Linear Solution Scheme for Microstructure Design with Process Constraints

This paper addresses a two-step linear solution scheme to find an optimum metallic microstructure satisfying performance needs and manufacturability constraints. The microstructure is quantified using the orientation distribution function, which determines the volume densities of crystals thatmake up the polycrystal microstructure. The orientation distribution function of polycrystalline alloys is represented in a discrete form using finite elements, and the volume-averaged properties are computed. The first step of the solution approach identifies the orientation distribution functions that lead to the set of optimal engineering properties using linear programming. This step leads tomultiple solutions, of which only a few can bemanufactured using traditional processing routes such as rolling and forging. In the second step, textures froma given process are represented in a space of reduced basis coefficients called the process plane. This step involves generation of orthogonal basis functions for representing spatial variations of the orientation distribution functions during a given process using proper orthogonal decomposition. Multiple orientationdistribution function solutions in step one are then projected onto these basis functions to identifywhich of the optimal textures are feasible through a given manufacturing process. This feasibility is determined with two approaches. The first approach finds the closest match to the orientation distribution function solutions in the material plane, whereas the second approach finds the closest match to a desired set of properties instead of the orientationdistribution functions. Themethod is explained throughan example of vibration tuning of a galfenol alloy, with the primary objective of maximizing the yield strength.