The Effect of Fiber Shape and Spacing on Stress Distribution in a Composite Monolayer with an Internal Crack

Document Type : Research Article

Authors

Abstract

The effect of inter-fiber spacing and shape on stress distribution is studied in a composite monolayer. The lamina is subjected to an internal crack while loaded by a force P along the fibers at infinity. Two models are postulated. In the first, fibers have circular cross section while in the second, a triangular shape is considered. By direct application of modified shear – lag model, the differential equations of equilibrium are derived and solved for displacements and stress fields. The results show that the ordinary shear – lag model can not well predict the stress distribution within the lamina. The modified model shows a noticeable decrease in both types of stresses once fiber spacing and shape are changed. This reduction is more pronounced for triangular fibers where a decrease in  causes more reduction in maximum shear stresses and no change in fiber normal stresses. The reduction in peak shear stress appears to be 32 percent for volume fraction of one at q = 30o. 

Keywords

References

[1] Hedgepeth, J. M., "Stress concentration in a filamentary structure", NASA TN D-882, 1961.
[2] Rossetoss, J. N. and Shishesaz, M., "Stress concentration in fiber composite sheets including matrix extension", Journal of Applied Mechanics,Vol. 54, p. 723, 1987.
[3] Bond, I., Hucker, M., Wear, P., Bleay, S. and Haq, S, "Mechanical behavior of circular and triangular glass fibers and their composites", Composite Science and Technology, Vol. 62, p. 1051, 2002.
[4] Park, S. J., Seo, M. K. and Shim, H. B., "Effect of Fiber Shapes on Physical Characteristics of Non-Circular Carbon Fibers-Reinforced Composites",Material Science and Engineering, A352, p. 34,2003.
[5] Kim, T. J. and Park, C. K., "Flexural and Tensile Strength Developments of Various Shape Carbon Fiber-Reinforced Lightweight Cementitious Composites", Cement and Concrete Research, Vol.28 No. 7, p. 955, 1998.
[6] Anagnostopoulos G., Parthenios J., Andreopoulos A.G., Galiotis C., " An Experimental and Theoretical Study of the Stress Transfer Problem in Fibrous Composites", Acta Materialia, Vol. 53, pp.4173–4183, 2005.
[7] Heuvel van den, P.W.J. Peijs T., Young R.J., "Failure Phenomena in Two-Dimensional Multi-Fiber Microcomposites. Part 4: a Raman Spectroscopic Study on the Influence of the Matrix Yield Stress on Stress Concentrations", Journal of Composites: Part A, Vol. 31, pp. 165–171, 2000.
[8] Grubb David T., Li Zong-Fu, and S. Leigh Phoenix,"Measurement of Stress Concentration in a Fiber Adjacent to a Fiber Break in a Model Composite",Composite Science and Technology, Vol.53 , pp.237-249, 1995.
[9] Hedgepeth J. H., and Van Dyke P., "Local Stress Concentration in Imperfect Filamentary Composite Materials", Journal of Composite Materials, Vol. 1,P. 294, 1967.
[10] Zhou X.-F., Wagner H.D., "Stress Concentrations Caused by Fiber Failure in Two-Dimensional Composites", Composites Science and Technology,Vol. 59, pp. 1063-1071, 1999.
[11] Wagner H. D. and Eitan A., " Stress Concentration Factors in Two-Dimensional Composites: Effects of Material and Geometrical Parameters", Composite Science and Technology, Vol. 46, pp. 353-362,1993.
[12] Sirivedin S., Fenner D.N., Nath R.B., Galiot C.,"Effects of Inter-Fiber Spacing and Matrix Cracks on Stress Amplification Factors in Carbon-Fiber/Epoxy Matrix Composites. Part I: Planar Array of Fibers",Composites: Part A, Vol. 34, pp. 1227–1234, 2003.
[13] Sirivedin S., Fenner D.N., Nath R.B., Galiot C., " Effects of Inter-Fiber Spacing and Matrix Cracks on Stress Amplification Factors in Carbon-Fiber/Epoxy Matrix Composites. Part II: Hexagonal Array of Fibers", Composites: Part A, Vol. 37, pp. 1936–
1943, 2006.
[14] Shishesaz, M., "The Effect of Mechanical and Physical Properties of Polymers on Stress Amplification Factor in Composites with an Internal Damage.", Iranian Journal of Polymers, Vol. 14, No.5, Issue No. 59, May 2005.

Files

Share

How to cite

Statistics