MECHANICAL PROPERTIES OF FIBER REINFORCED COMPOSITES · PDF fileMECHANICAL PROPERTIES OF FIBER REINFORCED COMPOSITES USING FINITE ... of the fiber reinforced composites for different

80

Int. J. Mech. Eng. & Rob. Res. 2015 Sri chandana Buddi et al., 2015

MECHANICAL PROPERTIES OF FIBERREINFORCED COMPOSITES USING FINITE

ELEMENT METHOD

Sri chandana Buddi1*, P Phani Prasanthi1 and P Srikanth1

*Corresponding Author: Sri chandana Buddi,[email protected]

The micromechanical analysis plays a very important role in the composite materials. Thesestudies explore average mechanical properties of composites materials with good accuracy.The properties of any composite material depends on the constituents, loading, geometry, interphase region and environmental conditions. The proposed work focus on the evaluation ofproperties of the fiber reinforced composite material with different volume fraction under differentloading conditions. The 3D finite element model with governing boundary conditions has beendeveloped from the unit cell of square pattern of the composite to evaluate engineering constantslike, longitudinal modulus (E1), transverse modulus (E2), major poissons ratio (12) and minorPoisson’s ratio (21) of the fiber reinforced composites for different fiber volume fractionsconsidering uniform and random distribution of reinforcement. The predictions of the presentwork are validated with analytical expressions. The present work will be useful to predict theengineering constants of uniform and random distribution of fiber in FRP composites subjectedto longitudinal and transverse loading.

Keywords: Mechanical properties, Fiber, Composite materials, Finite element method, FRPcomposties

INTRODUCTIONEngineering materials are classified into threebroad categories; metals, ceramics andpolymers. Composites are combinations oftwo or more materials from one or more ofthese categories. One of the phase is usuallydiscontinuous, stiffer, and stronger and iscalled reinforcement, whereas the less stiff and

ISSN 2278 – 0149 www.ijmerr.comVol. 4, No. 1, January 2015

© 2015 IJMERR. All Rights Reserved

Int. J. Mech. Eng. & Rob. Res. 2015

1 Department of Mechanical Engineering, PVP Siddhartha Institute of Technology, Kanuru, Vijayawada, India.

weaker phase is continuous is called thematrix. The combination results in superiorproperties not exhibited by the individualmaterials. Mostly the properties of interest incomposites are the mechanical properties. Acomposite material is composed ofreinforcement (fibers, particles, flakes, and/orfillers) embedded in a matrix (polymers,

Research Paper

81


metals, or ceramics). The matrix holds thereinforcement to form the desired shape whilethe reinforcement improves the overallmechanical properties of the matrix. The keyparameters of interest in fiber reinforcedcomposites are specific strength and specificmodulus. Specific strength is defined as theratio of tensile strength to the specific gravity.Specific modulus is defined as the ratio ofmodulus of elasticity to the specific gravity. Thefiber reinforced composites can be a tailormade, as their properties can be controlledby the appropriate selection of the substrataparameters such as fiber orientation, volumefraction, fiber spacing, and layer sequence.The required directional properties can beachieved in the case of fiber reinforcedcomposites by properly selecting fiberorientation, fiber volume fraction, fiber spacing,and fiber distribution in the matrix and layersequence. As a result of this, the designer canhave a tailor-made material with the desiredproperties. Such a material design reducesthe weight and improves the performance ofthe composite. Shokrieh and GhaneiMohammadi (2010), Lei et al. (2012) andSyam Prasad et al. (2013) have developedpredictive models for the uni-directional shortfiber-reinforced composites and investigatethe distribution effect of the short fibers.Sreedhar Kari et al. (2007), have developedpredictive models for micromechanicalanalysis of fiber reinforced composites withvarious types of constituents. Harald Bergeret al. (2007), Srivastava et al. (2011), AnuragBajpai et al. (2012) and Marek Romanowicz(2013) have developed the material propertiesof spherical particle reinforced composites fordifferent volume fractions upto 60%. DraganKreculj (2008), stresses in the models from uni-

directional carbon/epoxy composite materialare studied using Finite Element Method(FEM), can be used in order to predict stressdistribution on the examined model.

In this paper the material properties arepredicted for the uniform distribution of fiberreinforced composites and randomdistribution of fiber reinforced composites. Theengineering constants E1, E2, 12, 21, 13, 23

are determined for both the cases and arecompared with the rule of mixtures andHalphin-Tsai criteria.

METHODOLOGYThe present research work deals with theevaluation of engineering properties by theelastic theory based on finite element analysisof representative volume elements of fiber-reinforced composites. The fibers arearranged in the square array which is knownas the uni-directional composite. And this uni-directional fiber composite is shown in Figure1. It is assumed that the fiber and matrixmaterials are linearly elastic. A unit cell is

Figure 1: Concept of Unit Cells

82


adopted for the analysis. The measure of thevolume of fiber relative to that total volume ofthe composite is taken from the cross-sectional areas of the fiber relative to the totalcross-sectional area of the unit cell. Thisfraction is considered as an importantparameter in composite materials and iscalled fiber volume fraction (Vf).

Due to symmetry in the geometry, materialand loading of unit cell with respect to 1-2-3coordinate system it is assumed that one fourthof the unit cell is sufficient to carry out thepresent analysis. The 3D Finite Element meshon one fourth portion of the unit cell is shown inFigure 4.

Figure 2: Isolated Unit Cells of SquarePacked Array

Finite Element ModelIn the study of the Micromechanics of fiberreinforced materials, it is convenient to use anorthogonal coordinate system that has one axisaligned with the fiber direction. The 1-2-3Coordinate system shown in Figure 3 is usedto study the behavior of unit cell. The 1 axis isaligned with the fiber direction, the 2 axis is inthe plane of the unit cell and perpendicular tothe fibers and the 3 axis is perpendicular to theplane of the unit cell and is also perpendicularto the fibers. The isolated unit cell behaves asa part of large array of unit cells by satisfyingthe conditions that the boundaries of the isolatedunit cell remain plane.

Figure 3: One Fourth Portion of Unit Cell

Figure 4: Finite Element Mesh Model

83


GeometryThe dimensions of the finite element model aretaken as:

X = 100 units,

Y = 100 units,

Z = 10 units.

The radius of fiber is calculated is varied tothe corresponding fiber volume.

Element TypeThe element SOLID95 of ANSYS V13.0 usedfor present analysis is based on a general 3Dstate of stress and is suited for modeling 3Dsolid structure under 3D loading. SOLID95 isa higher-order version of the 3D 8-node solidelement SOLID45. It can tolerate irregularshapes without as much loss of accuracy.SOLID95 elements have compatibledisplacement shapes and are well suited tomodel curved boundaries. SOLID95 hasplasticity, creep, stress stiffening, largedeflection, and large strain capabilities. Theelement has 20 nodes having one degree offreedom, i.e., temperature and with threedegrees of freedom at each node: translationin the node X, Y, Z directions respectively.

Boundary ConditionsDue to symmetry of the problem, the followingsymmetric boundary conditions are used:

• At X = 0, UX = 0

• At Y = 0, UY = 0

• At Z = 0, UZ = 0

In addition, the following multi pointconstraints 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

Analytical SolutionThe mechanical properties of the lamina arecalculated using the following expressions ofTheory of elasticity approach and Halphin-Tsai’s formulae. Young’s Modulus in the fiberdirection and transverse direction.

E1 = 1/1

E2 = 2/2

Major poison’s ratio 12 = –2/1

where

1 = stress in X-direction

2 = stress in Y-direction

1 = strain in X-direction

2 = strain in Y-direction

Rule of MixturesLongitudinal young’s modulus: E1 = EfVf + Em

Vm

Transverse young’s modulus: E2 = EfVf +EmVm

Major poison’s ratio: 12 = fVf + mVm

RESULTSIn the present work finite element analysis hasbeen carried out to predict the engineeringconstants of uniform and random distributionfibers in fibre reinforced particulate composite.The results obtained are validated with theresults obtained by Rule of Mixtures andHalpin-Tsai.

84


Uniform Distribution of Fiber(Boron) in an FRP Composite

The variation of different engineering constantsof a uniform distribution of boron fiber/Epoxycomposite with respect to the different volumefractions is shown.

The variation of longitudinal Young’smodulus (E1) with respect to volume fractionof fiber. The response of E1 of compositematerial is increasing in linear manner with thevariation of fiber content (Vf). This is due tothe improvement in stiffness of resultingcomposite material (Figure 5). The variation

Figure 5: Variation of E1 with Fiber Volume Fraction


85


of Transverse modulus (E2) following the sametrend as that of longitudinal modulus but in nonlinear way (Figure 6). The longitudinal poissonsratios (12 and 13) are yielded same responseand their magnitude is decreases as thestiffness of composite material increases (Vf)(Figure 7). The transverse poissons ratio 21

is decreased sharply upto 40% Vf later nosignificant change is observed (Figure 8). Thetransverse poissons ratio 23 showed differentresponse compared with other poissonsratios. It is low at lower volume fractions andmaintained steady response with theincrement of volume fraction (Figure 9).

Figure 7: Variation of 12 with Fiber Volume Fraction


86




Random Distribution of Boron Fiberin an FRP CompositeThe variation in different engineering constantsof a random distributed Boron fiber in epoxymatrix with respect to the different fiber volumefractions is shown below. The properties forrandomly distribution of reinforcement is

mentioned in terms of bounds. The minimumand maximum properties for randomlydistributed reinforcement are presented. Theeffect of randomly distributed boron fibers isnot observed in longitudinal Young’s modulus(E1), i.e., the maximum and minimumproperties are same for concerned random

87


distribution (Figure 11). The transverseYoung’s modulus is considerable changes aregained due to random distribution and thechanges are minimum at lower and highervolume fraction of fiber reinforcement andmaximum deviation is observed atintermediate volume fractions (Figure 12). The

same trend is observed for longitudinalpoissons ratio (12, 13) and Transversepoissons ratio (23) (Figures 13, 14 and 16).Difference scenario is obtained for Transversemodulus (21) at fiber dominated volumefractions the maximum and minimum are quitealike (Figure 15).



88


Figure 13: Variation of 12 With Fiber Volume Fraction



89



CONCLUSIONThe finite element method is very useful tool toextract the average properties of compositematerials. The influence of reinforcementdistribution in mechanical properties ofcomposite material is presented by adoptingfinite element method and micromechanicsapproach. Compared with uniform distribution,the random distribution of boron fiber issignificant in terms of mechanical propertiesparticularly in transverse properties.

REFERENCES1. Anurag Bajpai, Sandeep Agarwal and

Suruchi (2012), “Mechanical Properties ofEpoxy Resin Based Polymer Concrete”,International Journal of MechanicalEngineering & Technology (IJMET),Vol. 3, No. 1, pp. 267-276.

2. Chen Y J Liu (2004), “SquareRepresentative Volume Elements forEvaluating the Effective MaterialProperties of Carbon Nanotube-Based

Composites”, Computational MaterialsScience, Vol. 29, pp. 1-11.

3. Dragan D Kreculj (2008), “Stress Analysisin a Unidirectional Carbon/EpoxyComposite Material”, FME Transactions,Vol. 36, No. 3, pp. 127-132.

4. Harald Berger, Sreedhar Kari, UlrichGabbert, Reinaldo Rodriguez Ramos andJulian Bravo Castillero (2007), “Evaluationof Effective Material Properties ofRandomly Distributed Short CylinderFiber Composites Using A NumericalHomogenization Technique”, Vol. 2,No. 8, Mathematical Science Publishers.

5. Lei H F, Zhang Z Q and Liu B (2012),“Effect of Fiber Arrangement onMechanical Properties of Short FiberReinforced Composites”, CompositesScience and Technology, Vol. 72,pp. 506-514.

6. Marek Romanowicz (2013), “NumericalHomogenization of Fiber-Reinforced

90


Composite with Complex Micro StructuralFeatures”, Journal of Theoretical andApplied Mechanics, Vol. 51, No. 4,pp. 883-890.

7. Shokrieh M M and Ghanei MohammadiA R (2010), “Finite Element Modeling ofResidual Thermal Stresses in Fiber-Reinforced Composites Using DifferentRepresentative Volume Elements”,Proceedings of the World Congress onEngineering, Vol. II, June 30-July 2, WCE,London, UK.

8. Sreedhar Kari , Harald Berger,Reinaldo Rodriguez-Ramos and UlrichGabbert (2007), “Computat ionalEvaluat ion of Ef fect ive Mater ia l

Properties of Composites Reinforcedby Randomly Distributed SphericalParticles”, Composite Structures ,Vol. 77, pp. 223-231.

9. Srivastava V K, Gabbert U, Berger H andShraddha Singh (2011), “Analysis ofParticles Loaded Fiber Composites forthe Evaluation of Effective MaterialProperties with the Variation of Shapeand Size”, International Journal ofEngineering, Science and Technology,Vol. 3, No. 1, pp. 52-68.

10. Syam Prasad A, Syed Altaf Hussainand Pandurangadu V (2013),“Micromechanical Analysis of FrpComposites”, Vol. 4, No. 2, pp. 272-285.

Documents

MECHANICAL PROPERTIES OF FIBER REINFORCED COMPOSITES · PDF fileMECHANICAL PROPERTIES OF FIBER REINFORCED COMPOSITES USING FINITE ... of the fiber reinforced composites for different