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
Wale
(warp)
Course
(weft)
TENSILE PROPERTIES: Knitted vs. Woven Fabrics
WOVENKNITTED
Region II
Region III
Region I
Region IRegion II
Region III
LOAD
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
Thermoforming with Knitted
Reinforcement
Use knitted reinforcement to:
1) improve thermoforming control
2) fabricate flexible composites for high impact resistance
Schematic View of Vacuum Thermoforming
Plastic Sheet
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
Plastic Sheet
Clamp Clamp
Vacuum
Mold
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°
100
110
120
130
140
150
160
0 2 4 6 8 10
A
B
R0
R
Distance (R/R0)
Te
mp
era
ture
(°C
)
0 0.2 0.4 0.6 0.8
1.0
Tem
pera
ture
°C
Comparison of final thickness distributions between optimized initial
temperatures with and without random temperature perturbation.
Temperature Perturbation Effects
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25
A
B
S
C.L.
R0
Th
ickn
ess (
H/H
0)
Arc Length (S/R0)
Thic
kness H
/H0
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
0
1
2
3
4
5
6
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
P*
stretch (l)
C01/C10=0.5
0.2
0.005
0.01
0.1
An Exercise on Thermoforming
010
0*
2
Pr
tCP =
)3()3( 201110 !+!= ICICW
d
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
Finite Element Models
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
Wale
Course
200 Beam Elements (Fiber)
9900 8-node 3D Brick Elements (Soft Exterior
Material) 2300 Contact Elements
Finite Element Models
0
10
20
30
40
50
60
70
80
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)
Finite Element Models
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 Stretch (%)
Walewise Uniaxial Testing
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50 60 70
Walewise Stretch (%)
1 2 3
4
5
Critical Stretch
Walewise Uniaxial Testing
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100 120
Lo
ad
(N
)
Walewise Stretch (%)
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
d d
Correction for Yarn Compression Effect
Determination of Critical Stretch
Net Result
Correction Fiber stretch behavior
Critical Stretch
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5 6 7 8
Cri
tical S
tretc
h (
%)
Wale Number (loops/cm)
d=0.033 cm
d=0.066 cm
d=0.099 cm
!"#$%&'())*+,-.'
1/C
1/W
Wale
Coursed
W/C=3.7 W/C=3.0675 W/C=2.3
W/C=1.938 W/C=1.5
W/C=0.85
FE Results: Walewise Loading
Correlation of Critical Stretch with Wale-Number
for different Yarn Diameters
•! /0-123+24'())*'420+567'89:!;'
+5<05=-306(7'()>21+'-15?-3('+6126-@$'
•! /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$'8#4EF,
9;'
•! G+50<'45H21206'420+567'*3I210+'50'6@2'+3.2'A3D15-J'<()D3('+6126-@'
D2@3B5)1'-30'D2'635()124$'
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
Thermoforming with Knitted
Reinforcement
Thermoformed Reinforced Structures
a) ! Thermoformed twin-sheet, foam filled, panel with
knitted reinforcement b)! Thermoformed twin-sheet panel with graded
reinforcement.
