Multi-scale modelling of thermal shock damage in refractory materials

Abstract

Refractories are high-temperature resistant materials used extensively in many engineering structures and assemblies in a wide spectrum of applications ranging from metallurgical furnace linings to thermal barrier coatings. Such structures are often exposed to severe thermal loading conditions in the form of rapid temperature changes (thermal shock) and/or temperature cycles. The understanding and modelling of the failure processes are definitely necessary to achieve reliable life-time predictions of the existing structures and to develop design rules for improvement. Due to their high temperature resistance, alumina based refractory ceramics with a porous granular microstructure being far from homogenous are commonly used in the applications as mentioned above. In such heterogeneous material systems, local thermal expansion (CTE) mismatches, non-uniformities and anisotropy of the different constituents naturally lead to the appearance of internal stresses which are essentially the driving mechanisms for micro-cracking and damage. Under highly transient external thermal loading conditions, the resulting heterogeneous temperature distribution may lead to a complicated mechanical response along with a nonuniform mechanical and physical property degradation accompanied by irreversible geometry changes. The altered distribution of the mechanical properties dictates the macroscopic response when the external loading is further varied. Therefore, a strong coupling between the evolving microstructure and the macroscopic response arises. Moreover, microstructural configurational changes may trigger a significant interaction between the mechanical and thermal fields, for instance due to a reduced heat transport across a damaged interface. Therefore, an approach taking into account these mechanisms sufficiently well would render a versatile tool to improve the understanding of the influence of mechanical and thermal properties at the constituent level and their mutual interaction from a microstructural perspective. In this thesis, a concurrent multi-scale framework for the thermo-mechanical analysis of heterogeneous materials is proposed, with a particular focus on coarse grained refractory ceramics. The framework is essentially based on a rigorous extension of the well established FE2 computational homogenization technique, where the local macroscopic response is determined through the solution of a boundary value problem defined on a representative volume of the underlying microstructure. At first, the computational homogenization ideas are explored in the context of pure heat conduction processes in heterogeneous solids. Subsequently, the framework for coupled thermo-mechanical analyses is constructed by combining the first order mechanical homogenization with the dual procedure developed for heat conduction, within an operator-split (or staggered) solution algorithm which is composed of incrementally uncoupled nested (FE2) solution blocks for thermal and mechanical equilibrium subproblems. For predictive computations, the mechanical and thermophysical properties of individual phases and interfaces at the microstructural level are required, which is a distinctive characteristic of such a multi-scale approach. Due to the lack of material data, particularly for interfaces, direct numerical simulations (DNS) are exploited to identify the parameters inversely by using a limited set of molten aluminium thermal shock test results. On the basis of a microstructure composed of mutually noncontacting large grains embedded in a homogeneous matrix reflecting a compound of very fine grains, molten aluminium thermal shock tests are reproduced in full detail under realistic boundary conditions and a computational procedure is developed to determine the damage distribution along the specimen which is compared to experimental results. The failure mechanisms at the matrix-grain interface level are resolved by introducing thermo–mechanical cohesive zone elements not only capable of accounting for the mechanical decohesion but also including the reduced heat transport through themechanically damaged interfaces. Fine scalemicro-cracks within the matrix are smeared out by using a well-established continuum damage mechanics formulation which is free of any pathological localization and mesh sensitivity problems. Direct numerical simulation of thermal shock tests has also served for the investigation of short range effects (due to the local CTE mismatch) and long range effects (elastic fields accompanying the temperature gradient) on the resulting thermo-mechanical damage profile, through variations of different microstructural material parameters. In the last part of the thesis, predictive capabilities of the developed analysis framework are assessed by means of the two–scale analysis of a real size ladle refractory lining, based on the microstructural parameters identified through direct numerical simulations.