Structure-unit cell-based approach on three-dimensional representative braided preforms from four-step braiding: Experimental determination of effects of structure-process parameters on predetermined yarn path

Abstract

The aim of this study was to understand the effects of braid pattern and the number of layers on three-dimensional (3D) braided unit cell structures. Various unit cell-based representative 3D braided preforms were developed. Data generated from these structures included unit cell dimensions, yarn angle, and yarn length in the unit cell structures.

It was shown that braid patterns affected the 3D braided unit cell structures. The 1 × 1 braid pattern made fully interconnected integral 3D braided unit cell structures, whereas the 2 × 1 braid pattern created disconnected braid layers that were connected to the structures edges. When the number of layers increased, 3D braided unit cell thickness also increased. Braid pattern slightly affected the braider yarn angle, whereas the number of layers did not influence it. It was observed that the number of layers considerably affected the yarn length in the unit cell structure. Increasing the layer number from five to 10 layers created a yarn path in the unit cell edge regions called the ‘multilayer yarn length’. This yarn path was not observed below five-layer 3D braided unit cell structures. In jamming conditions, minimum jamming decreased the width of the unit cell structure, but maximum jamming increased its width. On the other hand, minimum jamming decreased the surface angle of the unit cell structure, whereas maximum jamming increased the surface angle. In addition, it was realized that jamming conditions influenced the density of the unit cell but did not affect the yarn length in the unit cell structures.

Keywords

four-step braiding predetermined yarn path preform jamming conditions textile composites three-dimensional representative braided preform

Introduction

Three-dimensional (3D) braiding is a preform technique used in the multidirectional near-net shape manufacturing of high damage-tolerant structural composites for civilian and defense areas, such as aerospace and various industrial applications.¹^–⁴

3D braided preforms are fabricated by traditional maypole braiding (slotted horn gear matrix) or innovative four-step braiding (track and column), or more recently by 3D rotary braiding. In the four-step braiding process, there is one set of longitudinal yarns arranged in column and row directions in the cross-section. These yarns are all intertwined with each other by at least four distinct motions in each machine cycle. The braider carriers move simultaneously in predetermined paths relative to each other within the matrix to intertwine the braiding yarns to form the braided preform.⁵^–¹³ 3D rotary braiding is an extension of maypole braiding that allows the braider carrier to be independently and arbitrarily moved over a base plate so that each braider yarn is placed and interlaced into a 3D preform.¹⁴^–²³

The properties of 3D braided preform composite material depend on fiber and matrix, fiber orientation (θ), and fiber volume fraction (V_f). The fabric geometry model (FGM) was developed to characterize the 3D braided preform composite with regard to fiber and matrix, and processing parameters. 3D braided unit cell geometry in the FGM requires two basic components: fabric geometry and the determination of the fiber volume fraction. Fabric geometry is a function of the compacting (take-up rate) action during fabric formation, while yarn displacement values in terms of the number of yarns depend on row and column motions. The orientation of the yarns in a 3D preform depends on fabric construction, fabric shape, and the dimensions of the braiding loom.²⁴ The yarn orientation angle tends to decrease as the number of yarns in the fabric increases. For the same number of yarns in the fabric, the yarn orientation angle decreases as the linear density of the fabric decreases. It was reported that the maximum attainable V_f in a uniaxially aligned fiber structure is 90.6%, whereas the maximum fiber volume fraction of a 3D braided preform is 68%.^24,25 A computer-aided design (CAD) model was developed to describe representative volume elements for four-step braided composites. The model considered the unit cell in interior, surface, and corner volume elements for different yarn crimps and braiding take-up.²⁶ The effects of processing parameters on 3D braided preforms produced from four-step braiding were studied. It was claimed that the braider yarns carry loads in all directions, so the orientation angle must be adjusted to match the product’s end-use.²⁷

The research revealed that the strength of 3D braided preforms, for a given yarn, tends to increase as the number of yarns in the fabric increase.²⁸ The rate of increase is more rapid for fabrics with yarns of lower linear density. For the same number of yarns in the fabric, the axial strength of the fabric tends to increase as the linear density of the fabric decreases. On the other hand, fabric linear density is directly related to yarn orientation angle.²⁸ The effect of cut edges, filament bundle size, and braid pattern were examined through tensile, compressive, flexural, and shear tests. It was found that the specimens were sensitive to cut edges where the tensile strength of the cut and shaped graphite-epoxy preform composite was reduced.²⁹ The braid pattern also had an important effect on tensile strength. For instance, changing the yarn orientation from a 1 × 1 to a 1 × 3 braid pattern reduced the yarn orientation angle. As a result, the preform tensile strength was increased.²⁹ In general, it was found that the tensile strength and modulus of 3D braided composites tend to increase as filament bundle size increases. Although the strength and modulus of braided composites were significantly higher than those of the 0°/90° woven laminates, the Poisson’s ratio of the braided composites was very large, leading to instability in the transverse direction; by adding transverse yarns, the Poisson’s ratio of the braided composite was reduced, but at the cost of a reduction in strength and modulus.²⁹

The fiber inclination model was developed to predict the effective in-plane elastic moduli of 3D braided composites. A modified classical laminated plate analysis formed the basis of the approach. The model confirmed the influence of yarn orientation angle on composite elastic properties, with the performance approaching that of unidirectional laminae as the braiding angle becomes smaller, and the elastic shear modulus increasing as the braiding angle increases.³⁰ The elastic strain energy method was used to correctly predict the axial (braiding direction) elastic moduli to be functions of the yarn orientation and fiber volume fraction, and the elastic moduli were determined to be sensitive to the braid geometry, increasing as the yarn orientation angle decreases, that is, as the yarns become more aligned with the tensile axis.³¹ Another model was developed to characterize the yarn structures in 3D braided preform produced from four-step braiding. The method involved the general topology of the yarn structure based on the braiding processing parameters and then related the characterizing parameters to the final dimensions of the preform after consolidation. It was shown that the topological characteristics in both rectangular and tubular braided preforms were the same.³² On the other hand, modelingof the preform unit cell was carried out by a micromechanics procedure and related to the braiding parameters. It was demonstrated that the unit cells in the preform interior were different from those on the boundary.³³ A model using the digital element approach investigated the microstructure of 3D braided preforms and composites. The model calculated tensile and shear stiffness and the Poisson’s ratio more accurately compared to the topological model.³⁴ The multilayer interlock braided composites produced by traditional maypole braiding were analyzed as a function of material, braiding, and consolidation parameters by the Voight and Reuss bounds and cell methods.³⁵

The aim of this study was generally to understand the effects of braid pattern and the number of layers on developed representative 3D braided preform unit cell structures.

Materials and methods

Four-step braiding method

An experimental rig was constructed to make a representative 3D braided preform based on the four-step braiding method. This method involves four distinctive steps to braid three to 10 layer preforms. Figure 1 shows the 1 × 1 braid pattern (a1–e1), 2 × 1 braid pattern (a2–e2), 3 × 1 braid pattern (a3–e3), and 4 × 1 braid pattern (a4–e4). The 1 × 1 braid pattern means the braider carrier moves just one braider carrier distance in the row and column directions, whereas the 2 × 1 braid pattern means the braider carrier moves two and one braider carrier distance in the row and column directions, respectively. The same analogy can be applied to 3 × 1 and 4 × 1 braid patterns.³⁶

Figure 1.

Four-step braiding method to make representative braided preforms; braid pattern 1 × 1 (a1–e1), braid pattern 2 × 1 (a2–e2), braid pattern 3 × 1 (a3–e3), and braid pattern 4 × 1 (a4–e4).

In order to make the representative 3D braided preform in a 1 × 1 braid pattern, the braider carrier must be arranged in a matrix of rows and columns as presented in Figure 1(a1). The first step is sequential and the reversal movement of the braider carriers is in the column direction (b1). The second step is sequential and the reversal movement of the braider carriers is placed on the rapier in the row direction (c1). The third step is again sequential and the reversal movement of the braider carriers is in the column direction (d1). The fourth step is again sequential and the reversal movement of the braider carriers is placed on the rapier in the row direction (e1). These steps were repeated depending on preform length requirements. Braid patterns other than 1 × 1 are also shown in Figure 1 in steps a2–e2 for the 2 × 1 pattern, a3–e3 for the 3 × 1 pattern, and a4–e4 for the 4 × 1 patterns, where the braider carriers on the rapier move two, three, and four braider carrier distances in the row direction, respectively. The number of braider carrier can be expanded in row and column direction depending upon preform dimensions.

Three-dimensional representative braided preforms

3D representative braided preform structures with polyethylene tubes (diameter 5 mm and wall thickness 1 mm) using the four-step braiding method are shown in Figure 2. All tubes in the developed preforms were aligned in one direction. They were intertwined to form the braided structure. The braided structures were designed as 1 × 1 (Figure 2(a)), 2 × 1 (Figure 2(b)), 3 × 1 (Figure 2(c)), and 4 × 1 (Figure 2(d)) braided patterns.

Figure 2.

Three-dimensional representative braided preform structures where a polyethylene tube was used instead of high-modulus yarns. Front (left) and side (right) views of 10-layer braided preform in braid pattern 1 × 1 (a), front (left) and side (right) views of 9 layer braided preform structure in braid pattern 2 × 1 (b), front (left) and side (right) views of three-layer braided preform structure in braid pattern 3 × 1 (c), and front (left) and side (right) views of three-layer braided preform structure in braid pattern 4 × 1 (d).

Parameters measured in three-dimensional representative braided preform unit cell

Measurements of the 3D representative braided preform were performed in two states: (1) the ‘out of loom’ condition called normal; and (2) jamming conditions, the minimum and maximum conditions of which are shown in Figure 3. The state of the normal condition is defined as ‘after the 3D representative braided preform structure was fabricated, it was removed from the loom and left on the table without applying any force’. The state of the minimum jamming condition is defined as ‘after the 3D representative braided preform structure was fabricated, it was removed from the loom and left on the table and tensile force was applied at both ends (longitudinal direction) until the minimum braider angle is reached, and the structure is kept in this state’, whereas the state of the maximum jamming condition is defined as ‘after the 3D representative braided preform structure was fabricated, it was removed from the loom and left on the table and tensile force was applied at both edges (transverse direction) until to the maximum braider angle was reached, and the structure was kept in this state’. The measurements of the representative preforms in normal conditions were carried out in force-free environments (Figure 3(a)). However, measurements in jamming conditions were carried out with longitudinal (Figure 3(b)) and lateral force (Figure 3(c)) applied to the representative preform.

Figure 3.

Representative braided preform conditions; measurement on representative preform in the out-of-loom condition (or normal condition) (a), measurement of representative preforms in jamming conditions, minimum condition (b), and maximum condition (c).

Dimensions

Width and thickness measurements of the representative 3D braided preform structures were carried out. On the other hand, width, thickness, and length measurements were performed on the best representative unit cell in the 3D braided preform structures.

Angles

Surface angle (θ) and edge angles (θ_e) were measured on the surface of the 3D representative braided preform structures, as shown in Figure 4. Braider(+) and braider(−) angles (θ_b) were measured in the out-of-lane direction of the 3D representative braided preform structures by means of a 4 mm rod, as shown in Figure 5. It was also observed that when the braider layer increased from four to 10 layers, an additional yarn path called the ‘multilayer yarn length’ (l_m) occurred in the inside part of the edge of the 3D representative braided preform structure, as shown in Figure 6. This yarn was at an angle to the edge of the 3D braided structure. This yarn angle, called the multilayer angle (θ_m), was also measured.

Figure 4.

Measured angles on three-dimensional representative braid preform structures: surface angle (a); edge angle (b).

Figure 5.

Measured angle on three-dimensional representative braid preform structure: braider(–) angle (a); braider(+) angle (b).

Figure 6.

Measured yarn length on three-dimensional representative braid preform structure: corner yarn length (l_c) (a); edge yarn length (l_e) (b); multilayer yarn length (l_m) (c).

Density

The density of the braider(+) and braider(−) representative yarns was measured on the surface of the 3D representative braided preform structure and these were then added to find the total yarn density, which was denoted as ‘b’. In addition, total yarn ends for each braided structure were found in the following relations as:

(1)

where M is the number of layers, C is the number of columns, R is the braid carrier movement in the row direction based on the braid pattern, and N is the total yarn ends per braided preform structure.

Yarn lengths

Measured yarn lengths in the 3D representative braided preform structures are shown in Figures 6 and 7. These included surface yarn length (l), braider (l_b), and surface arc (l_a) lengths, as shown in Figure 7, and corner yarn length (l_c), edge yarn length (l_e), and multilayer yarn length due to the preform thickness (l_m), as shown in Figure 6.

Figure 7.

Measured yarn length on three-dimensional representative braid preform structure: surface yarn length (l) (a); schematic yarn path in the structure (b); braider yarn length (l_b) and surface arc length (l_a) (c).

Actual yarn length (l_l) and total yarn lengths for thin (l_tt) and thick (l_tk) preform structures were calculated in the following relations as:

(2)

(3)

(4)

Results and discussion

Unit cell structure results

A 3D braided unit cell structure using the four-step braiding process with a 1 × 1 braid pattern was developed for three to 10 layers. The representative braided preform structures and CAD drawings of their unit cells using Unigraphics NX6 are shown in Figure 8. Yarns in the 3D braided unit cell were intertwined with each other and all yarns were interlocked in each braid layer in the in-plane directions and in each adjacent layer in the out-of-plane directions. Therefore, the 3D braided unit cell structures were fully interlocked. In the 2 × 1 braid pattern, yarns in the 3D braided unit cell were intertwined with each other and all yarns were interlocked in each braid layer in the in-plane directions, whereas there was no interlocking in each adjacent layer in the out-of-plane direction except at the edge of the braid structure, where the first layer was locked to the second layer and the third layer was locked to the fourth layer on both edges of the braid structure. Therefore, there was an empty pocket between each braid layer in the structure, as shown in clearly Figure 9 for three-, six-, and nine-layer braided structures. The 3 × 1 and 4 × 1 braid pattern braided structures were similar to those of the 1 × 1 and 2 × 1 braid pattern braided structures, respectively. However, 3D braided structures in 3 × 1 and 4 × 1 braid patterns become coarse compared to those of 1 × 1 and 2 × 1 braid patterns due to long floating in the crossing regions in the 3D braided structure. These structures are shown in Figure 10. In addition, the dimensional specifications of 3D braided unit cell structures and jamming conditions are presented in Tables 1 and 2, respectively.

Figure 8.

Developed representative three-dimensional braided preform structures in 1 × 1 braid pattern using four-step braiding method: surface and side views of three-layer actual braided preform (left) and unit cell (right) (a); surface and side views of four-layer actual braided preform (left) and unit cell (right) (b); surface and side views of five-layer actual braided preform (left) and unit cell (right) (c); surface and side views of six-layer actual braided preform (left) and unit cell (right) (d); surface and side views of seven-layer actual braided preform (left) and unit cell (right) (e); surface and side views of eight-layer actual braided preform (left) and unit cell (right) (f); surface and side views of nine-layer actual braided preform (left) and unit cell (right) (g); surface and side views of 10-layer actual braided preform (left) and unit cell (right) (h).

Figure 9.

Developed representative three-dimensional braided preform structures in 2 × 1 braid pattern using four-step braiding method: surface, side and jamming condition views of three-layer actual braided preform (left) and unit cell (right) (a); surface, side and jamming condition views of six-layer actual braided preform (left) and unit cell (right) (b); surface, side, and jamming condition views of nine-layer actual braided preform (left) and unit cell (right) (c).

Figure 10.

Developed representative three-dimensional braided preform structures in 3 × 1 and 4 × 1 braid patterns using four-step braiding method: surface and side views of three-layer actual braided preform (left) and unit cell (right) (a); surface and side views of three-layer actual braided preform (left) and unit cell (right) (b).

Table 1.

Dimensional specifications of three-dimensional representative braided preform structures and unit cells

		Yarn	Structure	Unit cell
Braid pattern	Number of layers	Row × column	Width × thickness (cm)	Length × width × thickness (cm)	Density(ends/5 cm)
1 × 1	3	4 × 30	25.00 × 1.48	13.50 × 5.00 × 1.48	6
		4 × 60	45.50 × 1.68	14.50 × 4.00 × 1.68	7
	4	5 × 15	14.00 × 2.34	16.00 × 6.00 × 2.34	6
		5 × 30	24.50 × 2.30	16.50 × 5.00 × 2.30	6
	5	6 × 15	13.00 × 3.13	21.00 × 8.00 × 3.13	5
		6 × 30	25.50 × 3.00	20.00 × 8.00 × 3.00	5
	6	7 × 15	11.50 × 3.40	24.00 × 8.50 × 3.40	7
		7 × 30	24.50 × 3.38	21.00 × 8.00 × 3.38	7
	7	8 × 15	13.50 × 4.43	25.00 × 11.20 × 4.43	5
		8 × 30	23.50 × 3.94	26.00 × 10.50 × 3.94	7
	8	9 × 15	12.00 × 4.50	32.00 × 12.00 × 4.50	5
		9 × 30	29.00 × 4.72	35.00 × 15.50 × 4.72	6
	9	10 × 15	13.00 × 5.16	33.00 × 13.00 × 5.16	5
		10 × 30	29.50 × 5.02	38.00 × 14.00 × 5.02	6
	10	11 × 15	13.00 × 5.64	47.00 × 13.00 × 5.64	6
		11 × 30	32.00 × 6.42	54.00 × 20.00 × 6.42	5
2 × 1	3	4 × 15	10.50 × 3.20	28.00 × 10.00 × 3.20	5
		–	–	–	–
	6	7 × 15	11.00 × 6.94	41.00 × 9.00 × 6.94	4
		–	–	–	–
	9	10 × 15	11.50 × 9.09	41.00 × 9.00 × 9.09	4
		–	–	–	–
3 × 1	3	4 × 15	11.00 × 3.35	22.50 × 11.00 × 3.35	7
		–	–	–	–
4 × 1	3	4 × 15	8.20 × 5.22	35.00 × 8.20 × 5.22	7
		–	–	–	–

Table 2.

Dimensional specifications of jamming conditions of three-dimensional representative braided preform structures and unit cells

			Yarn	Structure	Unit cell
Jamming conditions of braided structures	Braid pattern	Number of layers	Row × column	Width × thickness (cm)	Length × width × thickness (cm)	Density (ends/5 cm)
Minimum	1 × 1	3	4 × 30	17.00 × 1.49	13.00 × 2.50 × 1.49	9
			4 × 60	32.50 × 1.69	15.00 × 2.50 × 1.69	9
		4	5 × 15	8.80 × 2.34	16.00 × 3.70 × 2.34	9
			5 × 30	16.50 × 2.30	16.50 × 3.30 × 2.30	10
		5	6 × 15	8.50 × 3.06	21.30 × 4.50 × 3.06	9
			6 × 30	17.00 × 3.01	20.00 × 5.00 × 3.01	9
		6	7 × 15	8.30 × 3.36	24.00 × 5.50 × 3.66	9
			7 × 30	16.00 × 3.50	20.50 × 5.00 × 3.50	10
		7	8 × 15	9.00 × 4.58	24.50 × 7.30 × 4.58	8
			8 × 30	16.50 × 4.11	26.00 × 7.00 × 4.11	10
		8	9 × 15	8.50 × 4.86	32.00 × 8.50 × 4.86	9
			9 × 30	19.50 × 4.90	35.00 × 10.50 × 4.90	9
		9	10 × 15	9.00 × 5.55	33.00 × 9.00 × 5.55	9
			10 × 30	20.00 × 5.13	38.00 × 10.00 × 5.13	9
		10	11 × 15	9.50 × 5.80	47.00 × 9.50 × 5.80	9
			11 × 30	20.50 × 6.64	54.00 × 12.00 × 6.64	8
	2 × 1	3	4 × 15	9.30 × 3.38	28.00 × 8.50 × 3.38	6
			–	–	–	–
		6	7 × 15	9.00 × 7.08	41.00 × 8.00 × 7.08	5
			–	–	–	–
		9	10 × 15	9.50 × 9.73	41.00 × 7.00 × 9.73	6
			–	–	–	–
	3 × 1	3	4 × 15	7.70 × 3.69	22.50 × 7.70 × 3.69	9
			–	–	–	–
	4 × 1	3	4 × 15	7.00 × 5.68	35.00 × 7.00 × 5.68	9
			–	–	–	–
Maximum	1 × 1	3	4 × 30	54.00 × 1.48	13.50 × 9.50 × 1.48	3
			4 × 60	120.00 × 1.66	15.00 × 10.00 × 1.66	3
		4	5 × 15	22.50 × 2.23	16.50 × 9.00 × 2.23	3
			5 × 30	46.50 × 2.30	16.50 × 11.00 × 2.30	4
		5	6 × 15	23.50 × 3.15	21.00 × 14.00 × 3.15	3
			6 × 30	48.50 × 3.01	20.00 × 15.00 × 3.01	3
		6	7 × 15	22.50 × 3.40	24.50 × 15.50 × 3.40	3
			7 × 30	46.50 × 3.28	21.00 × 14.50 × 3.28	4
		7	8 × 15	22.50 × 4.41	25.00 × 18.50 × 4.41	4
			8 × 30	46.00 × 3.74	26.00 × 20.50 × 3.74	4
		8	9 × 15	22.00 × 4.44	32.50 × 22.00 × 4.44	3
			9 × 30	44.50 × 4.61	35.00 × 22.00 × 4.61	4
		9	10 × 15	18.50 × 5.07	33.00 × 18.50 × 5.07	4
			10 × 30	45.00 × 4.95	38.00 × 22.00 × 4.95	3
		10	11 × 15	20.00 × 5.42	47.00 × 20.00 × 5.42	4
			11 × 30	45.00 × 6.30	54.00 × 27.00 × 6.30	4
	2 × 1	3	4 × 15	13.00 × 3.03	26.50 × 12.00 × 3.03	4
			–	–	–	–
		6	7 × 15	15.00 × 6.40	41.00 × 13.50 × 6.40	3
			–	–	–	–
		9	10 × 15	14.00 × 9.06	41.00 × 10.50 × 9.06	3
			–	–	–	–
	3 × 1	3	4 × 15	14.50 × 3.05	22.50 × 14.50 × 3.05	5
			–	–	–	–
	4 × 1	3	4 × 15	10.00 × 5.00	35.00 × 10.00 × 5.00	7
			–	–	–	–

Effect of number of layers, braid pattern, and jamming conditions on unit cell structure

As seen in Tables 1 and 2, when the number of layers increased in all braid patterns, the unit cell dimensions increased. The thickness of the unit cell structure increased proportionally for each additional layer of the 3D braid unit cell structure. For each number of layers, the unit cell structure dimension in the 1 × 1 braid pattern was small compared to those of the 2 × 1, 3 × 1, and 4 × 1 braid patterns due to small interlacement occurring in the 1 × 1 pattern. In jamming conditions, the dimensions of all braid unit cell structures in all braid patterns were different compared to those of the normal condition of the braid unit cell structure. In minimum conditions, the width of all braid unit cell structures decreased, while their density increased for all braid patterns and layer numbers. In maximum conditions, the width of all braid unit cell structures increased, while their density decreased for all braid patterns and layer numbers.

Unit cell angle results

The surface, braider, edge, and multilayer angles of the 3D braided unit cell structure for all braid patterns are presented in Table 3. Table 4 also presents the jamming conditions of the 3D braided unit cell structures.

Table 3.

Measured angles of three-dimensional representative braided preform structures in the normal condition

		Yarn
Braid pattern	Number of layers	Row × column	Surface angle (θ°)	Braider angle (θ_b°)	Edge angle (θ_e°)	Multilayer angle (θ_m°)
1 × 1	3	4 × 30	20	10	10	–
		4 × 60	15	10	10	–
	4	5 × 15	25	10	20	–
		5 × 30	20	15	20	–
	5	6 × 15	25	10	20	20
		6 × 30	22	11	15	15
	6	7 × 15	20	10	20	20
		7 × 30	23	10	20	20
	7	8 × 15	25	12	15	15
		8 × 30	20	15	20	20
	8	9 × 15	20	9	20	20
		9 × 30	30	11	15	15
	9	10 × 15	30	14	15	15
		10 × 30	20	10	17	17
	10	11 × 15	20	9	20	20
		11 × 30	25	9	15	15
2 × 1	3	4 × 15	30	11	13	–
		–	–	–	–	–
	6	7 × 15	30	12	10	15
		–	–	–	–	–
	9	10 × 15	30	7	20	25
		–	–	–	–	–
3 × 1	3	4 × 15	30	5	25	–
		–	–	–	–	–
4 × 1	3	4 × 15	30	6	11	–
		–	–	–	–	–

Table 4.

Measured angles of three-dimensional representative braided preform structures in jamming conditions

			Yarn
Jamming conditions of braided structures	Braid pattern	Number of layers	Row × column	Surface angle(θ°)	Braider angle(θ_b°)	Edge angle (θ_e°)	Multilayer angle (θ_m°)
Minimum	1 × 1	3	4 × 30	15	10	10	–
			4 × 60	10	10	10	–
		4	5 × 15	15	20	20	–
			5 × 30	10	20	20	–
		5	6 × 15	10	15	20	20
			6 × 30	13	17	15	15
		6	7 × 15	13	15	20	20
			7 × 30	15	15	20	20
		7	8 × 15	20	16	20	20
			8 × 30	13	16	21	21
		8	9 × 15	13	9	20	20
			9 × 30	20	11	20	20
		9	10 × 15	20	14	15	15
			10 × 30	15	11	17	17
		10	11 × 15	15	9	15	15
			11 × 30	15	10	20	20
	2 × 1	3	4 × 15	25	10	17	–
			–	–	–	–	–
		6	7 × 15	25	12	15	20
			–	–	–	–	–
		9	10 × 15	20	7	20	25
			–	–	–	–	–
	3 × 1	3	4 × 15	20	13	30	–
			–	–	–	–	–
	4 × 1	3	4 × 15	25	9	12	–
			–	–	–	–	–
Maximum	1 × 1	3	4 × 30	45	10	10	–
			4 × 60	50	8	10	–
		4	5 × 15	40	15	17	–
			5 × 30	40	10	20	–
		5	6 × 15	40	11	20	20
			6 × 30	45	10	15	15
		6	7 × 15	40	6	15	15
			7 × 30	45	10	20	20
		7	8 × 15	40	15	20	20
			8 × 30	45	10	14	14
		8	9 × 15	40	8	17	17
			9 × 30	40	11	20	20
		9	10 × 15	40	12	15	15
			10 × 30	35	9	16	16
		10	11 × 15	30	9	15	15
			11 × 30	35	10	15	15
	2 × 1	3	4 × 15	40	9	13	–
			–	–	–	–	–
		6	7 × 15	40	12	10	15
			–	–	–	–	–
		9	10 × 15	40	10	20	25
			–	–	–	–	–
	3 × 1	3	4 × 15	50	10	23	–
			–	–	–	–	–
	4 × 1	3	4 × 15	40	11	11	–
			–	–	–	–	–

Effect of braid pattern on unit cell angle

In the three-layer 3D unit cell structure, when the braid pattern changed from 1 × 1 to 3 × 1, the braid angle decreased, as shown in Figure 11. This is because thebraid yarns resulted in long floating in the in-plane direction of the 3D braid structure and inclined to the out-of-plane direction. In the three-layer 3D unit cell structure, when the braid pattern changed from 2 × 1 to 4 × 1, the braid angle decreased, where it occurred in the in-plane direction of each layer, due to no inter-yarn connection, as shown in Figure 11.

Figure 11.

Relationship between braid patterns and braider angle in three-layer three-dimensional braided unit cell structure for normal and jamming conditions.

In the three-layer 3D unit cell structure, when the braid pattern changed from 1 × 1 to 3 × 1, the edge angle increased, whereas when the braid pattern changed from 2 × 1 to 4 × 1, the edge angle slightly decreased, as shown in Figure 12. In the three-layer 3D unit cell structure, when the braid pattern changed from 1 × 1 to 3 × 1, the surface angle increased, whereas when the braid pattern changed from 2 × 1 to 4 × 1, the surface angle remained unchanged, as shown in Figure 13.

Figure 12.

Relationship between braid patterns and edge angle in three-layer three-dimensional braided unit cell structure for normal and jamming conditions.

Figure 13.

Relationship between braid patterns and surface angle in three-layer three-dimensional braided unit cell structure for normal and jamming conditions.

In jamming conditions, the braid, edge, and surface angles of all braid unit cell structures in all braid patterns were different compared to those of ‘normal condition’ braid unit cell structures. In minimum and maximum conditions, it was observed that the braid and edge angles changed irregularly for all braid unit cell structures, whereas the surface angle in normal conditions was between the minimum and maximum conditions.

Effect of number of layers on unit cell angle

The braider angle in 1 × 1 braid pattern 3D braided unit cell narrow and wide structures for different numbers of layers are shown in Figure 14, where the braider angle varied between 9° and 15°. In jamming conditions, the braider angles in narrow structures range between 9° and 20° and 9° and 15° for minimum and maximum conditions, respectively. Braider angles in wide structures range between 10° and 20° and 9° and 11° for minimum and maximum conditions, respectively.

Figure 14.

Relationship between number of layers and braider angle in three-dimensional (3D) narrow and wide braided preform structures for 1 × 1 braid pattern: 3D braided preform structures for normal (a) and jamming conditions (b).

The edge angle in 1 × 1 braid pattern 3D braided unit cell narrow and wide structures for different numbers of layers are shown in Figure 15, where the edge angle varied between 10° and 20°. In jamming conditions, the edge angles in narrow structures range between 10° and 20° in both minimum and maximum conditions. The edge angles in wide structures range between 10° and 21° and 10° and 20° for minimum and maximum conditions, respectively.

Figure 15.

Relationship between number of layers and edge angle in three-dimensional (3D) narrow and wide braided preform structures for 1 × 1 braid pattern: 3D braided preform structures for normal (a) and jamming conditions (b).

The surface angle in 1 × 1 braid pattern 3D braided unit cell narrow and wide structures for different numbers of layers are shown in Figure 16, where the surface angle varied between 20° and 30°. In jamming conditions, the surface angles in narrow structures range between 10° and 20° and 30° and 45° for minimum and maximum conditions, respectively. The surface angles in wide structures range between 10° and 20° and 35° and 45° for minimum and maximum conditions, respectively.

Figure 16.

Relationship between number of layers and surface angle in three-dimensional (3D) narrow and wide braided preform structures for 1 × 1 braid pattern: 3D braided preform structures for normal (a) and jamming conditions (b).

The multilayer angle in 1 × 1 braid pattern 3D braided unit cell narrow and wide structures for number of layers are shown in Figure 17, where the multilayer angle varied between 15° and 20°. In jamming conditions, the multilayer angles in narrow structures range between 10° and 20° for both minimum and maximum conditions. The multilayer angles in wide structures range between 15° and 21° and 14° and 20° for minimum and maximum conditions, respectively.

Figure 17.

Relationship between number of layers and multilayer angle in three-dimensional (3D) narrow and wide braided preform structures for 1 × 1 braid pattern: 3D braided preform structures for normal (a) and jamming conditions (b).

Unit cell density results

The density in 1 × 1 braid pattern 3D braided unit cell narrow and wide structures for different numbers of layers are shown in Figure 18, where density varied between 5 and 7 (ends/5 cm). In jamming conditions, the density in narrow structures ranges between 8 and 9 (ends/5 cm) and 3 and 4 (ends/5 cm) for minimum and maximum conditions, respectively. Density in wide structures ranges between 8 and 10 (ends/5 cm) and 3 and 4 (ends/5 cm) for minimum and maximum conditions, respectively.

Figure 18.

Relationship between number of layers and density in three-dimensional (3D) narrow and wide braided preform structures for 1 × 1 braid pattern: 3D braided preform structures for normal (a) and jamming conditions (b).

In the three-layer 3D unit cell structure, when the braid pattern changed from 1 × 1 to 3 × 1 and from 2 × 1 to 4 × 1, density slightly increased, as shown in Figure 19. On the other hand, it was observed that density in normal conditions was between minimum and maximum conditions.

Figure 19.

Relationship between braid patterns and density in three-layer three-dimensional braided unit cell structure for normal and jamming conditions.

Unit cell yarn length results

Yarn lengths, which include surface yarn length, braider yarn length, surface arc length, corner yarn length, edge yarn length, and multiple yarn lengths, were measured in 3D braided unit cell structures at various layers. Table 5 presents the measured yarn lengths. In addition, Table 6 presents the measured yarn lengths of the 3D braided unit cell structures in jamming conditions.

Table 5.

Measured yarn lengths of three-dimensional representative braided preform structures in normal conditions

		Yarn								Total yarn length
Braid pattern	Number of layers	Row × column	Surface yarn length (l, cm)	Braider yarn length (l_b, cm)	Surface arc length (l_a, cm)	Corner yarn length (l_c, cm)	Edge yarn length (l_e, cm)	Multilayer yarn length (l_m, cm)	Actual yarn length (l_l, cm)	Thin perform (l_tt, cm)	Thick perform (l_tk, cm)
1 × 1	3	4 × 30	13.5	1.50	6.0	–	4.8	–	7.50	12.3	–
	4	5 × 30	16.5	3.90	5.0	–	4.0	–	8.90	12.9	–
	5	6 × 30	20.0	5.10	4.8	4.0	4.0	1.7	9.90	–	19.6
	6	7 × 30	21.0	7.00	4.4	2.3	3.0	4.4	11.4	–	21.1
	7	8 × 30	26.0	9.00	4.2	2.5	3.0	3.8	13.2	–	22.5
	8	9 × 30	35.0	13.0	4.7	3.6	3.3	4.0	17.7	–	28.6
	9	10 × 30	38.0	15.5	4.4	2.5	3.3	4.8	19.9	–	30.5
	10	11 × 30	54.0	23.0	5.0	2.5	3.8	5.2	28.0	–	39.5

Table 6.

Measured yarn lengths of three-dimensional representative braided preform structures in jamming conditions

			Yarn								Total yarn length
Braided jamming conditions	Braid pattern	Number of layers	Row × column	Surface yarn length (l, cm)	Braider yarn length (l_b, cm)	Surface arc length (l_a, cm)	Corner yarn length (l_c, cm)	Edge yarn length (l_e, cm)	Multilayer yarn length (l_m, cm)	Actual yarn length (l_l, cm)	Thin perform (l_tt, cm)	Thick perform (l_tk, cm)
Minimum	1 × 1	3	4 × 30	13.0	1.60	5.5	–	4.8	–	7.10	11.9	–
		4	5 × 30	16.5	4.20	4.5	–	4.0	–	8.70	12.7	–
		5	6 × 30	20.0	5.60	4.5	4.0	4.0	1.7	10.1	–	19.8
		6	7 × 30	20.5	7.50	4.0	2.3	3.0	4.4	11.5	–	21.2
		7	8 × 30	26.0	8.60	4.1	2.5	3.0	3.8	12.7	–	22.0
		8	9 × 30	35.0	13.3	4.4	3.6	3.3	4.0	17.7	–	28.6
		9	10 × 30	38.0	15.9	4.2	2.5	3.3	4.8	20.1	–	30.7
		10	11 × 30	54.0	23.2	4.8	2.5	3.8	5.2	28.0	–	39.5
Maximum	1 × 1	3	4 × 30	13.5	1.60	6.0	–	3.9	–	7.60	11.5	–
		4	5 × 30	16.5	3.90	5.0	–	3.2	–	8.90	12.1	–
		5	6 × 30	20.0	6.00	4.8	3.5	3.5	1.2	10.8	–	19.0
		6	7 × 30	21.0	7.60	4.4	2.2	2.1	3.0	12.0	–	19.3
		7	8 × 30	26.0	9.50	4.0	2.5	2.5	3.1	13.5	–	21.6
		8	9 × 30	35.0	15.0	4.6	3.0	3.0	3.7	19.6	–	29.3
		9	10 × 30	38.0	16.5	4.2	2.0	2.5	2.7	20.7	–	27.9
		10	11 × 30	54.0	24.0	5.1	2.0	3.0	4.7	29.1	–	38.8

Effect of number of layers on unit cell yarn length

The surface arc length in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 20(a). The surface arc length decreased when the number of layers increased, due to the increase in unit cell structure thickness. Braider yarn length in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 20(b). As seen in the figure, the braider yarn length increased when the number of layers increased, due to the increasing thickness of the unit cell structure. In jamming conditions, braider yarn length and surface arch length remain between minimum and maximum conditions.

Figure 20.

Relationship between number of layers and surface arc length in three-dimensional (3D) braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (a). Relationship between number of layers and braider yarn length in 3D braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (b).

The edge yarn length in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 21(a). The edge yarn length decreased when the number of layers increased, due to the increasing of the braider yarn path. Corner yarn length appeared after four-layer braided unit cell structures, as shown in Figure 21(b). As seen in the figure, the corner yarn length decreased when the number of layers increased, due to the increasing of the braider yarn paths. In jamming conditions, the edge yarn length and corner yarn length remain between minimum and maximum conditions.

Figure 21.

Relationship between number of layers and edge yarn length in three-dimensional (3D) braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (a). Relationship between number of layers and corner yarn length in 3D braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (b).

The multiple yarn length in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 22. Multiple yarn length appeared after four-layer braided unit cell structures. As seen in the figure, the multiple yarn length increased when the number of layers increased, due to the increasing thickness of the unit cell structure. In jamming conditions, the multiple yarn length remains between minimum and maximum conditions.

Figure 22.

Relationship between number of layers and multilayer yarn length in three-dimensional braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions.

The surface yarn length in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 23(a). The surface yarn length increased when the number of layers increased, due to the increasing length of the braider yarn. The actual yarn lengths in 1 × 1 braid pattern 3D braided unit cell structures for different numbers of layers are shown in Figure 23(b). As seen in the figure, the actual yarn length increased when the number of layers increased, due to the increase in braider yarn lengths. In jamming conditions, surface yarn length and actual yarn length remain between minimum and maximum conditions.

Figure 23.

Relationship between number of layers and surface yarn length in three-dimensional (3D) braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (a). Relationship between number of layers and actual yarn length in 3D braided unit cell structures of 1 × 1 braid pattern for normal and jamming conditions (b).

The total yarn length for thin preform (three and four layers) in 1 × 1 braid pattern the 3D braided unit cell structures are shown in Figure 24(a). As seen in the Figure, thin preform total yarn length increased when the number of layers increased. There we can see that for thin preform total yarn length increased when the number of layers increased. The total yarn length for thick preforms (from 5 to 10 layers) in 1 × 1 braid pattern 3D braided unit cell structures are shown in Figure 24(b). As seen in the figure, the total yarn length for thick preforms increased when the number of layers increased. In jamming conditions, the total yarn length for thin preforms were outside minimum and maximum conditions, whereas the total yarn length for thick preforms remain between minimum and maximum conditions.

Figure 24.

Relationship between number of layers and total yarn length for thin preform in three-dimensional (3D) braided structures of 1 × 1 braid pattern for normal and jamming conditions (a). Relationship between number of layers and total yarn length for thick preform in 3D braided structures of 1 × 1 braid pattern for normal and jamming conditions (b).

Unit cell yarn path results

The braider yarn path on the edge and inside of the 3D representative braided unit cell structures with three and four layers is shown in Figure 25(a) and Figure 26(a). As seen in the figures, the braid(+) yarn on the edge changed its path from braid(+) to braid(−) at one step, as shown in Figure 25(a), and later braid(−) follows the out-of plane direction of the structure based on the predetermined path, as shown in Figure 26(a).

Figure 25.

Braider yarn path on edge of the three-dimensional (3D) representative braided preform with three and four-layers (a) and braider yarn path on the edge of the 3D representative braided preform with five to 10 layers (b).

Figure 26.

Braider yarn path on the edge and inside of the three-dimensional (3D) representative braided preform with three and four layers (a) and braider yarn path on the edge and inside of the 3D representative braided preform with five to 10 layers (b).

The braider yarn path on the edge and inside of the 3D representative braided unit cell structures with five and 10 layers is shown in Figure 25(b) and Figure 26 (b). Braid(+) yarn on the edge changed its path from braid(+) to braid(−) in two steps, as shown in Figure 25(b). After the ‘multilayer yarn path’ occurred due to the increasing number of layers in the 3D braided unit cell structures, braid(−) follows the out-of plane direction of the structure based on the predetermined path, as shown in Figure 26(b). It was observed that a one-step edge path occurred on both surfaces of the 3D braided structure, as seen in the three- and four-layer unit cell structures, whereas on the inside layers of the 3D braided structure, a two-step edge path occurred, as shown in Figure 26(b). This two-step edge path is called the ‘multilayer yarn path’.

General results

Unit cell structure

Braid patterns influence 3D braided unit cell structures. It was found that patterns on odd numbered rows resulted in fully interconnected integral unit cell structures, whereas patterns on even numbered rows resulted in layer-to-layer interconnection on the edge of the unit cell structure where there was an empty pocket between each braided layer. The unit cell structure has a fine intertwine in the 1 × 1 pattern, whereas it has a coarse intertwine for other braid patterns.

The number of layers affects 3D braided unit cell structures: when the number of layers increased the thickness of the unit cell structure increased for all braid patterns. On the other hand, with the same layer number, the thickness of the unit cell structure in the 1 × 1 pattern was less than that of other patterns. This indicated that all braid patterns except 1 × 1 resulted in a coarse form of unit cell structure.

Jamming conditions considerably affect the 3D braided unit cell structure for all braid patterns. Minimum jamming decreased the width of the unit cell structure, whereas maximum jamming increased its width. Width reduction of the unit cell structure in the 1 × 1 pattern was high compared to that of other patterns. However, the width increment of the unit cell structure in the 1 × 1 pattern was slightly higher than that of other patterns. In addition, minimum jamming increased the density of the 3D braided unit cell structure, whereas maximum jamming decreased its density.

Unit cell angle

Braid pattern slightly influences the yarn angles in 3D braided unit cell structures. The braider yarn slightly decreased when the braid pattern changed from 1 × 1 to 3 × 1, whereas the surface angle increased when the braid pattern changed from 1 × 1 to 3 × 1.

We found that increasing the number of layers from three to 10 did not considerably affect the braider angle.

Jamming conditions affect the yarn angles in 3D braided unit cell structures. Minimum jamming decreased the surface angle of the 3D braided unit cell structures, whereas maximum jamming increased the surface angle.

Unit cell yarn length

The number of layers affects yarn length in 3D braided unit cell structures. Increasing the layer numbers caused increased braider and surface yarn lengths, and multilayer yarn length in the 3D braided unit cell structures. However, increasing the layer numbers caused decreased surface arc length and corner yarn length, as well as edge yarn lengths.

We found that jamming conditions did not affect yarn length in 3D braided unit cell structures.

Unit cell yarn path

The most significant finding of this research was that increasing the layer number from five to 10 layers created an additional yarn path, the ‘multilayer yarn path’ on the edge of the 3D braided unit cell structure, and this could affect the mechanical behavior of the 3D braided composite. This was considered especially important for the manufacturing of near-net shape thick 3D braided preform and composites.

Conclusions

3D braided unit cell structures were developed. Basically, braid pattern and the number of layers were considered as processing parameters. Various 3D unit cell structures were made under these parameters. Data were generated. These included the unit cell dimensions, yarn angles, and yarn lengths in the unit cell structures. Unit cell yarn paths for developed unit cell structures were also identified.

We concluded that braid pattern influenced 3D braided unit cell structures. The number of layers and jamming conditions affected 3D braided unit cell thickness and width, respectively. We found that braid pattern and jamming conditions affected the yarn angle in 3D braided unit cell structures, where the braider angle decreased when the braid pattern changed from 1 × 1 to 3 × 1.

It was shown that number of layers affected the yarn length in 3D braided unit cell structures, where increasing the layers resulted in increased braider and surface yarn length, and multilayered yarn length; it resulted in decreased edge, corner yarn length, and surface arc length. Increasing the number of layers from five to 10 created a yarn path at the edge region of the 3D braided unit cell structures called the ‘multilayer yarn path’.

In light of these findings we plan to conduct future research on 3D braided preform structures using high-modulus fibers.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Conflict of interest statement

None declared.

Acknowledgements

This work is the product of the principal author’s continued research efforts since 1988. The authors acknowledge their gratitude to Prof Dr DW Lloyd from the Material Centre Laboratory at Leeds University; Prof Dr Frank Ko from the Fibrous Composite Research Laboratory at Drexel University; Prof Dr TW Chou from the Center for Composite Materials at the University of Delaware; and Prof Dr Aly El-Shiekh and MH Mohamed from the Textile Braiding Preform Composite Laboratory and Weaving Research Laboratory at the North Carolina State University at Raleigh.

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