SIMU L A T IO N S O F C O MP R E SS IO N , SH E A - PowerPoint PPT Presentation

SIMU L A T IO N S O F C O MP R E SS IO N , SH E A R A N D T E N SIO N O F G L A SS/P P WO VE N F A BR IC S Stepan Lomov, An Willems, Dirk Vandepitte, Ignaas Verpoest Katholieke Universiteit Leuven, Belgium Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 1

C ontents • Models • Materials and input data • Calculations – Compression – Biaxial tension – Shear • Conclusions Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 2

• Models • Materials and input data • Calculations – Compression – Biaxial tension – Shear • Conclusions Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 3

C ompression Compression: (un)bending + compression of yarns • The spacing of the yarns is not affected by compression. • The shape of the compressed yarn cross-sections can be modelled as an ellipse or lenticular shape. • The compression force is evenly distributed : over the fabric surface between regions of warp-weft contacts. over the region of contact between yarns. work of compressive force Q on change of thickness db = = change of bending energy of yarns dW Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 4

Biaxial tension test area F y X X Y Y X Y � � � � 0 0 ; � � � � � � x y X X Y Y 0 0 0 0 •The spacing of the warp F x F x and weft yarns is changed y, weft proportionally to the unit cell deformations. •Tension and deformation of F y individual yarns are averaged along the yarn x, warp length in the fabric repeat. Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 5

Biaxial tension: F orces p B � � � � Q Q h / p � � bending Wa 2 p h Wa � l l T � T 0 ; T T � � � � � � Q l 0 Q Q 2 T � sin � � h d Q d Q h � bending � � � � � � � � � Wa Wa We We Step 1 . Set initial deformations and tensions. Step 2 . Compute dimensions of yarns and transversal forces. Step 3 . Compute length of the yarns. Step 4. Compute deformations and tensions Step 5 . Check convergence for the deformations. If not, go to Step 2 . Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 6

Biaxial tension: A lgorithm Step 1. Compute p Wa = p Wa0 (1+ � y ); p We = p We0 (1+ � x ) Step 2. Set changes of weft crimp heights � h lj =0 Step 3. Compute fabric internal structure for h lj = h lj0 + � h lj Step 4. Compute average yarns strains � = l/l 0 -1 Step 5. Compute yarns tensions T=T( � ) Step 6. Compute transversal forces Q (due to bending and tension) Step 7 . Compute compression of the yarns under the forces Q Step 7. Compute � h lj using the condition of minimum of total (bending plus tension) energy of the yarns in the repeat. Step 8. Check convergence of � h lj ; if not, go to Step 3 . Step 9. Compute applied forces summing up the yarns tension Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 7

C omponents of the shear resistance F y M T XY YX cos � � � � X � T Y 0 1 A M � � F x 2 Y X 0 A A A A A � � � � friction disp bending torsion p h Wa � T T Q Q Q Q Q � � � Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 8 bending tension lateral compression

L ateral compression spacing 2.8 mm d � � 2 arccos max � � � � Vf 0 � � L � � p � � spacing 1.5 mm new d new � � � � P P Vf d , Q � 1 2 Vf Wa We Q P P d d � � � � � lateral compression Wa We 2 2 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 9

F riction and torsion M friction � fQr d 2 2 R 1 r ; R d Wa d � � 2 We 2 3 2 1 2 a 1 A torsion � C � a 2 2 t s a d � � 1 t a ds � � � � � � � 1 ds � � 0 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 10

Vertical displacement and bending after shear before shear � z 2 1 S 2 1 d z � � � A Q z ds A B ds � � � � � � � � � disp bending � � 2 l 2 ds � � contact 0 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 11

Input data • dimensions of the cross-section; • behaviour in compression; • bending and torsion resistance; • tension diagram; • coefficient of friction. Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 12

• Models • Materials and input data • Calculations – Compression – Biaxial tension – Shear • Conclusions Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 13

G lass/P P fabrics Yarns linear dens., Weave Ends / picks, Areal dens., spec/meas yarns/cm specified, g/m 2 tex 1 2x2400 twill 2/2 2.6/0.76 1816 2x2520 1900 2 1870/2x1870 twill 2/2 4.1/1.9 1485 2050/2x2050 1550 3 1870 - 2110 plain 1.9/1.9 743- 815 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 14

D imensions of the yarn cross-sections tex Warp & weft thickness x width, mm 2x2400 1 2.40 � 0.58 x 5.44 � 0.76 2x2400 1.56 � 0.16 x 7.16 � 0.42 1870 2 1.00 � 0.34 x 3.26 � 0.52 2x1870 1.60 � 0.17 x 5.27 � 0.15 3 1870 0.90 � 0.27 x 4.35 � 0.59 1870 1.17 � 0.16 x 4.96 � 0.33 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 15

Bending and torsion rigidity tex B, N mm 2 HB, N mm 1 2400 3.43 � 0.93 0.35 � 0.07 2 1870 1.14 � 0.07 0.14 � 0.03 3 1870 1.13 � 0.16 0.071 � 0.005 B nB � yarn strand B C � d d 1 2 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 16

Models of internal geometry 1 2 3 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 17

C ompression of yarns d d 1 eta1 1 2 1 ; � � 2 � � 1 2 d d 0.8 3 10 20 average 0.6 0.38 � � corrected � � 2 1 0.4 [G. Krupincova, T.U.Liberec ] 0.2 0 0 20 40 60 80 100 120 p, kPa Constraint correction: 1. KES-F measurements on one strand F * F /(1 ) � � � 2. Head size 4x4 mm 1 � � 2 � � Q , Q p d 3. Used in WiseTex as � � 1 � � � � � � � 1 1 2 1 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 18

T ension and friction 2 5 0 Instron measurement 1870 for one strand 1 2 0 0 2 2400 3 tex 1 5 0 F, N 1 2400 1 0 0 2 1870 5 0 e p s, % 3 1870 0 0 1 2 3 4 KES-F steel/fabric: f = 0.25 … 0.35 Input in the calculations: f = 0.3 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 19

• Models • Materials and input data • Calculations – Compression – Biaxial tension – Shear • Conclusions Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 20

C ompression 7 experiment 6 calculation 5 with constraint correction h, mm 4 1 3 2 2 1 3 0 0 20 40 60 80 100 120 140 160 180 p, kPa 200 Measurements on Instron, 1 mm/min, plate diameter 35 mm CV ~15% Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 21

U niaxial tension 0.12 0.25 0.25 Force, kN/mm Force, kN/mm Force, kN/mm F1 F2 F3 0.1 0.2 0.2 0.08 warp 0.15 0.15 0.06 warp 0.1 0.1 0.04 weft 0.05 0.05 0.02 weft Strain, % 0 0 Strain, % 0 Strain, % 0 1 2 3 4 5 6 0 1 2 3 4 5 0 1 2 3 4 5 6 7 • Not stable calculation for Fabric 2 • Good prediction of differences in behaviour: Instron; sample 50 x 210 mm Fabric 1: Stiffness warp vs weft pretension 0.56; 0.30; 0.26 N/mm Fabric 2: Initial stiffness warp vs weft • Overall satisfactory comparison Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 22 • Correct Poisson for Fabric 3: 1.0 … 1.3

Biaxial tension: F abric 2 0.1 weft Force, kN/mm 0.08 0.06 warp 0.04 0.02 0 Strain, % 0 1 2 3 4 Low initial stiffness – difficult positioning of the pretension 0.4 N/mm zero point Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 23

Shear pretension 0.4 N/mm no pretension Shear components, 10 -3 N/mm, F3, 45° Total B T L L � B T T � T T T T � T z B f f z T � 13 9 6 4 1 4 37 Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 24

• Models • Materials and input data • Calculations – Compression – Biaxial tension – Shear • Conclusions Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 25