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，日益受到重视。由于合金的凝固开裂倾向，大熔点合金的加工是一个挑战。凝固裂纹是由于枝晶组织与枝晶间熔体的临界应力和应变状态所致。尽管具有很高的工业相关性，但只有从冶金或结构上解决问题的单一方面的办法。“激光焊接过程中的凝固裂纹--高性能工艺的高性能计算”研究单元旨在发展对凝固开裂机理及其与工艺参数之间的关系的过程的定量理解。考虑到这里普遍存在的物理机理，考虑到这里普遍存在的物理机制，考虑到这里普遍存在的物理机制，对具有枝晶间熔体的枝晶微结构进行全场解析将导致极大的方程系统不能有效地模拟工艺，因此采用了一种直接的均匀化方法，即有限元-方法。这在微观尺度上的树枝晶凝固区和成分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模拟，该混合区是形成凝固裂纹的临界区。在热力耦合问题的有限元方法的多尺度方法中，在每个宏观积分点处附加并在能量一致的边界条件下求解微观边值问题(以代表性体积单元的形式)，并通过计算代表体积单元的适当的表面积分来获得宏观尺度上的相关材料响应。为了降低RVEs的复杂性，采用了统计相似的代表性体积单元(SSRVEs)，其构造基于对TP 6枝晶组织的相场模拟。借助热塑性材料定律，在微观尺度上记录了各相的材料行为。在宏观尺度上的建模需要考虑激光的影响以及从其他子项目中合并的进一步的边界条件。多尺度方法的有效实施需要特别是与申请者Klaonn/Lanser的合作，这使得算法能够在高性能计算机上使用。这种方法允许根据微观组织的局部状态变量作为宏观工艺参数的函数来预测凝固裂纹的形成。

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.