Statistically similar representative microstructures in elasto-plasticity

微异质高科技钢使雄心勃勃的工程建设成为可能。对于这类随机多相微观结构的设计，数值模拟程序对于宏观边值问题整体响应的可靠预测具有重要意义。为解决这类问题而设计的直接均质方案，只有当复杂的随机微观结构被明显不那么复杂的代表性体积元（RVEs）所近似时，才能有效地捕获微观尺度的基本形态属性。这是该项目的主要任务，其中几种统计度量（谱密度，线性路径函数，Minkowski估值等）用于构建统计相似的rve （ssrve）。这一时期的主要挑战是基于电子-背散射衍射（EBSD）结合聚焦离子束（FIB）测量的三维ssrve设计。针对具有代表性的宏观拉深过程，分析了利用所构建的ssrve直接均匀化方法的性能。

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.