Theoretical study on mechanical properties of two-dimensional composite model with circular filler under compressive load
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https://www.eduzhai.net International Journal of Composite Materials 2015, 5(3): 47-51 DOI: 10.5923/j.cmaterials.20150503.01 Theoretical Study on Mechanical Properties of 2-D Composite Models Containing Circular Fillers under Compression Load Widayani*, Sparisoma Viridi, Siti Nurul Khotimah Nuclear Physics and Biophysics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia Abstract This paper reports a theoretical study of stress distribution and factors that affect Young’s modulus of 2D composite model containing circular fillers under compression loads. The dimension used for the composite model containing 1 filler is (4x4) cm with filler radius of 1 cm. In the case of filler more rigid than matrix, the Young’s modulus values used for matrix, filler 1 and filler 2 are close to that of epoxy, Hemp fiber and glass, respectively. In the case of matrix more rigid than filler, we use the same Young’s modulus value of the matrix, and the Young’s modulus of filler 1 and filler 2 are close to LDPE and HDPE, respectively. The stress distribution for 2D composite model containing 2 circular fillers arranged in series and parallel has been carried out for the case filler more rigid than matrix. The dimension used for the composite model containing 2 fillers is (4x7) cm with filler radius of 1 cm. The stress is calculated using Excel and the data are taken for every increment X of 0.1 cm. The results are successfully showing the qualitative picture on stress distribution. The results show that stress is not uniform along X axis, but higher in the area containing the longer more rigid component. Young’s modulus of a specific total filler fraction has been calculated using the method used and compared with Voight and Reuss formulas. Keywords Composite model, Circular filler, Compression load, Stress distribution, Young’s modulus 1. Introduction Mostly, the studies on composites focus on the correlation of mechanical properties of the composites with that of its components. The studies are very important since generally researchers concern with new composite materials with specific properties which are actually formed as a combination of its component properties. Proper composition and technique in composites synthesis may result in a new composite with expected mechanical properties. Studies on mechanical properties of composites have been carried out via experiments, modeling and simulation [1-3]. Computational study on mechanical properties of composite containing uniform distribution of hard and soft components has been carried out . The computational results were then compared to calculations based on Voight and Reuss formulas, and the study shows that the Voight formula suits the composite with high fraction of particle. The Voight formula uses isostrain condition where the modulus Young * Corresponding author: email@example.com (Widayani) Published online at https://www.eduzhai.net Copyright © 2015 Scientific & Academic Publishing. All Rights Reserved of composites is formulated as follow: EC = Ef Vf + Em (1− Vf ) (1) Where EC, Ef, Vf and Em are Young’s modulus of composite, Young’s modulus of fiber, volume fraction of fiber, Young’s modulus of matrix, respectively. Reuss formula, based on isostress condition, is as follow: 1= Vf + (1− Vf ) EC Ef Em (2) Where EC, Ef, Em, Vf, and Vm are Young’s modulus of composite, Young’s modulus of filler, Young’s modulus of matrix, volume fraction filler and volume fraction of matrix, respectively. There are some other formulations to predict the Young’s modulus of composite based on Young’s modulus of its components such as Einstein formula which is then modified by Guth and Money, Hapin and Tsai formula, etc . Fillers can have form typically of spherical [6, 7], ellipsoidal , and arbitrary , where they can also be non-metallic , inorganic , or metallic . This paper presents a simple view on mechanical property of composite model 2-D containing circular fillers under external compression loads. This model can be considered as simplification of 3D composite model containing spherical 48 Widayani et al.: Theoretical Study on Mechanical Properties of 2-D Composite Models Containing Circular Fillers under Compression Load fillers, where spherical filler can be approximated by series 3. Method of cylinder in order to apply fiber refinforcement theory . It has been shown that residual stress in polymeric composites depends on filler shape . In this study, the Y stress distribution is calculated along X- axis (in horizontal direction) on 2D composite model with one and two fillers. There are two arrangements of filler for the model with two fillers: series and parallel. The basic concept used in this study is that the composites experience contraction under external compression load. 0 1 2 3 4 X Lm Lf X=2 2. Theory According to elasticity theory, the rigidity of materials is represented by its modulus of elasticity. For normal loads, modulus elasticity is named as Young’s modulus. There are two types of normal load: tensile and compression. In general, response of materials to external tensile load is different with that of compression load. Therefore, Young’s modulus of a material under tensile load may different with that of under compression load. Young’s modulus (E) is a ratio of stress (σ = F ) to strain (ε =∆L) of a material A L under an external normal load. For a material containing two components connected in series, the external force will be equally transmitted for the two components, thus if there is no difference in area, the two components will experience same stress. σ = σ1 = σ2 E1 ∆L1 L1 = E2 ∆L2 L2 ∆Ltotal = ∆L1 + ∆L2 σ = ( ∆Ltotal L1 + L2 E1 E2 ) (3) A composite material consists of two components: matrix and filler. This study concerns with 2D composite models with one and two circular fillers. Schematic figure of the composite models are shown in Figure 1. Figure 2. Illustration of X-axis used for 2D composite model containing 1 filler. At X=2, there are two parts of matrix and one part of filler arranged in series Table 1. The length of matrix (LM) and filler (LF) containing 1 circular filler X (cm) 0
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