Halpin-Tsai equations parameter

The modulus and yield kinetic parameters of the block polymer B can be related to those of the homopolymer in terms of a microcomposite model in which the silicone domains are assumed capable of bearing no shear load. Following Nielsen (10) we successfully applied the Halpin-Tsai equations to calculate the ratio of moduli for the two materials. This ratio of 2 is the same as the ratio of the apparent activation volumes. Our interpretation is that the silicone microdomains introduce shear stress concentrations on the micro scale that cause the polycarbonate block continuum to yield at a macroscopic stress that is half as large as that for the homopolymer. The fact that the activation energies are the same however indicates that aside from this geometric effect the rubber domains have little influence on the yield mechanism. 

The parameter is a measure of fibre reinforcement of the composite materials that depends on several factors, such as fibre geometry and fibre arrangement. The exact elasticity calculations predict the moduli to rise faster with increasing fibre volume fraction above 0.7 as compared to the Halpin-Tsai equation [25]. The following empirical expressions were suggested by others [26] ... 

There are no adjustable parameters. Such models include the Kemer equation [68], Halpin-Tsai equation [69] and Chow equation [70]. The second group of equations, on the other hand, incorporate adjustable parameters to account for interactions between particles as well as between the matrix and the particles. Factors such as critical solid volume fraction, degree of agglomeration and powder-matrix adhesion are taken into account. Equations and models under this group would include the Nielsen generalized equation [71] and the modified Kemer equation [72,73]. 

Detailed Expressions for the Parameter in Halpin-Tsai Equations Depending on Filler Particle s Geometry... 

Typical curves as calculated with Halpin-Tsai equations and parameters for short glass fiber-polypropylene composites parameters used in calculation short glass fibers = 77.0 GPa,... 

A7.2.6 Average Orientation Parameters from Halpin-Tsai Equations for Short Fibers Filled Systems... 

The Chow equations, which constitute a large set that is too long and complex to reproduce here, are sometimes more accurate. Both of these sets of general-purpose equations (Halpin-Tsai and Chow) are applicable to many types of multiphase systems including composites, blends, immiscible block copolymers, and semicrystalline polymers. Their application to such systems requires the morphology to be described adequately and reasonable values to be available as input parameters for the relevant material properties of the individual phases. 

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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