DETERMINATION OF NONSYMMETRICAL 3-D FIBER-ORIENTATION DISTRIBUTION AND AVERAGE FIBER LENGTH IN SHORT-FIBER COMPOSITES

A mathematical procedure is proposed for recovering from image analysi s the three-dimensional (3-D) non-symmetric density distribution of fi ber orientation and the average fiber length in short-fiber composites . The determination of fiber-orientation distribution and average fibe r length is essential for assessing the mechanical and physical proper ties of a short-fiber composite. The average fiber length can be obtai ned from one micrograph, while the determination of 3-D fiber orientat ion requires micrographs from two orthogonal planar faces of a composi te sample. In addition, a simple procedure is proposed to obtain the s ingle-angle fiber-orientation distribution from one micrograph. This d istribution is often needed for predicting the mechanical and physical properties in the direction normal to the plane of the photographed s ample cross section. In processing the fiber-orientation density data obtained from a micrograph, a cumulative fiber-orientation density cur ve is used to derive the fiber-orientation function, which is simpler and more accurate than the histogram that has been commonly used. Prev iously 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.