Compositionally graded alloys can realize multiple conflicting properties in the same part, but the formation of secondary phases can often lead to cracks or deleterious properties. In prior work, a computational methodology was presented that can design compositional gradients to avoid these phases at any temperature in high dimensions [1]. The methodology also optimizes paths for a specified cost function, but prior work only considered minimizing path length or maximizing obstacle clearance. In this work, a new cost function is presented to produce compositional paths with optimal property gradients. Specifically, monotonicity is presented as the optimal quality of a pathwise property gradient because monotonic property gradients can be transformed to nearly any form on the part by controlling deposition rate. The proposed cost function uses a metric for non-monotonicity to find the shortest path with monotonic properties and is shown to be compatible with optimal path planners. A synthetic case study examines the effect of a cost function parameter on the trade-off between length and monotonicity. The cost function is also demonstrated in the Fe-Co-Cr system to find a compositional path with monotonic gradients in Coefficient of Thermal Expansion (CTE). The deposition of the path on a hypothetical part is then planned subject to a maximum deposition rate and CTE gradient. Future work is proposed to extend the framework to optimize multiple properties at once and to incorporate Multi-Material Topology Optimization (MMTO) techniques into a complete design methodology for functionally graded metal parts.

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