On the Effects of Fiber Length and Spatial Distribution on the Stiffness of Short-Fiber Reinforced Composites

Abstract

We report on the results of a computational investigation of the effect of fiber aspect ratio (a_r) on the stiffness of composite rods reinforced with rigid spheroidal inclusions. The reinforcing spheroids are randomly placed within the containing rod and are also perfectly aligned with the tensile axis. Attention is focused in the interesting region of low (a_r), where the stiffness of the composite rod is known to be most sensitive on (a_r). Use of low aspect ratio fibers makes the results of this analysis suitable for a class of processed materials, such as whisker-reinforced metal-matrix composites and extruded or molded short-fiber-reinforced polymers. We consider steady-state three-dimensional deformations of composite rods containing up to 50 individual, randomly placed aligned spheroids. The equations of elasticity for the entire multi-fiber assembly are solved using the Boundary Element Method (BEM), implemented on a four-processor server and the force needed to impose a certain tensile deformation on the composite is computed. From this, an effective tensile modulus is obtained. Statistical averages of the computed effective moduli are compared to the predictions of the Mori-Tanaka model for the stiffness of short fiber composites. We find a good agreement at low values of (a_r). Additionally, we investigate the effect on stiffness of random perturbations in fiber length around a mean value.

References

Hashin

, “Analysis of Composite Materials”, J. of Applied Mechanics, 50(1983), 481–505.

Brooks

, “Materials property modeling and design of short fibre composites”, in “Flow-induced alignment in composite materials”, edited by T.D. Papathanasiou and D. D. Guell, Woodhead Publishing Limited (1997), 293–321.

Tucker

C.L.

and Liang

, “Stiffness predictions for unidirectional short-fiber composites: Review and evaluation”, Composite Science and Technology, 59(1999), 655–671.

Eduljee

R.F.

, Mccullough

R.L.

and Gillespie

J.W.

, “The influence of aggregated and dispersed textures on the elastic properties of discontinuous-fiber composites”, Compos. Sci. Tech., 50/3(1994), 381–391.

Chou

T.W.

, Nomura

and Taya

“A self-consistent approach to the elastic stiffness of short-fibre composites”, J. Comp. Mater., 14(1980), 178.

Laws

and Mclaughlin

, “The Effect of Fibre Length on the Overall Moduli of Composite Materials”, J. Mech. Phys. Solids, 27(1979), 1–13.

Pettermann

H.E.

, Bohm

H.E.

and Rammerstorfer , “Some direction-dependent properties of matrix-inclusion type composite with given reinforcement orientation distributions”, Composites Part B 28B(1997), 253–265.

Choy

C. L.

, Leung

W. P.

and Kowk

K. W.

, “Elastic moduli and thermal conductivity of injection-molded short-fiber-reinforced thermoplastics”, Polymer Composites, 13/2(1992), 69–80.

Hine

P. J.

, Wire

, Duckett

R. A.

and Ward

I. M.

, “Hydrostatically extruded glass fiber reinforced polyoxymethylene. 2. Modeling the elastic properties”, Polymer Composites, 18/5 (1997), 634–641.

10.

Withers

P. J.

, “The Determination of the Elastic Field of an Ellipsoidal Inclusion in a Transversely Isotropic Medium, and its relevance to composite materials”, Philosophical Magazine A, 59(1989), 759–781.

11.

Warner

T. J.

and Stobbs

W. M.

, “Modulus and yield stress anisotropy of short fiber metal matrix composites”, Acta Metal., 37(1989), 2873–2881.

12.

Bettess

, “Operation counts for boundary integral and finite element methods”, Int. J. Numer. Meth. Eng., 17(1981), 306–308.

13.

Mukherjee

and Morjaria

, “On the efficiency and accuracy of the boundary element method and the finite element method”, Int. J. Numer. Meth. Eng., 20(1984), 515–522.

14.

Mammoli

A.A.

and Bush

M.B.

, “A boundary element analysis of metal-matrix composite materials”, Int. J. Numer. Meth. Eng., 36/14(1993), 2415–2433.

15.

Ingber

M. S.

, Papathanasiou

T.D.

, “A Parallel-Supercomputing Investigation of the Stiffness of Aligned, Short-Fiber-Reinforced Composites using the Boundary Element Method”, Int. J. Numer. Meth. Eng., 40(1997), 3477–3491.