Halpin-Tsai equations fiber aspect ratio

These equations are suitable for single calculation and were employed previously for the single ply and angle ply properties. The short fiber composite properties are also given by the Halpin-Tsai equations where the moduli in the fiber orientation direction is a sensitive function of aspect ratio (1/d) at small aspect ratios and has the same properties of a continuous fiber composite at large but finite aspect ratios. 

Maximum strain theory may be modified to predict the strength of randomly oriented short-fiber composites (22). llie Halpin-Tsai equations (14) have established relations for the stiffness of an oriented short-fiber ply from the matrix and fiber properties. These nations show that the longitudinal stiffness of an oriented short-fiber composite is a s itive function of the aspect ratio. 

The well known Tsai-Halpin equation [1] describes the dependence of the modulus of a composite on that of the basis materials, the volume fraction of the fibers and their aspect ratio. In these composites the fibers carry the load and the matrix distributes it. Fiber reinforced thermosets have a wide range of technical applications and play an important role in self-supporting, low-weight constructions. 

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