International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 5, May 2017, pp. 651 655, Article ID: IJMET_08_05_071 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=5 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAEME Publication Scopus Indexed MODELING AND ANALYSIS OF HEXAGONAL UNIT CELL FOR THE PREDICTION OF EFFECTIVE THERMAL CONDUCTIVITY Kamala Priya B Assistant Professor, Department of Mechanical Engineering, KL University, Vaddeswaram, Andhra Pradesh, India ABSTRACT The importance of this work is to determine effective thermal conductivities of Unidirectional fibre reinforced composites by means of accomplishing Finite Element Method. The determination of effective thermal conductivity of composites where individual composites are taken into account were computed with the representative volume element of hexagonal model unit cell which is being incorporated with the Finite Element Software Ansys 12.0. The effect of fibre type and fibre arrangements of effective thermal conductivities in transverse and through thickness directions are thoroughly examined. Considering finite element method with respect to Representative Volume Element, thermal conductivities of Fibre reinforced composites are determined which are interpreted in the form of Hexagonal models are presented. From the results it is shown that the effective thermal conductivities of composites can be improved with voids in a matrix and random arrangement of fibres in a matrix. Key words: Thermal Conductivity, Finite Element Method, Representative Volume Element, Fibre Reinforced Composite. Cite this Article: Kamala Priya B, Modeling and Analysis of Hexagonal Unit Cell for the Prediction of Effective Thermal Conductivity. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp. 651 655. http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=5 1. INTRODUCTION Fibre and matrix of high strength are together called as fibre reinforced composites in which dispersed phase (or) discontinuous phase comes under fibre region and continuous phase comes under matrix region. And the region of fibre and matrix is called as interface. Because of high specific strength and stiffness, in structural applications and in some thermal load applications, composite materials are used. Coming to the thermal load, it is required to resolve the temperature distribution in the structure for which the valuation of structure response in which thermal conductivity of material is to be provided. Thermal Conductivity along transverse direction for ideal FRP Composites are examined by Islam and Pramila [1] which includes composites with interfacial Thermal Barrier Resistance and Composites with http://www.iaeme.com/ijmet/index.asp 651 editor@iaeme.com
Modeling and Analysis of Hexagonal Unit Cell for the Prediction of Effective Thermal Conductivity cracks. The evaluation of effective thermal conductivties for both square and hexagonal unit cells of long circular cylinders with appropriate thermal boundary conditions has been done by G. Sambasiva Rao [2] et al. T. J. Lu and J. W. Hutchinson[3] supposed the general longitudinal thermal conductivity of unidirectional fibre bolstered composite in a mixture of matrix cracking with an interfacial perfect debonding together with a verbal exchange of warmth transfer mechanisms across the cracks and debonded interfaces. A numerical method is proposed with the aid of Springer and Tsai[4] for evaluating Transverse thermal conductivity based totally on shear loading analogy. Transverse thermal conductivities supposed for square Array of Unit cell taking into account circular filaments are resolute through Tsai[5]. future mechanics foundation and the consequences of interfacial fracture mechanics theories for the evaluation of debonding and delamination in composite substances are discussed through Xiaomin Deng[6]. considering on rectangular and Hexagonal arrays, Yaun Lu[7] computed the transverse thermal conductivity by using Boundary series approach for both square and round cylinders. The effective thermal conductivities,k 2 and K 3 of Unidirectional Fibre Reinforced Composites by placing a thin third phase material between fibre and matrix are verified by Kamala Priya B[8]. 2. PROBLEM MODELING 2.1. Problem Statement The goal of this research is to determine effective thermal conductivities, K2 & K3 of Unidirectional Fibre Reinforced Composites for complete range of fibre volume fraction. 2.2. Methodology In the present part of the discussion, Hexagonal Model with regular arrangement of fibres are verified for fibre volume fractions ranging from 0.1 to 0.6 with appropriate thermal boundary conditions based on the direction of heat flow. 2.3. Geometry The cross-sectional area of fiber relative to the total cross- sectional area of unit cell is a measure of volume of fiber relative to the total volume of the composite which is called fiber volume fraction (Vf) = Where r is radius of fiber a is edge length of square unit cell Vf volume fraction of fiber 3. ASSUMPTIONS In the literature, the indicated micromechanical models standardly build some assumptions that fibre and matrix constituents are homogenous as well as isotropic materials and the composites are macroscopically homogenous. The assumption made that the composites are of void free. So according to the thermal conductivities of fibre and matrix constituents, volume fraction of fibre and fibre distribution are spread out aligned and staggered. The geometry, material and loading of unit cell which are taken into consideration are symmetrical about the axes. On that account one forth portion of Unit cell is modelled. http://www.iaeme.com/ijmet/index.asp 652 editor@iaeme.com
Kamala Priya B 4. FINITE ELEMENT MODELS Normally it is sufficient to draw conclusions for the complete arrangement of periodic fibres by considering only unit cell which is called as representstive volume element (RVE) for a composite which is shown in figure 1 had taken into account for the analysis. Figure 1 Hexagonal Unit cell with Fibre Matrix interface Figure 2 Isolated Hexagonal Unit cell with Fibre Matrix interface Figure 3 One forth portion of Isolated Hexagonal Unit cell with Fibre Matrix interface 4.1. Boundary and Loading Conditions Thermal conductivity is acquired from the Fourier equation 1.1 by means of substituting the heat flow within the required direction in Watts that's obtained through giving suitable Thermal boundary conditions. Temperature Boundary situations for a one-fourth model are as follows: For prediction of K 2 : T(0,y) =T 1 ; T(a,y) = T 2 All other faces are subjected to adiabatic boundary conditions. For prediction of K 3 : T(x,0) =T 1 ; T(x,a) = T 2 All other faces are subjected to adiabatic boundary conditions. http://www.iaeme.com/ijmet/index.asp 653 editor@iaeme.com
Modeling and Analysis of Hexagonal Unit Cell for the Prediction of Effective Thermal Conductivity 4.2. Material Properties Fiber Conductivity On this evaluation, thermal conductivity values are expected to be in the variety of 5 to 100. The materials in this predicted variety are Carbon and Glass fibers. Matrix Conductivity Polymer is considered for the existing analysis. The effective thermal conductivity of Fiber Matrix interface with and without debond are studied with the expected matrix thermal conductivity value. 4.3. Hexagonal Unit Cell with Fiber Matrix Debond From figure 4 & 5, for both Transverse (K 2 ) and through Thickness (K 3 ) directions, a similar variation in Thermal Conductivity is observed with increase in volume fraction upto 0.2. A wide divergence of Thermal Conductivity values are identified from 0.2 to 0.6. Figure 4 Thermal Conductivity K 2 (W/m-k) V s Volume Fraction V f plot for Hexagonal Unit Cell. Figure 5 Thermal Conductivity K 3 (W/m-k) V s Volume Fraction V f plot for Hexagonal Unit Cell. 5. RESULTS AND DISCUSSIONS Figure 6 ANSYS Plot shows the temperature variation in Hexagonal Unit Cell with Fibre Matrix interface for Staggered Fibres in Transverse Direction Figure 7 ANSYS Plot shows the temperature variation in Hexagonal Unit Cell with Fibre Matrix interface for Staggered Fibres through Thickness Direction http://www.iaeme.com/ijmet/index.asp 654 editor@iaeme.com
Kamala Priya B 6. CONCLUSION 6.1. Hexagonal Unit Cell with Fiber Matrix interface for Staggered Fibers From figure 6 & 7, in Transverse (K 2 ) and through Thickness (K 3 ) directions, a similar variation in Thermal Conductivity is observed with increase in volume fraction upto 20%. A wide divergence of Thermal Conductivity values are identified from 20% to 60%. REFERANCES [1] Islam, R. Md. And Pramila, A., Thermal Conductivity of Fiber reinforced Composites by the FEM, Journal of Composite Materials, vol. 33, 1999, pp. 1699-1715. [2] G. Sambasiva Rao1, T. Subramanyam2 and V. Balakrishna Murthy., 3D finite element models for the prediction of effective transverse thermal conductivity of Unidirectional fiber reinforced composite, International Journal of Applied Engineering Research, ISSN 0973-4562 Volume 3, Number 1 (2008), pp. 99 108. [3] Lu, T. and Hutchinson, J., Effect of matrix cracking on the overall thermal conductivity of Fiber reinforced composites, Philosophical Transactions of Royal Society (London) A, 351, 1995, pp. 595-610. [4] Springer, G. S. and T Sai S. W., Thermal Conductivities of Unidirectional Materials, Journal of Composite Materials, vol. 1, 1967, pp. 166. [5] Tsai, H., On the Thermal Model of Transverse Flow of Unidirectional Materials, 2002, NASA/TM-2002-211649. [6] Xiaomin, D., Mechanics of debonding and delamination in composites: asymptotic studies, Composites Engineering, vol. 5, 1995, pp. 1299-1315. [7] Yaun Lu-shih, 1995, The Effective Thermal Conductivities of Composites with 2D arrays of circular and square cylinders, Journal of Composite Materials, 29, pp. 483-505. [8] Kamala Priya B., Design and Analysis of Square Model Unit Cell for the prediction of Thermal Conductivity of Fibre Reinforced Composites, International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11,Number 10 (2016) pp 7166-7170. [9] Abdulrahman A. Alghamdi. The Influence of Shape and Spatial Distribution of Metal Particles on the Thermal Conductivity of Metal-Polymer Composites, International Journal of Mechanical Engineering and Technology, 6(12), 2015, pp. 30-35 [10] Vikas Mukhraiya, Raj Kumar Yadav and Sachendra Kori, Thermal Conductivity Analysis in Various Materials Using Composite Wall Apparatus. International Journal of Mechanical Engineering and Technology, 7(3), 2016, pp. 342 350. http://www.iaeme.com/ijmet/index.asp 655 editor@iaeme.com