An inverse design framework for prescribing precipitation heat treatments from a target microstructure

Highlights: • A precipitation model and a nonlinear optimization tool were coupled to prescribe heat treatments in thermally aged alloys. • The figure of merit in this coupled framework compares size distributions of Ni₄Ti₃ precipitates in NiTi shape memory alloys. • The framework analyzes complex precipitate size distributions to prescribe times and temperatures of heat treatment stages. • This paper establishes the top-down structure processing link necessary for goal driven design of thermally aged alloys. The computer-aided materials design process is highly iterative in nature and as such requires flexible tools that have the ability to link processing, properties, and performance not only in the usual forward direction but also in the inverse direction more associated with a goal-oriented/design framework of Integrated Computational Materials Engineering (ICME). While many computational techniques exist that relate properties to performance in both forward/inverse directions, tools that prescribe a process when given a desired microstructure have not been developed in detail. This research fills that gap by coupling physics-based precipitation models with "mesh adaptive direct search" optimization techniques as a strategy to develop (inverse) microstructure-processing relations. This framework is demonstrated by prescribing heat treatments in Ni-rich NiTi shape memory alloys that will result in a desired size distribution of Ni ₄Ti ₃ precipitates. This prescriptive technique provides a rigorous strategy for the identification of materials processing schedules—provided the forward models connecting processing and microstructure are available—that yield specific microstructural features and that can significantly reduce the experimental search space that needs to be explored, accelerating the materials development process.