as a matrix, and UHMWPE fibers oriented in the x-axis direction. The volume fractions of the UHMWPE fiber and matrix were set to 5% and 95%, respectively. An analysis model was constructed using the homogenization method. An ANSYS Material Designer was used to construct this composite material analysis model using the homogenization method. According to a comparative analysis of E₁₁, which is the modulus of elasticity in the longitudinal direction of the fiber, when the aspect ratio of the UHMWPE fiber was 0.2 and 30, the modulus of elasticity was calculated to be 1518 MPa and 2365 MPa, respectively. Theoretical numerical analysis indicated that the modulus of elasticity was 2415 MPa when the aspect ratio was 100. The higher the aspect ratio of the UHMWPE fibers, the higher the elastic modulus (E₁₁) is in the longitudinal direction. Analyzing the tendency of the elastic modulus to increase together with the theoretical analysis results confirmed that the rate of increase in elastic properties decreased above UHMWPE aspect ratios of 40 and converged to 2400 MPa. Based on these characteristics, an aspect ratio above 40 can be interpreted as a continuous fiber. In addition, a comparative analysis of the elastic modulus in the E₂₂ direction indicated that, in the low aspect ratio range, the anisotropy property of the existing anisotropic material in the x-axis direction was reversed to the y-axis longitudinal direction. This was owing to the reversal of the aspect ratio, such that the elastic modulus of E₂₂ was increased. Therefore, the E₂₂ elastic modulus with an aspect ratio of 0.2 was the highest at 1620 MPa. Furthermore, the elastic modulus of E₂₂ converged to a constant value because it was related to the cross-sectional shape of the UHMWPE. A comparative analysis of the shear modulus (G₁₂) confirmed that the larger the aspect ratio, the greater the convergence to 510 MPa. The shear modulus (G₁₂) is related to the fiber cross-section of the UHMWPE because it is a shear modulus that occurs in the cross-section in which the fibers of the composite material are oriented. The UHMWPE modeled in this study had a circular cross-section, and the number of fibers added was limited according to the volume fraction, resulting in a convergent outcome. If the volume fraction is 50% or more, a curved graph will be obtained rather than one that converges to a constant value. When developing a PP/UHMWPE composite material based on these research results, the expected elastic properties can be calculated for UHMWPE short-fiber reinforcement to secure injection moldability. The expected elastic behavior can be predicted when developing long and continuous-fiber composite materials to secure elastic properties. This can be used to develop various materials and components based on the characteristics of the PP/UMHWPE composite material derived in this study. Since the PP/UHMWPE composite material is lightweight and high-strength, it can be used for developing parts in the automobile field and can be used for various lightweight components. In addition, it can be manufactured by adjusting the volume fraction and aspect ratio of the UHMWPE additive according to the required properties of the component. To commercialize these composites, it is necessary to conduct a study to analyze and predict the elastic behavior when the volume ratio of UHMWPE changes from 0 to 50%.