Theoretical Consideration of Fiber Orientation in Flow

The rheological properties of fiber-reinforced thermoplastic composites depend on fiber orientation. Therefore, it is very important to understand fiow-induced fiber orientation. For this reason, in this section we first present briefly the approach of Dinh and Armstrong (1984), who developed a constitutive equation for concentrated fiber suspensions in a solvent on the basis of a general formulation proposed earlier by Batchelor (1970). We then present expressions predicting the shear viscosity of fiber-reinforced thermoplastic composite, where the suspending medium is assumed to follow 

Newtonian behavior. Finally, we describe a computational procedure to solve a system of equations predicting the extent of fiber orientation in a shear flow field. 

Batchelor (1970) formulated a general constitutive equation for a suspension of particles in a solvent and presented the following form for the total extra stress tensor a  

Dinh and Armstrong (1984) simplified Eq. (12.12) further by replacing the quantity [itgff n]dA , describing the drag force on the surface of the test fiber, with the product 

Note that for semiconcentrated suspensions, the motion of a fiber is limited because of the presence of other fibers. Fibers cannot pass through each other and thus the bulk rheological properties of the suspension would depend strongly on the structural 

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