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Micromechanical analysis of frp composites 2
1.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 272 MICROMECHANICAL ANALYSIS OF FRP COMPOSITES Syam Prasad.A1 , Syed Altaf Hussain2 , Pandurangadu.V3 1 (Department of Mechanical Engineering, Regency Institute of Technology, Yanam-533464, India) 2 (School of Mechanical Engineering, RGM College of Engineering & Technology, Nandyal- 518501, India) 3 (Department of Mechanical Engineering, JNTU College of Engineering, Anantapur, Anantapur-512002, India) ABSTRACT Fiber reinforced composite materials are now an important class of an engineering materials. They offer outstanding mechanical properties, unique flexibility in design capabilities, and ease of fabrication. Additional advantages include light weight and corrosion resistance, impact resistance, and excellent fatigue strength. Today fiber composites are routinely used in such diverse applications as automobiles, aircraft, space vehicles, offshore structures, containers and piping, sporting goods, electronics, and appliances. In the present work, micromechanical behavior of a square unit cell of uni-directional fiber reinforced composite with orthotropic fibers (viz., Hexply Im7-8552, Kelvar and Carbon T300) embedded in epoxy resin has been analyzed under tensile loading using Finite element analysis software package Ansys 13.0. The 3-D Finite Element Model with governing boundary conditions has been developed from the unit cell of square pattern of the composite to evaluate the engineering constants like, Longitudinal modulus (E1), Transverse modulus (E2), In-plane shear modulus (G12) and Major Poisson’s ratio (ν12) of the above FRP composites for various fiber volume fractions. Also, interfacial stresses induced at the fiber- matrix interfaces due to longitudinal loading for various fiber volume fractions has been estimated. Finally the results obtained from finite element analysis (Numerical method) are validated with benchmark results. The present work will be useful to predict the engineering constants of uni-directional fiber reinforced composite materials subjected to longitudinal loading. INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 2, March - April (2013), pp. 272-285 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET © I A E M E
2.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 273 Keywords: Epoxy, Finite Element Analysis, FRP, Interface, Lamina, Micromechanics. 1. INTRODUCTION A Composite is a material system consisting of two or more phases on a macroscopic scale, whose mechanical performance and properties are designed to be superior to those of constituent materials acting independently. One of the phase is discontinuous, stiffer, and stronger and is called reinforcement. Where the less stiff and weaker phase is continuous and is called matrix. The low density, high strength, high stiffness to weight ratio, excellent durability and design flexibility of fiber-reinforced composite materials are the primary reasons for their extended use. The fiber reinforced composites can be a tailor made, as their properties can be controlled by the appropriate selection of the substrata parameters such as fiber orientation, volume fraction, fiber spacing, and layer sequence. The required directional properties can be achieved in the case of fiber reinforced composites by properly selecting fiber orientation, fiber volume fraction, fiber spacing, and fiber distribution in the matrix and layer sequence. As a result of this, the designer can have a tailor-made material with the desired properties. Such a material design reduces the weight and improves the performance of the composite. For example, the carbon-carbon composites are strong in the direction of the fiber reinforcement but weak in the other direction. Chen and Chang [1], Hussain S.A. et.al [2], have developed predictive models for micromechanical analysis of fiber reinforced composites with various types of constituents. Tandon [3] has evaluated the interfacial normal strength in unidirectional SCS-0/ epoxy composites by using single fiber specimens. These model specimens are incrementally loaded in tension to failure with a specifically built loading device mounted on the straining stage of the microscope. Qing Wang et al [4] has presented in situ strain measurement is performed at a submicron scale using a newly developed micromechanics technique SIEM (Speckle Interferometer with Electron Microscopy). The global mechanical response of metal-matrix composite and transverse tension is related with the micro mechanical behaviour of the interface. Nimmer [5] investigated that, analytical models are presented and are used to explore the mechanics of transversely loaded, high temperature composites with a thermally induced residual stress field and a vanishingly weak fiber-matrix interface strength. Robertson et al [6] has presented the formulation of a new 3-dimensional micromechanical model for fiber reinforced material. It is based on the relaxation of the coupling effect between the normal and shear stress. Asp, L.E, Berglund, L.A., [7] developed failure initiation in polymer-matrix composites loaded transverse to the fibers is investigated by a numerical parametric study where the effects of constituent properties, interphase properties and thickness are examined. Dragan, [8] stresses in the models from unidirectional carbon/epoxy composite material are studied using Finite Element Method (FEM), can be used in order to predict stress distribution on the examinated model. N. Krishna Vihari [9] adopted micromechanical approach to predict the stresses at the fiber-matrix interface of Boron/S-G/E-G fiber and Epoxy matrix composites due to temperature gradient across the lamina. In this paper the finite element method has been adopted for predicting various engineering constants uni-directional fiber reinforced composites and the results of Ex, Ey, υ12 and G12 are compared with the rule of mixtures and Halphin-Tsai criteria. Also, interfacial stresses induced at the interface of fiber and resign for various volume fractions have been estimated.
3.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March 2. METHODOLOGY The present research work deals with the evaluation of engineering properties by the elasticity theory based finite element anal reinforced composites. The fibers are arranged in the square array which is known as the unidirectional fiber composite. And this unidirectional fiber composite is shown in Fig. 1. It is assumed that the fiber and matrix materials are linearly elastic. A unit cell is adopted for the analysis. The measure of the volume of fiber relative to the total volume of the composite is taken from the cross sectional areas of the fiber relative to the total cross sectional area of the unit cell. This fraction is considered as an important pa is called fiber volume fraction (V Fig.2: 2.1 Numerical solution Finite element method is an approximate numerical method which has been successfully used for solutions of problems in various fields, including solid mechanics, fluid mechanics and heat transfer. In the present work, the computational numerical analysis i done using ANSYS version 13.0 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 274 present research work deals with the evaluation of engineering properties by the elasticity theory based finite element analysis of representative volume elements of fiber The fibers are arranged in the square array which is known as the unidirectional fiber composite. And this unidirectional fiber composite is shown in Fig. 1. It is assumed that the fiber and matrix materials are linearly elastic. A unit cell is adopted for the analysis. The measure of the volume of fiber relative to the total volume of the composite is taken from the cross sectional areas of the fiber relative to the total cross sectional area of the unit cell. This fraction is considered as an important parameter in composite materials and Vf). Fig.2 shows an isolated unit cell. Fig.1: Concept of Unit Cells Isolated Unit Cells of Square packed array Finite element method is an approximate numerical method which has been successfully used for solutions of problems in various fields, including solid mechanics, fluid mechanics and heat transfer. In the present work, the computational numerical analysis i 13.0 running on an Intel i3 processor system. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – April (2013) © IAEME present research work deals with the evaluation of engineering properties by the ysis of representative volume elements of fiber- The fibers are arranged in the square array which is known as the unidirectional fiber composite. And this unidirectional fiber composite is shown in Fig. 1. It is assumed that the fiber and matrix materials are linearly elastic. A unit cell is adopted for the analysis. The measure of the volume of fiber relative to the total volume of the composite is taken from the cross sectional areas of the fiber relative to the total cross sectional area of rameter in composite materials and Finite element method is an approximate numerical method which has been successfully used for solutions of problems in various fields, including solid mechanics, fluid mechanics and heat transfer. In the present work, the computational numerical analysis is
4.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 275 Assumptions made for the present analysis were Fibers are uniformly distributed in the matrix; Fibers are perfectly aligned; There is perfect bonding between fibers and matrix; The composite lamina is free of voids and other irregularities; and The load is within the linear elastic limit. 2.2 Finite Element Model In the study of the Micromechanics of fiber reinforced materials, it is convenient to use an orthogonal coordinate system that has one axis aligned with the fiber direction. The 1- 2-3 Coordinate system shown in Fig.3 is used to study the behavior of unit cell. The 1 axis is aligned with the fiber direction, the 2 axis is in the plane of the unit cell and perpendicular to the fibers and the 3 axis is perpendicular to the plane of the unit cell and is also perpendicular to the fibers. The isolated unit cell behaves as a part of large array of unit cells by satisfying the conditions that the boundaries of the isolated unit cell remain plane. Due to symmetry in the geometry, material and loading of unit cell with respect to 1- 2-3 coordinate system it is assumed that one fourth of the unit cell is sufficient to carry out the present analysis. The 3D Finite Element mesh on one fourth portion of the unit cell is shown in Fig.4. Fig.3: One-fourth portion of unit cell Fig.4: Finite Element mesh 2.2.1 Geometry The dimensions of the finite element model are taken as X=100 units, Y=100 units, Z=10units. The radius of fiber is calculated is varied to the corresponding fiber volume. Vf = ୡ୰୭ୱୱ ୱୣୡ୲୧୭୬ ୟ୰ୣୟ ୭ ϐ୧ୠୣ୰ ୡ୰୭ୱୱ ୱୣୡ୲୧୭୬ ୟ୰ୣୟ ୭ ୳୬୧୲ ୡୣ୪୪ Vf = π ర ୰మ ୟమ (1) r radius of fibre a edge length of square unit cell Vf volume fraction of fibre
5.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 276 2.2.2 Element type The element SOLID186 of ANSYS V13.0 used for the present analysis is based on a general 3D state of stress and is suited for modeling 3D solid structure under 3D loading. The element has 20 nodes having one degree of freedom i.e. temperature and with three degrees of freedom at each node: translation in the node x, y and z directions respectively. 2.2.3 Boundary conditions Due to the symmetry of the problem, the following symmetric boundary conditions are used At x = 0, Ux = 0 At y = 0, Uy = 0 At z = 0, Uz = 0 In addition, the following multi point constraints are used. The Ux of all the nodes on the Area at x =100 is same The Uy of all the nodes on the Area at y =100 is same The Uz of all the nodes on the Area at z = 10 is same 2.3 Analytical solution The mechanical properties of the lamina are calculated using the following expressions of Theory of elasticity approach and Halphin - Tsai’s formulae. Young’s Modulus in the fiber direction and transverse direction E1 = σ1 /ε1 (2) E2 = σ2 /ε2 (3) Major Poison’s ratio ν12 = - ε2 /ε1 (4) where σ1 = Stress in x-direction ε1 = Strain in x-direction σ2 = Stress in y-direction ε2 = Strain in y-direction 2.3.1 Rule of mixtures Longitudinal young’s Modulus: E1 = Ef Vf +Em Vm (5) Transverse young’s Modulus: E2 = Ef Vf +Em Vm (6) Major Poisson’s Ratio: ν12 = νf Vf + νm Vm (7) In-Plane Shear Modulus: G12 = Gf Vf + Gm Vm (8) 2.3.2 Semi-empirical model (Halphin- Tsai’s) The values obtained for transverse young’s modulus and in-plane shear modulus through equations (6) and (8) do not agree with the experimental results. This establishes the need for better Modeling techniques, which include finite element method, finite difference method and boundary element methods. Unfortunately, these models are available for complicated equations. Due to this, semi-empirical models have been developed for the design purposes. The most useful of these semi-empirical models includes those of Halphin
6.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 277 and Tsai, since they can be used over a wide range of elastic properties and fiber volume fractions. Halphin and Tsai developed their models as simple equations by curve fitting to results that are based on elasticity. The equations are semi-empirical in nature since involved parameters in the curve fitting carry physical meaning. Longitudinal Young’s Modulus (E1) The Halphin-Tsai equation for the longitudinal Young’s modulus is the same as that obtained through the strength of materials approach, that is, E1 = Ef Vf + Em Vm (9) Transverse Young’s Modulus (E1) The transverse Young’s modulus, E2 , is given by E2 /Em = (1+ξηVf )/ (1-ηVf ) (10) where η = ((Ef /Em )-1)/ ((Ef /Em ) +ξ) (11) The term “ξ”is called the reinforcing factor and depends on the following; Fiber geometry Packing geometry Loading conditions Major Poisson’s Ratio (ν12 ) The Halphin and Tsai equation for the Major Poisson’s ratio is the same as that obtained using the strength of materials approach, that is, ν12 =νf Vf +νm Vm (12) In-Plane Shear Modulus (G12) The Halphin and Tsai equation for the in-plane shear Modulus G12 is G12 /Gm =(1+ξηVf )/(1-ηVf ) (13) where η = ((Gf /Gm )-1)/((Gf /Gm ) + ξ (14) The value of reinforcing factor ξ depends on fibre geometry, packing geometry and loading conditions. 2.3.3 Materials Three different types of fiber reinforced composite materials considered in this investigation, they are Carbon T300/ Epoxy composite Hexply 8555 IM7/ Epoxy composite Kevlar/Epoxy composite The typical properties of the three different composite materials are illustrated in table 1.
7.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 278 Table- 1: Typical properties of Fibers and Epoxy Property Symbo l Units Carbon T300 Hexply 8555 IM7 Kelvar Epoxy Axial Modulus E1 Gpa 230 161 131 4.62 Transverse Modulus E2 Gpa 15 11.4 7 4.62 Axial Poisson’s Ratio ν12 - 0.2 0.32 0.33 0.32 Transverse Poisson’s Ratio ν13 - 0.2 0.32 0.33 0.32 Axial Shear Modulus G12 Gpa 27 5.17 21 1.308 Transverse Shear Modulus G13 Gpa 27 5.17 21 1.308 3. RESULTS In the present work finite element analysis has been carried out to predict the engineering constants of three different types of uni-directional fiber reinforced composite materials viz., Hexply Im7-8552, Kelvar and Carbon T300 embedded in epoxy resin. The results obtained are validated with the results obtained by rule of mixtures and Halpin-Tsai. In addition to that the interfacial stresses which are induced at the interface of fiber and matrix for various fiber volume fractions are also determined. σf n = Normal stress intensity in the fiber at the fiber matrix interface. τf n = Shear stress intensity in the fiber at the fiber matrix interface. 3.1 Finite Element Analysis of Carbon T300/Epoxy Composite The variation of different engineering constants of a uni-directional Carbon T300/Epoxy composite with respect to the different fiber volume fractions are shown from Fig.5~8 and the variation of normal stresses and also interfacial shear stresses with respect to the fiber volume fraction are shown in Fig. 9~10. Fig.5: Variation of E1with fiber volume fraction. 0 50 100 150 200 20 30 40 50 60 70 LongitudinalModulus,E1 (GPa) % Fiber volume fraction Longitudinal Modulus, E1 (GPa) Halpin-Tsai FEM Rule of Mixtures
8.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 279 Fig.6: Variation of E2with fiber volume fraction. Fig.7: Variation of G12with fiber volume fraction. Fig.8: Variation of ν12with fiber volume fraction. Fig.9: Variation of Interfacial Normal Stress with fiber volume fraction. 0 20 40 60 20 30 40 50 60 70 Transverse Modulus,E2(GPa) % Fiber volume fraction Transverse Modulus, E2 (GPa) Halpin-Tsai FEM Rule of Mixtures 0 10 20 30 20 30 40 50 60 70 ShearModulus,G12 (GPa) % Fiber volume fraction Shear Modulus, G12 (GPa) Halpin-Tsai Rule of Mixtures FEM 0 0.5 1 1.5 20 30 40 50 60 70 MajorPoisson's Ratio,ν12 % Fiber volume fraction Major Poisson's Ratio, ν12 Halpin-Tsai FEM Rule of Mixtures 0 0.1 0.2 0.3 20 30 40 50 60 70 InterfacialNormalStress (GPa) % Fiber volume fraction Interfacial Normal Stress (GPa) Normal stress
9.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 280 Fig.10: Variation of Interfacial Shear Stress with fiber volume fraction 3.2 Finite Element Analysis of Hexply 8555 IM7/Epoxy Composite The variation of different engineering constants of a uni-directional Hexply 8555 IM7/Epoxy composite with respect to the different fiber volume fractions are shown from Fig.11~14 and the variation of normal stresses and also interfacial shear stresses with respect to the fiber volume fraction are shown in Fig.15~16. Fig.11: Variation of E1with fiber volume fraction Fig.12: Variation of E2with fiber volume fraction 0 0.05 0.1 0.15 20 30 40 50 60 70 InterfacialShearStress (GPa) % Fiber volume fraction Interfacial Shear Stress (GPa) Shear Stress 0 10 20 30 40 20 30 40 50 60 70 TransverseModulus,E2 (GPa) % Fiber volume fraction Transverse Modulus, E2 (GPa) Halpin-Tsai FEM Rule of Mixtures 0 50 100 150 20 30 40 50 60 70 LongitudinalModulus,E1 (GPa) % Fiber volume fraction Longitudinal Modulus, E1 (GPa) Halpin-Tsai FEM Rule of Mixtures
10.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 281 Fig.13: Variation of G12with fiber volume fraction Fig.14: Variation of ν12with fiber volume fraction. Fig.15: Variation of Interfacial Normal Stress with fiber volume fraction. Fig.16: Variation of Interfacial Shear Stress with fiber volume fraction. 0 5 10 20 30 40 50 60 70ShearModulus,G12 (GPa) % Fiber volume fraction Shear Modulus, G12 (GPa) Halpin-Tsai FEM Rule of Mixtures 0 0.5 1 1.5 20 30 40 50 60 70 MajorPoisson's Ratio,ν12 % Fiber volume fraction Major Poisson's Ratio, ν12 Halpin-Tsai FEM Rule of Mixtures 0 0.05 0.1 0.15 0.2 0.25 20 30 40 50 60 70 InterfacialNormalStress (GPa) % Fiber volume fraction Interfacial Normal Stress (GPa) Normal Stress 0 0.05 0.1 0.15 20 30 40 50 60 70 InterfacialShearStress (GPa) % Fiber volume fraction Interfacial Shear Stress (GPa) Shear Stress
11.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 282 3.3 Finite Element Analysis of Kevlar/Epoxy Composite The variation of different engineering constants of a uni-directional Kevlar/Epoxy composite with respect to the different fiber volume fractions are shown from Fig.17~20 and the variation of normal stresses and also interfacial shear stresses with respect to the fiber volume fraction are shown in Fig.21~22. Fig.17: Variation of E1with fiber volume fraction. Fig.18: Variation of E2with fiber volume fraction. Fig.19: Variation of G12with fiber volume fraction. 0 50 100 150 20 30 40 50 60 70 LongitudinalModulus,E1 (GPa) % Fiber volume fraction Longitudinal Modulus, E1 (GPa) Halpin-Tsai FEM Rule of Mixtures 0 10 20 30 20 30 40 50 60 70 TransverseModulus,E2 (GPa) % Fiber volume fraction Transverse Modulus, E2 (GPa) Halpin-Tsai FEM Rule of Mixtures 0 5 10 15 20 20 30 40 50 60 70 ShearModulus,G12(GPa) % Fiber volume fraction Shear Modulus, G12 (GPa) Halpin-Tsai FEM Rule of Mixtures
12.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 283 Fig.20: Variation of ν12with fiber volume fraction. Fig.21: Variation of Interfacial normal stress with fiber volume fraction. Fig.22: Variation of Interfacial Shear stress with fiber volume fraction. 3.3.1 ANALYSIS OF RESULTS Figures 5-22 show the variation of various properties with the fiber volume fraction. The observations are made from the plot are: 1. The longitudinal young’s modulus and E1 increases linearly with increase in fiber volume fraction up to 60 % thereafter it increases rapidly for all the three types of composites materials; 2. The transverse young’s modulus E2 increases linearly with increase in fiber volume fraction for all the three types of composites materials; 0 0.5 1 1.5 20 30 40 50 60 70MajorPoisson'sRatio,ν12 % Fiber volume fraction Major Poisson's Ratio, ν12 Halpin-Tsai FEM Rule of Mixtures 0 0.1 0.2 0.3 0.4 20 30 40 50 60 70 InterfacialNormalStress (GPa) % Fiber volume fraction Interfacial Normal Stress (GPa) Normal Stress 0 0.05 0.1 0.15 20 30 40 50 60 70 InterfacialShearStress (GPa) % Fiber volume fraction Interfacial Shear Stress (GPa) Shear Stress
13.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 284 3. In plane Shear modulus G12 increases linearly with increase in fiber volume fraction for all the three types of composites materials; 4. Interfacial normal stress intensities are almost same with increase in fiber volume fraction up to 50% thereafter it increases rapidly for all the three types of composites materials; 5. Interfacial shear stress intensities decreases with increase in fiber volume fraction for all the three types of composites materials; 4. CONCLUSION In this paper micromechanical analysis of three different types of composite (Viz., Carbon 300T/Epoxy, Hexply 8555 IM7/Epoxy and Kevlar/ Epoxy) materials has been carried out using FEA software, ANSYS 13 to evaluate several elastic constants. The results of elastic moduli E1, E2, G12 and ν12 are compared with the results obtained by using the Rule of Mixture and Semi-empirical Model (Halpin-Tsai’s). It is seen that the results from the Finite Element simulation are little bit deviating with the analytical results. Interfacial normal stress and Interfacial shear stress intensities are also evaluated which are otherwise difficult to evaluate by using conventional methods. Also several properties for which simple and accurate analytical methods are not available are evaluated. Hence finite element method is a viable alternative to perform better analysis of fiber reinforced composite materials. 5. ACKNOWLEDGMENT It is my privilege to express my profound gratitude and thanks to my guide Dr. S. ALTAF HUSSAIN, M.Tech, Ph.D., Professor in Mechanical Engineering, R.G.M College of Engineering and Technology, for his valuable guidance and encouragement. REFERENCES Journal Papers [1] Chen C H & Cheng S, Trans ASME J Appl Mech, 37 (1970) 186-189 [2] Syed Altaf Hussain, B.Sidda Reddy.B and Nageswar Reddy.V, “prediction of elastic properties of FRM composite lamina for Longitudinal loading” Asian Research Publishing Network (ARPN), vol. 3(6), 2008, pp. 70-75. [3] Tandon, G.P., “Evaluation of interfacial normal strength in a SCS-0/Epoxy composite with cruciform specimens.” Composites Science and Technology, vol. 60, 2000, pp. 2281-2295. [4] Wang, Q. and Chiang, F.P., “Experimental characterization of interface mechanical properties of composites.” Composites, part: B, vol. 27B, 1996, pp. 123-128. [5] Nimmer, R.P., “Fiber-Matrix interface stresses in the presence of thermally induced residual stresses”, Journal of Composites Technology and Research, JCTRER, Vol. 12(2), summer 1990, pp. 65-75. [6] Robertson, D. D. and mall, S., “Fiber-Matrix Inter phase Effects upon Transverse Behavior in metal-Matrix Composites”, Journal of Composites Technology & Research, JCTRER, vol.14 (1), spring 1992, pp. 3-11.
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International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME 285 [7] Asp, L.E, Berglund. L.A., “Effects of fiber and interface on matrix-initiated transverse failure in polymer composites.” Composites Science and Technology, vol. 56, 1996, pages 657-665. [8] Dragan D. Kreculj, “Stress Analysis in a Unidirectional Carbon/Epoxy Composite Material”, FME Transactions, vol. 36(3), 2008, pp. 127-132. [9] Krishna Vihari.N, Phani Prasanthi.P and Bala Krishna Murthy .V “Micromechanical Analysis of FRP Composites Subjected to Thermal Loading” International Journal of Mechanics and Solids, vol. 6, (3) 2011, pp. 167-174. [10] Siddhant Datta, B.M. Nagabhushana and R. Harikrishna, “A New Nano-Ceria Reinforced Epoxy Polymer Composite With Improved Mechanical Properties” International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 248 - 256, ISSN Print: 0976-6480, ISSN Online: 0976- 6499. [11] Hargude N.V and Ghatage k.D, “An Overview of Genetic Algorithm Based Optimum Design of an Automotive Composite (E-Glass / Epoxy and Hm-Carbon/Epoxy) Drive Shaft”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 1, 2012, pp. 110 - 119, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. [12] Anurag bajpai, Sandeep Agarwal and Suruchi, “Mechanical Properties of Epoxy Resin Based Polymer Concrete”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 1, 2012, pp. 267 - 276, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. Books [13] M W Hyer. 1998. Stress Analysis of Composite Materials. WCB McGraw-Hill. [14] R M Jones. 1975. Mechanics of Composite Materials. Scripta Book Company. [15] Autar K.Kaw.2006. Mechanics of Composite Materials. CRC Press. [16] Issac M Danial. 1994 Engineering Mechanics of Composites. Oxford University Press. [17] ANSYS Reference Manuals, 2012.
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