Numereical Microstructure Optimisation of Melt-Infiltrated Metal-Ceramics Composites

具有层状微观结构的熔融渗透金属/陶瓷复合材料是处于发展阶段的材料，其宏观热力学性能与层状畴的取向分布密切相关。创建其微观结构的虚拟模型，并因此将其用于执行微观结构优化的应用，将支持这些材料的定向生产。微观结构建模和数值优化使得在不同设计变量的组合下数值再现复合材料的行为成为可能，从而减少生产和实验的工作量。这样，就有可能指导进一步的材料开发。在宏观尺度上，将采用有限元方法进行MMC建模。在微观尺度上，代表微观结构的单畴的有效性质将使用数值均匀化程序计算。本项目前期提出了金属内部塑性流动和陶瓷内部损伤的均匀化和建模方法。为了完善这些模型，将对微观结构的三维性以及识别一些缺失的输入参数进行具体的实验研究。通过对陶瓷预制体进行计算机层析成像，将提供这些区域的三维表示，然后直接用于创建真实微观结构的有限元模型和生成三维合成微观结构。这些模型将用于改进已开发的均质化程序。在下面，将提供有限元建模和均匀化，以计算畴的热性能。在对微尺度模型进行实验验证后，所开发的方法将用于宏观尺度上的微观结构优化。由于两相的热性能差异较大，因此MMC组件的热流优化在理论和材料开发方面都具有重要意义。我们考虑了三个优化问题：首先，热传导问题的局部最高温度（热点）的最小化；其次，热弹性问题的有效热膨胀最小；最后，将所提出的优化程序扩展到具有两个弱耦合场（热传导和弹性）的多物理场问题的求解中。

Melt-infiltrated metal/ceramic composites with lamellar microstructure are materials in the de-velopment stage and show strong dependence of their macroscopic thermo-mechanical properties on the orientation distribution of the lamellar domains.The creation of a virtual model of their microstructure and, consequently, their application for performing microstructural optimization will support the well-directed production of these materials. The microstructure modeling and numerical optimization make it possible to reproduce numerically the behavior of the composite for different combinations of the design variables and, thereby, to reduce the production and experiment efforts. In this way, it will be possible to direct the further material development. MMC modeling at the macroscale will be provided by means of the finite element method. The effective properties of the single domains representing the microstructure on the microscale will be calculated using the numerical homogenization procedure. The suitable homogenization and mod-eling of the plastic flow in the metal and damage in the ceramics were proposed in the previous phase of this project. For refining these models, specific experimental studies will be performed with regard to the three-dimensionality of the microstructure as well as for the identification of some missing input parameters. The 3D representation of the domains by means of computer tomogra-phy of the ceramic preform will be provided and after that directly utilized for creation of the FE models of the real microstructure and for generation of the 3D synthetic microstructure. These models will be utilized for improvement of the developed homogenization procedure. In the follow-ing, the FE modeling and homogenization will be provided for calculation of the thermal properties of the domains. After the experimental verification of the micro-scale modeling, the developed methods will be used for microstructure optimization on the macroscale. Due to the large difference between the thermal properties of the two phases, the optimization of the heat flow in MMC components is important both theoretically and in relation to problems of the material development. We consider three optimization problems: firstly, the minimization of the highest local temperature (hot spot) for the heat conduction problem; secondly, the minimization of the effective thermal expansion for the thermo-elastic problem; finally, the proposed optimization procedures will be extended for the solution of the multiphysics problem with two weakly-coupled fields (heat conduction and elasticity).