Fiber reinforced polymers are key materials across different industries. The manufacturing processes of those materials have typically strong impact on their final microstructure, which at the same time controls the mechanical performance of the part. A reliable virtual engineering design of fiber-reinforced polymers requires therefore considering the simulation of the process-induced microstructure. One relevant microstructure descriptor in fiber-reinforced polymers is the fiber orientation. This work focuses on the modeling of the fiber orientation phenomenon and presents a historical review of the different modelling approaches. In this context, the article describes different macroscopic fiber orientation models such as the Folgar-Tucker, nematic, reduced strain closure (RSC), retarding principal rate (RPR), anisotropic rotary diffusion (ARD), principal anisotropic rotary diffusion (pARD), and Moldflow rotary diffusion (MRD) model. We discuss briefly about closure approximations, which are a common mathematical element of those macroscopic fiber orientation models. In the last section, we introduce some micro-scale numerical methods for simulating the fiber orientation phenomenon, such as the discrete element method (DEM), the smoothed particle hydrodynamics (SPH) method and the moving particle semi-implicit (MPS) method.

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.

This study aims to evaluate how fiber orientation results are dependent on fluctuations in input parameters, such as the average fiber length, fiber volume content, and initial alignment of fibers. The range of parameters is restricted to deviations within one specific short fiber reinforced thermoplastic and is not set up to investigate the differences between materials. The evaluation was conducted by a virtual shear cell based on a mechanistic modeling approach. The fiber orientation prediction model discussed is the pARD-RSC (principal anisotropic rotary diffusion-reduced strain closure) model implemented as a user routine in AUTODESK MOLDFLOW INSIGHT^® (AMI^®). The material investigated was discontinuous short glass fiber reinforced PBT (polybutylene-terephthalate), which is often used for housings in various industries. It is shown that variation in the input parameters, although having an influence on the fiber orientation model parameters, only affects the final orientation moderately.

The simulative prediction of fiber orientation for injection-molded short fiber-reinforced thermoplastics is an important step in prediction warpage and failure of injection molded parts. There exists a variety of phenomenological macroscopic fiber orientation models, which are computationally very efficient but strongly dependent on phenomenological parameters. This research focuses on a mechanistic fiber orientation model for concentrated short fiber-reinforced thermoplastics. A fully coupled computational fluid dynamics particle simulation is used to estimate the lubrication forces between two fibers in different configurations (angles between fibers, velocities) with varying fiber length and surrounding fluid viscosity. Based on these data, a calibrated lubrication model is developed and implemented in a mechanistic fiber orientation simulation. In addition, the fiber orientation estimated by the enhanced mechanistic fiber model is compared to experimental fiber orientation data obtained with a glass fiber-reinforced thermoplastic industrial grade, which showed an improvement over a simulation that did not include the lubrication force.