*Article* **Experimental Validation of a Direct Fiber Model for Orientation Prediction**

#### **Sara Andrea Simon \*, Abrahán Bechara Senior and Tim Osswald**

Polymer Engineering Center (PEC), University of Wisconsin-Madison, 1513 University Ave, Madison, WI 53706, USA; bechara@wisc.edu (A.B.S.); tosswald@wisc.edu (T.O.)

**\*** Correspondence: ssimon9@wisc.edu; Tel.: +1-608-265-2405

Received: 24 April 2020; Accepted: 19 May 2020; Published: 25 May 2020

**Abstract:** Predicting the fiber orientation of reinforced molded components is required to improve their performance and safety. Continuum-based models for fiber orientation are computationally very efficient; however, they lack in a linked theory between fiber attrition, fiber–matrix separation and fiber alignment. This work, therefore, employs a particle level simulation which was used to simulate the fiber orientation evolution within a sliding plate rheometer. In the model, each fiber is accounted for and represented as a chain of linked rigid segments. Fibers experience hydrodynamic forces, elastic forces, and interaction forces. To validate this fundamental modeling approach, injection and compression molded reinforced polypropylene samples were subjected to a simple shear flow using a sliding plate rheometer. Microcomputed tomography was used to measure the orientation tensor up to 60 shear strain units. The fully characterized microstructure at zero shear strain was used to reproduce the initial conditions in the particle level simulation. Fibers were placed in a periodic boundary cell, and an idealized simple shear flow field was applied. The model showed a faster orientation evolution at the start of the shearing process. However, agreemen<sup>t</sup> with the steady-state aligned orientation for compression molded samples was found.

**Keywords:** fiber reinforced plastics; long fiber reinforced thermoplastics (LFT); sliding plate rheometer; fiber microstructure; fiber orientation; direct fiber simulation; mechanistic model
