Modeling and evaluation of thermo-mechanical properties of open-cell ceramic foams for metal melt filtration

Abstract

Open-cell ceramic foams are used in metal melt filtration processes to clean and calm the liquid melt. Due to the high temperatures and pressure of the melt, thermo-mechanical stresses occur in the filter structures, which require a corresponding evaluation of strength, deformation, and failure. The ceramic materials used no longer behave elastically and brittle at operating temperatures of up to 1650 ◦ C, but exhibit viscoplastic behavior. Experimental investigations of the deformation of filter structures during the filtration process are difficult or even impossible, which is why simulation methods are used to investigate the filtration process and the filter loading. The filters considered in this work are manufactured using a replica process in which a ceramic slurry is applied to an open-cell polyurethane foam, which is dried and fired in a thermal process. Real filter structures consist of a network of several thousand struts with varying geometries. Direct numerical simulation of these geometries is possible in principle, but it is very complex and expensive, which is why homogenization methods are used. Representative volume elements of the ceramic foams are generated and analyzed using the finite element method. The micro-macro relations determined in the process are mapped using corresponding continuum mechanical models. These models allow the evaluation of the thermo-mechanical behavior of filter materials and filter structures. This thesis provides a critical overview of methods for generating, characterizing, and homogenizing foam structures. The generation of realistic foam structures is carried out using various methods from the fields of mathematics and mechanics and is described in detail. Analytical and data-driven approaches are used for the actual homogenization. The analytical approaches use adaptations of continuum mechanical models from the field of granular media. The data-driven approaches use neural networks, which replace or supplement hard-to-describe thermodynamic potentials used in material modeling. Both approaches can be used in a developed general framework for the modeling of any porous structures. As a result of the research and modeling work carried out, generic and real foams are compared in terms of their topological and geometrical properties. It is discussed how local geometrical variations of foam structures affect the macroscopic behavior, considering different thermo-mechanical properties such as elasticity, viscoplasticity, and fracture strength. The developed homogenization concepts are compared with each other and with other concepts from the scientific literature and evaluated with respect to their accuracy, flexibility, and efficiency. Finally, possible further developments and applications are discussed.:1. Introduction 1.1. Motivation and objectives 1.2. Structure of the thesis 2. State of the art research 2.1. Integration of sub-project B05 into the CRC 920 2.2. Manufacture of open-cell foam structures 2.2.1. Schwartzwalder process 2.2.2. Additive manufacturing 2.2.3. Additional coatings 2.2.4. Bulk material properties 2.3. Characterization of open-cell foam structures 2.3.1. Topological and geometrical characteristics 2.3.2. Thermo-mechanical characteristics 2.3.3. Fluid dynamical characteristics 2.4. Modeling of open-cell foam structures 2.4.1. Geometrical models of foams 2.4.2. Direct numerical simulation 2.4.3. Homogenization approaches 2.4.4. Data-driven and machine-learning approaches 2.4.5. Constitutive models for open-cell foam structures 3. Modeling of open-porous ceramic foams 3.1. Foam surfaces of strut networks based on implicit functions 3.2. Sphere packings and Laguerre tessellations 3.3. Surface evolver, dry foams, wet foams, and foam froth 3.4. Voxel models and isosurfaces of foams 3.5. Finite element model 3.5.1. Models with structural elements 3.5.2. Unstructured tetrahedral meshes 3.5.3. Structured meshes 3.6. Generating foam structures using FoamGUI 3.7. Homogenized constitutive models 3.7.1. Scale bridging, meso and micro models 3.7.2. Effective elastic properties 3.7.3. Elastic limit surfaces 3.7.4. Effective yield surfaces 3.7.5. Modified Ehlers model 3.7.6. Constitutive model for viscoplastic behavior 3.7.7. Constitutive framework for plastic behavior 3.7.8. General return algorithm 3.7.9. Application to the phenomenological models 3.7.10. Hybrid models 3.7.11. Neural networks 3.7.12. Data sampling for the neural network training 3.7.13. Parameter identification for the modified Ehlers model 4. Results 4.1. Geometrical foam models 4.1.1. Foam models based on implicit functions 4.1.2. Foam models based on sphere packings 4.2. Effective thermo-mechanical properties 4.2.1. Geometry dependent elastic properties 4.2.2. Yield and failure surfaces 4.2.3. Fracture mechanical properties 4.2.4. Fracture mechanical properties for thermo-shock loading 4.2.5. Visco-plastic properties 4.2.6. Effective plastic properties 5. Conclusions & Discussio