Mechanical Properties of Thermoformed Structures with Knitted...

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B. Bekisli and H. F. Nied

Mechanical Engineering and Mechanics

Lehigh University

RTS 2009 Ecole des Mines d’Albi (France)

March 13, 2009

Mechanical Properties of

Thermoformed Structures with

Knitted Reinforcement

Lehigh University in Bethlehem PA

Packard #1, 1899

Packard Lab

Thermoforming with Knitted

Reinforcement

KNITTED FABRICS

Weft Knit Warp Knit Weft Rib Knit

•! Yarn looping through itself to make a chain-

like structure •! Initially loose, interlocking with deformation

•! Hundreds of patterns •! Net-shape structures (2D fabrics onto 3D

shapes), seamless tubular forms, cones,

domes, T-pipe junctions •! Full 3D knits are also available

Mixed Interlock

Textile Fabrics

(warp)

Course

(weft)

TENSILE PROPERTIES: Knitted vs. Woven Fabrics

WOVENKNITTED

Region II

Region III

Region I

Region IRegion II

Region III

Displacement

Region I : Inter-yarn and intra-yarn friction resistance

Region II : Bending of yarns; straightening in the load

direction (knitted), in-plane shear (woven)

Region III: Fiber extension, transverse compression

Textile Fabrics

Reinforcement

Use knitted reinforcement to:

1) improve thermoforming control

2) fabricate flexible composites for high impact resistance

Schematic View of Vacuum Thermoforming

Plastic Sheet

Clamp Clamp

Vacuum

Mold Mold

Heater

(1) Pre-Heated Stage (2) Vacuum Stage

Advantages: Easy to form large parts with low pressure

Disadvantages: Forming with high precision is very difficult

Thermoforming of Large Structures

Source: “Design With Plastic And Composites, A Handbook.”, Rosato, DiMattia and Rosato, 1991

Boat Hull

Thermoforming of Large Structures

Liger (European) “Microcar” Body Panels are Thermoformed

Thermoformed Prototype Mariner Rocker Molding

“Claddings”

2006 Ford Mercury Mariner

Finite Element Simulations

Membrane Elements

Forming Thickness Variations

fig 22: Plug example fig 21: Corner contact

Full 3-D Elements

Source: De Vries, A. J., Bonnebat, C. and Beautemps, J., 1977, J. Poly. Sci.:

Polym. Symp., 58, 109

Material Behavior of Polystyrene

Thermoforming with Zone Heating

Upper Heating Zones

IR Thermal Image

640oF 200oF

~175oF

~220oF

Plastic Sheet

Clamp Clamp

Vacuum

Heater

(1) Pre-Heated Stage (2) Vacuum Stage

Infrared Imaging in Thermoforming

Non-dimensional final thickness distributions for thermoformed cylinders Numerical Solution of Inverse Problem

Isothermal initial boundary conditions Optimal thermal boundary conditions

T0 = 115.6 oC

Temperature Perturbation Effects

Comparison of optimized initial temperature distribution with

random temperature perturbation within ± 3°

0 2 4 6 8 10

Distance (R/R0)

0 0.2 0.4 0.6 0.8

Comparison of final thickness distributions between optimized initial

temperatures with and without random temperature perturbation.

Temperature Perturbation Effects

0 5 10 15 20 25

Arc Length (S/R0)

kness H

0 0.5 1.0 1.5 2.0 2.5

Case A

Analytical Solution for inflation of a hyperelastic sphere*

2-P Mooney-Rivlin model

Non-dimensional Pressure

When C10 is constant, material with higher C01 behaves more like a flexible

composite with denser knit architecture (stiffening at earlier stretch).

Rough assumption for demonstration purposes : Model will be used to

simulate a flexible composite, with C01 defining the density of the knits.

* “Finite Element Simulation of Thick Sheet Thermoforming”, Mercier, PhD Diss., Lehigh University, 2006

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

stretch (l)

C01/C10=0.5

An Exercise on Thermoforming

)3()3( 201110 !+!= ICICW

Analysis of Uniaxial Walewise Stretching of

a Plain Knitted Glass-Fiber Fabric

Plain Knitted Fabric Geometric Unit Cell

W: Wale Number- Number of loops per length of course direction

C: Course Number- Number of loops per length of wale direction d: Yarn Diameter

Load-Displacement Behavior

Knitted Thermoforming Exercise

Initially Uniform Knit Architecture

Optimized Knit Architecture (10x10

sub-sections)

•!Finite Element Analysis

•!Experimental Measurements

•!Comparison

Uniaxial Walewise Stretching of a

Plain Knitted Glass-Fiber Yarn

Finite Element Models

Linear Elastic Beam Elements:

A Single Glass-Fiber d= 9 !m

Ex=Ey=Ez= 74 GPa Gxy=Gyz=Gzx=30 GPa

Linear Elastic 8-Node Brick

Elements: A Soft Exterior Material

Ex=Ey=Ez= 74 kPa Gxy=Gyz=Gzx=30 kPa

Yarn with Core Fiber Model

Outer Surface is covered with

Contact (or target) elements

Point Loading at

Fiber ends

Periodic Boundary Conditions

on Wale Direction End Surfaces

No fixed point in the wale

direction : Friction holds the

yarns together (!=0.1)

Symmetry Conditions in the Coursewise Direction

Course

200 Beam Elements (Fiber)

9900 8-node 3D Brick Elements (Soft Exterior

Material) 2300 Contact Elements

0 20 40 60 80 100 120 140

Walewise Stretch (%)

Run1: Single Fiber + Soft Filling Material Run2: All Soft Filling

Material

Net Result: Run1-Run2 (Single Fiber)

Load is the total load on the knitted fabric;

Load found for a single fiber x number of fibers in a yarn (2800) x number of loops in coursewise direction (7)

Equipment and Testing

Silver Reed SK840

Manual Knitting Machine

Uniaxial Testing of

a Glass Fiber Knitted Specimen

1- Relaxed Fabric

2- Translation of Loops

3- Bending Domination starts

4- Critical Stretch Point

5- Fiber Stretch Region

Walewise Uniaxial Testing

0 10 20 30 40 50 60 70

Critical Stretch

Walewise Uniaxial Testing

0 20 40 60 80 100 120

Three other sets were also tested: (d=0.066 cm for all)

•! W = 1.62 loops/cm, C=3.47 loops/cm •! W = 2.30 loops/cm, C=4.09 loops/cm

•! W = 2.47 loops/cm, C=4.26 loops/cm

W= 1.94 loops/cm

C= 4.12 loops/cm d=0.066 cm

Test length=10 cm

Test width= 3.6 cm

(curls to below 1cm)

10 specimens:

Effect of Inter-yarn and Intra-yarn Friction:

Effect of Friction

Experiment Set 1, 13 similar specimens;

10 tested dry, 3 tested after a lubricant applied on yarns to reduce friction.

Lubricated yarns Dry yarns

Correction for Yarn Compression Effect

Determination of Critical Stretch

Net Result

Correction Fiber stretch behavior

Critical Stretch

0 1 2 3 4 5 6 7 8

tical S

Wale Number (loops/cm)

d=0.033 cm

d=0.066 cm

d=0.099 cm

!"#$%&'())*+,-.'

Coursed

W/C=3.7 W/C=3.0675 W/C=2.3

W/C=1.938 W/C=1.5

W/C=0.85

FE Results: Walewise Loading

Correlation of Critical Stretch with Wale-Number

for different Yarn Diameters

•! /0-123+24'())*'420+567'89:!;'

+5<05=-306(7'()>21+'-15?-3('+6126-@$'

•! /0-123+24'7310'453.2621'84;'

42-123+2+'-15?-3('+6126-@'A)1'3'<5B20'

>3(2'0C.D21'89;'304'-)0+61350+'6@2'

42+5<0'130<2'<2).2615-3((7$'8#4EF,

•! G+50<'45H21206'420+567'*3I210+'50'6@2'+3.2'A3D15-J'<()D3('+6126-@'

D2@3B5)1'-30'D2'635()124$'

Experimental Observations

Results: FE vs. Experiments

K26' 9'8())*+,-.;' !'8())*+,-.;'!15?-3('K6126-@'8L;'

M11)1'8L;''

M:*215.206+' NC.215-3('

F' F$OP' Q$#R' &Q$P#' F%F$Q' S$O#'

P' F$&#' #$FP' &F$OO' &&$T' S$TT'

Q' P$Q' #$%&' OO$ST' R#$F&' F%$&S'

#' P$#R' #$PO' T&$#&' OR$#T' FQ$QS'

Possible Sources of Error:

•! Significant Scatter in Experiments

•! Hypothetical Yarn Diameter from Manufacturer Data, Theoretical Predictions give Higher

Diameters

•! Effect of Friction between yarns and between fibers

Future Work

•! Analyze knitted fabric subjected to multiaxial deformation

•!Global Scale FE Model for the Knitted Fabric using Hexagonal

Symmetry* and Hyperelastic Material Models

* M.de Araujo, R.Fangueiro, H.Hong, Autex Research Journal, March 2004.

•! Extension to Flexible Composites; Knitted Fabrics embedded in

flexible matrices (Polyurethane)

•! Applications in Forming, High-Energy Impact Performance

FEM Simulations of Knitted Materials

Multiaxial Characterization Testing with Knitted Fabric Embedded in Urethane Matrix

Testing with Knitted Fabric Stretched over Rubber Sheet

Reinforcement

Thermoformed Reinforced Structures

a) ! Thermoformed twin-sheet, foam filled, panel with

knitted reinforcement b)! Thermoformed twin-sheet panel with graded

reinforcement.

Mechanical Properties of Thermoformed Structures with Knitted...

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