*Article* **A Flow-Dependent Fiber Orientation Model**

**Susanne Katrin Kugler 1,2,\*,†, Argha Protim Dey 1,3,†, Sandra Saad 1,4, Camilo Cruz 1, Armin Kech 1 and Tim Osswald 2**


Received: 24 June 2020; Accepted: 17 July 2020; Published: 22 July 2020

**Abstract:** The mechanical performance of fiber reinforced polymers is dependent on the process-induced fiber orientation. In this work, we focus on the prediction of the fiber orientation in an injection-molded short fiber reinforced thermoplastic part using an original multi-scale modeling approach. A particle-based model developed for shear flows is extended to elongational flows. This mechanistic model for elongational flows is validated using an experiment, which was conducted for a long fiber reinforced polymer. The influence of several fiber descriptors and fluid viscosity on fiber orientation under elongational flow is studied at the micro-scale. Based on this sensitivity analysis, a common parameter set for a continuum-based fiber orientation macroscopic model is defined under elongational flow. We then develop a novel flow-dependent macroscopic fiber orientation, which takes into consideration the effect of both elongational and shear flow on the fiber orientation evolution during the filling of a mold cavity. The model is objective and shows better performance in comparison to state-of-the-art fiber orientation models when compared to μCT-based fiber orientation measurements for several industrial parts. The model is implemented using the simulation software Autodesk Moldflow Insight Scandium® 2019.

**Keywords:** fiber orientation; modeling; polymer composites
