Theoretical And Numerical Studies Of Flow-induced Short Fiber Orientation Distribution

A common practice in injection molding is reinforcing the polymer matrix with short fibers, the purpose being to improve the mechanical properties of the material. Properties are affected by the presence of the fibers include the elastic modulus, the tensile strength, and the thermal and electrical conductivities. The size of fiber varies. Usually the typical injection molded short-fiber dimension is about ten to twenty microns in radius and ten to fifty in aspect ratio. There are about roughly 10,000 fiber per cubic millimeter oriented in various direction.During the injection molding filling process, the suspended fibers orient in response to the kinematics of the flow. The orientation state of fibers changes with time and position. Consequently, the final microstructure of the solidified composite is complex. And the mechanical properties of the material are anisotropic. Fiber orientation can significantly affect the mechanical properly of parts, which either made parts developing anisotropic property or develop residual stress due to which solidified in the parts cause parts to warp deformation. Fiber orientation is the main properties of the parts' microstructure. Due to the role of the microstructure in determining the mechanical properties of composite product, it is very significant to catch on and predict the oriented behavior of fibers indeed to control it.For the short fiber reinforced composites, the motion of a single fiber was studied analytically in simple shear flow and extensional flow with Jeffery dynamics equation. Besides, we analyze that the fiber motion and oriented behavior was affected by the shear velocity , the time, the aspect ratio and the original orientation angles.At the same time, we describe the state of orientation fiber with the statistics fiber distribution function, and set up the differential coefficient equation provides the evolution of the distribution function with time, as Fokker-Plank equation. Appending the Jeffery's model taking into account the motion caused only by fluid movement, .Finally we obtained the differential coefficient equation to predict the fiber orientation by taking into account two factors, the fluid flow and the fiber-fiber interactions, which induced the orientation motion based on the suspension rheology.