Effiziente Multiskalen-Methode für Viskoelastizität und Ermüdung von kurzfaserverstärkten Polymeren

Short fiber reinforced polymers are of central importance in many industrial applications such as lightweight constructions. This is mainly due to their exceptional weight to stiffness ratio. The processing of these composite materials by injection molding to components with complex geometries makes them a cost-efficient alternative to metallic materials, primarily in large-scale production. However, the complex microstructure of short fiber reinforced polymers makes their experimental characterization difficult and time consuming. Especially the design of short fiber reinforced components with regard to their long-term behavior, such as their lifetime under cyclic loading or creep, is a complex task. The mechanical behavior of these components depends on the complex morphological parameters of the underlying microstructures. In many applications a conventional simulation on the macroscopic scale without consideration of the material properties caused by the underlying microstructures is therefore not sufficient. A multi scale simulation of short fiber reinforced components is necessary to precisely predict the material behavior of these components and thus to support their experimental char acterization. In chapter 3 of the present work, an efficient data-based multi-scale method is presented, which takes into account the influence of the microstructure in component-scale simula tions. In order to enable the multi-scale simulation of components of industrially relevant sizes, effective or reduced models are used in this thesis. The multi-scale approach consists of two steps. Firstly, effective models are generated for given fiber orientation states.
In this thesis fast Fourier transform (FFT) based numerical homogenization methods are used for this purpose. These methods are particularly suitable for the simulation
of short fiber reinforced polymers. Due to its efficiency, the micro-scale boundary value problem can be solved quickly for large volume elements.
In the second stage of the multi-scale method, the generated effective models are inter polated to predict the material response for a general fiber orientation state. In chapter 4, Schapery’s collocation method together with FFT-based homogenization is used to identify an effective model for predicting the creep behavior of short glass fiber reinforced polyamide. The multi-scale method using these fiber orientation dependent effective models is applied in a macroscopic finite element (FE) simulation, where the commercial FE-solver Abaqus is used on the component-scale. In chapter 5, a model for the prediction of the stiffness degradation in short fiber re inforced polymers under cyclic loading is presented. This model is based on a simple isotropic non-local fatigue model for the matrix material with a very small number of
parameters. The influence of the numerical and material parameters on the effective stiffness is studied extensively in chapter 5. Furthermore, the influence of morphological properties, such as fiber volume content and fiber orientation, is investigated. Due to the special structure of this model, a reduced order model is identified by Galerkintype model order reduction. Moreover, this reduced model is applied in a macroscopic FE-simulation within the multi-scale framework.