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Research Papers: Design Automation

Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials

[+] Author and Article Information
Tanner Kirk

Design Systems Laboratory
Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: tannerkirk@tamu.edu

Edgar Galvan

Quantitative Modeling and Analysis,
Sandia National Laboratories,
Livermore, CA 94551
e-mail: egalvan@sandia.gov

Richard Malak

Design Systems Laboratory
Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: rmalak@tamu.edu

Raymundo Arroyave

Computational Materials Science Laboratory,
Materials Science and Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: rarroyave@tamu.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 1, 2018; final manuscript received July 4, 2018; published online September 7, 2018. Assoc. Editor: Andres Tovar.

J. Mech. Des 140(11), 111410 (Sep 07, 2018) (9 pages) Paper No: MD-18-1274; doi: 10.1115/1.4040816 History: Received April 01, 2018; Revised July 04, 2018

Additive manufacturing (AM) has enabled the creation of a near infinite set of functionally graded materials (FGMs). One limitation on the manufacturability and usefulness of these materials is the presence of undesirable phases along the gradient path. For example, such phases may increase brittleness, diminish corrosion resistance, or severely compromise the printability of the part altogether. In the current work, a design methodology is proposed to plan an FGM gradient path for any number of elements that avoids undesirable phases at a range of temperatures. Gradient paths can also be optimized for a cost function. A case study is shown to demonstrate the effectiveness of the methodology in the Fe–Ni–Cr system. Paths were successfully planned from 316 L Stainless Steel (316 L SS) to pure Cr that either minimize path length or maximize separation from undesirable phases. Examinations on the stochastic variability, parameter dependency, and computational efficiency of the method are also presented. Several avenues of future research are proposed that could improve the manufacturability, utility, and performance of FGMs through gradient path design.

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References

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Figures

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Fig. 5

Rapidly exploring random tree created to plan a path between Pure Cr and 316 L SS that minimizes path length. Optimal path emphasized.

Grahic Jump Location
Fig. 6

Ten runs of the path planning algorithm with various random seeds and their respective costs. All attempt to plan a path between Pure Cr and 316 L SS that minimizes path length, as calculated in Eq. (4).

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Fig. 4

The effect of the number of function evaluations on the performance of the CSA [14] as measured by (a) misclassification rate, (b) precision, and (c) recall

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Fig. 3

Undesirable phase boundaries determined from multiple runs of the CSA with various maximum function evaluations. The solid black line represents the boundary obtained from a 505,000 sample, full-factorial grid sampling of calphad considered here as the “ground truth.” The points used to initialize the CSA for the CrNi2 phase at 600 K (triangles) and the sigma phase at 1000 K (squares) are also shown.

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Fig. 2

Approximate locations of CrNi2 phase (left) and sigma phase (right) are shown in three-dimensional composition-temperature space as determined from an evenly discretized (100 intervals in each dimension) grid of 505,000 samples of calphad. The maximum amount of each phase along the temperature dimension is also projected below the displayed phase regions onto same two-dimensional composition space.

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Fig. 1

(a) An example of the connection of randomly selected points to the tree in a general RRT algorithm. Point z1 demonstrates a point sampled from the obstacle region (Zobs). A collision check is made between point z1 and all neighboring nodes in the tree. If no potential connection passes the collision check, the point is not added to the tree. Point z2 is a point randomly sampled from the free region (Zfree). Such a point passes a collision check to one of its nearest neighbors and is therefore added to the tree. (b) An excerpt that highlights the nearest neighbors of point z2. (c) An example of the rewiring step of RRT* [16] in which nodes are connected to new parent nodes to reduce total path cost. (d) An example of the removal step of RRT*FN [15] in which certain nodes are deleted if the fixed nodes threshold is exceeded.

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Fig. 7

Rapidly exploring random tree created to plan a path between Pure Cr and 316 L SS that maximizes distance from the undesirable phase regions. Optimal path emphasized.

Grahic Jump Location
Fig. 8

Ten runs of the path planning algorithm with various random seeds and their respective costs. All attempt to plan a path between Pure Cr and 316 L SS that maximizes distance from the undesirable phase regions, as calculated in Eq. (5).

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Fig. 9

Rapidly exploring random tree created to plan a path between Pure Cr and 316 L SS that maximizes distance from the undesirable phase regions. Maximum nodal separation restricted to 0.05. Optimal path emphasized.

Grahic Jump Location
Fig. 10

Ten runs of the path planning algorithm with various random seeds and their respective costs. All attempt to plan a path between Pure Cr and 316 L SS that maximizes distance from the undesirable phase regions, as calculated in Eq. (5), and were planned with a maximum nodal separation of 0.05.

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Fig. 11

The number of constraint model evaluations performed by the path planning algorithm (RRT*FN) as a function of algorithm iterations for paths that minimize length, maximize clearance (distance from the undesirable phase regions), and maximize clearance at a higher resolution (nodal separation restricted to 0.05)

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