Analysis Of Flow-induced Fiber Orientation Using Finite Element Method

Short-fiber reinforced composites (SFRPS) are one kind of very important engineering material. Because the convenient processing and the low cost, they are widely used in our industry. During injection molding of the fiber reinforced composites, for one hand, fiber orientation can significantly affect the mechanical property of parts, which either made the parts develop anisotropic property or develop residual stress due to which cause the parts to warp deformation; for the other hand, fiber orientation is the main properties of the parts' microstructure. Therefore, an accurate prediction of fiber orientation became very important.For predicting flow induced alignment, we could use two different methods. The fist one is based on using a fiber distribution function, which provides the probability of orienting particle in certain direction and is computationally intensive. A second approach is based on using the moments of the orientation distribution function (orientation tensor). We can get the fiber orientation in the parts by solving the evolution equation of the fiber orientation tensor. This approach requires a closure model since the equation governing the second moment of the orientation distribution function involves an unclosed fourth order tensor.Orientation tensor is mainly used in this dissertation to study the fiber orientation. We construct the orientation tensor using the inner product of orientation vector and fiber distribution function by studying the fiber orientation behavior. Based on this, the property of the second and fourth order tensor, and the eigenvalues and invariants of orientation tensor which under different orientation states are discussed.Some of the closure model is discussed in this dissertation and has been pursued in this work. We get the evolution equation of the fiber orientation tensor by taking into account the interaction between fibers and the movement equation of fibers. We get the finite element equation of fiber orientation by Galerkin method. A VC++ code has been developed to solve film-gated strip and center-gated disk problems using the two closure model (Linear model of Hand and H&L1 model). The results reveal the flow induced fiber orientation behavior during the mold-filling process.