Functionally Graded Materials (FGMs) are materials that exploit spatially varying properties to achieve conflicting performance objectives in the same part.  Compositionally graded alloys are FGMs that can exhibit the high performance of metals while also producing larger gradients in properties than varying structure alone. Directed energy deposition (DED) has enabled rapid development of these materials through layer-by-layer control of composition, but the formation of secondary phases during this process can often lead to cracks or deleterious properties.

In prior work, a computational methodology was developed that can design compositional gradients to avoid these phases at any temperature in high dimensions. In short, the methodology builds a surrogate model of phase regions from CALPHAD software and then uses a path planning algorithm to design compositional paths that avoid undesirable phase regions while optimizing a specified cost function. However, prior work only considered cost functions that minimize path length or maximize 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, by controlling deposition rate, monotonic property gradients can be used to make parts with nearly any properly bounded linear, monotonic, or even non-monotonic property gradient. Lack of Monotonicity is introduced from the literature as a metric of measuring the non-monotonicity of general functions. The proposed cost function uses this metric to find the shortest path with a monotonic property profile and is shown to be compatible with optimal path planners.

A synthetic case study is conducted to demonstrate the cost function’s ability to find the shortest path with monotonic properties in a simple environment.  The case study also 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 straight-line, shortest length path is shown to produce a non-monotonic property profile that might produce problematic discontinuities in CTE. In contrast, the new cost function produces the shortest path with a monotonic property profile. The deposition of the monotonic path on a hypothetical part is then planned subject to a maximum CTE gradient and maximum deposition rate.

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.


Computational Design of Compositionally Graded Alloys for Property Monotonicity

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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