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May 17, 2023 371 likes •648 views

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,

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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

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C

  • ntents
  • Models
  • Materials and input data
  • Calculations

– Compression – Biaxial tension – Shear

  • Conclusions
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  • Models
  • Materials and input data
  • Calculations

– Compression – Biaxial tension – Shear

  • Conclusions
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C

  • mpression

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:
  • ver the fabric surface

between regions of warp-weft contacts.

  • ver the region of contact between yarns.

work of compressive force Q on change of thickness db = = change of bending energy of yarns dW

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Biaxial tension

y, weft

Fx Fx Fy Fy

test area x, warp

; Y Y Y Y Y X X X X X

y x

  • The spacing of the warp

and weft yarns is changed proportionally to the unit cell deformations.

  • Tension and deformation of

individual yarns are averaged along the yarn length in the fabric repeat.

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Biaxial tension: F

  • rces
  • p

h Q p B Q

Wa bending

/

2

  • T

T Q hWa p

  • sin

2T Q Q

bending

  • T

T l l l

  • ;

We We Wa Wa

h Q d Q d h

  • 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.

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Biaxial tension: A lgorithm

Step 1. Compute pWa = pWa0(1+y); pWe = pWe0(1+ x) Step 2. Set changes of weft crimp heights hlj=0 Step 3. Compute fabric internal structure for hlj= hlj0 + hlj Step 4. Compute average yarns strains = l/l0 -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 hlj using the condition of minimum of total (bending plus tension) energy of the yarns in the repeat. Step 8. Check convergence of hlj ; if not, go to Step 3. Step 9. Compute applied forces summing up the yarns tension

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C

  • mponents of the shear

resistance

X Y X0 Y0 Fx Fy T

  • cos

YX XY T M

  • M

A 2 1

  • T

T Q hWa p

bending tension lateral compression

Q Q Q Q

  • torsion

bending disp friction

A A A A A

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L ateral compression

spacing 2.8 mm spacing 1.5 mm Vf0 Vf Q

  • new

new d

d Vf P P

2 1

,

  • 2

2 Wa We lateral compression Wa We

Q P P d d

  • p

d

L 2

max arccos

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F riction and torsion

fQr M friction

2 2

2 1 ; 3 2

We Wa d

d R R r

  • d2

t a2 a1

  • s

ds ds d

1 1

a a t

  • 2

2 1

  • C

Atorsion

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Vertical displacement and bending

z

before shear after shear

  • contact

disp

ds z l Q A

  • 1
  • S

bending

ds ds z d B A

2 2 2

2 1

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Input data

  • dimensions of the cross-section;
  • behaviour in compression;
  • bending and torsion resistance;
  • tension diagram;
  • coefficient of friction.
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  • Models
  • Materials and input data
  • Calculations

– Compression – Biaxial tension – Shear

  • Conclusions
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G lass/P P fabrics

743-815 1.9/1.9 plain 1870 - 2110 3 1485 1550 4.1/1.9 twill 2/2 1870/2x1870 2050/2x2050 2 1816 1900 2.6/0.76 twill 2/2 2x2400 2x2520 1 Areal dens., specified, g/m2 Ends / picks, yarns/cm Weave Yarns linear dens., spec/meas tex

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D imensions of the yarn cross-sections

0.90 0.27 x 4.35 0.59 1.17 0.16 x 4.96 0.33 1.00 0.34 x 3.26 0.52 1.60 0.17 x 5.27 0.15 2.40 0.58 x 5.44 0.76 1.56 0.16 x 7.16 0.42 Warp & weft thickness x width, mm

1870 1870 1870 2x1870 2x2400 2x2400

3 2 1 tex

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Bending and torsion rigidity

0.071 0.005 1.13 0.16 1870 3 0.14 0.03 1.14 0.07 1870 2 0.35 0.07 3.43 0.93 2400 1 HB, N mm B, N mm2 tex

1 2 yarn strand

B nB B C d d

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Models of internal geometry

1 2 3

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C

  • mpression of yarns

0.2 0.4 0.6 0.8 1 20 40 60 80 100 120

p, kPa eta1

1 2 3 average corrected

1. KES-F measurements on one strand 2. Head size 4x4 mm 3. Used in WiseTex as

1 1 2

, Q Q p d

  • 1

2 1 2 10 20 0.38 2 1

; d d d d

  • [G. Krupincova, T.U.Liberec ]

* /(1 ) F F

  • 2

1

1 1

  • Constraint correction:
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T ension and friction

5 1 1 5 2 2 5 1 2 3 4 e p s, % F, N 1 2 3

Instron measurement for one strand KES-F steel/fabric: f = 0.25 … 0.35 Input in the calculations: f = 0.3 1870 3 1870 2 2400 1 tex 2400 1870

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  • Models
  • Materials and input data
  • Calculations

– Compression – Biaxial tension – Shear

  • Conclusions
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C

  • mpression

Measurements on Instron, 1 mm/min, plate diameter 35 mm CV ~15% 1 2 3 4 5 6 7 20 40 60 80 100 120 140 160 180 200

p, kPa h, mm

1 2 3

experiment calculation with constraint correction

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U niaxial tension

0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 6 Strain, % Force, kN/mm 0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 6 7 Strain, % Force, kN/mm 0.02 0.04 0.06 0.08 0.1 0.12 1 2 3 4 5 Strain, % Force, kN/mm F3 weft warp warp weft F1 F2

Instron; sample 50 x 210 mm pretension 0.56; 0.30; 0.26 N/mm

  • Not stable calculation for Fabric 2
  • Good prediction of differences in behaviour:

Fabric 1: Stiffness warp vs weft Fabric 2: Initial stiffness warp vs weft

  • Overall satisfactory comparison
  • Correct Poisson for Fabric 3: 1.0 … 1.3
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Biaxial tension: F abric 2

0.02 0.04 0.06 0.08 0.1 1 2 3 4

Strain, % Force, kN/mm weft warp

pretension 0.4 N/mm

Low initial stiffness – difficult positioning of the zero point

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Shear

no pretension pretension 0.4 N/mm 37 4 1 4 6 9 13 Total

B T f

T

  • L

f

T

B T z

T

  • L

z

T

B

T

T

T

Shear components, 10-3 N/mm, F3, 45°

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  • Models
  • Materials and input data
  • Calculations

– Compression – Biaxial tension – Shear

  • Conclusions
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C

  • nclusions

1. Testing protocol established for input of yarn and fabric data into meso- mechanical models of deformability of woven fabrics 2. Comparison with experiments validates the models of deformability for “benchmarking” glass/PP fabrics 3. The models can be used for creation of input for forming simulations 4. Main sources of the uncertainty of the simulation:

  • High compressibility of the yarns
  • Low initial stiffness in tension
  • Unknown pretension in the picture frame test

5. The same factors may cause numerical instabilities in calculations