Figure 3.13:Chomarat 800S4-F1
Chomarat 800S4-F1 is glass fibre 4 harness satin woven fabric (Figure 3.13).. This fabric is more challenging to model due to its higher tightness.
Fabric thickness measurements4 are shown in Table 3.7 using the various methods available. Yarn spacing5 and width6 measurements are shown in Table 3.8 and Table 3.9 respectively. In this case the spacings between warp and weft yarns are the same, thus only one spacing measurement appears in the table. With these measurements and visual observation of the fabric weave pattern, the yarn path is described by spec- ifying points at crossovers alone. The cross-section is defined as an ellipse all along the yarn as with the initial Chomarat 150TB model and the yarn path is interpolated with a Bézier spline.
Figure 3.14 shows the TexGen model created. Although the model looks similar to the real fabric, after analysis it is clear that there are intersections between the yarn volumes. The measurements taken above cannot be modified since they have been measured from the real fabric. The only parameters which can be changed are the assumed yarn path and section shape.
4The average of the KES-f and µCT values rounded to 1 decimal place is used to generate the model 5The values measured by ruler rounded to 2 decimal places are used to generate the model
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
Table 3.7:Chomarat 800S4-F1 thickness measurements
Method Mean (mm) Pressure (gf/cm2) STD (mm) Samples
KES-f 1.146 0.5 0.210 3
KES-f 0.978 50 0.0762 3
µCT 0.904 0 0.0334 10
Microscopy 0.828 0 0.0551 6
Manufacturer 0.75 100 - 260 N/A 10
Table 3.8:Chomarat 800S4-F1 yarn spacing measurements
Method Mean (mm) STD (mm) Samples
Ruler 3.158 0.0382 3
µCT 3.322 0.354 10
Microscope 3.167 0.245 5
Table 3.9:Chomarat 800S4-F1 yarn width measurements
Method Mean (mm) STD (mm) Samples
µCT 3.314 0.182 10
Microscope 2.920 0.0857 6
Figure 3.14:Basic Chomarat 800S4-F1 TexGen model
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
First the yarn cross-section shapes will be refined at the crossovers in an attempt to remove intersections. By displaying a cross-section through the textile at the crossovers the intersections are clearer. From Figure 3.15 three types of crossovers can be identified labelled 1, 2 and 3. The first is when the crossing yarn changes position on both sides, the second is when the crossing yarn changes position on only one side and the third case is when the crossing yarn does not change position on either side. Cases 1 and 2 intersect with the crossing yarn, while case 3 does not.
1
2
3
2
Figure 3.15:Cross-section of basic Chomarat 800S4-F1 TexGen model
For case 1, the half of the yarn cross-section that is in contact with the crossing yarn (the lower half in this case) will be modified to follow the yarn path. This is done numeri- cally by obtained a number of points Pi lying on the edge of the yarn cross-section. If the line segment from the centre of the yarn Pcto point Piintersects with the transverse yarn then the point is moved. The new position of the point is the intersection of the line with the transverse yarn surface.
For case 2, the section is rotated before the point positions are adjusted in order to minimise cross-section deformation (these rotations can be observed in micrographs and µCT images, as presented in Section 3.5.1). The angle of rotation θ is calculated as:
θ =tan−1 h 2s
(3.9) The resulting cross-section of the textile is shown in Figure 3.16.
θ
2s
h
Figure 3.16:Cross-section of refined Chomarat 800S4-F1 TexGen model
The full refined TexGen model can be seen in Figure 3.17. The number of intersections has been reduced, but they have not been completely eliminated. The model is trans- parent such that the intersections can be seen, illustrated as small white spheres. The intersections can be seen more clearly by taking a cross-section diagonally across the fabric where the intersections occur (Figure 3.18).
The remaining intersections occur between crossovers rather than at the crossovers themselves. With some further refinement of the yarn cross-section, these intersections can be removed. First of all it is necessary to ensure that the centreline of the yarn
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
Figure 3.17:Refined Chomarat 800S4-F1 TexGen model with intersections shown
Figure 3.18:Diagonal cut of refined Chomarat 800S4-F1 TexGen model
half way between crossovers lies exactly on the mid-plane of the fabric. This can be achieved by adding an additional node at this position, however a more convenient alternative is to create a spline that passes through this point without specifying addi- tional nodes. This is done by using a Bézier spline and specifying that the tangents at all the nodes lie in the horizontal plane. It is not possible to specify the tangents for the cubic periodic spline. Secondly the section shape half way between crossovers must be specified such that it does not intersect with crossing yarns. The section shape is created as the intersection of the two unrotated sections at the master nodes between which it lies (Figure 3.19).
Master node
Master node
Mid-node section
Figure 3.19:Section specified between crossovers
With these refinements, an intersection free model can be created and is shown in Fig- ure 3.20.
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
Figure 3.20:Final Chomarat 800S4-F1 TexGen model
3.5.1 Validation
µCT analysis
Figure 3.21:Chomarat 800S4-F1 µCT reconstruction
Figure 3.21 shows the reconstructed fabric from the µCT data. Firstly, a comparison of the differences between Bézier and periodic cubic splines is shown in Figure 3.22. The figure shows a section taken from the µCT data, with points on the crossing yarn identified manually and interpolated by a Bézier spline and a periodic cubic spline re- spectively. The root mean square drmsvalue between the Bézier spline and the periodic cubic spline is 11.96×10−3mm which is far greater than for the Chomarat 150TB plain weave. This is due to the fact that this fabric is not a plain weave and the tangents at the nodes will be different between the two splines as a result. The root mean square drms fit for the Bézier spline is 9.59×10−3 mm, whereas the periodic cubic spline has a drms of 17.4×10−3 mm. Both paths provide a good fit; in this case the Bézier spline is preferred because it gives control over the node tangents which are used to prevent interference in the model.
With image analysis the positions and rotations of the longitudinal yarns were deter- mined for several cross-sections along the centre of the transverse yarns. Three such cross-sections are shown in Figure 3.23. An assumed elliptical shape was used for the algorithm, with rotations ranging from±10◦at 20 intervals.
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
Figure 3.22:Yarn path comparison for 800S4-F1
Figure 3.23:Yarn path and cross-section fits for 800S4-F1
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
have been applied at certain positions. It is possible to verify that this use of rotations is correct by comparing with the µCT cross-section images. The average rotation over 10 cross-sections of type 2 (see Figure 3.15) is 3.87 degrees with a standard deviation of 0.54 degrees. The assumed rotation was 3.04 from Equation 3.9. Agreement is close enough to suggest that the revised model is accurate.
Cross-sections taken between longitudinal yarns (where the longitudinal yarns cannot be seen) are also extracted from the µCT data. Three such cross-sections are shown in Figure 3.24. To compare against the TexGen model, a cross-section is also taken be- tween yarns and shown side by side with a representative µCT cross-section in Figure 3.25. Similarities between the two can be seen, with the rotations of the sections in the same directions. The two lower left cross-sections form a sharp edge where they meet which is not present in the two upper right cross-sections. Again variability ex- ists within the real fabric that is not captured within the TexGen model, but overall the shape agreement is good.
Figure 3.24:Cross-section fits for 800S4-F1
Figure 3.25:Cross-section comparison for 800S4-F1
In conclusion, a method to create a geometric model of an interference free tightly packed 2D weave has been generated that is applicable to any 2D weave. The revised algorithms to define yarn rotations and to modify cross-sections (avoiding interference) have been implemented as advanced options in TexGen.
The geometry created for the Chomarat 800S4-F1 has been verified against µCT mea- surements, showing good agreement.
CHAPTER3: TEXTILE GEOMETRY MODEL CASE VALIDATIONS
Table 3.10:Chomarat 800S4-F1 properties
Fabric properties
Total areal density 780 g/m2 Fibre density 2.62 g/cm3 Geometric model properties
Unit cell area 159.7 mm2 Total yarn volume 115.6 mm3
Volume fraction calculations Volume of fibres Vf 47.54 mm3 Volume fraction VF 0.411
Volume fraction
From the fabric properties and the geometric model properties the volume fraction of the yarns is calculated and shown in Table 3.10. As an additional validation a threshold is applied to a cross-sectional image obtained by optical microscope such that 41% of the brightest pixels are highlighted (Figure 3.26). Individual fibres are clearly visible, providing confidence in the accuracy of the volume fraction calculation.
Original grayscale image
41% white pixels
Figure 3.26:Threshold applied to Chomarat 800S4-F1 micrograph