Can the Strength of Brittle Materials be Enhanced?
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CAN THE STRENGTH OF BRITTLE MATERIALS BE ENHANCED? L. MONETTE, M. P. ANDERSON AND G. S. GREST Corporate Research Science Laboratory, Exxon Research and Engineering Company, Annandale, NJ 08801 ABSTRACT We have employed a two-dimensional computer model to study the effect of volume fraction of second phase constituents on load transfer (stiffness) and strength in brittle short-fiber composites, i.e. composites containing a random distribution of aligned fibers, and brittle particulate composites. We find that the efficiency of load transfer to the second phase consituent increases with volume fraction in particulate composites, while it decreases for short-fiber composites. The strength of brittle particulate composites is found to decrease, while the strength of brittle short-fiber composites marginally increases only at fiber volume fractions equal or greater than 0.25. INTRODUCTION Short-fiber composites are becoming increasingly attractive as engineering materials, not only for their light weight or potential corrosion resistance, but particularly for their low manufacturing cost. Contrary to continuous fiber composites, the understanding and prediction of elastic properties of short-fiber composites is not so advanced[1]. In this paper, we investigate the stiffness and strength of perfectly aligned short-fiber composites as well as particulate composites, (in the limit of a fiber aspect ratio of unity) as a function of the fiber/particle volume fraction. Composite strength a.• is defined in this work as cc. the product of composite stiffness Ec and the composite strain at failure e:: a* = c is the value of applied strain at which catastrophic failure occurs, i.e. the material ruptures into two distinct parts. The composite strain at failure is determined in large part by the "fracture resistance", or fracture toughness of the matrix and/or the second phase constituent. The issue of toughness will not be explicitly investigated in this paper. The methodology consists of two-dimensional computer simulations in which we assume that the second phase and matrix are perfectly brittle materials, that the fiber/matrix or particle/matrix interface is perfect (same properties as the matrix), and that the matrix is an elastic continuum with no microstructure. THEORY Short-Fiber Composites Stiffness The problem of load transfer to the fibers was first addressed from a theoretical point of view by Cox[2], for an ideal system consisting of a single fiber embedded in a matrix. Cox made use of a few simplifying assumptions: the matrix tensile stress is constant, hence it has no radial or axial dependence, and the displacement at a distance R away from the fiber is equal to the applied displacement. The distance R can be viewed as a correlation length: other fibers and/or matrix material at or beyond this distance R do not "feel" the presence of the fiber. Cox obtained the following expression for the fiber tensile stress in three-dimensions for a constant applied composite strain cc: a (z) = Ef E,1
cosh/3z/rfi cosh,8s IJ
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