Determination of Non-Symmetric 3-D Fiber-Orientation Distribution and Average Fiber Length in Short-Fiber Composites

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Abstract
A mathematical procedure is proposed for recovering from image analysis the three-dimensional (3-D) non-symmetric density distribution of fiber orientation and the average fiber length in short-fiber composites. The determination of fiber-orientation distribution and average fiber length is essential for assessing the mechanical and physical properties of a short-fiber composite. The average fiber length can be obtained from one micrograph, while the determination of 3-D fiber orientation requires micrographs from two orthogonal planar faces of a composite sample. In addition, a simple procedure is proposed to obtain the single-angle fiber-orientation distribution from one micrograph. This distribution is often needed for predicting the mechanical and physical properties in the direction normal to the plane of the photographed sample cross section. In processing the fiber-orientation density data obtained from a micrograph, a cumulative fiber-orientation density curve is used to derive the fiber-orientation function, which is simpler and more accurate than the histogram that has been commonly used. Previously reported procedures all assume symmetries in fiber-orientation distribution, and are therefore highly idealized. Without assuming any symmetry, the present procedure improves upon previous works.