A micromechanics model to predict extensional viscosity of aligned long discontinuous fiber suspensions

A micromechanical unit cell model is formulated to investigate the deformation in a unit cell of highly concentrated suspension of long discontinuous aligned fibers. The periodic unit cell is many fiber lengths long to allow for microstructural variations due to random fiber length overlaps and end-to-end gap distances between the fibers. This feature of the unit cell makes it possible to examine the effect of such variabilities on the macroscopic material behavior (effective viscosity) during the forming process. The influence of microstructure variability on viscosity is predicted. The standard deviation of the effective extensional viscosity is significant and increases with material extensional deformation and the variation of the end to end fiber spacing. This could have ramifications on the forming process and the final physical properties of the materials of interest. The predicted dependence of the mean extensional viscosity value on the usual material parameters (fiber aspect ratio, fiber volume fraction) is found to be consistent with the relations predicted by reported models using deterministic periodic unit cells. The behavior of standard deviation of our model follows the same dependence as the mean value. On the other hand, it shows negligible variability of effective longitudinal-transverse shearing viscosity of such materials, regardless of the random perturbations of fiber length overlaps and end to end fiber spacings within the unit cell.