Halpin-Tsai equations longitudinal

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. 

By analogy, the Halpin-Tsai equation type of expression can be used to predict elastic moduli of the composite containing randomly oriented anisometric (nonspherical) inclusions with engineered interphases (30). This is a plausible model of the 3-D randomly oriented Mg(OH)2 platelets or 2-D randomly oriented SGF in the PP matrix. In the first step, the modified Halpin-Tsai equation is used to calculate the longitudinal and transverse moduli of the composites with unidirec-tionally oriented nonspherical inclusions ... 

The Halpin-Tsai equations and the Mori-Tanaka model are the most used to predict mechanical properties of composites. The Halpin-Tsai equations predict stiffness of the unidirectional composites as a function of aspect ratio. In this model, the longitudinal stiffness and transverse engineering moduli are expressed in the following general form ... 

The Halpin-Tsai equation predicts a linear variation of the longitudinal modulus with increasing fiber volume fraction such a behavior is not exhibited by commercial PP + SGF composites likely because fibers are far to be perfectly aligned in such materials. 

Tensile Modulus. The Halpin-Tsai equations relate the composite tensile modulus E ) to the volume fraction of the fiber (Vf), the fiber and matrix moduli E ) and ( ), and L and D, the average fiber length and diameter [19]. In the longitudinal direction, the modulus ( n) is... 

Curve-fitting parameters are used in semiempirical and generalized equations to predict experimental results. The most common model was developed by Halpin and Tsai, and it has been modified for aligned discontinuous fiber composites to produce such results as the following for the longitudinal modulus ... 

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