Fiber-dependent injection molding simulation of discontinuous reinforced polymers

This work presents novel simulation techniques for injection molding of fiber reinforced polymers. These include approaches for anisotropic flow modeling, hydrodynamic forces from fluid on fibers, contact forces between fibers, a novel fiber breakage modeling approach and anisotropic warpage analysis. Due to the coupling of fiber breakage and anisotropic flow modeling, the fiber breakage directly influences the modeled cavity pressure, which is validated with experimental data

Fiber-dependent injection molding simulation of discontinuous reinforced polymers

Diese Arbeit präsentiert neuartige Simulationstechniken für Spritzgusssimulationen mit faserverstärkten Polymeren (FRPs). Spritzguss ist einer der meistverbreiteten Prozesse zur Massenproduktion von diskontinuierlich faserverstärkten Polymerbauteilen. Die Prozessparameter (Füllrate, Temperatur, etc.) beeinflussen die Bauteileigenschaften signifikant. Für eine adäquate Vorhersage der finalen Bauteileigenschaften muss eine Simulation alle Prozessschritte (Formfüllung, Nachdruck, Abkühl-/Aushärtungsphase, Abkühlung außerhalb des Werkzeuges) beinhalten. Während der Formfüllung hat die Strömungsmodellierung oberste Priorität. Das komplexe Matrixverhalten muss unter Beachtung von Scherrate, Temperatur und, falls vorhanden, chemischer Reaktion modelliert werden. Die sich ausprägende Faserorientierung, die von Strömungsfeld, Faserlänge und Volumengehalt abhängt, sollte aus zwei Gründen berechnet werden. Einer ist das Ausprägen von anisotropen Material- und somit auch Bauteileigenschaften aufgrund der Fasern. Zudem rufen die Fasern auch während der Formfüllung anisotropes Verhalten im flüssigen Material hervor. Auch die Faserlänge beeinflusst das mechanische und Fließverhalten des Materials und wird im Umkehrschluss durch das Strömungsfeld während der Formfüllung beeinflusst. Die Faserlänge hat großen Einfluss auf die Schlagzähigkeit des Bauteils, aber auch auf die effektive Viskosität in Faserrichtung im flüssigen Material. Umgekehrt erzeugt das Strömungsfeld aber auch Kräfte auf die Fasern, die diese zum Brechen bringen können. Stand der Technik Simulationen beachten den Einfluss der Faserorientierung und -länge auf das Strömungsfeld nicht. Diese Arbeit präsentiert einen neuartigen Ansatz, in welchem Viskosität, Faserorientierung, Faserlänge und Geschwindigkeit gekoppelt sind. Zur Berücksichtigung der Fasereigenschaften in der Viskositätsmodellierung und somit auch in der Geschwindigkeit wird die Viskosität als Tensor vierter Stufe, der als Funktion von Matrixviskosität, Faserorientierung, -länge und -volumengehalt definiert ist, modelliert. Der Viskositätstensor wird für eine homogenisierte Matrix-Faser-Suspension auf Basis von mikromechanischen Modellen berechnet. Für die Modellierung des Faserbruchs werden die hydrodynamischen Schlepp- und Auftriebskräfte beachtet. Zusätzlich werden makroskopische Ansätze zur Berechnung der Faser-Faser Interaktionskräfte (Schmier- und Reibkraft) gezeigt und verifiziert. Neben der Formfüllung beeinflussen die weiteren Prozessschritte Nachdruck, Abkühl-/Aushärtungsphase und Abkühlung außerhalb des Werkzeuges ebenfalls die Bauteileigenschaften. Durch das anisotrop visko-elastische Verhalten können Verzug und Eigenspannungen aufkommen. Stand der Technik Software simuliert diese Phänomene in der Regel anisotrop mit linear elastischen Modellen. Diese Arbeit präsentiert einen Ansatz zur Berechnung von Verzug und Eigenspannungen für FRPs mit duromerer Matrix und thermo-visko-elastischen Modellen. Relevante Prozessdaten wie Faserorientierung, Temperatur und Aushärtungsgrad werden übertragen um diese in der Verzugssimulation mit zu betrachten. Faser- und Matrixeigenschaften werden zur Homogenisierung verwendet und unter Beachtung der Faserorientierung wird ein orthotropes Material definiert. Das Matrixverhalten wird als Funktion von Aushärtungsgrad und der Temperatur modelliert. Zusätzlich werden thermische und chemische Schwindung beachtet. Die vorgestellten Methoden sind für Formfüllsimulationen in der open-source, finite Volumen basierten Software OpenFOAM und für die Verzugsanalyse in die kommerziellen finiten Elemente basierten Software Simulia Abaqus implementiert. Numerische Studien verifizieren die Implementierung und Methoden. Die Formfüllsimulationen zeigen eine gute Übereinstimmung mit experimentellen Ergebnissen, was die neu entwickelten Ansätze validiert

Charge-induced conformational changes of dendrimers

We study the effect of chargeable monomers on the conformation of dendrimers of low generation by computer simulations, employing bare Coulomb interactions. The presence of the latter leads to an increase in size of the dendrimer due to a combined effect of electrostatic repulsion and the presence of counterions within the dendrimer, and also enhances a shell-like structure for the monomers of different generations. In the resulting structures the bond-length between monomers, especially near the center, will increase to facilitate a more effective usage of space in the outer-regions of the dendrimer.Comment: 7 pages, 12 figure

Fiber-dependent injection molding simulation of discontinuous reinforced polymers

This work presents novel simulation techniques for injection molding of fiber reinforced polymers. These include approaches for anisotropic flow modeling, hydrodynamic forces from fluid on fibers, contact forces between fibers, a novel fiber breakage modeling approach and anisotropic warpage analysis. Due to the coupling of fiber breakage and anisotropic flow modeling, the fiber breakage directly influences the modeled cavity pressure, which is validated with experimental data

Numerical Study on Uncertainty Effects in Injection Molding

Injection molding is one of the most widely used processes to manufacture polymer parts, but due to uncertainties in material and process, the part quality scatters, which leads to a raising of safety factors and therefore to inefficient material use. Although current simulation approaches predict the manufacturing process and resulting part behavior quite well, the approaches are deterministic, and the simulated material is based on average data in most cases. This work presents an approach for fast approximation of cavity pressure under the consideration of uncertainties in material state and process temperatures. The approach is based on interpolation and superposition of a few process simulations and enables fast data creation for uncertainty studies. The results are in good agreement with deterministic simulations and experimental data

Untangling the Role of Assortative Mating in Educational Reproduction in Twelve European Countries

In this study, we explore how educational differences in demographic behavior – in particular, mating patterns and fertility – mediate the intergenerational reproduction of educational inequality in twelve European countries. Although this research interest itself is not new, we contribute to this debate by adopting a prospective approach and scaling it to include multiple countries and cohorts. To this end, we leverage a series of complementary datasets and the inferential method developed by Song and Mare (2015) and advanced by Skopek and Leopold (2020) to estimate the components of a stylized educational reproduction model. We then employ a simple decomposition analysis to quantify the contributions of different pathways to prospective educational reproduction rates across educational backgrounds and explore the differences across cohorts and countries. We report several findings. Most notably, (1) the intergenerational reproduction of educational inequality persists in all twelve countries and is barely offset by small (and declining) negative educational gradients in fertility, (2) educational differences in selection into partnership are small and do not account for much inequality, and (3) the role of assortative mating, where present, is ambiguous because it both reinforces inequality via its effects on resources within the family and offsets it via its effects on fertility. * This article belongs to a special issue on “Changes in Educational Homogamy and Its Consequences”

Assembly of Nanoparticles into “Colloidal Molecules”: Toward Complex and yet Defined Colloids with Exciting Perspectives

In line with atoms being the elementary units of molecules and crystals, colloidal particles can be used as building blocks for organized materials. A major benefit in doing so is that joining colloids in a defined manner comes along with structuring. In view of opening avenues to more complex structural motifs, significant efforts must be geared to colloids with specific shapes and symmetries. A straightforward strategy is joining equal‐sized spherical particles into stable clusters. Such clusters are called “colloidal molecules” because they may exhibit configurations resembling pretty much those of molecules. Their preparation can be based on the agglomeration of particles dispersed in an emulsion. The particles adsorb on the emulsion droplets and coagulate in a defined way during the evaporation of the droplet phase. Using this method originally applied to microscale particles, one can produce clusters with submicron‐sized global dimensions. Variable parameters such as radii and concentration of cluster constituents provide the framework needed to obtain “colloidal molecules” that differ in size, shape, and physical properties. This opens up exciting perspectives for tailor‐made colloids as building units for hierarchically organized materials. Moreover, new physical properties such as plasmonic “hotspots” may emerge from packing particles into assemblies of specific configurations

Theoretical approximation of hydrodynamic and fiber-fiber interaction forces for macroscopic simulations of polymer flow process with fiber orientation tensors

Flow processes of discontinuous fiber reinforced polymers (FRPs) are the essence of several polymer-based manufacturing processes. FRPs show a transient chemo-thermomechanical matrix behavior and fiber-induced anisotropic physical properties. Therefore, they are one of the most complex materials used in volume production. The general flow behavior is influenced by fibers and their interactions with the matrix and other fibers. The consideration of individual fibers is numerically not capable for process simulation of FRP parts. Therefore, orientation tensors are used in macroscopic simulations, leading to a loss of information about the fiber network. Within this work, novel approximation schemes are presented to determine hydrodynamic and fiber-fiber contact forces with information provided by the second order fiber orientation tensor. Approximation of these forces can henceforth facilitate fiber breakage modeling in macroscopic process simulations. The results are verified by numerical simulations with individual fibers of different orientation states and lengths, showing good agreement with the verification results

Modeling Approach for Reactive Injection Molding of Polydisperse Suspensions with Recycled Thermoset Composites

Recycling production waste in the reactive injection molding (RIM) process is a step towards sustainability and efficient material usage. The recycled thermoset composite (RTC) material obtained by shredding the production waste is reused with a virgin thermoset composite (VTC). This study presents a mold-filling simulation approach considering this polydisperse suspension of RTC and VTC. Mold-filling simulations can assist in predicting processability and assessing the impact of reinforced RTC on the final part of production. State-of-the-art mold-filling simulations use the Cross–Castro–Macosko (CCM) model or anisotropic fiber-orientation-dependent viscosity models. The rheological parameters are determined either for the VTC or neat resin. However, these models do not account for changes in viscosity due to the reinforcing of fillers such as RTC. An effective viscosity model is developed by extending the CCM model using the stress–strain amplification approach to overcome this gap. This model is implemented in the computational fluid dynamics code OpenFOAM, and simulations are performed using an extended multiphase solver. To validate the simulations, experimental trials were executed using a two-cavity mold equipped with pressure sensors. Molding compounds with different compositions of VTC and RTC were injected at different speeds. Reinforcing VTC with RTC increases the viscosity. Results demonstrate that RTC-reinforced compounds require higher injection pressure for mold filling than VTC alone. The qualitative agreement of pressure profiles from simulations and experiments for different proportions of reinforcing RTC and different injection speeds shows that the implemented viscosity model can reproduce the experimental mold-filling behavior

Using microscale SPH-simulations to parameterize macroscopic fiber orientation models for discontinuous fiber reinforced polymers

The orientation of discontinuous fibers in injection or compression molded parts has crucial impact on the thermo-mechanical properties of the part. Therefore, the prediction of these orientation states is of high importance and has been the focus of research for several years. Today’s models often represent the orien-tation evolution by a semi-empirical tensor evolution equation, which needs at least one empirical parame-ter. More complex models need more parameters. The determination of these parameters often entails a high experimental effort, especially if data over time is needed. This work presents a multiscale approach, where microscale simulations of individual and interacting fibers in a simple shear flow are used to pa-rameterize macroscopic orientation models. The microscale simulations are performed with the smoothed particle hydrodynamics method. The macroscopic models, being the Folgar-Tucker and ARD-RSC model, are fitted according to the microscale results and are compared to state-of-the-art approaches for parame-ter determination. For experimental validation, injection molding trials of a 20 weight-% short glass fiber reinforced phenolic are used, showing the benefits of the micro-macro coupling especially when predict-ing the orientation evolution over time. The main advantage of the multiscale approach is the parameteri-zation of the ARD-RSC approach without the need of experimental data for a wide range of fiber-polymer materials