Modified hybrid closure approximation for prediction of flow-induced fiber orientation

Abstract

Distribution of fiber orientation in flow molding processes with short-fiber reinforcements is of great importance because it affects the mechanical properties of molded parts. Due to trade-off between the computational efficiency and accuracy, a second-order orientation tensor has been widely used to describe the fiber orientation distribution. For calculation of this fiber orientation tensor, a closure approximation has been introduced to reduce a higher fourth-order orientation tensor to a lower second order. In the present investigation, a hybrid closure approximation has been modified. Two parametric forms of the distribution function, which accurately describe the random-in-space, random-in-plane, and uniaxial distributions of the fiber orientation were linearly interpolated. The interpolating factor was obtained as a function of the fiber interaction coefficient by fitting the distribution function calculations. Test simulation in homogeneous flow and nonhomogeneous flow fields, respectively, showed that the proposed closure approximation gives good performance for a wide range of CI values without showing nonphysical behavior.