MONOFILAMENT TECHNICAL TEXTILES FOR SCREEN PRINTING: EXPERIMENTAL - - PowerPoint PPT Presentation

MONOFILAMENT TECHNICAL TEXTILES FOR SCREEN PRINTING: EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE MECHANICAL BEHAVIOUR

Valter Carvelli

Politecnico di Milano

SCREEN PRINTING

Printing technique, also known as serigraphy, involving stencils to transfer pictures. The ink is applied to the textile and penetrates areas of the screen not filled by the stencil.

Deposit of the stencil

Plain screen-printing

Exposure of the stencil

a) frame b) stencil c) ink d) squeegee e) substrate

a b c d e

Frame preparation tension and tie

SCREEN PRINTING

The mechanical response of the textile tied in the frame involves both

• the mechanical properties of the DRY TEXTILE and
• the mechanical properties of the FILLED WITH STENCIL TEXTILE

DRY TEXTILE

FILLED TEXTILE

(textile composite)

Experimental Results

• n dry textiles
• First-Scale Numerical Modelling

Numerical Modelling

34 m 45 m 70 m 30 m 34 m 45 m 70 m 30 m

• Second-Scale Numerical Modelling

OUTLINE

Numerical applications and comparisons Open discussion Analytical model

ANALIZED TECHNICAL TEXTILES

Two polyester plain weave monofilament textiles A 200 m B 200 m

Textile A  150 polyester fibres per cm  34 m fibre nominal diameter Textile B  62 polyester fibres per cm  64 m fibre nominal diameter

EXPERIMENTAL INVESTIGATION OF THE DRY TEXTILES

Carvelli V., Corazza C., Poggi C. Computational Materials Science, 2008

Geometric parameters

EXPERIMENTAL RESULTS: dry textiles

Scansion Electronic Microscopy (SEM)

30 m 20 m 20 m

Textile A

Optical Microscopy (OM)

33 m 40 m 70 m 28 m 33 m 40 m 70 m 28 m 34 m 45 m 70 m 30 m 34 m 45 m 70 m 30 m

Cross-section of warp fibres Cross-section of weft fibres

30 m 30 m 100 m

Scansion Electronic Microscopy (SEM)

73 m 56 m 148 m 47 m 73 m 56 m 148 m 47 m 70 m 62 m 146 m 48 m 70 m 62 m 146 m 48 m

Textile B

Optical Microscopy (OM)

Cross-section of warp fibres Cross-section of weft fibres

Geometric parameters

EXPERIMENTAL RESULTS: dry textiles

200 400 600 800 10 20 30 40 50 Strain [%] Stress [MPa] warp weft 200 400 600 800 10 20 30 40 Strain [%] Stress [MPa] warp weft

diameter 34 m

diameter 64 m

Fibres mechanical properties

warp weft warp weft

R : 26.58 m R : 24.99 m R : 25.14 m R : 32.44 m R : 17.77 m

Fibres extracted from the textile MTS (0.1kN load cell)

EXPERIMENTAL RESULTS: dry textiles

Uniaxial and Biaxial tensile tests of textiles

Home made biaxial tensile device

60 60 145mm 145mm 145 145 25mm 25 clamping zones

15 15

markers

r=20

 Two independent servo-motors  Speed range: 1÷280mm/min  Maximum load per direction: 5kN digital camera for DIC

EXPERIMENTAL RESULTS: dry textiles

load cells

UNIAXIAL TENSILE TESTS

10 20 30 40

• longit. strain [%]

100 200 300 400 500

force [N]

• 10
• 8
• 6
• 4
• 2
• transv. strain [%]

warp weft textile A 10 20 30 40

• longit. strain [%]

100 200 300 400 500

force [N]

• 10
• 8
• 6
• 4
• 2
• transv. strain [%]

warp weft textile B

EXPERIMENTAL RESULTS: dry textiles

20 40 60 80

shear strain [%]

100 200 300 400 500

force [N]

textile A

fibres oriented ±45o to the load direction

UNIAXIAL TENSILE TESTS EXPERIMENTAL RESULTS: dry textiles

• 15
• 10
• 5

5 10 15

warp direction

• 15
• 10
• 5

5 10 15

weft direction

21 22 23

weft strain component

• 15
• 10
• 5

5 10 15

warp direction

• 15
• 10
• 5

5 10 15

weft direction

1 2 3

in-plane shear strain component

Textile A

BIAXIAL TENSILE TEST

(displacement speeds ratio = 1)

3 6 9 12 15

strain [%]

100 200 300 400 500

force [N]

warp weft textile A 3 6 9 12 15

strain [%]

100 200 300 400 500

force [N]

warp weft textile B

• 200
• 100

100 200

warp direction [pixels]

• 200
• 100

100 200

weft direction [pixels]

0% 8.5% textile A 60 60 145mm 145mm 145 145 25mm 25 clamping zones

15 15

markers

r=20

EXPERIMENTAL RESULTS: dry textiles

BIAXIAL TENSILE TEST

(displacement speeds ratio = 1)

EXPERIMENTAL RESULTS: dry textiles

• 15
• 10
• 5

5 10 15

warp direction [mm]

• 15
• 10
• 5

5 10 15

weft direction [mm]

• 15
• 10
• 5

5 10 15

warp direction [mm]

• 15
• 10
• 5

5 10 15

weft direction [mm]

• 15
• 10
• 5

5 10 15

warp direction [mm]

• 15
• 10
• 5

5 10 15

weft direction [mm]

Map of the strain components

strain in the warp direction strain in the weft direction

60 60 145mm 145mm 145 145 25mm 25 clamping zones

15 15

markers

r=20

in-plane shear strain

STATIC FRICTION COEFFICIENT EXPERIMENTAL RESULTS: dry textiles

Test according to ASTM D3412

In the numerical model, Coulomb friction for fibre-fibre contact interaction static friction coefficient s  5 d=0.56 dynamic friction coefficient

Yarn PacKage Yarn Guide Adjustable Input tension Yarn Tension Gages Yarn Takeup Yarn helix Yarn Guide

Experimental device average dynamic friction coefficient 0.112 coefficient of variation (%) 3.2

1 1 2 d

T T ln



           

T1 mean input tension T2 mean output tension  wrap angle

NUMERICAL MODELLING AT TWO SCALES

Carvelli V., Corazza C., Poggi C. Computational Materials Science, 2008

BACKGROUND

FUNDAMENTALS OF HOMOGENIZATION THEORY FOR PERIODIC MEDIA

Homogenized Material Representative Volume Heterogeneous Material

Hypothesis: periodic distribution of the fibres in the textile Heterogeneous Periodic Material

FIRST-SCALE NUMERICAL MODELLING (HOMOGENIZATION at the yarn scale) SECOND-SCALE NUMERICAL MODELLING (textile structure scale) REPRESENTATIVE VOLUMES (RV)

DRY TEXTILE

NUMERICAL MODELLING

FILLED WITH STENCIL TEXTILE

PROBLEM FORMULATION FOR THE HOMOGENIZATION The homogenized constitutive law is predicted solving the incremental problem defined on the RV

V in div   

V   

• n

periodic

• anti

n t   





V dV

V     1





V dV

V 1    E

Volume of the RV Macroscopic stress Macroscopic strain Microscopic stress Microscopic strain Microscopic constitutive law Periodic part of the microscopic displacement

V    

• n

periodic ~ x E u u     V F in )) ( ( u      

Boundary

• f the RV

KINEMATIC BOUNDARY CONDITIONS

) ( ~ ) ( x u x E x u x u       

rigid displacement

antisymmetric tensor periodic displacement component symmetric strain tensor position vector

Carvelli V, Taliercio A. Mechanics Research Communications, 1999

GENERAL 3D MICROSCOPIC DISPLACEMENT FIELD Macroscopic displacement gradient

E Ω Ψ  

FIRST-SCALE NUMERICAL MODELLING

in the textile plane

 

2 2

1 2

 

   

B A D C

) ( ) (

B 2 A 2 D 1 C 1

      u u u u FIRST-SCALE NUMERICAL MODELLING

FINITE ELEMENT MODEL: KINEMATIC BOUNDARY CONDITIONS

) ( ~ ) ( x u x E x u x u       

periodic displacement no rigid rotation

=0

no rigid displacement

u0=0

) , , ( ) , , ( ) , , ( ) , , (

2 1

    D C B A  

B A K H

u u u u   

D C X Y

u u u u   

(H, K) – (Y, X) couples of nodes corresponding in the periodicity

Material of fibres is considered:  isotropic  nonlinear Ramberg-Osgood nonlinear model

n

E E                 | |

200 400 600 800 10 20 30 40 Strain [%] Stress [MPa] warp weft

Experiment: diameter 64 m

Approximation of the fibres constitutive behaviour by

strain stress Young’s modulus stress at linear limit hardening exponent

• ffset

parameter

FIRST-SCALE NUMERICAL MODELLING

FINITE ELEMENT MODEL: CONSTITUTIVE BEHAVIOUR OF THE FIBRES

Fitting of the experimental data by the Ramberg-Osgood model

10 20 30

strain [%]

200 400 600 800

stress [MPa]

warp weft fibres 34m experimental analytical 10 20 30 40

strain [%]

200 400 600 800

stress [MPa]

warp weft fibres 64m experimental analytical

FIRST-SCALE NUMERICAL MODELLING

FINITE ELEMENT MODEL: CONSTITUTIVE BEHAVIOUR OF THE FIBRES

34 m 45 m 70 m 30 m 34 m 45 m 70 m 30 m

Hypothesis: constant elliptic fibre cross section Kinematic conditions:

• no penetration between fibres
• no adhesion at the fibres crossovers (due to the thermal treatment)
• Coulomb friction contact between fibres.

FIRST-SCALE NUMERICAL MODELLING

FINITE ELEMENT MODEL: two DRY TEXTILE representative volumes

RV1 RV2

FINITE ELEMENT MODEL: two DRY TEXTILE representative volumes

Textile Elements Nodes A 25920 6380 B 26880 6612 Textile Elements Nodes A 19200 5330 B 26880 7410 (4-nodes tetrahedral elements)

FIRST-SCALE NUMERICAL MODELLING

RV1 RV2

Textile Elements Nodes A 81312 15162 (4-nodes tetrahedral elements)

• Perfect adhesion between

fibres and matrix

• Matrix elastic behaviour:

E = 2000 MPa n = 0.32

FIRST-SCALE NUMERICAL MODELLING

FINITE ELEMENT MODEL of the FILLED TEXTILE representative volume

NUMERICAL APPLICATIONS AND COMPARISONS

UNIAXIAL TENSILE TEST in the principal directions

Textile A

10 20 30 40

strain [%]

100 200 300 400 500

load [N]

exp.

• num. RV1
• num. RV2

textile A warp 10 20 30 40

strain [%]

100 200 300 400 500

load [N]

exp.

• num. RV1
• num. RV2

textile A weft

weft warp

Textile B

10 20 30 40

strain [%]

100 200 300 400 500

load [N]

exp.

• num. RV1
• num. RV2

textile B warp 10 20 30 40

strain [%]

100 200 300 400 500

load [N]

exp.

• num. RV1
• num. RV2

textile B weft

weft warp

FIRST-SCALE NUMERICAL MODELLING

RV2 RV1

DRY TEXTILES: RESULTS AND COMPARISONS

BIAXIAL TENSILE TEST in the principal directions

Textile A Textile B

4 8 12 16 20

strain [%]

100 200 300 400 500

load [N]

• exp. warp
• exp. weft
• num. RV1 warp
• num. RV2 warp
• num. RV1 weft
• num. RV2 weft

textile B 4 8 12 16 20

strain [%]

100 200 300 400 500

load [N]

• exp. warp
• exp. weft
• num. RV1 warp
• num. RV2 warp
• num. RV1 weft
• num. RV2 weft

textile A

FIRST-SCALE NUMERICAL MODELLING

RV2 RV1

DRY TEXTILES: RESULTS AND COMPARISONS

undeformed and deformed geometry at the strain level 9.5%

Free surface for ink penetration

200 400 600 800 1000 2.0% 5.0% 9.5%

Strain Free Area [m2]

variation initial area

Textile A

2000 4000 6000 8000 10000 2.0% 5.0% 9.5%

Strain Area libera [m2]

variation initial area

Free Area [m2]

Textile B

FIRST-SCALE NUMERICAL MODELLING

BIAXIAL TENSILE TEST geometry variation at different strain levels in the principal directions

Textile A

DRY TEXTILES: RESULTS AND COMPARISONS

deformed undeformed

1 2 3 4 5 macro strain [%] 50 100 150 200 macro stress [MPa]

• num. warp
• num. weft

filled textile A uniaxial traction

FIRST-SCALE NUMERICAL MODELLING

FILLED TEXTILE: RESULTS AND COMPARISONS

UNIAXIAL TENSILE TEST in the principal directions (linear elastic range)

Filled Textile A

Filled Textile A

deformed undeformed

1 2 3 4 5 macro strain [%] 50 100 150 200 macro stress [MPa]

• num. warp
• num. weft

filled textile A biaxial traction

FIRST-SCALE NUMERICAL MODELLING

FILLED TEXTILE: RESULTS AND COMPARISONS

BIAXIAL TENSILE TEST in the principal directions (linear elastic range)

TEXTILE PLANE STRUCTURE FOR SCREEN-PRINTING

Textile A Metallic frame

Textile structure geometry (academic application)

SECOND-SCALE NUMERICAL MODELLING

Finite Element simulation of the textile traction in the frame

Elements Nodes 1814 5720

• Loading condition:

6mm biaxial traction (working strain level 2%)

• MESH:
• 8-nodes quadrilateral;
• thickness = 0.057mm.

SECOND-SCALE NUMERICAL MODELLING

TEXTILE PLANE STRUCTURE FOR SCREEN-PRINTING

MATERIALS PROPERTIES in the elastic range from the first-scale numerical modelling results

E1 = 2992 MPa E2 = 3542 MPa v12 = 0.14 v21 = 0.22 G12 = 113 MPa Homogenized dry textile A E1 = 3825 MPa E2 = 3762 MPa v12 = 0.31 v21 = 0.30 G12 = 1126 MPa

1=warp 2=weft

Homogenized filled textile A

SECOND-SCALE NUMERICAL MODELLING

TEXTILE PLANE STRUCTURE FOR SCREEN-PRINTING

Mises’s stress contour plot

max 97.8 MPa

SECOND-SCALE NUMERICAL MODELLING

TEXTILE PLANE STRUCTURE FOR SCREEN-PRINTING

200 400 600

stress warp [MPa]

200 400 600

stress weft [MPa]

experimetal Tsai-Hill textile A FAILURE DOMAIN

Contour plot of the axial strain components E22 ≈ 2.4% E22 ≈ 2% E11 ≈ 1.6% E11 ≈ 1.8%

200 400 600 800 1000 2.0% 5.0% 9.5%

Strain Free Area [m2]

variation initial area

SECOND-SCALE NUMERICAL MODELLING

TEXTILE PLANE STRUCTURE FOR SCREEN-PRINTING

SECOND-SCALE NUMERICAL MODELLING

TEXTILE CYLINDRICAL STRUCTURE FOR ROTATING SCREEN-PRINTING

Textile Overlap

Geometric features [mm] Metallic frame Monofilament plain weave textile

as Discontinuous surface

SECOND-SCALE NUMERICAL MODELLING

TEXTILE CYLINDRICAL STRUCTURE FOR SCREEN-PRINTING

Finite Element simulation of the textile traction in the frame

• MESH:
• finite elements S3R;
• thickness = 0.057mm.

Elements Nodes 19770 6380

• Boundary conditions

Clamping at bottom Metallic Rings no radial displacements Imposed displacement at top 10mm

• Homogenized material

properties of Textile A,

from the first-scale numerical modelling results

SECOND-SCALE NUMERICAL MODELLING

TEXTILE CYLINDRICAL STRUCTURE FOR SCREEN-PRINTING

CONTINUOUS SURFACE DISCONTINUOUS SURFACE

Mid cross section: measured displacement 8mm

Contour plot of the displacement magnitude

SECOND-SCALE NUMERICAL MODELLING

TEXTILE CYLINDRICAL STRUCTURE FOR SCREEN-PRINTING

Mises’s stress contour plot for the discontinuous surface

200 400 600

stress warp [MPa]

200 400 600

stress weft [MPa]

experimetal Tsai-Hill textile A FAILURE DOMAIN

ANALYTICAL MODEL

Carvelli V. Mechanics Research Communications, 2009 Carvelli V. Chapter 10 in “Composite reinforcements for optimum performance”. Woodhead, 2011

ANALYTICAL MODEL

MODEL FOR THE HOMOGENIZATION AT THE SCALE OF THE TEXTILE RV

x1 x2 x3 p2

 max

p1

 min

RV

Hypotheses on fibres geometry: circular cross-section parabolic longitudinal shape

ANALYTICAL MODEL

MODEL FOR THE HOMOGENIZATION AT THE SCALE OF THE TEXTILE RV Fibre-fibre transversal contact is simulated by elastic springs The fibres are modelled by a set of curved beams MAIN FEATURES

ANALYTICAL MODEL

Theory of curved beam: main features

Toniolo, 1978

d bz cz x   

2

global and local reference systems

                         

n n n n n n n n n n

F' M' φ' Δ' S F M φ Δ S '

displacements rotations moments forces n n

' S T S 

cross-section n

                sin cos 1 cos sin ) (s T

ANALYTICAL MODEL

Theory of curved beam: main features

k n

s s S H S S ) ( ) (  

                 I A I A A I A A A I H ) (

34 24 23 14 13 12

s The behaviour of the cross-section n depends on the cross-section k

Transmission function Aij are functions of the geometry and material features

ANALYTICAL MODEL

                         

  

k n k n k n s i i k n s s i i i i i n k n k n

d d d F F F U M M M V φ φ F V M V U U φ U Δ Δ

1 2 1

) ( The current state of the cross-section n is function of the cross-section k as:

             

n n n n n n n

x y x z y z U

                     

n ' z n ' y n n 2 n ' z n ' y n n 1

GA / 1 GA / 1 EA / 1 ' EI / 1 EI / 1 GJ / 1 ' V V

T n 2 n 2 T n 1 n 1

T V' T V T V' T V  

                                   

   

s i i 1 24 s i 1 23 s i 2 i i 1 i n 14 s i 1 i n 13 n 34 12

d ) ( d d ) ) ( )) ( ) ( (( d )) ( ) ( ( ) s ( U V A V A V U V U U A V U U A U A A

Transmission functions

Theory of curved beam: main features

ANALYTICAL MODEL

Theory of curved beam: main features Assembly of the linear elastic problem

S K F 

K = stiffness matrix of the beam between n and k cross-sections             

n k n k

M M F F F               

n k n k

Δ Δ S

ANALYTICAL MODEL

Prediction of the textile behaviour up to failure

Isotropic fibres material according to experimental stress-strain behaviour

10 20 30 40 50

strain [%]

200 400 600 800

stress [MPa] warp fibres 34m weft

Step by step procedure

A B uAi uBi vCi C Pi Pi+1 gi gi+1 x z y

yA i 1 i Ci i 1 i Bi Ai i 1 i

g g v H H 2 ) u u P 2 ( P        

  

) (

1 i i

E E  



Material and geometry data at the beginning of the current step (i+1) are known from the results of the previous step (i)

In each step (i+1) a linear elastic problem is solved: A strain based criterion is assumed to establish the textile failure The procedure ends when the longitudinal strain in a fibre is equal or higher them the failure strain obtained from the experimental tests.

1 1    i i i

S K F

ANALYTICAL MODEL

FIBRE-FIBRE TRANSVERSE CONTACT

elastic springs spring stiffness

P P r1 r2

) ( ) ( 4652 . ) (

2 1 2 2 1 2 1 2 2 1

r r E E r r E E K   

(see e.g. Belluzzi, 1947)

ANALYTICAL MODEL

Comparison of analytical and experimental uniaxial tensile test

Textile A

10 20 30

strain [%]

100 200 300 400 500

load [N]

experimental analitycal

Textile A: weft

10 20 30

strain [%]

100 200 300 400 500

load [N]

experimental analitycal

Textile A: warp

ANALYTICAL MODEL

Comparison of analytical and experimental uniaxial tensile test

Textile B 200 400 600 800 10 20 30 40 Strain [%] Force [N]

experimental warp experimental weft numerical weft numerical warp

• Exp. warp
• Exp. weft
• Analyt. warp
• Analyt. weft

ANALYTICAL MODEL

Comparison of analytical and experimental biaxial tensile test

Buet-Gautier K, Boisse P. Experimental Mechanics, 2001

Balanced plane weave glass textile

(0.22 yarns/mm)

for different ratio k (k = warp strain/weft strain)

Unbalanced plane weave glass textile

(0.22 and 0.16 yarns/mm)