Fiber orientation due to processing and its prediction

Flow-induced fiber orientation in complex moldings can be quantitatively predicted by considering a combination of four types of basic flows along streamlines [1]. Fibers will tend to align in the streamline direction at regions of shear and converging flows, but across the 

There are three types of fiber suspensions for predicting fiber orientation due to flow. They are dilute, semiconcentrated and concentrated suspensions defined as follows /, id/TF, dilute (d/l) =fv = d/t, semiconcentrated d/l f concentrated. Here d is the diameter of fibers and I is the length of fibers, and is the volume fraction of fibers. 

For the dilute suspension, fibers are free to rotate without interactions between fibers. The volume necessary for the free rotation of a fiber must be greater than the volume of a sphere, the diameter of which equals the fiber length. On the other hand, fibers interact with other fibers in the concentrated region. Fibers interfere via their rotation, when the average space occupied by a fiber is less than the volume of a cylinder whose diameter and height equal the fiber length and the fiber diameter, respectively. In the semiconcentrated region, interactions between fibers are frequent. 

The diameter of glass fibers is generally about 13 xm and their length is about 250 ixm. Thus, the aspect ratio, l/d, is 19. According to the above classification, the volume fraction is less than 0.27% for a dilute suspension and is greater than 5.2% for a concentrated suspension. The volume fraction of fibers is converted to the weight fraction of fibers / y by the equation  

Motion of a fiber in flow is described by Jeffery s model [3]. It is assumed that the fiber is a single rigid ellipsoidal partide suspended in a viscous fluid, the flow is a creeping flow of a Newtonian and incompressible fluid, and Brownian motion and inertia terms of the fiber are neglected. Jeffery s model was used for prediction of fiber orientation in the early period of injection molding CAE. Since it is, however, for dilute suspension, the model is replaced with the Folgar-Tucker model for concentrated suspension. 

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