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