Computational Design of Compositionally Graded Alloys

Abstract

In this work, a new computational methodology is presented for the design of compositionally graded alloys. Compositionally graded alloys are a class of functionally graded materials, or materials which exhibit spatially varying properties. While the introduction of additive manufacturing has accelerated interest in these materials, there are many challenges that impede their development like the formation of deleterious phases and material compositions that are incompatible with manufacturing processes. Previous design methods have attempted to design gradients that avoid these issues, but such methods have been limited to the analysis and interpretation of two-dimensional diagrams and are therefore hindered by the limits of human visualization and ideation. The proposed methodology is made possible by the novel formulation of gradient design as a path planning problem. This formulation allows the use of path planning algorithms to optimize gradient paths in composition space. Such algorithms can optimize gradients with any number of constituent elements to meet specified design requirements or objectives. To make the gradient design problem tractable for such algorithms, surrogate modeling techniques are employed to represent design constraints and objectives. Constraints, like deleterious phase formation, can be predicted by CALPHAD software and then modeled by a machine learning classifier. Similarly, regression models can be trained to evaluate cost functions in an efficient manner. Several unique problem formulations are demonstrated to showcase the advantages of the methodology in gradient design. Among these are constraints to avoid deleterious phase regions and other regions of the state space with poor predicted manufacturability. Common cost functions in the path planning community, like path length and obstacle clearance, are shown to be useful for some problems, while including constraint violation as penalty term is demonstrated to satisfy constraints that might otherwise be unachievable. Lastly, a novel cost function is proposed to design gradients with monotonic properties, which can achieve nearly any bounded property distribution on a gradient part. All proposed problem formulations are demonstrated in the design of authentic compositionally graded alloys and experiments are used to validate predicted results.