Fracture behavior of short-fiber reinforced materials
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H. Daniel Wagner Department of Materials and Interfaces, The Weizmann Institute of Science, Rehovot 76100, Israel (Received 31 January 1992; accepted 14 July 1992)
A discrete model of springs with bond-bending forces is proposed to simulate the fracture process in a composite of short stiff fibers in a softer matrix. Both components are assumed to be linear elastic up to failure. We find that the critical fiber length of a single fiber composite increases roughly linearly with the ratio of the fiber elastic modulus to matrix modulus. The finite size of the lattice in the direction perpendicular to the fiber orientation considerably alters the behavior of the critical length for large values of the modulus ratio. The simulations of the fracture process reveal different fracture behavior as a function of the fiber content and length. We calculate the Young's modulus, fracture stress, and the strain at maximum stress as a function of the fiber volume fraction and aspect ratio. The results are compared with the predictions of other theoretical studies and experiments.
I. INTRODUCTION Composite materials combining the outstanding features of two or more components are in wide use. One example of such a composite is a soft matrix reinforced with stiff and/or high strength fibers. Advanced engineering uses of these composites involve custom-tailored materials with layers of continuous unidirectional fibers oriented in directions optimized for the specific end use. Another example concerns fiber reinforced composites made up of short fibers (several millimeters long) dispersed randomly in the matrix with or without a preferred orientation. A theoretical understanding of the mechanical properties of discontinuous fiber reinforced materials, including their fracture behavior, is extremely difficult. This is due to the fact that the random spatial distribution of the fibers and the stress concentration at the fiber ends render the stress distribution within the material very complicated. Theoretical approaches that neglect the stress at the fiber ends, the so-called "rule-of-mixture" theories,1 describe the elastic properties rather successfully. However, fracture behavior is influenced by the spatial fluctuations of the stress distribution rather than by the average stress.2 Therefore an understanding of the fracture properties should start from the investigation of the microscopic stress distribution, at the level of the characteristic length scale, which for this case is the fiber diameter. In a series of papers, Termonia has investigated both the elastic 34 and the fracture5 properties of short fiber reinforced polymers using a microscopic approach. His model is based upon a finite difference solution of the equations of mechanical equilibrium. For any applied 3120 http://journals.cambridge.org
J. Mater. Res., Vol. 7, No. 11, Nov 1992 Downloaded: 08 Jan 2015
external strain, these equations are solved for the local strains. Bonds are then broken according to the kinetic theory of fracture at a rate that depends upon t
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