Statistically similar representative microstructures in elasto-plasticity

微观不均匀的高科技钢使雄心勃勃的工程建设成为可能。对于这种随机多相微结构的设计，数值模拟程序对于可靠地预测宏观边值问题的整体响应是很重要的。为这类问题设计的直接均匀化方案只有在复杂的随机微结构用明显不那么复杂的代表性体积元素(RVEs)来捕捉微尺度的基本形态属性来逼近时才是有效的。这是该项目的主要任务，其中有几个统计指标(谱密度、线性路径函数、Minkowski估值等)。这一时期的一个主要挑战是基于电子背散射衍射(EBSD)和聚焦离子束(FIB)测量的三维SSRVEs的设计。针对典型的宏观拉深成形过程，分析了利用所构造的SSRVEs进行直接均匀化的性能。

Micro-heterogeneous high-tech steels enable ambitious engineering constructions. For the design of such random multi-phase microstructures numerical simulation procedures are important for the reliable prediction of the overall response of macroscopic boundary value problems. Direct homogenization schemes, which are designed for such kind of problems, can only be efficient if the complex random microstructure is approximated by significantly less complex representative volume elements (RVEs) capturing the basic morphological attributes of the microscale. This is the main task in the project, where several statistical measures (spectral-density, lineal-path function, Minkowski valuations, etc.) are applied for the construction of statistically similar RVEs (SSRVEs) A main challenge in this period is the design of three-dimensional SSRVEs based on the Electron- Backscatter Diffraction (EBSD) combined with Focused-Ion-Beam (FIB) measurements. The performance of the direct homogenization approach using the constructed SSRVEs is analyzed for representative macroscopic deep-drawing processes.