Multiscale thermoplastic analysis in the solidification zone

激光焊接作为一种柔性、无接触的连接技术，越来越受到人们的重视。由于具有大熔化范围的合金的凝固开裂倾向，其加工提出了挑战。凝固裂纹的形成是由于枝晶组织与枝晶间熔体的临界应力和应变状态。尽管具有高度的工业相关性，但只有解决问题的单一方面的方法，无论是从结构上还是从功能上。研究单位“激光焊接中的凝固裂纹--高性能工艺的高性能计算”旨在发展对凝固裂纹机制及其与工艺参数关系的定量工艺理解。由于枝晶间熔体的枝晶微观结构的全场分辨率，考虑到这里流行的物理机制，将导致非常大的方程组，不允许有效的模拟过程，直接均匀化方法，FE²-方法，被应用。这在微观尺度上的枝晶凝固区和部件水平上的宏观尺度之间建立了联系。该项目与TP 5密切合作，致力于对固液界面前沿混合区的过程进行多尺度和多物理建模，其中凝固裂纹形成的关键区域位于该区域。在热机械耦合问题的FE²方法的多尺度方法中，在每个宏观积分点处，附加微观边界值问题（以代表性体积元的形式，RVE）并在能量一致的边界条件下求解，并且通过评估RVE的适当表面积分来获得宏观尺度上的相关材料响应。为了减少RVE的复杂性，统计相似的代表性体积元素（SSRVE），其建设是基于TP 6的枝晶微观结构的相场模拟。通过热塑性材料定律，在微观尺度上记录各个相的材料行为。宏观尺度上的建模需要考虑激光束的影响以及进一步的边界条件，这是从其他子项目中纳入的。多尺度方法的有效实施需要特别是与申请人Klawonn/Lanser的合作，这使得能够在高性能计算机上使用算法。该方法允许基于微观结构的局部状态变量作为宏观工艺参数的函数来预测分析凝固裂纹的形成。

As a flexible and contact-free joining technology, laser beam welding has increasingly gained importance. Processing of alloys with large melting range poses a challenge due to their solidification cracking tendency. Solidification cracks form due to critical stress and strain states of the dendritic microstructure with interdendritic melt. Despite the high industrial relevance, there are only approaches addressing single aspects of the problem, metallurgically or structurally oriented. The research unit “Solidification Cracking during Laser Beam Welding – High Performance Computing for High Performance Processes” aims at developing quantitative process understanding of the mechanisms of solidification cracking and their relation to process parameters.Since a full-field resolution of the dendritic microstructure with interdendritic melt, taking into account the physical mechanisms prevailing here, would lead to immensely large systems of equations that do not allow efficient simulation of the process, a direct homogenization method, the FE²-method, is applied. This establishes a link between the dendritic solidification zone on the microscale and the macroscale on the component level. In close cooperation with TP 5 this project is dedicated to multi-scale and multiphysical modelling of the processes in the mixture zone in the forefront of the solid-liquid interface, where the critical zone for the formation of solidification cracks is located. In the multi-scale approach of the FE²-method for thermomechanically coupled problems, at each macroscopic integration point microscopic boundary value problems (in the form of representative volume elements, RVEs) are attached and solved under energetically consistent boundary conditions and the associated material response on the macroscale is obtained through evaluation of suitable surface integrals of the RVEs. To reduce the complexity of the RVEs, statistically similar representative volume elements (SSRVEs) are used, whose construction is based on the phase field simulations of the dendritic microstructure of TP 6. By means of thermoplastic material laws, the material behaviour of the individual phases is recorded on the microscale. The modelling on the macroscale demands the consideration of the influence of the laser beam as well as further boundary conditions, which are incorporated from the other subprojects. The efficient implementation of the multiscale approach requires the cooperation especially with the applicants Klawonn/Lanser, which enables the use of the algorithms on high performance computers. This approach allows a predictive analysis of the formation of solidification cracks on the basis of local state variables of the microstructure as a function of macroscopic process parameters.