Finite Element Micromechanical Modeling of FRP Composite with Orthotropic Fibers Subjected To Longitudinal Loading

Finite Element Micromechanical Modeling of FRP Composite with Orthotropic Fibers Subjected To Longitudinal Loading

Finite Element Micromechanical Modeling of FRP Composite with Orthotropic Fibers Subjected To Longitudinal Loading

M. Gowtha Muneswara Rao and P. Phani Prasanthi*

Mech. Engg. Dept., P. V. P. Siddhartha Institute of Technology, Vijayawada, A.P., India.

ABSTRACT

The present research work deals with the micromechanical analysis of fiber reinforced composites reinforced with orthotropic fibers under fiber directional tensile loading using three- dimensional finite element method. The problem is modeled in ANSYS software and the FE model is validated with bench mark results. Longitudinal Youngs modulus and corresponding Poissons ratios are predicted. The distribution of interfacial stresses around the circumference of the fiber is also determined for three different fiber-matrix combinations. The present work will be useful to find the static behavior of FRP lamina subjected to longitudinal load.

1 Introduction

Mechanics of materials deals with stresses, strains, and deformations in engineering structures subjected to mechanical and thermal loads. A common assumption in the mechanics of conventional materials, such as steel and aluminum, is that they are homogeneous and isotropic continua. For a homogeneous materials, properties do not depends on the location, and for an isotropic materials, properties do not depend on the orientation. Fiber-Reinforced composites, on the other hand, are microscopically inhomogeneous and nonisotropic. As a result, the mechanics of fiber reinforced composites are far more complex than that of conventional materials.

One of the approaches is used in the mechanics of fiber- Reinforced composites materials are Micromechanics approach, in which the interaction of the constituent materials is examined on a microscopic scale. Equations describing the elastic and thermal characteristics of a lamina are, in general, based on micromechanics formulations. An understanding of the interaction between various constituents is also useful in delineating the failure modes in fiber-reinforced composites materials. Good number of publications are available on this area. Zheng-Ming Huang [1] has implemented a micromechanical model to

simulate the overall thermal and mechanical properties of a fibrous composite out of an elastic deformation range. This micromechanics model is called the Bridging model. Application of the model to predict various properties of unidirectional lamina and multidimensional laminates, including thermoelastic behaviour, elasto-plastic response, and ultimate failure strength, strength at elevated temperature and fatigue strength and S-N curve is demonstrated. Anifantis [2] studied that, variations in topology, material properties and adhesion characteristics, the micro mechanical stress states developed within fibrous composites that contain a heterogeneous interface region has been predicted numerically. 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 Interferometry with Electron Microscopy). The global mechanical response of metal-matrix composite and transverse tension is related with the micro mechanical behavior 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. Hussain et.al [9] studied on unidirectional continuous fiber lamina at different fiber volume fractions using the finite element method. Salvatore et.al [10] studied the elastic moduli and structure of boron carbide/ aluminum (B4C/Al) multiphase composites using rigorous bounding and experimental characterization techniques. V. Nassehi, J. Dhillon & L. Mascia [11] adopted finite element analysis has been applied to study the mechanical behavior of composites with ductile thermoplastic and rubbery interlayer between fibers and matrix. N. Krishna Vihari[12] 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.

The aim of the current work is to predict elastic modulus three different fibers reinforced plastic laminas subjected to longitudinal loading and the interfacial stresses for a fixed volume fraction of 50%.

1. SQUARE ARRAY OF UNIT CELLS

   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 is called fiber volume fraction (Vf).

   . Fig.1 Concept of Unit Cells

   Fig.2 Isolated Unit Cell of Square packed array

2. PROBLEM STATEMNT

   The analysis deals with the evaluation of the stresses at the fiber-matrix interface for a fiber volume fraction of 50% with various material combinations using 3D finite element method.

3. 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.2 is used to study the behaviour 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.

   1,z

   3,y

   2,x

   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 as 79.788 units, so that the fber volume fraction becomes 0.5. (Fig. 3). Z denoted the fiber direction, x,y represents inplane and out of plane directions.

        Fig.3. Finite element mesh on one-eighth portion of the unit cell

   2. Element type

      The element used for the present analysis are SOLID 95 of ANSYS defined by

      20 nodes having one degree of freedom i.e. temperature and three degrees of freedom at each node: translation in the node x, y and z directions respectively.

   3. Materials

      The properties of the constituent materials used for the present analysis are given in (Table 1.)

   4. Loading

      A pressure load of -1 MPa is applied in the Z-direction.

      Table1. Properties of Constituent

   5. 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

        S . N O	Mate rial	E	E	V	v	G (Gpa)	G (Gpa)
        1	Carb on Fibe r(T3 00)	E1	230	12	0.2	G12	27
        		E2	15	13	0.2	G13	27
        		E3	15	23	0.07	G23	7
        2	Carb on Fibe r(IM 7)	E1	290	12	0.2	G12	14
        		E2	21	13	0.2	G13	14
        		E3	21	23	0.04	G23	8.75
        3	Kevl ar Fibe r	E1	131	12	0.33	G12	21
        		E2	7	13	0.33	G13	21
        		E3	7	23	0.04	G23	2.63
        4	Epo xy (Mat rix)	E	4.6 2		0.32	—	—-

      • 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

      E=Youngs Modulus V=Poissons Ratio

4. RESULTS

   Sufficient number of convergence tests is made and the present finite element model is validated by comparing the Youngs modulus that is computed from the results obtained to the values from rule of mixtures and found in close agreement. This comparision is shown in (Table 2).

   Materia ls	E	E from FEM GPa	E from Rule of Mixt ures GPa	% Err or	(FE M)
   T-300-	E1	118.0	117.	0.63	0.73
   Epoxy		637	310	8	7
   Carbon	E1			0.06	0.46
   (IM7)-		147.4	147.	73	3
   Epoxy		1	31
   Kevlar	E1	68.01	67.8	0.30	0.55
   -Epoxy		7	1	43	3

   Table 2 Youngs Modulus E (GPa) for 50% Vf

   The following stresses are computed at the fiber-matrix interface.

   epoxy and lm-7-epoxy lamina as shown in Fig.7.

   n

   • f = Normal stress in the fiber at the

     Variation of circumferential stress in the

     interface

     c

   • f = Circumferential stress in the matrix at the interface

     1

   • f = Directional stress in the fiber at the interface.

     nc

     f = Shear stress in the fiber at the interface.

     matrix is shown in Fig. 8, from which we can observe that the carbon lm7 had minimum stress values also that the carbon T300 and Kevlar materials had approximately equal stresses. Negative stresses developed from 0 to 630 positions and later positive directional stresses are observed.

     The variation in fiber directional stress

     c

   • m

     = Circumferential stress in the

     of matrix is shown in Fig. 9. All the three

     matrix at the interface

     1

   • m = Directional stress in the matrix at the interface

5. ANALYSIS OF RESULTS

   Fig. 4 shows the normal stress in fiber at the interface for three different reinforced composite materials. The normal stress is maximum at 00 and is minimum at 900 positions. Curve of the carbon lm7 reinforced composite material shows the minimum stress values because its longitudinal directional properties are superior then those of other two materials and same matrix is used in three combinations. The same stresses in T-300 reinforced and Kevlar reinforced composites are approximately equal from =450 to 900 positions of the fiber. From Fig. 5, we can

   materials have different stress values. Maximum fiber directional stresses are developed in Kevlar reinforced matrix followed by carbon T300, Carbon lm7.

   The circumferential stresses in matrix had given the tensile stress from630 to 900 positions whereas the same stresses in fiber had shown compression nature.

   The variation in stresses with angle is due to the geometrical arrangement of fiber and matrix in unit cell and the constraints imposed on boundaries.

   The variation of stresses with material is due to the variation of mismatch in fiber to matrix Youngs modulus.

   c

   observe that the values of f

   obtained for

   carbon (lm7) material are minimum and these stress is maximum at 900 position and minimum at 00. Similar type of response is observed in other two reinforced composites.

   The variation of fiber directional stress in fiber for all the three composites is nearly same and almost constant with angular position as shown in Fig. 6. The shear stresses are zero at the starting and ending positions of the fibers, maximum at the center of the fiber matric interface. This phenomenon is same for all the three reinforced composites and magnitude is ultimate for T300-epoxy followed by Kevlar-

   n

   Fig. 2 Variation of f

   with respect to

   nc

   Fig. 3 Variation of f

   1

   with respect to

   Fig.6 Variation of f

   with respect to

   c

   Fig. 4 Variation of f

   with respect to

   1

   Fig. 7 Variation of m

   with respect to

6. CONCLUSIONS

c

Fig. 5 Variation of m

with respect to

Micromechanical analysis of continuous fiber reinforced composite is performed using three-dimensional FEM. The following conclusions are drawn:

• The normal stress is maximum at 00 and minimum at 900 for all three materials.

• A reverse trend to normal stress isobserved in circumferential stress in fiber is maximum at 900 and minimum at 00 for all three materials.

• The fiber directional stresses are almost same at all locations of interface.

• The fiber directional stress in matrix is minimum for carbon (lm7) composite.

• The normal and shear stresses are same for both fiber and matrix at the fiber-matrix interface for all the three composites and hence only normal and shear stress of fiber are shown.

REFERENCES

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2. Anifantis, N.K., Micromechanical stress analysis of closely packed fibrous composites, Composites Science and Technology, Vol. 60, 2000, pp. 1241- 1248.

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, pages 2281-2295.

4. Wang, Q. and Chiang, F.P., Experimental characterization of interface mechanical properties of composites. Composites, part: B, vol. 27B, 1996, pages 123-128.

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6. Robertson, D. D. and mall, S., Fiber- Matrix Interphase Effects upon Transverse Behavior in metal-Matrix Composites, Journal of Composites Technology & Research, JCTRER, vol.14(1), spring 1992, pp. 3-11.

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.

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10. Salvatore Torquato, Christofer L. Y. Yeong, Mark D. Rintoul, David L. Milius and Ilhan A. Aksay, Elastic Properties and Structure of Interpenetrating Boron Carbide/Aluminum Multiphase Composites, Journal of the American Ceramic SocietyTorquato et al., Vol. 82(5), May 1999, pp. 126368.

11. Fiber Reinforced Composites by L.L. Faulkner and S.B. Menkes.

12. N. Krishna Vihari, P. Phani Prasanthi and Dr. V. Bala Krishna Murthy, Micromechanical Analysis of FRP Composites Subjected to Thermal Loading International Journal of Mechanics and Solids, Volume 6, Number 3 (2011), pp. 167-174.

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