Characterization of nesting effects on compression processes for plain woven fabrics in composites manufacturing

Abstract

Nesting and compression processes of plain woven fabrics are the most important features in the composites manufacture of fiber-reinforced composite components, while their relationships are still not reported. Here, in this work, we clearly reveal nesting and compression characteristics of typical fabrics through systematical compression experiments. We present the theoretical expression of the nesting effects on the initial thickness h and experimentally demonstrate its effectiveness. We find that nesting decreases the h and the minimum h appears in the maximum nesting condition. Meanwhile, we experimentally demonstrate that for plain woven fabrics, nesting has relationships with the thickness in compression t, while it has no effects on the thickness deformation Δ in the whole compression processes. Thus, we reveal the relationships between the nesting and h, t, Δ in the compression processes. Moreover, the applicability of these results for other types of fiber is also illustrated by comprehensive analysis. These obtained results provide the references for thickness evolution rules, volume fraction, and molding process of the fiber-reinforced composite components.

Keywords

Composites plain woven fabric nesting compression processes thickness deformation

Introduction

Fiber reinforcements polymer (FRP) composites, such as carbon fiber and E-glass fiber, have been used in the manufacture of composites parts for the difference applications in automotive body, marine, aerospace, and so on. Notably, the application of composite to the automotive body is a widely acknowledge approach to realize lightweight design.^1,2On the other hand, resin transfer molding is the most common molding process for FRP composite components.^3,4 It is widely known that increasing the fiber volume fraction can significantly improve the mechanical properties of the composites parts. Thus, in order to obtain a higher fiber volume fraction, the fabrics should be well compressed in the thickness direction in the composites manufacture. Meanwhile, the compression of the fabrics changes the internal structures of the fibers and the yarns configurations which have significant effects on the FRP composite permeability and molding processes.^5,6 Therefore, it is quite important to explore the compressibility of the fabrics, which has a significant influence on the forming of the corresponding FRP components.

On one hand, the prediction of nesting and compression processes for the fabrics was studied through various theoretical analysis, experiments, and numerical simulation. For the theoretical analysis and experiments, the detailed micro-structural changes that take place under compression was presented.^7–9 Some micromechanical models were established to investigate the structure of plain woven fabrics and the effects of structural elements at different levels.^10,11 Nesting effects become more remarkable with the decrease in the fabric tightness and its effects on the compression of woven fabrics and the permeability of their laminates were also studied.^12–14 On the other hand, numerical simulation provides enlightening insights into the compression of plain woven fabrics and gave impetus to the development of predictive models. Finite element models to predict nesting and the compression processes were established and experimentally verified.^15,16 It should be noted that nesting and compression processes have significant effects on the preform process and the thickness of the FRP composite. However, the corresponding studies about the relationship between nesting and compression processes, the evolution of the nesting in compression deformation processes have never been reported. Meanwhile, the compressibility of natural fabric, carbon fabric, glass fabric, and other types have been studied separately.^17–20 Most of researches only involved one type of fiber and the general applicability of conclusions for other types of fibers were not revealed. In addition, compression processes involve many uncertainties caused by fiber architecture variations and matrix material uncertainties, and some delicate features that conventionally neglected may have significant impacts on thickness and yarn crimp inside the composite.^21,22 Compression processes, as important processes after lay-up, have significant effects on the fiber volume fraction. Meanwhile, nesting, especially for plain woven fabric, can reduce the thickness of layers during layer up. There must be connections between nesting and compression processes in composites manufacture. Therefore, it is of great significance to find the relationship between nesting and compression processes for generally used fabrics.

Thus, in this paper, the objective is to find the relationship between nesting and compression processes that include the initial thickness h, the thickness in compression t, and the thickness deformation Δ, for plain woven fabrics in various types of fibers. In “Experiments” section, systematical experiments of the initial thickness and compression for three carbon fiber fabrics and two kinds of E-glass fiber fabrics were presented. A unit cell for plain woven fabric was established for theoretical analysis of initial thickness and nesting conditions. In “Results and discussion” section, we conducted a detailed study on the compression processes by analyzing compression curves and the influences of nesting on h, t, and Δ were discussed. Meanwhile, the relationships between nesting and compression processes were revealed and the applicability of the obtained conclusions for other types of fibers were demonstrated. Finally, conclusions were summarized in “Conclusion” section.

Experiments

Fabrics

Carbon fiber fabrics and E-glass fiber fabrics are the most common fiber-reinforced fabrics in the FRP composites. Thus, as shown in Figure 1, in this work, we selected three kinds of carbon fiber fabrics: CC-P200-3 (fabric C-1), CC-P400-12 (fabric C-2), and C-LT400-12 (fabric C-3) and two E-glass fiber fabrics E-G0601(fabric E-1) and E-D1301(fabric E-2). Fabrics C-1, C-2, E-1, and E-2 are plain woven fabrics, while fabric C-3 is non-crimp fabric(NCF). As NCF of E-glass has the same compression properties with carbon fiber, it is not mentioned in this paper for reducing duplication of work. The corresponding parameters are listed in Table 1. There are significant differences among these fabrics in yarns specifications and weaving methods. Yarns of fabric C-1 and E-1 have a fiber count of 3 k, while yarns of fabric C-2, E-2, and C-3 are 12 k. Moreover, these fabrics are woven in different ways. Fabric C-3 is NCF and the axial angles are 0° and 90°, while the others are in the way of plain woven. Non-crimp is easy to meet the paving layer of the direction and order requirements, while plain woven fabric has better surface. Both of them are widely used in composite components.

Figure 1.

Photographs of fabrics: (a) plain woven fabric C-1 (3 k), (b) plain woven fabric C-2 (12 k), (c) non-crimp fabric C-3 (12 k), (d) plain woven fabric E-1 (3 k), and (e) plain woven fabric E-2 (12 k).

Table 1.

Parameters including fiber type and weave of the fabrics (200 tex = 3 k, 800 tex = 12 k).

Fabric ID	Fiber type	Specification	Weave	Areal density (g m⁻²)	Warp/weft
C-1	Carbon	CC-P200-3	Plain	200	3 k
C-2	Carbon	CC-P400-12	Plain	400	12 k
C-3	Carbon	C-LT400-12	Unidirectional	400	12 k
E-1	E-glass	E-G0601	Plain	160	200 tex
E-2	E-glass	E-D1301	Plain	400	800 tex

Initial thickness tests

The initial thickness of these five kinds of fabrics were tested according to the standard ASTM D1777²³ for thickness measurement of fabrics and the loading pressure was 4.14 ± 0.21 kPa. The specimen is placed on the base of a thickness gage and a weighted presser foot with the diameter 28.7 ± 0.02 mm lowered. The displacement between the base and the presser foot is measured as the thickness of the specimen. In the experiments, the fabrics were cut into 100 × 100 mm, which were in accordance with the size of bottom plate. In order to prevent the edge of the fabrics from shedding which can have negative effects on testing processes and results, two or three yarns, which located at the ends of the fabrics, were removed before tests. Actually, the effective size of the specimen must be less than 100 × 100 mm. Typically, the effective size of the fabric C-2, C-3, and E-2 is about 80 × 80 mm, the effective size of the fabric C-1 and E-1 is about 90 × 90 mm. All fabrics were compacted with the layer number n of 1, 2, and 4. Particularly, the layer angles of the fabric C-3 were [0/90]_n. Nesting is a common phenomenon for plain woven fabrics expected for NCFs, thus, experiments for fabric C-3 were treated as calibration tests to make the results more reasonable in this work. Nesting can affect the initial thickness for plain woven fabrics.^24–26 So, it is necessary to test the initial thickness of layers in certain nesting conditions. These nesting conditions will be illustrated in “ Nesting” section.

Compression experiments

Compression experiments for the fabrics were systematically conducted. As shown in Figure 2, the fabrics were positioned on the bottom plate with a diameter of 100 mm, and the top plate is a 50 mm diameter steel plate. The top plate covers enough unit cells, which can reflect the compressibility of specimen and the effective area is the surface of top plate in each experiment. Therefore, the size of the top plate can be smaller than the specimen and the bottom plate. Before compression experiments, a constant 4.14 kPa pressure was applied to ensure the initial thickness as well as the sufficient contact between top plate and the fabrics. During compression experiments, the loading speed of the top plate was 0.5 mm/min and each experiment was repeated 3 times. Relationships between the pressure P and the distance s of the top plate were recorded. The thickness t can be calculated as follows:

t = h - Δ

(1)

Figure 2.

Compression experiments for fabrics: (a) experimental setup and (b) schematic diagram.

where t is the thickness in compression, h is the initial thickness, and Δ is the thickness deformation. Here, h and Δ are directly measured on the experiments. The initial thickness h was tested according to the standard ASTM D1777 in “Initial thickness tests” section. As the top plate is sufficient contact to the fabric before the compression experiments, the top plate moves downward in the compression experiments, and the distance s of top plate is the thickness deformation Δ of specimen. Thus, Δ can be directly measured in the compression processes. In order to make the obtained results more clearly, the above parameters are divided by the number of layers n, and the corresponding expressions of per layer are presented as:

t_{p} = t / n, h_{p} = h / n, Δ_{p} = Δ / n

(2)

where t_p is the thickness in compression of per layer, h_p is the initial thickness of per layer, and Δ_p is the thickness deformation of per layer. In this work, h_p, t_p, and Δ_p are used to characterize the compression processes of the fabrics.

Nesting

Here, a mesoscopic model for predicting the initial thickness of plain woven fabrics was established. Figure 3(b) shows a cross-sectional view of the unit cell of plain woven fabric with single layer. In the theoretical analysis, the unit cell repeats in the plane of fabric, and the cross section of yarns is regarded as ellipse and no gaps exit between the contact surface of the yarn. H and L represent the thickness and length of the unit cell, respectively. 2a and 2b are the lengths of the long axis and short axis of the ellipse cross section of the yarn.

Figure 3.

Unit cell of plain woven fabric: (a) plain woven fabric and (b) unit cell.

To illustrate the nesting as shown in Figure 4, the edge of one yarn is measured with respect to the edge of one yarn of the next layer. According to the shift S_x in x direction of two adjacent layers, nesting can be classified into three cases. When S_x = L/2 as shown in Figure 4(a), this is the maximum nesting. When 0 < S_x < L/2 or L/2 < S_x < L as shown in Figure 4(b), this is the random nesting. When S_x = 0 as shown in Figure 4(c), this is the minimum nesting. The effects of nesting on the initial thickness of per layer h_p, the thickness in compression of per layer t_p, and the thickness deformation of per layer Δ_p will be discussed in “Nesting and initial thickness,” “Nesting and thickness in compression,” and “Nesting and thickness deformation” sections.

Figure 4.

Illustration of nesting between two layers: (a) maximum nesting, (b) random nesting, and (c) minimum nesting.

Compression processes

The characteristics of a typical compression curve of fabric are shown in Figure 5(a).^15,26 The compression processes can be divided into three typical stages. Stage 1: the linear stage, stage 2: the experiential stage, and stage 3: the linear stage. The main changes of the fabrics in the compression processes are as follows:^27,28 In the stage 1 of the compression, as shown in Figure 5(b), stage 1, the gap l caused by the warping of the fabrics reduces to zero rapidly, and this leads to a corresponding decrease in the thickness in compression t. During the stage 2, the main characteristics are the changes in yarns cross section. The fibers begin to move toward the voids formed by the fabric structure and the yarns become thinner, this is the main stage of the thickness deformation as shown in Figure 5(b), stage 2. As the compressive force increases to the stage 3, the fiber starts resisting the external pressure and begin to bear the compression as shown in Figure 5(b), stage 3.

Figure 5.

A typical compression processes: (a) a representative compression curve and (b) the main changes of the fabrics.

Results and discussion

Compression processes

Figure 6 shows compression curves for carbon fiber and E-glass fiber fabrics with four layers. The variation characters of these curves agree well with the typical stages as mentioned in Figure 5, demonstrating the effectiveness of our experimental procedure. In stage 1, yarns offer limited resistance to the compression through bending deformation at the low pressure and that can be negligible. As the pressure increases, the deformation comes into stage 2. The curves are no longer linear as the geometric shapes of the yarns change significantly, leading to obvious reduction in the thickness of fabrics. In stage 3, the compression curves become linear again. The voids between yarns reach its limit and the fibers begin to bear the compression. In this work, we mainly focus on the compression processes of multilayer fabrics.

Figure 6.

Compression curves in minimum nesting (the layers are four): (a) carbon fiber fabrics and (b) E-glass fiber fabrics.

Nesting and initial thickness

Nesting has an effect on the initial thickness h of the layers. For multilayer fabrics, the initial thickness of the fabric is

h_{n} = 2 h_{top} + (n - 2) H - (n - 1) z

(3)

where h_n is the initial thickness of fabric, n is the number of layers, h_top denotes the thickness of top and bottom layers, and z is the thickness reduction due to nesting between two adjacent layers. The thickness reduction z of two adjacent layers can be expressed as follows:^10,11

z = z_{x - z} + z_{y - z}; z_{x - z} = 2 (b - z_{s_{x}}); z_{y - z} = 2 (b - z_{s_{y}})

(4)

x_{S_{x}} = S_{x} / 2 = a \cos θ, z_{S_{x}} = b \sin θ; y_{S_{y}} = S_{y} / 2 = a \cos φ, z_{S_{y}} = b \sin φ

(5)

where z_x_-z and z_y_-z stand for thickness reduction in the plane x-z and y-z, respectively. Here, S_x and S_y are the shift distances of the two adjacent layers in the x and y directions. In this work, only two conditions, S_x = S_y = 0 and S_x = S_y = L/2, are considered. As mentioned in “Nesting” section, when S_x = S_y = 0, it is the minimum nesting case, S_x = S_y = L/2 is the maximum nesting case. For these two cases, it can be calculated that the thickness reductions are:

z_{max} = 4 b (1 - \sqrt{1 - (L / 4 a)^{2}}), z_{min} = 0

(6)

Similarly, the top and bottom layers are the same as those inner layers and thus:

h_{top} = H

(7)

Substitute equations (6) and (7) into equation (3), the initial thickness of the fabric with the mentioned two nesting conditions can be expressed:

h_{max} = nH - (n - 1) z_{max}, h_{min} = nH

(8)

where h_max and h_min are the initial thickness for maximum and minimum nesting conditions. For an n-layers plain woven fabric with maximum and minimum nesting, the average initial thickness of per layer can be written as:

h_{max} = H - \frac{n - 1}{n} z_{max}, h_{p, min} = H

(9)

where h_p,max and h_p,min are initial thickness of per layer for maximum and minimum nesting conditions. With the increase in the number of layers, the h_p,max will become smaller and it can be illustrated by experiments in “Nesting and thickness in compression” section.

Table 2 gives the initial thickness h of single layer, two layers and four layers of all test fabrics under a certain pressure. Nesting can reduce the h of the multilayer fabrics, while if there is no nesting between two layers, h is a certain value. For multilayer fabrics of plain woven fabrics, such as two or four layers listed in Table 2, there exits nesting and h is in certain ranges. When there is no nesting, namely, the layer is single layer or the fabric is NCF, h is a fixed value for all fabrics as listed in Table 2. Thus, nesting is the main contribution to the difference of h for plain woven fabrics.

Table 2.

The initial thickness of fabrics with various layers.

Number of Layers	Initial thickness/mm
Number of Layers	Fabric C-1	Fabric C-2	Fabric C-3	Fabric E-1	Fabric E-2
1	0.25	0.50	0.54	0.2	0.54
2	0.45–0.49	0.86–1.00	1.07	0.37–0.40	0.98–1.10
4	0.90–1.04	1.72–2.02	2.15	0.72–0.82	1.96–2.24

The initial thickness h for plain woven fabric can be calculated according to equation (8). The per layer fabric parameters were measured through direct measurement by an optical mesoscope (VHX1000, Keyence). The mesoscopic structures of all fabrics were observed and calibrated, the sizes of the unit cell, a, b, H, and L, have been measured three times and rounded off three significant figures The parameters are as follows, fabric C-1: a = 0.82 mm, b = 0.07 mm, H = 0.25 mm, L = 2.00 mm; fabric C-2: a = 1.50 mm, b = 0.13 mm, H = 0.50 mm, L = 4.00 mm; fabric E-1: a = 1.10 mm, b = 0.05 mm, H = 0.20 mm, L = 2.50 mm; fabric E-2: a = 1.50 mm, b = 0.13 mm, H = 0.54 mm, L = 4.00 mm. As mentioned in equation (8), h_max is associated with all the parameters of the unit cell and it can reflect the accuracy of the model. The comparison between analytical predictions and experimental results in maximum nesting are listed in Table 3. Clearly, the experimental measurements agree well with the analytical predictions as the maximum error is no more than 10%, which demonstrated the effectiveness and correctness of the initial thickness tests.

Table 3.

The experimental and theoretical values of initial thickness of plain-woven fabrics (with maximum nesting).

Layers	Fabric C-1		Fabric C-2		Fabric E-1		Fabric E-2
Layers	2	4	2	4	2	4	2	4
Experimental value/mm	0.45	0.90	0.86	1.72	0.37	0.72	0.98	1.96
Theoretical value/mm	0.44	0.82	0.87	1.61	0.36	0.69	0.95	1.81
Error (%)	2.3	9.6	1.2	6.4	2.8	4.3	3.2	8.3

Nesting and thickness in compression

The thickness in compression of per layer t_p is affected by the initial thickness of per layer h_p that has relationship with nesting conditions. Figure 7 shows compression curves of all the tested fabrics with maximum and minimum nesting, and the numbers of the layers are two and four. It is not mentioned the compression curves of single layer. Firstly, the compression curves of three typical of carbon fiber fabrics were analyzed. With the same number of the layers, the compression curves are quite different in these two nesting cases. For example, In Figure 7(b), when the number of the layers is four, h_p of fabric C-2 are 0.42 and 0.50 mm for the maximum and minimum nesting, respectively. When the pressure reaches up to 0.15 MPa, t_p is compressed to 0.28 and 0.35 mm, respectively. This result clearly reveals that under these two different nesting conditions, t_p is different at a given pressure. However, there is no difference in t_p for different layers with no nesting. For instance, as shown in Figure 7(c), the compression curves almost coincide with each other, as there is no nesting exists. Therefore, these results present that h_p is affected by the nesting, which further influences the compression curves. Meanwhile, as the different of h_p, which has illustrated in equation (9) in maximum nesting, the t_p of two layers is higher than that of four layers as shown in Figure 7(a) and (b). Obviously, it is sure that the above conclusions about the relationship between h_p and t_p are also applicable to the evolutions of the E-glass fiber fabrics as shown in Figure 7(d) and (e). For illustrating the relationship between h_p and t_p, it can be expressed by the following relation:

t_{p} (P) = h_{p} - Δ_{p} (P)

(10)

where t_p(P) changes in relation to Δ_p(P) and h_p. And h_p is related to the parameters of fabric and nesting as mentioned in “Nesting and initial thickness” section, it keeps as constant once the layers are established. At a given P, Δ_p(P) is constant. So, t_p(P) is significantly affected by h_p, which is then determined by the nesting as expressed in equation (10).

Figure 7.

Compression curves with maximum and minimum nesting: (a) fabric C-1, (b) fabric C-2, (c) fabric C-3, (d) fabric E-1, and (e) fabric E-2.

Nesting and thickness deformation

In order to explore the influence of nesting on the thickness deformation of per layer Δ_p and exclude the influence of the initial thickness of per layer h_p, the thickness deformation curves about Δ_p are discussed here. As the compression curves with different number of layers are the same as mentioned in “Nesting and thickness in compression” section, the following analysis of thickness deformation curves are for the four layers. Figure 8 shows the thickness deformation curves of all fabrics with maximum and minimum nesting conditions. Figure 8(a) and (b) is for carbon fiber fabrics and Figure 8(c) and (d) is for E-glass fabrics. Compared the curves in Figure 8(a) and (b), it is known that nesting has no influence on Δ_p in compression processes. For example, in Figure 8(a), the curves of thickness deformation are the same in maximum and minimum nesting cases. This conclusion can be also found in Figure 8(b) for fabric C-2 with different nesting conditions. For E-glass fiber fabrics, we have the same conclusion that nesting has no effect on Δ_p in compression processes. Moreover, the way of weaving also has no influence on Δ_p of the fabrics with same yarns specification for carbon fiber. As shown in Figure 8(b), fabric C-2 is plain woven fabric and C-3 is NCF as mentioned in “Fabrics” section, and their thickness deformation curves show no difference. Thus, these two comparisons conclude that nesting and weaving models show little effects on Δ_p for fabrics. On the other hand, the specification of the yarns has a significant effect on the thickness deformation of the fabrics. At a given pressure P, Δ_p of different yarns specification are not the same. For instances, Δ_p of fabric C-1 and C-2 is 0.06 and 0.14 mm at 0.15 MPa, and when the pressure reach to 0.6 MPa, Δ_p is 0.09 and 0.20 mm, respectively. Thus, it can be concluded that Δ_p has nothing to do with nesting and weaving methods except for yarns specification in compression processes. Furthermore, whether for the E-glass fiber or the carbon fiber, nesting is a common phenomenon that occurs in the lay-up and Δ_p is essentially reflects the fabric compression processes. Lay-up and compression processes are two different parameters of the fabric, there is no inner relationship between them.

Figure 8.

Thickness deformation curves: (a) fabric C-1, (b) fabric C-2 and C-3, (c) fabric E-1, and (d) fabric E-2.

Effects of fiber types

According to the above discussion, the type of different fibers, namely whether carbon or glass fiber, has no effect on the relationship between nesting and compression process. To further verify this conclusion about the effects of nesting on t_p and Δ_p, as shown in Figure 9, the curves of compression experiments for other types of fibers are discussed here. Figure 9(a) and (b) presents the results of compression for carbon nanotube plain woven fabric reported in the study by Stepan et al.²⁹ It contains three random nesting conditions, which are B, BC, and BG. The values of the nesting coefficients of B, BC, and BG are 16.2%, 13.4%, and 9.6%, respectively. Figure 9(c) and (d) illustrate the results of compression for nanofiber-grafted alumina fabric reported in the study by Lomov et al.,³⁰ which also contains three random nesting cases: C, V, and CVDN. The values of the nesting coefficients of C, V, and CVDN are 10%, 15%, and 13%, respectively. Carbon nanotube fabric and nanofiber-grafted alumina fabric are two fibers which have differences with carbon and glass fibers investigated in this work. In Figure 9(a), compression curves of different nesting cases are not the same. At a given pressure, t_p of these nesting cases are not equal, which means nesting has an effect on t_p. While, as shown in Figure 9(b), the thickness deformation curves are the same, which clearly demonstrates that nesting has no effect on the thickness deformation of per layer Δ_p. Moreover, Figure 9(c) and (d) provide further evidences for these two conclusions. Thus, Figure 9 demonstrates the effectiveness of the conclusions that nesting affects the thickness in compression of per layer t_p but has no effect on the thickness deformation of per layer Δ_p, and also definitely illustrate the applicability of these conclusions for plain woven fabrics with different fibers including carbon, glass, carbon nanotube, and nanofiber-grafted alumina fibers.

Figure 9.

Curves of compression experiments:^29,30 (a) and (c) compression curves, (b) and (d) thickness deformation curves.

Conclusions

In this work, we conducted studies for plain woven fabrics on nesting and compression processes through systematic experiments and detailed analysis. The relationship between nesting and the initial thickness h, the thickness in compression t, and the thickness deformation Δ were respectively revealed. The general applicability of these relationships for different types of fibers were fully demonstrated. The main conclusions are summarized as follows:

A unit cell of plain woven fabric was established, the theoretical expressions of nesting effects on the initial thickness h were presented. The correctness and effectiveness have been demonstrated. We find that nesting will decrease the initial thickness and the minimum initial thickness appears in the maximum nesting condition.

For carbon fiber or E-glass fiber, we experimentally figure out that nesting has no effect on the Δ in the whole compression processes. Thus, for plain fabric, even with different initial thicknesses caused by nesting, the thickness deformations are kept the same at given pressures.

The thickness in compression t of minimum nesting is higher than that of maximum nesting at the same layers, exhibiting the same interrelation as that between nesting and h. As nesting has no effect on the Δ, at a given pressure, the relationship between nesting and t can be precisely described as the relationship between nesting and h.

The conclusions of nesting and compression processes drawn from carbon fiber and E-glass fiber are also applicable to other types of fibers, such as carbon nanotube and nanofiber-grafted alumina fibers. Generally, nesting reduces the t through the h but has no effect on Δ.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are grateful for the support by National Natural Science Foundation of China under grants #11602081, #51405150. This work is also supported by the fundamental research funds for the central universities under grants #531107040934.

Appendix 1

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