Inverse Monte Carlo Grain Growth Analysis for Process Design

In this work, we solve the inverse problem to determine the required processing conditions to create a prescribed columnar microstructure in a metal film. Thermal processing is used by metals manufacturers to generate desired microstructural features and thus, properties. However, the processing conditions are typically specified based on experience and trial and error, leading to a longer development cycle and resulting process parameters that may not be optimized. In this work, we develop an approach to determine the processing parameters that will create a columnar grain structure. The columnar grain structure results from a slowly moving temperature gradient applied to the metal, and creates a creep resistant material along the elongated grain direction. To model the forward problem, we developed a new parallel Monte Carlo method for modeling microstructure evolution in manufacturing processes that involves a time-dependent local temperature gradient. To capture the effects of the temperature gradient, the site selection probability in each Monte Carlo step is biased accordingly across the domain. This new biased sampling strategy is built upon the scaling relation between the Potts Monte Carlo method and physical observations. The inverse problem of determining the process parameters to create a columnar microstructure is posed as a binary classifier. To improve the computing performance, a reduced model or classifier is built from the new Monte Carlo method, and it is used as the forward model in the inverse problem. The forward grain growth model takes as inputs the temperature field calculated by a heat transfer finite element model. A genetic algorithm is used to drive the heat transfer model and the forward grain growth model to search for the optimal process parameters under constraints such that columnar growth can be created. The manufacturing design parameters that control the temperature field are solved for in this inverse analysis. Some examples demonstrating the algorithm will be presented.