Application and evaluation of the method of ellipses for measuring the orientation of long, semi-flexible fibers

The method of ellipses (MoE) is a common experimental technique utilized to quantitatively determine the orientation state of a population of rigid fibers within a fiber–polymer composite. In this research, the validity of applying the MoE to long, semi‐flexible fiber systems in which the majority of fibers are flexible is discussed. The components of the orientation tensor were first determined for a composite formed by a homogenous, simple shear field. The minimum acceptable image analysis width, or bin width, for the selected geometry was found to be ∼5.5 mm, or 1.4 times the average fiber length. This modified bin width was then used to determine the orientation at multiple percentages of flow within an injection‐molded, center‐gated disc, and compared to orientation values obtained utilizing the traditional, 0.7‐mm bin width. The results show that the traditional, 0.7‐mm bin width is sufficient for analysis of the center‐gated geometry. This fortuitous result is attributed to the axisymmetric nature of the center‐gated geometry, and the highly transverse fiber alignment seen within the samples, especially at moderate to high percentages of flow. In more complex flows, it is expected that the conventional bin width will not apply. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers