Interfacial Strain Distribution of a Unidirectional Composite with Randomly Distributed Fibers under Transverse Loading

Abstract

The micromechanical approach was used to investigate the interfacial strain distributions of a unidirectional composite under transverse loading in which fibers were usually found to be randomly packed. Representative volume elements (RVEs) for the analysis were composed of both periodic fiber arrays, such as a square array and a hexagonal array, and a random fiber array. The finite element analysis was performed to analyze the normal, tangential, and shear strains at the interface. In order to verify the RVE for describing a random fiber array, the generated RVE was statistically compared with the one constructed from typical images of a transverse cross-section of a unidirectional composite. Since the strain distributions at the interface experienced periodic characteristics along with its circumference, the Fourier series approximation with proper coefficients was utilized to evaluate the strain distributions at the interface for the periodic and random fiber arrays with respect to fiber volume fractions. From the analysis, it was found that the random arrangement of fibers had a significant influence on the strain distribution at the interface, and the strain distribution in the periodic arrays was one of special cases of that in the random array.

Keywords

interfacial strains micromechanics representative volume element (RVE)random fiber array transverse loading statistical approach strain invariant failure theory (SIFT)

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References

Tucker III, C.L. and Erwin, L. (1999). Stiffness Predictions for Unidirectional Short-fiber Composites: Review and Evaluation , Composites Science and Technology, 59(5): 655–671 .

Bednarcyk, B.A. and Arnold, S.M. (2001). Micromechanics-based Deformation and Failure Prediction for Longitudinally Reinforced Titanium Composites , Composites Science and Technology, 61(5): 705–729 .

Kok, de J.M.M. and Meijer, H.E.H. (1999). Deformation, Yield and Fracture of Unidirectional Composites in Transverse Loading-I: Influence of Fiber Volume Fraction and Test-temperature , Composites: Part A-Applied Science and Manufacturing, 30(7): 905–916 .

Laird II, G. and Kennedy, T.C. (1995). Micromechanics of Composite Materials under Compressive Loading , Engineering Fracture Mechanics, 51(3): 417–430 .

Berryman, J.G. and Berge, P.A. (1996). Critique of Two Explicit Schemes for Estimating Elastic Properties of Multiphase Composites , Mechanics of Materials, 22(2): 149–164 .

Lamon, J. (2001). A Micromechanics-based Approach to the Mechanical Behavior of Brittlematrix Composites , Composites Science and Technology, 61(15): 2259–2272 .

Kwon, Y.W. and Berner, J.M. (1995). Micromechanics Model for Damage and Failure Analyses of Laminated Fibrous Composites , Engineering Fracture Mechanics, 52(2): 231–242 .

Brinson, L.C. and Lin, W.S. (1998). Comparison of Micromechanics Methods for Effective Properties of Multiphase Viscoelastic Composites , Composite Structures, 41(3/4): 353–367 .

Sun, C.T. and Vaidya, R.S. (1996). Prediction of Composite Properties from a Representative Volume Element , Composites Science and Technology, 56(2): 171–179 .

10.

Caiazzo, A.A. and Costanzo, F. (2000). On the Effective Elastic Properties of Composites with Evolving Microcracking , Journal of Reinforced Plastics and Composites, 19(2): 152–163 .

11.

Dong, M. and Schmauder, S. (1996). Modeling of Metal Matrix Composites by a Self-consistent Embedded Cell Model , Acta Materialia, 44(6): 2465–2478 .

12.

Sun, H. , Di, S. , Zhang, N. and Wu, C. (2001). Micromechanics of Composite Materials using Multivariable Finite Element Method and Homogenization Theory , International Journal of Solids and Structures, 38(17): 3007–3020 .

13.

Gosse, J.H. and Christensen, S. (2001). Strain Invariant Failure Criteria for Polymers in Composite Materials, AIAA-2001-1184.

14.

Gosse, J.H. (2002). An Overview of the Strain Invariant Failure Theory (SIFT) , In: Proceeding 10th US-Japan Conference on Composite Materials, pp. 989–997 , Stanford, USA, 16–18 September.

15.

Li, R. , Kelly, D. and Ness, R. (2003). Application of a First Invariant Strain Criterion for Matrix Failure in Composite Materials , Journal of Composite Materials, 37(22): 1977–2000 .

16.

Li, R. , Kelly, D. and Croksy, A. (2002). An Evaluation of Failure Criteria for Matrix Induced Failure in Composite Materials , Composite Structures, 57(1/4): 385–391 .

17.

Gosse, J.H. , Christensen, S. , Wollschlager, J.A. and Llanos, A.S. (2005). A Strain Invariant Failure Theory (SIFT) for Composite Materials , Journal of Composite Materials (to be published).

18.

Yang, S. , Tewari, A. and Gokhale, M.A. (1997). Modeling of Non-uniform Spatial Arrangement of Fibers in a Ceramic Matrix Composite , Acta Materialia, 45(7): 3059–3069 .

19.

Bulsara, V.N. , Talreja, R. and Qu, J. (1999). Damage Initiation under Transverse Loading of Unidirectional Composites with Arbitrary Distributed Fibers , Composites Science and Technology, 59(5): 673–682 .

20.

Ha, S.K. (2002). Micromechanics in the Analysis of Composite Structures , 6th Composites Durability Workshop (CDW-6), Tokyo, Japan, 14–15 November.