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THE MATRIX: EVOLUTIONS II
Pearl SullivanComposites and Adhesives Group
Department of Mechanical EngineeringUniversity of Waterloo
IPR 28th Annual Symposium, 16 May 2006
Scope: Multi-scale Analyses
meters10–10 10–9 10–8 10–7 10–6 10–5 10–4 10–3 10–2 10–1 10–0 101 102
materials science
applied mechanics
engineering
Atomic/Nanoscale Micro-scale Macro-scale Structural
[Adapted from Broek, 1974]
Structure + mechanics are critically linked to function at all scale lengths.
Performance depends on :• Inherent polymer structure (materials selection)• Processing• Mechanical/thermal loading on part design• Environmental effects
THERMOSETSAdvanced Composites
Adhesives
THERMOPLASTICSAmorphous
Semi-crystalline
Polymeric Materials Program
Network 3-D Structure Amorphous - discrete linear chains
Semi-crystalline – orderedpacking in amorphous matrix
Mod
u lus
, E
Temperature
TgEg
Mod
u lus
, E
Temperature
TgEg
PART I: Thermoset Program
Transitions During Cure of a Thermoset
• Polymerization
• Cross-linking
• 3-D Network
Edv
ViscoelasticMechanical Properties
Phase Transformations
Cure Kinetics
Glass Transition
TemperatureUnrelaxed
Modulus, Eg
GOAL: A Unified Model for Modulus Development during Thermoset Cure
Relaxed Modulus, E∞
( ) [ ]E t E E E et
R g iii
n= + − −
⎡
⎣⎢
⎤
⎦⎥∞ ∞
=∑ exp
τ1
Relaxation Time Spectra, ER
Case I. Composite Patch Repair of Metallic Structures
CF-18
Y470.5 Bulkhead
X-19 Repair Patch
In collaboration with Dr. Andrew Johnston The Institute of Aerospace Research, Ottawa
ThermosetThermoset Adhesives ProgramAdhesives ProgramTeam:• Drazen Djokic (MScE)• Angela Rogers (PhD)• Pearl Sullivan
Project Objectives
• Investigate residual stress development during patch repair• Characterize adhesive cure kinetics during cure process• Develop simulation model (viscous-elastic) for predicting:
Specimen deformation
Specimen Warpage *, δ
Cured adhesive interface Substrate in tension
Patch in compression
*exaggerated deformation
WARPAGE MEASUREMENT
•• SingleSingle--sided repair sided repair
•• PrePre--cured unidirectional carbon cured unidirectional carbon fibrefibre/epoxy patch/epoxy patch
•• Aluminum substrateAluminum substrate
•• FM 73 film adhesiveFM 73 film adhesive
304.8 mm
101.6 mm
50.8 mm
101.6 mm
3.30mm0.20mm
[010]
Al 2024-T3 Substrate Pre-Cured Composite Patch,AS4-3501/6 [0°]10 + 1 ply of FM 73
Adhesive Film, 1 ply FM 73
1.50mm
Fixture
Instrumented Cantilever Beam
Al Substrate
Scale:50 mm
Composite Patch
Cantilever-Specimen Contact Point
Djokic, D. et. al. American Society for Composites AnnualMeeting, Austin, Texas, Sept 2000, 12 pgs.
Tg
DSC for Cure Kinetics Determination
T
Tem perature (°C)
Hea
t Flo
w (W
/g)
Q res
• Perform a dynamic temperature scan on uncured and partially cured specimens with DSC.
• Calculate Tg from the heat flow data for each sample.
• Calculate the degree of conversion for each specimen.
Tg
Tg = A1 + B1α + C1α2 α < αc
Tg = A2 + B2(α - αc) + C2(α – αc)2
for α > αc
αc
Analytical Models: Cure Kinetics Equation
85.18.1
21 ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ −+= ααααfKKdt
d
An existing semiAn existing semi--empirical model (empirical model (KamalKamal and Sourour,1973) and Sourour,1973)
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛×−×=
RTK
4111
10353.9exp1038.1
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛×−×=
RTK
441
10694.3exp1062.6
Temperature dependent reaction rate constantsTemperature dependent reaction rate constants:Model Predictions and Experimental MeasurementsModel Predictions and Experimental Measurements
Degree of Cure, α
0.0 0.2 0.4 0.6 0.8 1.0
Rat
e of
Cur
e, d
α/d
t (1/
min
)
0.00
0.01
0.02
0.03
0.04
ExperimentModel
Degree of Cure, α
0.0 0.2 0.4 0.6 0.8 1.0
Rat
e of
Cur
e, d
α/d
t (1/
min
)
0.00
0.02
0.04
0.06
0.08
0.10
0.12ExperimentModel
T=95 °CT=95 °C T=120 °CT=120 °C
Analytical Models: Viscoelastic Response
Time (min)
0 50 100 150 200 250 300 350 400
E (G
Pa)
0.0
0.5
1.0
1.5
2.0
2.5
Tem
pera
ture
(°C
)
20
40
60
80
100
120
DMA Stress Relaxation Test Data:DMA Stress Relaxation Test Data:
Log(t) (min)
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
E (G
Pa)
0.0
0.5
1.0
1.5
2.0
2.530°C45°C60°C75°C90°C105°C
Log(ξ) (min)
-2 0 2 4 6 8 10 12
E (G
Pa)
0.0
0.5
1.0
1.5
2.0
2.530°C45°C60°C75°C90°C105°C
Time Time --Temperature Superposition:Temperature Superposition:
Log (ξ) (min)
-2 0 2 4 6 8 10 12
E (G
Pa)
0.0
0.5
1.0
1.5
2.0
2.5α=0.99α=0.95α=0.87α=0.74Model (α=0.99)Model (α=0.95)Model (α=0.87)Model (α=0.74)
Master Curves, Master Curves,
Model and Experimental ResultsModel and Experimental Results:
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−−+=
∞∞19.0
)(),(exp)()()(),,(ατα
αααα TatEEEtTE
T
u
TCCaT
)()()(log 21
αα +=
073.3512.3735.01333.1)(log 2 −+
−= αα
ατ
Shift FunctionShift Function:
Relaxation TimeRelaxation Time:
Relaxation ModulusRelaxation Modulus:
Results: Single-Step Cure CyclesTest 1: Test 1: TTcurecure=121 °C, =121 °C, ttholdhold=60 min=60 min
20
40
60
80
100
120
0 50 100 150 200Time [min]
Tem
pera
ture
[°C
]
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Spe
cim
en w
arpa
ge, δ
[mm
]
•• Negligible Negligible warpagewarpage during heating and isothermal holdduring heating and isothermal hold
•• NonNon--linear linear warpagewarpage until 100 °C (until 100 °C (TTgfgf ))
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
25 45 65 85 105 125
Temperature [°C]S
peci
men
War
page
, δm
odel
[mm
]
ExperimentModel
TSF(sim.) = 99.6 °C
TSF(exp.) = 102.2 °C
Tgf = 100 °C
Djokic, D. et. al. Composites A:Applied Sci and Manuf.Vol 33(2), 2001, pp. 277-288.
Results: Single-Step Cure CyclesExperimentExperiment ModelModel
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
25 45 65 85 105 125
Tem perature [°C ]
Spe
cim
en W
arpa
ge, δ
exp.
[mm
]
121°C , 1hr
104°C , 1hr
82°C ,4hr
77°C , 6hr
T SF ≈ T gfT SF ≈ T cure
125
-1 0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
25 45 65 85 105 12
Temperature [°C]
Spe
cim
en W
arpa
ge, δ
mod
el [m
m]
121°C , 1hr
104°C,1hr
82°C ,4hr
77°C , 6hr
TSF ≈ TgfTSF ≈ Tcure
125
3.0
-1.0
Next Steps
1.1. Patch repair model for multiPatch repair model for multi--step cure can be improved by:step cure can be improved by:
•• Including diffusion effects in cure kinetics modelIncluding diffusion effects in cure kinetics model
•• Including Including viscoelasticviscoelastic response within response within gelationgelation--vitrificationvitrification rangerange
2.2. Modulus development needed:Modulus development needed:
•• Integrate models into FE codeIntegrate models into FE code
Degree of Conversion (α)0.0 0.2 0.4 0.6 0.8 1.0
dα/d
t (m
in-1
)
0.000
0.005
0.010
0.015
ExperimentalModel 3Model 4Proposed Model
0.85 0.90 0.950.000
0.001
0.002
Comparison of Models
( ) ( )( )[ ]
ddt
k m n nα α α α
α α =
1 - + k2m2 1- a
+ exp C - c
11 1 2
1
This model: • Suggests that chemical curing is primarily the result of a combination of two autocatalytic reactions;
• Includes a diffusion factor in the denominator.
Refined Cure Kinetics Model
Rogers, A. and Lee-Sullivan, P., Polymer Engineering and ScienceVol. 43(1), Jan 2003, pp 14-25
Case II. Dimensional Stability of Microelectronic Bonds
• Epo-tek H20E two-part epoxy
• Silver filled; sub micron-size• Electrically Conductive
Adhesive (ECA)• Thermally conductive• Applications:
– Microelectronics– Optoelectronics
Cure Conversion with Time
0
0.2
0.4
0.6
0.8
1
1.2
0 50 100 150 200 250 300 350 400
Time (min)
Deg
ree
of C
ure
(%)
8090100110120
Cure kinetics for Electrically Conductive Adhesive (ECA)
Garvin, M. and Lee-Sullivan, P., Canadian Themal Analysis Meeting,
Toronto, May 2006
120 deg. Iso Cure (6h)
-0.001
0
0.001
0.002
0.003
0.004
0.005
0.006
0 0.2 0.4 0.6 0.8 1
a(t)
da/d
t
Run 1Run 2Run 3Iterative Model
Tg Advancement with Degree of Cure
Tg advancement with DOC
0
10
20
30
40
50
60
70
80
90
97.00% 97.50% 98.00% 98.50% 99.00% 99.50% 100.00%
DOC (%)
Tg (o C
)
Ultimate Goal of Thermoset Cure Modeling Program
( ) ( ) ( ) ( ) ( )E t T E T E T E T e t
a TR g i
T ii
n
, , , , , exp,,
α α α ατ αα
= + −⎡⎣⎢
⎤⎦⎥
−⎡
⎣
⎢⎢⎢
⎤
⎦
⎥⎥⎥
∞ ∞
=∑
1
For application in computational modeling:• adhesive bonding processes • composite processing• microelectronic assembly, e.g. underfill, encapsulation
Part II : Thermoplastic Program
Goals• Characterize time-, temperature- and moisture
effects on stability of thin-walled moldings– Creep and Stress Relaxation
• Develop phenomenological model to predict the intrinsic viscoelastic constitutive behaviour(e.g. time-dependent bulk modulus).
Post-Molding Dimensional Stability
Does your part warp after molding?
Case 1: Polypropylene (PP)
Cooling rate effects on part warpage during injection molding
Post-molding thin-wall warpage• Warpage in thin-walled plates due to
unsymmetrical residual stress during uneven cooling
• Can be minimized through part-cavitydesign and processing conditions
Measuring Post-Molding Warpage
using Coordinate Measuring Machine
• Circularity was calculated from 50 measurements: D0
Deviation = ∆ diameter/ d
• Flatness was calculated from 150 measured points on the surface: D1, D2, D3
Deviation = ∆ height/ dDisk diameter, d ~ 10 in
27
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40 50 60
Circ
ular
ity a
nd F
latn
ess
(mm
)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Dev
iatio
n fr
om R
ound
and
Fla
t (%
)
Circularity Flatness
Average Circularity Average Flatness
Warpage after one week after molding
Lower WarpageLower Warpage Variability
With lower 5 L/min cooling rate:
28
0.000
0.200
0.400
0.600
0.800
1.000
1.200
0 1 2 3 4 5 6 7
Days after Molding
Flat
ness
and
Circ
ular
ity (m
m)
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
Dev
iatio
n fr
om R
ound
and
Fla
t (%
)
Flatness 30 L/min Circularity 30 L/minFlatness 5 L/minCircularity 5 L/min
Increasingly more warpage as the part ages for higher cooling rate
Evolution of Warpage over 1 Week
30 C
30 F
5
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