µCT analysis
Using µCT, a reconstructed image of the Chomarat 150 TB fabric was created (Figure 3.7).
Figure 3.8 shows a single slice of the µCT data before and after image analysis. The analysis (as described in Section 3.3.5) was done with an assumed elliptical shape, with
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Figure 3.7:Chomarat 150TB µCT reconstruction
rotations ranging from -0.1 to 0.1 radians in 20 intervals.
Figure 3.8:Chomarat 150TB µCT slice, original (top) analysed (bottom)
From image analysis the yarn path fits the interpolated path constrained at the cross- overs alone very well. The root mean square drmsof the distances between points cho- sen along the yarn centreline and the analytical spline is 6.20×10−3mm (Note the value is the same for both Bézier and Natural cubic spline).
The high resolution images of the fabric cross-sections obtained from microscopy are ideal for determining yarn cross-section shape. Unfortunately the cross-section fitting algorithm described in Section 3.3 is not suitable for microscopy images, thus the fit must be done manually. One such image is shown in Figure 3.9 with a lenticular section fitted to it. As can be seen by the image, the lenticular section is more suitable than an elliptical section. Although the cross-section fit may be improved by using a polygon or a spline, both require many more parameters. The lenticular section described in Section 2.4.3 only requires 3 parameters to define it: width, height and distortion. Due to the variable nature of the cross-sectional shape, it is necessary to take measurements from several sections and average the parameters. This task is simplified by choosing a simple shape such as the lenticular cross-section.
The lenticular shape parameters can be obtained by measuring 4 points P1, P2, P3and P4on the yarn cross-section as shown in Figure 3.9. A fifth point P5 is defined as the intersection between the line segments created between points P1-P2 and P3-P4. The
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P1 P2
P3
P4 P5
Figure 3.9:Chomarat 150TB yarn cross-section shape at crossover
width w, height h and distortion d can then be calculated as follows:
w = kP2−P1k (3.4)
h = kP4−P3k (3.5)
d = kP5−P3k − h
2 (3.6)
However, only the width and height of the section are strictly necessary. The distortion parameter d can be calculated such that points P1and P2are in contact with the crossing yarn (this is the approach used). Since the section is not symmetric about the x axis it is necessary to invert it from one crossover to the next along the length of the yarn. This is done as described in Section 2.5.2. Figure 3.10 illustrates the comparison of a TexGen generated cross-section and a micrograph cross-section half way between two crossovers. The full TexGen model is shown in Figure 3.11.
Figure 3.10:Chomarat 150TB yarn cross-section shape between crossovers
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Table 3.5:Chomarat 150TB distortion measurements
Method Mean (mm) STD (mm) Samples Microscope 0.0284 0.00528 5
For completeness Table 3.5 shows the average distortion parameter obtained from a series of cross-section measurements.
Volume fraction
It is necessary to ensure that the yarn volumes in the geometric model do not intersect. This validation can be done without any further knowledge of the textile (see Section 2.11.2). In the model created above, there are no intersections between the yarn vol- umes. This is due in part to the fact that the ratio of yarn width to yarn spacing is large.
It is possible to perform some consistency checks between the mass m and volume Vy of yarns in a unit cell (see Section 2.10). The areal density ρAof the fabric was obtained from the manufacturer’s data sheet, the density ρ of E-glass fibres was obtained from Reinhard et al. [101] and the yarn volumes and unit cell area are calculated from the geometric model.
Table 3.6:Chomarat 150TB properties
Fabric properties
Total areal density ρA 150 g/m2 Warp areal density 82 g/m2 Weft areal density 68 g/m2 Fibre density ρf 2.62 g/cm3 Geometric model properties
Unit cell area A 13.333 mm2 Total yarn volume V.Y. 1.384 mm3 Warp yarn volume 0.755 mm3 Weft yarn volume 0.630 mm3
Volume fraction calculations Volume of fibres V.F. 0.763 mm3
Volume fraction Vf y 0.552
The total volume of the fibres V.F. within a unit cell of fabric is calculated with the
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS following equation: V.F.= m ρf = ρAA ρf (3.7) The ratio of fibre volume to yarn volume Vf yis then calculated with:
Vf y= V.F.
V.Y. (3.8)
The results are shown in Table 3.6.
The absolute maximum acceptable volume fraction for circular fibres would be 0.907, assuming the fibres are arranged in a hexagonal array and all fibres are just touching each other. This is a rather idealised case; in actual yarns the fibres are not organised in a regular array. In order to verify the calculation a threshold is applied to a cross- sectional image obtained by optical microscopy such that 55% of the brightest pixels are highlighted (Figure 3.12). The boundaries of the fibres are not clearly visible indicating that the threshold may be too high. The threshold was then manually adjusted until the boundaries of the fibres were clearly visible without losing pixels corresponding to fibres. The best fit was found at approximately 41%. This indicates that there may have been some innacuracies in the volume fraction calculation. A possible cause for the innacuracies may be that the volume of the yarns V.Y. in the model is smaller than in reality. However since the contrast between the fibres and matrix in the micrograph was not sufficient to clearly distinguish between the two, this method should not be considered reliable.
As a further consistency check the ratio of warp/weft yarn masses (1.206) obtained from the manufacturers data should be approximately equal to the ratio of warp/weft yarn volumes (1.198) calculated from the geometric model. There is less than a 0.7% difference between these two ratios.
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Original grayscale image
55% white pixels
41% white pixels
Figure 3.12:Threshold applied to Chomarat 150TB micrograph
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