A Subspace-Inclusive Sampling Method for the Computational Design of Compositionally Graded Alloys

Abstract

Compositionally graded alloys, a special class of functionally graded materials (FGMs), utilize localized variations in composition within a single metal part to achieve higher performance than traditional single-material parts. In previous work [1], the authors presented a computational design methodology that avoids common issues which limit a gradient alloy’s usefulness or feasibility, such as deleterious phases or properties, and also optimizes gradients for performance objectives. However, the previous methodology only samples the interior of a composition space, meaning designed gradients must include all elements in the space at every step in the gradient. Because the addition of even a small amount of an alloying element can introduce a new deleterious phase, this characteristic often neglects potentially simpler solutions to otherwise unsolvable problems and, consequently, discourages the addition of new elements to the state space. The present work improves upon the previous methodology by introducing a sampling method that includes subspaces with fewer elements in the design search. The new sampling method samples within an artificial expanded form of the state space and projects samples outside the true region to the nearest true subspace. This method is evaluated first by observing the distribution of samples in each subspace of a 2-D, 3-D, and 4-D state space. Next, a parametric study in a synthetic 2-D problem compares the performance of the new sampling scheme to the previous methodology. Lastly, the updated methodology is applied to design a gradient from stainless steel to equiatomic NiTi that has practical uses such as embedded shape memory actuation and for which the previous methodology fails to find a feasible path.