Analysis and Evaluation of Fiber Orientation Reconstruction Methods

Abstract

The calculation of the fiber orientation of short fiber-reinforced plastics with the Fokker–Planck equation requires a considerable numerical effort, which is practically not feasible for injection molding simulations. Therefore, only the fiber orientation tensors are determined, i.e., by the Folgar–Tucker equation, which requires much less computational effort. However, spatial fiber orientation must be reconstructed from the fiber orientation tensors in advance for structural simulations. In this contribution, two reconstruction methods were investigated and evaluated using generated test scenarios and experimentally measured fiber orientation. The reconstruction methods include spherical harmonics up to the 8th order and the method of maximum entropy, with which a Bingham distribution is reconstructed. It is shown that the quality of the reconstruction depends massively on the original fiber orientation to be reconstructed. If the original distribution can be regarded as a Bingham distribution in good approximation, the method of maximum entropy is superior to spherical harmonics. If there is no Bingham distribution, spherical harmonics is more suitable due to its greater flexibility, but only if sufficiently high orders of the fiber orientation tensor can be determined exactly.