*Article* **Calibration of Fiber Orientation Simulations for LFT—A New Approach**

#### **Fabian Willems \*, Philip Reitinger \* and Christian Bonten**

Institut für Kunststofftechnik (IKT), University of Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, Germany; christian.bonten@ikt.uni-stuttgart.de

**\*** Correspondence: fabian.willems@ikt.uni-stuttgart.de (F.W.); philip.reitinger@ikt.uni-stuttgart.de (P.R.); Tel.: +49-711-685-62883 (F.W.); +49-711-685-62870 (P.R.)

Received: 18 August 2020; Accepted: 26 October 2020; Published: 30 October 2020

**Abstract:** Short fiber reinforced thermoplastics (SFT) are extensively used due to their excellent mechanical properties and low processing costs. Long fiber reinforced thermoplastics (LFT) show an even more interesting property profile and are increasingly used for structural parts. However, their processing by injection molding is not as simple as for SFT, and their anisotropic properties resulting from the fiber microstructure (fiber orientation, length, and concentration) pose a challenge with regard to the engineering design process. To reliably predict the structural mechanical properties of fiber reinforced thermoplastics by means of micromechanical models, it is also necessary to reliable predict the fiber microstructure. Therefore, it is crucial to calibrate the underlying prediction models, such as the fiber orientation model, within the process simulation. In general, these models may be adjusted manually, but this is usually ineffective and time-consuming. To overcome this challenge, a new calibration method was developed to automatically calibrate the fiber orientation model parameters of the injection molding simulation by means of optimization methods. This optimization routine is based on experimentally determined fiber orientation distributions and leads to optimized parameters for the fiber orientation prediction model within a few minutes. To better understand the influence of the model parameters, different versions of the fiber orientation model, as well as process and material influences on the resulting fiber orientation distribution, were investigated. Finally, the developed approach to calibrate the fiber orientation model was compared with a classical approach, a direct optimization of the whole process simulation. Thereby, the new optimization approach shows a calculation time reduced by the factor 15 with comparable error variance.

**Keywords:** lightweight design; long fiber reinforced thermoplastics; process simulation; fiber microstructure; parameter-optimization; fiber orientation models; calibration
