Experimental study on mechanical properties for a three - Phase polymer composite reinforced by glass fibers and titanium oxide particles

Vietnam Journal of Mechanics, VAST, Vol. 33, No. 2 (2011), pp. 105 – 112 EXPERIMENTAL STUDY ON MECHANICAL PROPERTIES FOR A THREE - PHASE POLYMER COMPOSITE REINFORCED BY GLASS FIBERS AND TITANIUM OXIDE PARTICLES Nguyen Dinh Duc1, Dinh Khac Minh2 1University of Engineering and Technology 2Shipbuilding Science and Technology Institute Abstract. Nowadays, composite materials are applied in many fields. The physico - mechanical properties of the material can be improved by adding reinforced fibers and particles. Many scientists pay attention to the calculation for elastic modules of three - phase composite materials. This report presents the experimental results for some elastic modules of three - phase polymer composite reinforced with glass fibers and titanium oxide particles of different volume ratios. A comparison between experimental and the- oretical results shows good agreement. Key words: Three - phase composite (polyester, glass fiber, titanium oxide), elastic modulus, experimental. 1. INTRODUCTION Composite material consists of two or more component materials to obtain a new material with better properties. The components are matrix material and filled materials (reinforced or additive). The function of matrix material is to unite the components, assure the resistance to heat and physicochemical loads, while the filled components are used to improve the mechanical properties (stiffness and strength) of the composite [5, 6, 7, 10]. The reinforced components used usually are fibers and particles. Fibers can increase the stiffness, while particles can decrease the fracture, plastic strain and improve the water and gas proof ability of the composite. Thus, the addition of fibers and particles can make composite become more perfect, to satisfy more and more requirements of modern technology. Having advantages such as: light weight, resistance to heat and environmental loads, composite materials are widely applied in many fields: from industry, construction, ma- chine - building, transportation to aerospace engineering and medical engineering. In Viet- nam, within the past ten years, many researches and applications for composite have been done, especially for polymer composites. The properties of polymer composites is indicated in [5, 6, 9]. In ship building industry, guard ship, passenger ship, fishing vessel of small and medium sizes are mainly made of composite materials. To improve the water - proof, fire 106 Nguyen Dinh Duc, Dinh Khac Minh - proof, corrosion - proof and crack resistant properties of the material, particles often be added to the matrix besides fibers. This leads to the appearance of three - phase composite which having three phases: polymer matrix, reinforced fibers and particles. To deal with the structural problems, we need to know the mechanical behavior of the material, which means firstly determining the elastic modules of the composite (Fig. 1). Fig. 1. Model of three - phase composite with reinforced fiber and particle 2. DETERMINE THE ELASTIC MODULES OF THREE - PHASE COMPOSITE There are two main methods for determining the elastic modules of three - phase composite material: experimental and analytical methods. The advantage of experimental method is that it can provide the exact result for the material’s modules. However, since three - phase composite is a multi - component material, the experiment can not illustrate the effect that the component phases have on the overall mechanical properties of the material. The analytical method often uses a mechanical model of a three-phase composite material reinforced with fibers (normally in cylindrical shape) and particles (in spherical shape) to calculate the material’s elastic modules. It has a principal advantage: the modules are explicitly determined from the properties and aspect ratios of the component phase. When these factors are changed, new composite is obtained and their physicomechanical properties can be predicted, thus this method provides the foundation for optimal design of new material and structure. Another method is the inductive method, in which the predicted formulas for the elastic modules are derived based on a large number of experiments. Such formulas are often suggested by the scientists in experimental physics. But with the appearance of the third phase, the experiments and the prediction for the variation of the elastic modules from the component phases’ parameters become very complex. So far we have only seen publications [10] using this method for two - phase composites (matrix and reinforced particles). In our previous reports, the elastic modules of three - phase composites are estimated using two theoretical models of the two - phase composite consecutively: nDm = Om+nD Experimental study on mechanical properties for a three - phase polymer composite... 107 [3, 4, 12]. This paper considers three - phase composite reinforced with particles and unidirectional fibers, so the problem’s model will be: 1Dm = Om +1D. The researches on determining the elastic modules for composite material with re- inforced particles are reported in [1, 2, 10, 11, 12]. In our papers [11, 12], the interaction between matrix and particles is taken into account. Firstly, the modules of the effective matrix Om which called "effective modules" are calculated. In this step, the effective matrix consists of the original matrix and particles, it is considered to be homogeneous, isotropic and have two elastic modules. The next step is estimating the elastic modules for a composite material consists of the effective matrix and unidirectional reinforced fibers. Thus, the result for the three - phase composite problem depends much on the models for the two - phase composite problem and it can have different accuracy for different composites. For composite reinforced with particles, several methods for determining elastic modules have been proposed [1, 2, 10, 11, 12]. In this research, we chose the method which takes into account the interaction between matrix and particle [2, 12]. There are also researches on determining the elastic modules for composite reinforced by unidirectional fibers [1, 7, 8, 11]. This type of material is often considered orthotropic with 5 elastic modules [1, 7]. The most modern reports with two independent approaches by Pobedrya B.E. [8] and Vanin G.A. [11] have calculated the sixth modulus of this material, and their results show good agreement to each other. Assume that all the component phases (matrix, fiber and particle) are homogeneous and isotropic, we will use Em, νm, Ea, νa, Ec, νc to denote Young modulus and Poisson ratio for matrix, fiber and particle, respectively. According to [2], we can obtain the modules for the effective composite as below: G¯ = Gm 1− ξc (7− 5νm)H 1 + ξc (8− 10νm)H (1) K¯ = Km 1 + 4ξcGmL (3Km) −1 1− 4ξcGmL (3Km) −1 (2) here, L = Kc −Km Kc + 4Gm 3 , H = Gm/Gc − 1 8− 10νm + (7− 5νm) Gm Gc . (3) E¯, ν¯ can be calculate from (G¯, K¯) as below E¯ = 9K¯G¯ 3K¯ + G¯ , ν¯ = 3K¯ − 2G¯ 6K¯ − 2G¯ (4) The modules for three - phase composite reinforced with unidirectional fiber are chosen to be calculated using Vanin’s formulas [11]: 108 Nguyen Dinh Duc, Dinh Khac Minh E11 = ξaEa + (1− ξa) E¯ + 8G¯ξa (1− ξa) (νa − ν¯) 2− ξa + x¯ξa + (1− ξa) (xa − 1) G¯ Ga , E22 =   ν2 21 E11 + 1 8G¯   2 (1− ξa) (χ− 1) + (χa − 1)(χ− 1 + 2ξa) G¯ Ga 2− ξa + χξa + (1− ξa)(χa − 1) G¯ Ga + +2 χ (1− ξa) + (1 + ξaχ) G¯ Ga χ+ ξa + (1− ξa) G¯ Ga     −1 , G12 = G¯ 1 + ξa + (1− ξa) G¯ Ga 1− ξa + (1 + ξa) G¯ Ga , G23 = G¯ χ+ ξa + (1− ξa) G¯ Ga (1− ξa)χ+ (1 + χξa) G¯ Ga , ν23 E22 = − ν2 21 E11 + 1 8G¯  2 (1− ξa) x¯ + (1 + ξax¯) G¯ Ga x¯+ ξa + (1− ξa) G¯ Ga − − 2 (1− ξa) (x¯− 1) + (xa − 1) (x¯− 1 + 2ξa) G¯ Ga 2− ξa + x¯ξa + (1− ξa) (xa − 1) G¯ Ga   , ν21 = ν¯ − (χ+ 1) (ν¯ − νa) ξa 2− ξa + χξa + (1− ξa) (χa − 1) G¯ Ga . (5) in which x¯ = 3− 4ν¯. One of the goals of this research is to do the experiments to verify the results for the modules E11, E22, G12 of three - phase composite materials calculated using the formulas (5) above. 3. EXPERIMENT AND RESULT To verify Young modules for three - phase composite, we tested the samples made of polyester AKAVINA (made in Vietnam), fibers (made in Korea) and titanium oxide (made in Australia) with the properties as in Table 1. The experiments were done on HOUNSFEILD H50K-S tester (Fig. 2) using BS EN ISO 527-1: 1997 method. Room’s temperature was (20±50C), humidity was 65%±20%. The samples were made according to Vietnamese standard code: TCVN 6282:2008 [13]. The dimension of the samples is given in Fig. 3. The experiments were done at the Labo- ratory of Shipbuilding Technology Institute, Nha Trang University. Experimental study on mechanical properties for a three - phase polymer composite... 109 Table 1. Properties of component phases for the three - phase composite Component phase Young modulus E Poisson ratio ν Matrix polyester AKAVINA (Vietnam) 1,43 Gpa 0.345 Glass fiber (Korea) 22 Gpa 0.24 Titanium oxide TiO2 (Australia) 5,58 Gpa 0.20 Fig. 2. HOUNSFEILD H50K-S Tester Fig. 3. Dimension of three - phase composite sample Totally more than 60 samples were tested for 8 different cases of fibers and particle’s volume ratios (as in the first column of Table 2). Tensile test was done for estimating E11, E22 and in 45 degree direction for estimating E45 and G12. The experiments’ results is given in Table 2. According to the tests’ results, fiber has much effect on improving Young modulus, while particle has much effect on shear modulus. 110 Nguyen Dinh Duc, Dinh Khac Minh Table 2. Experiment results for three - phase composite’s elastic modules Elastic Modulus Composite E45 E1 E2 G12 20%TiO2 + 15%W800 + 65% polyester 3012.36 4548.25 2750.58 742.07 2996 4673.56 2678.5 720.138 2977.7 4695.67 2670.26 700.504 2879.5 4825.34 2740.79 700.18 20%TiO2 + 20%W800 + 60% polyester 3768.89 6208.64 2828.56 719.518 3752.2 6330.28 2931.42 715.799 3527.23 6347.5 2815.96 713.146 3340.08 6191.18 2923.98 712.51 20%TiO2 + 25%W800 + 55% polyester 3725.65 7270.8 3018.02 701.868 4001.73 6981 3158.63 702.952 3791.82 6959.8 3377.35 705.731 3582.3 6911 3045.76 701.31 3889.3 6956 3072.91 702.432 20%TiO2 + 30%W800 + 50% polyester 4330 7658.5 3230.54 677.701 4275 7580.4 3267.62 697.542 4106.81 7604 3254.59 700.201 30%TiO2 + 15%W800 + 55% polyester 2046.11 4725 2939.3 818.577 2467.39 4774 2932.81 800.125 2614.2 5073 3033.59 844.859 2244.17 5231 2997.34 801.6411 30%TiO2 + 20%W800 + 50% polyester 4025 6341 3278.59 807.049 3819.55 6423 3146.34 801.252 3738.52 6582.5 3178.75 803.382 30%TiO2 + 25%W800 + 45% polyester 3661.27 6875 3425.62 799.966 3992.65 6465 3462.25 805.524 3623.84 7012 3659.15 791.349 3707.86 6609 3547.13 786.753 30%TiO2 + 30%W800 + 40% polyester 4342.58 8230 3655.53 768.72 4229.44 8308 3708.33 761.511 4090 8092 3602.52 775.503 4111.5 8792 3670.48 801.844 The comparison between experimental results (average values from Table 2) with theoretical result ( formulas (5)) is shown in Table 3. 4. CONCLUSION From Table 3, we can obtain that the theoretical analysis and experiment have good agreement for elastic modules of three - phase composite made of polyester matrix, glass fibers and titanium oxide particles. This conclusion allows us to apply the algorithm and formulas proposed in this research for estimating the elastic modules and other structure and material problems using three - phase composite. The authors would like to thank the Laboratory of Shipbuilding Technology Insti- tute, Nha Trang University for their assistance on experiments. Experimental study on mechanical properties for a three - phase polymer composite... 111 Table 3. Comparison between experiment and analysis Composite E1 E2 G12 20%TiO2 + 15%W800 + 65% polyester Experimental 4685.70 2709.95 715.72 Theoretical 4787.5 2791.0 673.8 Error 2.1% 2.9% 6.2% 20%TiO2 + 20%W800 + 60% polyester Experimental 6269.4 2874.98 715.24 Theoretical 5781.7 2996.7 666.9 Error 8.4% 4.1% 7.3% 20%TiO2 + 25%W800 + 55% polyester Experimental 7015.72 3152.55 708.65 Theoretical 6778.4 3221.7 659.3 Error 3.5% 2.2% 7.5% 20%TiO2 + 30%W800 + 50% polyester Experimental 7614.3 3250.91 691.8 Theoretical 7777.5 3468.9 650.7 Error 2.1% 6.7% 6.3% 30%TiO2 + 15%W800 + 55% polyester Experimental 4950.75 2975.76 816.30 Theoretical 4980.5 3091.6 766.5 Error 0.6% 3.7% 6.5% 30%TiO2 + 20%W800 + 50% polyester Experimental 6348.6 3201.22 803.9 Theoretical 5962.1 3310.4 757.7 Error 6.5% 3.4% 6.1% 30%TiO2 + 25%W800 + 45% polyester Experimental 6717.75 3523.54 795.90 Theoretical 6946.3 3549.1 747.9 Error 3.4% 0.7% 6.4% 30%TiO2 + 30%W800 + 40% polyester Experimental 8355.5 3659.22 776.89 Theoretical 7933.1 3810.6 737.0 Error 5.3% 4.1% 5.4% The results of researching presented in the paper have been performed according to scientific research project of Vietnam National University, Hanoi (VNU, Hanoi), coded QGTĐ.09.01. 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