Supplementary Information

Microstructural design and additive manufacturing and characterization

of 3D orthogonal short carbon fiber/acrylonitrile-butadiene-styrene

preform and composite

Zhenzhen Quana, b, Zachary Larimorec, Amanda Wud, Jianyong Yua, Xiaohong Qina, *, Mark

Mirotznikc, Jonghwan Suhre, Joon-Hyung Byunf, Youngseok Ohf, Tsu-Wei Choub, *

a. College of Textiles, Donghua University, Shanghai 201620, P. R. China

b. Department of Mechanical Engineering, and Center for Composite Materials, University of

Delaware, Newark, DE 19716, United States

c. Department of Electrical and Computer Engineering, University of Delaware, Newark, DE

19716, United States

d. Materials Engineering Division, Lawrence Livermore National Laboratory, CA 94550, USA

e. Department of Polymer Science and Engineering and Department of Energy Science,

Sungkyunkwan University, 440-746 Suwon, South Korea

f. Composites Research Center, Korean Institute of Materials Science, Changwon 641831, South

Korea

** Corresponding authors. E-mail address: xhqin@dhu.edu.cn (X. Qin) ; chou@udel.edu (T.-W.

Chou)

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Contents:

1. Topological feature of 3D orthogonal preforms

2. Equivalency among various combinations in Cartesian system

3. Topological design of 3D orthogonal preforms in cylindrical and spherical systems

4. FFF process for the demonstration of microstructural design

1. Topological feature of 3D orthogonal preforms

According to their alignment directions, yarns in a 3D orthogonal preform can be categorized

into three mutually perpendicular groups as shown in Fig. S1. Each group consists of a certain

number of unidirectional yarn sheets, each of which is further composed of a continuous yarn

oscillating back and forth along a specific direction.

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Fig. S1 - 3D orthogonal preform. Yarns of a 3D orthogonal preform are orientated along three

mutually perpendicular directions.

2. Equivalency among various combinations in Cartesian system

For the eight possible combinations in the Cartesian system, due to the interchangeability among

the X, Y and Z directions, they are not all unique and some of them actually give identical 3D

architectures.

Take X(Y):Y(Z):Z(X) for example. Given the interchangeability between X and Y, if exchanging

the “X” and “Y” designations (denoted as “X ⇔ Y”), the resulting combination is

X(Z):Y(X):Z(Y). The preforms corresponding to these two combinations are illustrated in Fig. S2

a(i). It is obvious that they possess identical microstructures and one can be obtained by simply

rotating the other one with respect to the Z-axis by 90°. The topological equivalency between

X(Y):Y(Z):Z(X) and X(Z):Y(X):Z(Y) is denoted as

Similarly, the topological equivalency between X(Y):Y(Z):Z(X) and X(Z):Y(X):Z(Y) can also be

demonstrated by exchanging the “Y” and “Z” designations as well as the “Z” and “X”

designations, as denoted in the following:

These results are also shown in Fig. S2 a(ii).

As to the other six possible combinations, it can be readily shown that they are all topologically

equivalent (Fig. S2 b). For instance, X(Y):Y(Z):Z(Y) can be converted to X(Z):Y(X):Z(X),

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X(Z):Y(Z):Z(Y) and X(Y):Y(X):Z(Y) by exchanging the designations of X⇔Y, Y⇔Z and Z⇔X,

respectively:

Consequently, out of the eight possible combinations in the Cartesian system, there are only two

types of topologically different 3D orthogonal preforms.

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(a)

ii

i

Fig. S2 - Topological equivalency among different combinations. (a(i)) Due to the

interchangeability between X and Y (“X ⇔ Y”), X(Y):Y(Z):Z(X) and X(Z):Y(X):Z(Y) represent the

identical 3D architecture. (a(ii)) The equivalency between X(Y):Y(Z):Z(X) and X(Z):Y(X):Z(Y).

(b) The other six combinations represent another identical preform topology.

3. Topological design of 3D orthogonal preforms in cylindrical and spherical systems

3.1 Cylindrical coordinate system

Yarn orientation: If orienting three yarn groups along the three coordinate axes in a cylindrical

coordinate system (Fig. S3 a), 3D cylindrically orthogonal preforms can be designed. Here,

yarns along the radial direction are termed as R-yarn, circumferential direction as θ-yarn and

cylinder axial direction as Z-yarn.

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(b)

Sheet alignment: Similar to the considerations in Cartesian coordinate system, continuous R-

yarns and Z-yarns can form yarn sheets. A sheet of R-yarns can be lying in the R-θ plane

(denoted as a R(θ)-sheet), or the R-Z plane (denoted as a R(Z)-sheet). Analogously, Z-yarns can

form a Z(R)-sheet or a Z(θ)-sheet. In contrast, θ-yarns cannot be aligned continuously in the form

of a yarn sheet; they only assume the shape of circles without ends. Thus, they are not considered

in the following design steps.

Combination of sheet alignments: In cylindrical preforms, since θ-yarns cannot assume the

form of a yarn sheet, the preform topology is determined only by the combinations of sheet

alignments with aligned R-yarns and Z-yarns (Fig. S3 b); there are 22=4 combinations.

Equivalency among various combinations: In cylindrical coordinate system, since there is no

interchangeability among R, θ and Z directions, each possible combination of sheet alignments

represents a topologically distinct 3D orthogonal preform. Therefore, there exist four kinds of 3D

cylindrical preforms.

Fig. S3 - Topological design of 3D orthogonal preforms in cylindrical coordinate system: (a)

yarn orientation, along θ, R and Z direction, and (b) four possible combinations of sheet

alignments.

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(a) (b)

3.2 Spherical coordinate system

Yarn orientation: Aligning yarns along the three principal axes of a spherical coordinate system

(Fig. S4 a) will enable the topological design of spherical 3D orthogonal preforms. Here, yarns

along the R, θ and β direction are denoted as R-yarns, θ-yarns and β-yarns, respectively.

Sheet alignment: In spherical preforms, all yarns can assume the form of continuous yarn sheets.

R-yarns can form an R(θ)-sheet or an R(β)-sheet, θ-yarns can form a θ(R)-sheet or a θ(β)-sheet,

and β-yarns can form a β(R)-sheet or a β(θ)-sheet.

Combination of sheet alignments: The topology of spherical preforms is determined by the

combination of sheet alignments of R-yarns, θ-yarns and β-yarns; there are 23=8 possible

combinations, as presented in Fig. S4 b.

Equivalency among various combinations: Due to the interchangeability between θ and β

directions, the possible topological equivalency among the 8 different combinations of sheet

alignments is checked following the same approach used for Cartesian coordinate system.

Consider R(θ):θ(R):β(R) for instance, by exchanging the “θ” and “β” designations (i.e., “θ ⇔

β”), it is converted to R(β):θ(R):β(R). The preforms of R(θ):θ(R):β(R) and R(β):θ(R):β(R) are

depicted in Fig. S4 c; both possess identical microstructures, since the R(θ):θ(R):β(R)

combination can be obtained by rotating the R(β):θ(R):β(R) combination with respect to the R-

direction by 90° and vice versa:

Similarly, the following equivalencies can be established:

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Therefore, there are altogether four distinct types of 3D spherical preforms.

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(a)

(b)

(c)

Fig. S4 - Topological design of 3D orthogonal preform in spherical coordinate system: (a)

yarn orientation, along R, θ and β direction, (b) the eight possible combinations of sheet

alignments, and (c) the equivalency between R(θ):θ(R):β(R) and R(β):θ(R):β(R).

3.3 Combination of different coordinate systems

The combination of different coordinate systems enables flexibility in preform design. The

Chinese lantern-shaped design with a hollow shaft (Fig. S5) can be designed by using spherical

coordinates and cylindrical coordinates at the central and end portions, respectively.

Fig. S5 - A Chinese lantern-shaped shaft with 3D orthogonal architecture, designed by

combining cylindrical and spherical architectures.

4. FFF process for the demonstration of microstructural design

The fabrication procedure includes four major steps: 3D model construction, model orientating

and slicing, layer-by-layer printing and post-processing. More specifically, a model with

designed 3D structural features was first constructed using computer aided design software.

Then, the designed 3D model was inputted into the processing software of 3D printer which

allows the preform to be scaled and oriented with respect to printing substrate. After scaling and

orienting, the solid model was sliced into a stack of 2D layers, each with a given thickness, and

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the printing path of each layer was determined by an optimizing algorithm built into the

processing software. Subsequently, a thermoplastic material (in the form of wire spool) was

supplied as the building material, melted and extruded through the printing head to fabricate the

preform layer by layer. In order to realize the printing of overhangs, as well as for the ease of

removing printed parts from substrate, dissolvable plastics were used as support materials.

Finally, after printing was finished, the as-fabricated part was immersed into water to remove the

support material.

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