Computational Design of Compositionally Graded Alloys for Property Monotonicity

Functionally graded materials (FGMs) exhibit spatial gradients in properties that can be exploited to satisfy multiple conflicting performance objectives in the same part. Compositionally graded alloys are a subclass of FGMs that have received increased attention with the development of metal additive manufacturing. However, the formation of secondary phases can often lead to cracks or deleterious properties in these materials. In prior work, a computational methodology was presented that can design compositional gradients to avoid these phases at any temperature without the need to visualize phase diagrams (Kirk et al., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” ASME J. Mech. Des., 140(11), p. 111410). The methodology optimizes gradient paths through composition space for a specified cost function, but prior work only considered minimizing path length or maximizing the distance from undesirable phases. 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.