Material Characterization for Processing: ACG MTM45-1 MTM45-1... · 2009-11-15 · Degree of Cure...

Material Characterization for Processing:

ACG MTM45-1Material Model Development

Final Project Wrap-Up

Prepared by: A. Shahkarami and D. Van EeReviewed by: D. Van EeApproved: A.PoursartipDate: November 15th, 2009Version: 1.0

2

Project Definition

Modeling performed for:

• Cure Kinetics

• Heat Capacity (Cp)

• Viscosity

Material: ACG MTM45-1

3

Material Description• MTM45-1 is a variable cure temperature, medium toughness, high service temp modified epoxy system

• Material forms received from ACG are as follows:- Fabric Prepreg (HTS5630-145-32%RW, received Aug 22, 2006)- UD Prepreg (CFO 526A-36%RW, received Aug 22, 2006)

• Tests were done on UD prepreg and comparison drawn with fabric

• Manufacturer’s recommended cure cycles are:

Autoclave1-3ºCpm20hr @ 80ºC or4hr @ 120ºC2hr @ 130ºC2hr @ 180ºC

Vacuum Bag1-3ºCpm20hr @ 82ºC or4hr @ 120ºC2hr @ 130ºC

Pre-Cure3ºCpm to initial cure temp0.3ºCpm to post-cure tempHold at 180ºC -0/+5ºC for 2hr -0/+30 minCool at 2ºCpm to 70ºC

Post-Cure

4

Material DescriptionManufacturer’s recommended cure cycles are:

Autoclave1-5ºCpm20hr @ 82ºC or4hr @ 120ºC2hr @ 130ºC2hr @ 180ºC

Vacuum Bag1-5ºCpm20hr @ 82ºC or4hr @ 120ºC2hr @ 130ºC

Pre-Cure

3ºCpm to initial cure temp0.3ºCpm to post-cure tempHold at 180ºC -0/+5ºC for 2hr -0/+30 minCool at 2ºCpm to 70ºC

Post-Cure

Autoclave20hr @ 80ºC or4hr @ 120ºC3hr @ 135ºC2hr @ 180ºC

Pre-Cure (at 3Cpm max)

2 hr at 200±2ºC (for max Tg)2 hr at 180ºC (for 140C wet service T)(max temp rate 20ºC per hr from 80ºC

Post-Cure

PREPREG

RESIN

5

Cure Kinetics Model

6

NomenclatureIso

Int

Dyn

RES

x

x&

gT

CC

Holdx

or Isothermal: Conditioned isothermal DSC tests where the specimen is held at a constant temperature long enough so that the reaction slows down significantly due to diffusionor Interrupted: Isothermal tests where the hold segment terminates before the reaction stops due to diffusionor dynamic: DSC tests where the specimen temperature is increased at a constant rate until the reaction completesor Residual: Dynamic DSC tests performed after the hold segment of Iso and Int tests to complete the remainder of the chemical reaction

or DoC: Degree of Cure

or xdot: Cure Rate

Glass transition temperature

or CureCycle: DSC tests designed to recreate the recommended cure cycles for the material, interrupted at certain points to investigate the cure advancement during the cure cycle

Degree of cure at the end of the hold segment of isothermal tests

7

Nomenclature

ModelHR

preTestHR

HoldHR

RampHR

TestHR

TotalHR

avgIsoHR

avgDynHR

avgTotalHR

Model heat of reaction; the nominal value of total heat of reaction used in the model (J/g)

The heat of reaction released during the cure advancement in material before the start of the test (material handling, storing, etc.) (J/g)

The heat of reaction released during the hold segment of the DSC tests (mostly in all variation of isothermal tests) (J/g)

The heat of reaction released during the ramp segment of the DSC tests (in dynamic tests and the residual ramps of the isothermal tests) (J/g)

The total heat of reaction measured through the two stages of the DSC test (J/g)

The total heat of reaction of the material tested (J/g)

The average of the total heat of reaction measured through the various stages of the isothermal DSC tests (J/g)

The average of the total heat of reaction measured through the various stages of the dynamic DSC tests (J/g)

The average of the total heat of reaction measured through the various stages of all the DSC tests(J/g)

HF Heat Flow, measured in the DSC experiments (W)

( )RampHold HRHR +=

( )TestpreTest HRHR +=

8

HR Definition

-20ºC

Handling &Storage

Making Samples

DSC Test

Hold

Ramp

Time

preTestHR TestHR

HoldHR RampHR

TotalHR

9

Summary

• Differential Scanning Calorimetry (DSC) tests were performed to characterize the cure kinetics of ACG MTM45-1. A Q1000 TA Instrument DSC was used for this purpose.

• Normal pans were used to perform the DSC tests on unidirectional prepreg form.

• Characterization was performed on UD tape and comparison to fabric prepreg response was done.

10

DSC Test ProcedureIsothermal TestsIn isothermal tests, the sample is equilibrated at a very low temperature and then heated up to a predefined hold temperature at a very high rate. The sample is held at this temperature for a predetermined duration of time (i.e. until the reaction stops due to diffusion or full cure in the case of conditioned isothermal tests, or earlier as predefined for interrupted isothermal tests).The sample is then cooled down, followed by a residual ramp at a known rate (typically 1-4 cpm). The residual ramp ensures that the material is fully cured, and provides the material Tg at the end of hold, as well as the residual heat of reaction. A second ramp is also performed to determine the final (full cure) Tg.Dynamic TestsIn dynamic tests, the sample is equilibrated at a very low temperature and then heated up at a predetermined rate. The goal is to fully cure the sample on the ramp. A second ramp follows to determine the final glass transition temperature (fully cured Tg).

11

DSC Tests Performed

The DSC tests were performed are summarized below:

• Dynamic tests: 19 tests @ 0.25 to 4ºCpm• Isothermal tests: 43 tests 100ºC to 205ºC• Interrupted Isothermal tests: 7 tests at 160ºC• Other: 2 cure cycle tests, 2 dynamic on fabric

After careful examination of the results and investigation of the consistency of the data, the temperature range of interest was chosen to be 100ºC to 200ºC. However, a number of tests were dismissed due to anomalies and the remaining isothermal and dynamic tests (see table on next slide) were considered in the analysis.

12

DSC Test Matrix

Mass Temp Time(mg) (ºC) (min)

MTM45-100-02 14.1 100 600MTM45-110-03 13.3 110 600MTM45-120-02 10.9 120 480MTM45-130-02 11.7 130 420MTM45-140-01 4.6 140 360MTM45-150-03 14 150 360MTM45-155-03 12.5 155 360MTM45-160-03 13.7 160 360MTM45-170-01 5.2 170 240MTM45-175-02 3.8 175 240MTM45-180-01 6.38 180 240MTM45-180-04 14.6 180 240MTM45-190-03 13.3 190 180MTM45-200-02 18 200 180

Test

Hold

Mass Temp Time(mg) (ºC) (min)

MTM45-160C-INT10-01 4.00 160 10MTM45-160C-INT20-01 6.10 160 20MTM45-160C-INT30-01 5.70 160 30MTM45-160C-INT35-01 5.10 160 35MTM45-160C-INT40-01 5.80 160 40MTM45-160C-INT45-01 6.40 160 45MTM45-160C-INT50-01 5.30 160 50

Test

Hold

Mass(mg)

MTM45-CureCycle-S3-01 5.80MTM45-CureCycle-S2-01 6.70

Test

Mass Rate Tempmax

(mg) (ºC/min) (ºC)MTM45-025cpm-02 14.5 0.25 280MTM45-05cpm-02 12.9 0.5 250

MTM45-075-02 13 0.75 260MTM45-1cpm-01 6.19 1 250MTM45-1cpm-02 4.1 1 260

MTM45-1_5cpm-01 6.09 1.5 250MTM45-1_5cpm-02 5.09 1.5 250MTM45-1_5cpm-03 5.7 1.5 260MTM45-2cpm-02 5.4 2 250MTM45-3cpm-02 14.5 3 300MTM45-4cpm-02 13.2 4 300

Test

13

Degree of Cure Calculation

Raw DSC data was linearly sparsedand smoothed.

A bi-linear baseline was considered for

dynamic tests in order to calculate the total heat of

reaction and degree of cure.

Baselines fitted to Isothermal tests

were chosen to be linear.

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000 10000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)

14

Cure Rate vs. DoC – Dyns

15

Cure Rate vs. DoC – Isos

16

0.25 Cpm Tests

17

0.50 Cpm Tests

18

0.75 Cpm Tests

19

1 Cpm Tests

20

1.5 Cpm Tests

21

2 Cpm Tests

22

3 Cpm Tests

23

4 Cpm Tests

24

HR – All Dynamics

0

20

40

60

80

100

120

140

160

180

200

MTM

45-0

25-0

1

MTM

45-0

25cp

m-0

2

MTM

45-0

5cpm

-01

MTM

45-0

5cpm

-02

MTM

45-0

75-0

1

MTM

45-0

75-0

2

MTM

45-1

cpm

-01

MTM

45-1

cpm

-02

MTM

45-1

_5cp

m-0

1

MTM

45-1

_5cp

m-0

2

MTM

45-1

_5cp

m-0

3

MTM

45-2

cpm

-01

MTM

45-2

cpm

-02

MTM

45-2

cpm

-03

MTM

45-2

cpm

-04

MTM

45-3

cpm

-01

MTM

45-3

cpm

-02

MTM

45-4

cpm

-01

MTM

45-4

cpm

-02

0

20

40

60

80

100

120

140

160

180

MTM

45-1

00-0

1M

TM45

-100

-02

MTM

45-1

10-0

2M

TM45

-110

-03

MTM

45-1

15-0

1M

TM45

-120

-01

MTM

45-1

20-0

2M

TM45

-125

-01

MTM

45-1

30-0

1M

TM45

-130

-02

MTM

45-1

35-0

1M

TM45

-140

-01

MTM

45-1

45-0

1M

TM45

-150

-01

MTM

45-1

50-0

2M

TM45

-150

-03

MTM

45-1

55-0

1M

TM45

-155

-02

MTM

45-1

55-0

3M

TM45

-160

-02

MTM

45-1

60-0

3M

TM45

-165

-01

MTM

45-1

65-0

2M

TM45

-170

-01

MTM

45-1

75-0

1M

TM45

-175

-02

MTM

45-1

80-0

1M

TM45

-180

-02

MTM

45-1

80-0

3M

TM45

-180

-04

MTM

45-1

85-0

1M

TM45

-185

-02

MTM

45-1

85-0

3M

TM45

-190

-01

MTM

45-1

90-0

2M

TM45

-190

-03

MTM

45-1

95-0

1M

TM45

-195

-02

MTM

45-1

95-0

3M

TM45

-200

-01

MTM

45-2

00-0

2M

TM45

-205

-01

MTM

45-2

05-0

2

25

0.000

0.004

0.008

0.012

0.016

0.020

10000 20000 30000 40000 50000 60000 70000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)

Heat Flow Response – 0.25cpm

0.25ºCpm Dynamic TestHRRamp = 117.5 J/g

26

0.0

0.2

0.4

0.6

0.8

1.0

10000 20000 30000 40000 50000 60000 70000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)

DoC and Cure Rate – 0.25cpm

0.25ºCpm Dynamic Test

27

0.000

0.010

0.020

0.030

0.040

0 10000 20000 30000 40000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

Cur

e ra

te (1

/s)



28

0.0

0.2

0.4

0.6

0.8

1.0

0 10000 20000 30000 40000

Time (s)

Deg

ree

of c

ure

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

Cur

e ra

te (1

/s)



29


-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0 5000 10000 15000 20000 25000 30000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


30


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000 30000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


31

Heat Flow Response – 1cpm-1

-0.01

0.00

0.01

0.02

0.03

0.04

0 5000 10000 15000 20000 25000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

Cur

e ra

te (1

/s)

1ºCpm-1 Dynamic TestHRRamp = 106.7 J/g

32

DoC and Cure Rate – 1cpm-1

0.00

0.20

0.40

0.60

0.80

1.00

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

Cur

e ra

te (1

/s)

1ºCpm-1 Dynamic Test

33


0.00

0.02

0.04

0.06

0.08

0 5000 10000 15000 20000 25000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)

1ºCpm-2 Dynamic TestHRRamp = 140.5 J/g

34


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


35

Heat Flow Response – 1.5cpm-1

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 3000 6000 9000 12000 15000 18000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)

1.5ºCpm-1 Dynamic TestHRRamp = 149.4 J/g

36

DoC and Cure Rate – 1.5cpm-1

0.00

0.20

0.40

0.60

0.80

1.00

0 3000 6000 9000 12000 15000 18000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)

1.5ºCpm-1 Dynamic Test

37


0.00

0.02

0.04

0.06

0.08

0.10

0 3000 6000 9000 12000 15000 18000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)


38


0.0

0.2

0.4

0.6

0.8

1.0

0 3000 6000 9000 12000 15000 18000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)


39


0.00

0.02

0.04

0.06

0.08

0.10

0 3000 6000 9000 12000 15000 18000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)


40


0.0

0.2

0.4

0.6

0.8

1.0

0 3000 6000 9000 12000 15000 18000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)


41


0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 2000 4000 6000 8000 10000 12000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)

2ºCpm Dynamic TestHRRamp = 144.7 J/g

42


0.0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000 12000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)

2ºCpm Dynamic Test

43

Heat Flow Response – 3cpm

0.00

0.04

0.08

0.12

0.16

0 2000 4000 6000 8000 10000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)

3ºCpm Dynamic TestHRRamp = 149. 97 J/g

44

DoC and Cure Rate – 3cpm

0.0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)

3ºCpm Dynamic Test

45

Heat Flow Response – 4cpm

0.00

0.04

0.08

0.12

0.16

0.20

0 1000 2000 3000 4000 5000 6000 7000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

1.5E-03

Cur

e ra

te (1

/s)

4ºCpm Dynamic TestHRRamp = 147.99 J/g

46

DoC and Cure Rate – 4cpm

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000 6000 7000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

1.5E-03

Cur

e ra

te (1

/s)

4ºCpm Dynamic Test

47

Heat Flow Response – 100ºC

-0.001

0.000

0.001

0.002

0.003

0.004

0 10000 20000 30000 40000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

Cur

e ra

te (1

/s)

100ºC Isothermal TestHRHold = 78.2 J/g

48

DoC and Cure Rate – 100ºC

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10000 20000 30000 40000

Time (s)

Deg

ree

of c

ure

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

Cur

e ra

te (1

/s)

100ºC Isothermal TestDoCHold = 0.60

49


-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0 10000 20000 30000 40000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

Cur

e ra

te (1

/s)


50


0.0

0.2

0.4

0.6

0.8

0 10000 20000 30000 40000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

Cur

e ra

te (1

/s)


51

Heat Flow Response – 120ºC-1

0.000

0.003

0.006

0.009

0.012

0 5000 10000 15000 20000 25000 30000 35000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

Cur

e ra

te (1

/s)


52

DoC and Cure Rate – 120ºC-1

0.0

0.2

0.4

0.6

0.8

0 5000 10000 15000 20000 25000 30000 35000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

Cur

e ra

te (1

/s)


53


-0.005

0.000

0.005

0.010

0.015

0.020

0 5000 10000 15000 20000 25000 30000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)


54


0.0

0.2

0.4

0.6

0.8

0 5000 10000 15000 20000 25000 30000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)


55


-0.01

0.00

0.01

0.02

0.03

0 5000 10000 15000 20000 25000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

1.8E-04

Cur

e ra

te (1

/s)


56


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

1.8E-04

Cur

e ra

te (1

/s)


57


-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0 5000 10000 15000 20000 25000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

Cur

e ra

te (1

/s)


58


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

Cur

e ra

te (1

/s)


59


-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0 5000 10000 15000 20000 25000 30000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


60


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


61


-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 5000 10000 15000 20000 25000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


62


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)


63


-0.02

0.00

0.02

0.04

0.06

0.08

0 5000 10000 15000 20000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)

170ºC Isothermal TestHRHold = 119 J/g

64


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

Cur

e ra

te (1

/s)


65


0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 5000 10000 15000 20000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


66


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


67

Heat Flow Response – 180-1ºC

-0.02

0.02

0.06

0.10

0 5000 10000 15000 20000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


68

DoC and Cure Rate – 180-1ºC

0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


69

Heat Flow Response – 180ºC-4

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5000 10000 15000 20000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


70

DoC and Cure Rate – 180ºC-4

0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


71


-0.02

0.01

0.04

0.07

0.10

0.13

0.16

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)


72


0.0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)


73


-0.02

0.02

0.06

0.10

0.14

0.18

0.22

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Spec

ific

heat

flow

(W/g

)

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

1.5E-03

1.8E-03

Cur

e ra

te (1

/s)


74


0.0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

1.5E-03

1.8E-03

Cur

e ra

te (1

/s)

200ºC Isothermal TestDoCHold =1.0

75

Heat of Reaction Tables

Pre-Test Ramp TotalMTM45-025cpm-02 0 117.5 117.5MTM45-05cpm-02 0 123.1 123.1

MTM45-075-02 0 118.4 118.4MTM45-1cpm-01 0 106.7 106.7MTM45-1cpm-02 0 140.5 140.5

MTM45-1_5cpm-01 0 149.4 149.4MTM45-1_5cpm-02 0 128.6 128.6MTM45-1_5cpm-03 0 173.8 173.8MTM45-2cpm-02 0 144.7 144.7MTM45-3cpm-02 0 150.0 150.0MTM45-4cpm-02 0 148.0 148.0

Test Heat of Reaction (J/g)Iso-Ramp Hold Ramp Total

MTM45-100-02 0.0 78.2 52.6 130.8MTM45-110-03 0.0 88.2 41.9 130.2MTM45-120-02 0.0 97.4 37.9 135.3MTM45-130-02 1.0 102.3 32.6 135.9MTM45-140-01 1.0 101.3 25.1 127.4MTM45-150-03 1.7 115.8 22.1 139.6MTM45-155-03 2.5 114.5 18.0 135.0MTM45-160-03 2.8 121.2 14.8 138.9MTM45-170-01 4.0 119.1 9.5 132.6MTM45-175-02 5.4 136.9 9.4 151.7MTM45-180-01 4.5 103.4 4.0 111.9MTM45-180-04 6.5 133.2 6.2 145.9MTM45-190-03 8.3 117.2 2.4 127.9MTM45-200-02 10.1 116.6 0.0 126.7

Test Heat of Reaction (J/g)

76

Total Heat of Reaction

0

20

40

60

80

100

120

140

160

180

100C

110C

120C

130C

140C

150C

155C

160C

170C

175C

180C

-118

0C-4

190C

200C

0.25

cpm

0.5c

pm0.

75cp

m1c

pm-1

1cpm

-21.

5cpm

-11.

5cpm

-21.

5cpm

-32c

pm-2

3cpm

4cpm

Hea

t of R

eact

ion

(J/g

)

Ramp (dynamic) HR

Isothermal HR

Pre-Hold HR

J/g 133.6 =avgIsoHR

J/g 136.4 =avgDynHR

77

Heat of Reaction - Model

J/g 133.6 =avgIsoHR

J/g 136.4 =avgDynHR

J/g 140 =AvgTotalHR

For uni prepreg:

Heat of reaction of neat resin:

Resin content (uni prepreg): 32% (wt)

J/g 437.5 140/0.32 ==ModelHR

(for prepreg)

78

Tg TablesDoC Tg (ºC) DoC Tg (ºC)

MTM45-025cpm-02 0 3.3 1 -MTM45-05cpm-02 0 5.3 1 198.9

MTM45-075-02 0 3.7 1 188.2MTM45-1cpm-01 0 3.1 1 204.3MTM45-1cpm-02 0 3.2 1 -

MTM45-1_5cpm-01 0 3.8 1 210.5MTM45-1_5cpm-02 0 4.0 1 208.5MTM45-1_5cpm-03 0 1.8 1 -MTM45-2cpm-02 0 2.3 1 205.7MTM45-3cpm-02 0 3.3 1 -MTM45-4cpm-02 0 2.2 1 -

Test Initial FinalDoC Tg (ºC) DoC Tg (ºC)

MTM45-100-02 0 3.0 0.60 118.0MTM45-110-03 0 2.6 0.68 136.4MTM45-120-02 0 2.9 0.72 148.7MTM45-130-02 0 3.5 0.76 160.4MTM45-140-01 0 4.9 0.80 171.1MTM45-150-03 0 3.4 0.84 183.3MTM45-155-03 0 3.4 0.87 183.3MTM45-160-03 0 2.9 0.89 192.2MTM45-170-01 0 - 0.93 198.2MTM45-175-02 0 3.7 0.94 204.5MTM45-180-01 0 - 0.96 206.7MTM45-180-04 0 4.2 0.96 206.6MTM45-190-03 0 4.5 0.98 213.6MTM45-200-02 0 5.3 1.00 209.3

Test Initial Post-Hold

Test ModelMTM45-160C-INT10-01 15.8 23.7MTM45-160C-INT20-01 52.1 61.1MTM45-160C-INT30-01 107.0 102.5MTM45-160C-INT35-01 122.6 120.3MTM45-160C-INT40-01 130.6 134.8MTM45-160C-INT45-01 146.0 146.2MTM45-160C-INT50-01 150.1 155.0

Post-Hold Tg (ºC)Test

79

0

50

100

150

200

250

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Degree of Cure

Gla

ss T

rans

ition

Tem

pera

ture

(C)

Isothermal-post holdIsothermal-finalIsothermal-initialDynamic-finalDynamic-initialModelInterrupted PostHold

Glass Transition Temperature

CTg °= 30

CTg °=∞

220

7.0=λ Drop in Tg due to degradation

80

Cure Kinetics Model

dkeff kkk111

+=

⎟⎠⎞

⎜⎝⎛−

= RTE

kk

a

ekk 0

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= fB

dd ekk0

( ) bTTaf g +−=

Cure kinetics model (CK13):

where

Kinetics model

Diffusion model

where

( ) ( )∑=

+⎟⎟⎠

⎞⎜⎜⎝

⎛−−=+=

2

121

211i

n

in

m

i

lieff

ii

i

i bxxr

xkxxdtdx

&&

1If f<small then f=small (=1E-30 see CMT_vars2.f90)

81

Cure Kinetics Model

and⎪⎩

⎪⎨

⎧

<<<

<+=

gag

aggag

agg

aga

TTTTT

TT

aCTS

aa

2

21

1

2

1

⎪⎩

⎪⎨

⎧

−=−−

=

11

12

12

agaa

agaga

TSaCTTaaS

with

and with⎪⎩

⎪⎨

⎧

<<<

<+=

gbg

bggbg

bgg

bgb

TTTTT

TT

bCTS

bb

2

21

1

2

1

⎪⎩

⎪⎨

⎧

−=−−

=

11

12

12

bgbb

bgbgb

TSbCTTbbS

( ) ( )00 11 gggg TT

xxTT −−−

+=∞λ

λand the DeBenedetto equation:

82

Cure Kinetics Model8.1

892.1

11 105.11 xxkx eff ⎟

⎠⎞

⎜⎝⎛ −=&

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= fd ek

35.0

1 2000

⎟⎠⎞

⎜⎝⎛−

= RTk ek

52938

1 8506

( ) bTTaf g +−=

⎪⎩

⎪⎨

⎧

°>°<<°

°<=

CTCTC

CTb

g

g

g

14014070

70

030.00.030 and 0.025 bwLinear

025.0

4108.4 −×=a


83

Cure Kinetics Model

( ) 171.0627.5

757.02 193.0

11 xxxkx eff ⎟⎠⎞

⎜⎝⎛ −−=&

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−×= fd ek

34.03

2 107

⎟⎠⎞

⎜⎝⎛−

= RTk ek

65946

2 115.4

( ) bTTaf g +−=

⎪⎩

⎪⎨

⎧

°>°<<°

°<=

CTCTC

CTb

g

g

g

220220100

100

040.00.040 and 0.025 bwLinear

025.0

4108.4 −×=a


84

Cure Kinetics Model

C30 °=gT 0.7=λC022 °=∞gT

Total Heat of Reaction (Prepreg):

Glass Transition (Tg) Model (DeBenedetto):

J/g 140 =AvgTotalHR

J/g 437.5 =ModelHR

85

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0022 0.0024 0.0026 0.0028 0.003 0.0032 0.0034

1/T (1/s)

Ln(x

dot)

Test Data-IsosTest Data-DynsModel-KineticModelTg x = 0.02

86

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)

Test Data-IsosTest Data-DynsModel-KineticModelTg

x = 0.1

87

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)

Test Data-IsosTest Data-DynsModel-KineticModel x = 0.2

88

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)

Test Data-IsosTest Data-DynsModel-KineticModel x = 0.3

89

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)

Test Data-Isos

Test Data-Dyns

Model-Kinetic

Model

Tg x = 0.4

90

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)


91

Ln(xdot)-1/T

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)


92

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)


x = 0.7

93

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028

1/T (1/s)

Ln(x

dot)

Test Data-IsosTest Data-DynsModel-KineticTgModel

x = 0.8

94

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.0019 0.00195 0.002 0.00205 0.0021 0.00215 0.0022 0.00225 0.0023

1/T (1/s)

Ln(x

dot)


x = 0.9

95

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.0019 0.00195 0.002 0.00205 0.0021 0.00215 0.0022 0.00225 0.0023

1/T (1/s)

Ln(x

dot)


x = 0.98

96

Ln(xdot)-1/T

-14

-13

-12

-11

-10

-9

-8

-7

-6

-50.0019 0.00195 0.002 0.00205 0.0021 0.00215 0.0022 0.00225 0.0023

1/T (1/s)

Ln(x

dot)


x = 0.98

97

Model Parameters

1.800

0.0001.0001.8921.1050.000529388506

R1

0.0001.0005.627

0.171

0.1930.757

65946 (J/mol)4.115 (1/s)

R2 (unit)Parameter

14070

0.0300.0251000

0.000480.00048

0.352000

R1

220 (ºC)100 (ºC)

0.025100 (ºC)0 (ºC)

0.040

4.8E-4 (1/ºC)4.8E-4 (1/ºC)

0.347E-3 (1/s)

R2 (unit)Parameter

0.7220 (ºC)3 (ºC)

Value (unit)Parameter

aE

l

rm

2n

b

n

0dk

B

1a

2a

1agT

2agT

1b2b

1bgT

2bgT0gT

∞gT

λ

0k

Model’s range of validityIso: 100ºC < Temperature < 200ºC

Dyn: ºC < Temperature < ºC

98

Dynamic Tests – 0.25cpm

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)

Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model


99


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

Cur

e ra

te (1

/s)



100


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)



101

Dynamic Tests – 1cpm-1

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

Cur

e ra

te (1

/s)



102


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)



103

Dynamic Tests – 1.5cpm-1

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)



104


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)



105


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Cur

e ra

te (1

/s)



106


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)


2ºCpm Dynamic Test

107

Dynamic Tests – 3cpm

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

Cur

e ra

te (1

/s)


3ºCpm Dynamic Test

108


0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of C

ure

0.0E+00

3.0E-04

6.0E-04

9.0E-04

1.2E-03

1.5E-03

Cur

e ra

te (1

/s)


4ºCpm Dynamic Test

109

Isothermal Tests - 100ºC

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10000 20000 30000 40000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

Cur

e ra

te (1

/s)



110


0.0

0.2

0.4

0.6

0.8

0 10000 20000 30000 40000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

Cur

e ra

te (1

/s)



111


0.0

0.2

0.4

0.6

0.8

0 5000 10000 15000 20000 25000 30000 35000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

Cur

e ra

te (1

/s)



112


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000 30000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

Cur

e ra

te (1

/s)



113


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

1.8E-04

Cur

e ra

te (1

/s)



114


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

Cur

e ra

te (1

/s)



115


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)



116


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000 25000

Time (s)

Deg

ree

of c

ure

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

Cur

e ra

te (1

/s)



117


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

Cur

e ra

te (1

/s)



118


0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

Cur

e ra

te (1

/s)



119

Isothermal Tests - 180ºC-1

0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

Cur

e ra

te (1

/s)


180ºC-1 Isothermal TestDoCHold = 0.964

120

Isothermal Tests - 180ºC-4

0.0

0.2

0.4

0.6

0.8

1.0

0 5000 10000 15000 20000

Time (s)

Deg

ree

of c

ure

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

Cur

e ra

te (1

/s)


180ºC-4 Isothermal TestDoCHold = 0.958

121

Isothermal Tests – 190ºC

0.0

0.2

0.4

0.6

0.8

1.0

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Deg

ree

of c

ure

0.0E+00

4.0E-04

8.0E-04

1.2E-03

Cur

e ra

te (1

/s)



122


0.00

0.20

0.40

0.60

0.80

1.00

0 2000 4000 6000 8000 10000 12000 14000

Time (s)

Deg

ree

of c

ure

0.0E+00

4.0E-04

8.0E-04

1.2E-03

1.6E-03

2.0E-03

Cur

e ra

te (1

/s)



123

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

9.0E-05

Cur

e ra

te (1

/s)


Isothermal Tests - 100ºC-R

124


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

Cur

e ra

te (1

/s)


125


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

Cur

e ra

te (1

/s)


126


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

Cur

e ra

te (1

/s)


127


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

Cur

e ra

te (1

/s)


128


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

8.0E-05

Cur

e ra

te (1

/s)


129


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

Cur

e ra

te (1

/s)


130


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

7.0E-05

Cur

e ra

te (1

/s)


131


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

Cur

e ra

te (1

/s)


132


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

Cur

e ra

te (1

/s)


133

Isothermal Tests - 180ºC-R-1

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

Cur

e ra

te (1

/s)


134

Isothermal Tests - 180ºC-R-4

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

4.5E-05

5.0E-05

Cur

e ra

te (1

/s)


135


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

Cur

e ra

te (1

/s)


136


0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300

Temperature (°C)

Deg

ree

of c

ure

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

9.0E-06

Cur

e ra

te (1

/s)


137

Dynamic Tests – All

0.00

0.20

0.40

0.60

0.80

1.00

0 50 100 150 200 250 300 350

Temperature (°C)

Deg

ree

of C

ure

DOC (0.25cpm, expt)DOC (0.25cpm, model)DOC (0.5cpm, expt)DOC (0.5cpm, model)DOC (0.75cpm, expt)DOC (0.75cpm, model)DOC (1cpm-1, expt)DOC (1cpm-1, model)DOC (1cpm-2, expt)DOC (1cpm-2, model)DOC (1.5cpm-1, expt)DOC (1.5cpm-1, model)DOC (1.5cpm-2, expt)DOC (1.5cpm-2, model)DOC (1.5cpm-3, expt)DOC (1.5cpm-3, model)DOC (2cpm-1, expt)DOC (2cpm-1, model)DOC (2cpm-2, expt)DOC (2cpm-2, model)DOC (3cpm, expt)DOC (3cpm, model)DOC (4cpm, expt)DOC (4cpm, model)

138

Dynamic Tests – All

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 50 100 150 200 250 300 350

Temperature (°C)

Cur

e ra

te (1

/s)

Cure rate (0.25cpm, expt)Cure rate (0.25cpm, model)Cure rate (0.5cpm, expt)Cure rate (0.5cpm, model)Cure rate (0.75cpm, expt)Cure rate (0.75cpm, model)Cure rate (1cpm-1, expt)Cure rate (1cpm-1, model)Cure rate (1cpm-2, expt)Cure rate (1cpm-2, model)Cure rate (1.5cpm-1, expt)Cure rate (1.5cpm-1, model)Cure rate (1.5cpm-2, expt)Cure rate (1.5cpm-2, model)Cure rate (1.5cpm-3, expt)Cure rate (1.5cpm-3, model)Cure rate (2cpm-1, expt)Cure rate (2cpm-1, model)Cure rate (2cpm-2, expt)Cure rate (2cpm-2, model)Cure rate (3cpm, expt)Cure rate (3cpm, model)Cure rate (4cpm, expt)Cure rate (4cpm, model)

139

Isothermal Tests – All

0.00

0.20

0.40

0.60

0.80

1.00

0 10000 20000 30000 40000 50000

Time (s)

Deg

ree

of C

ure

DOC 100C (expt) DOC 100C (model)DOC 110C (expt) DOC 110C (model)DOC 120C (expt) DOC 120C (model)DOC 130C (expt) DOC 130C (model)DOC 140C (expt) DOC 140C (model)DOC 150C (expt) DOC 150C (model)DOC 155C (expt) DOC 155C (model)DOC 160C (expt) DOC 160C (model)DOC 170C (expt) DOC 170C (model)DOC 175C (expt) DOC 175C (model)DOC 180C-1 (expt) DOC 180C-1 (model)DOC 180C-4 (expt) DOC 180C-4 (model)DOC 190C (expt) DOC 190C (model)DOC 200C (expt) DOC 200C (model)

140

Isothermal Tests – All

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Time (s)

Cur

e ra

te (1

/s)

Cure rate (100C, expt) Cure rate (100C, model)










Cure rate (180C-1, expt) Cure rate (180C-1, model)

Cure rate (180C-4, expt) Cure rate (180C-4, model)



141

Post-Hold Tg - IsosTg values at the end of the hold segment of the isothermal tests were compared to the predictions of the cure kinetics model. Good agreement was observed.

Test ModelMTM45-100-02 118.0 117.6MTM45-110-03 136.4 131.8MTM45-120-02 148.7 142.9MTM45-130-02 160.4 153.7MTM45-140-01 171.1 164.7MTM45-150-03 183.3 177.0MTM45-155-03 183.3 183.3MTM45-160-03 192.2 189.4MTM45-170-01 198.2 199.2MTM45-175-02 204.5 204.9MTM45-180-01 206.7 210.3MTM45-180-04 206.6 210.3MTM45-190-03 213.6 217.5MTM45-200-02 209.3 220.0

Test Post-Hold Tg (ºC)

0

50

100

150

200

250

MTM

45-1

00-0

2

MTM

45-1

10-0

3

MTM

45-1

20-0

2

MTM

45-1

30-0

2

MTM

45-1

40-0

1

MTM

45-1

50-0

3

MTM

45-1

55-0

3

MTM

45-1

60-0

3

MTM

45-1

70-0

1

MTM

45-1

75-0

2

MTM

45-1

80-0

1

MTM

45-1

80-0

4

MTM

45-1

90-0

3

MTM

45-2

00-0

2

Tg (C

)

Model

Test

142

Post-Hold Tg - Ints

0

50

100

150

200

MTM

45-1

60C

-IN

T10-

01

MTM

45-1

60C

-IN

T20-

01

MTM

45-1

60C

-IN

T30-

01

MTM

45-1

60C

-IN

T35-

01

MTM

45-1

60C

-IN

T40-

01

MTM

45-1

60C

-IN

T45-

01

MTM

45-1

60C

-IN

T50-

01

Tg (C

)

Model

Test

Test ModelMTM45-160C-INT10-01 15.8 23.7MTM45-160C-INT20-01 52.1 61.1MTM45-160C-INT30-01 107.0 102.5MTM45-160C-INT35-01 122.6 120.3MTM45-160C-INT40-01 130.6 134.8MTM45-160C-INT45-01 146.0 146.2MTM45-160C-INT50-01 150.1 155.0

Post-Hold Tg (ºC)Test

143

Post-Hold Tg – Cure Cycle

0

50

100

150

200

250

MTM45-CureCycle-S2-01 MTM45-CureCycle-S3-01

Tg (C

)

ModelTest

CC-S2 CC-S3

Test ModelMTM45-CureCycle-S2-01 204.6 199.2MTM45-CureCycle-S3-01 207.6 206.3

Test Tg (ºC)

144

Goodness of Fit - Overview

• Goodness of fit is measured by comparing the test to the model prediction at several key points in the cure history.

• Both timing and DOC error are considered.

145

Goodness of Fit – Key Points

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5000 10000 15000 20000 25000 30000 35000Time (s)

Deg

ree

of C

ure

0.00E+00

2.00E-05

4.00E-05

6.00E-05

8.00E-05

1.00E-04

1.20E-04

1.40E-04

1.60E-04

1.80E-04

Cur

e R

ate

(1/s

)Degree of Cure - ExptDegree of Cure - ModelCure Rate (1/s) - ExptCure Rate (1/s) - ModelStart/End ThresholdKickoff/Slow Threshold

Peak Cure Rate

146

Goodness of Fit – Peak

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2000 3000 4000 5000 6000 7000 8000 9000 10000Time (s)

Deg

ree

of C

ure

1.20E-04

1.30E-04

1.40E-04

1.50E-04

1.60E-04

1.70E-04

1.80E-04

Cur

e R

ate

(1/s

)

Degree of Cure - ExptDegree of Cure - ModelCure Rate (1/s) - ExptCure Rate (1/s) - Model

Model Peak

Expt Peak

147

Goodness of Fit – Other

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5000 10000 15000 20000 25000 30000 35000Time (s)

Deg

ree

of C

ure

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

4.00E-05

Cur

e R

ate

(1/s

)

Degree of Cure - ExptDegree of Cure - ModelCure Rate (1/s) - ExptCure Rate (1/s) - ModelStart/End ThresholdKickoff/Slow Threshold

Expt Slow

Model Slow

Model End

Expt End

Model/Expt Start

Model/Expt Kickoff

148

Goodness of Fit – Iso Timing

-900

-600

-300

0

300

600

900

MTM

45-M

ISO

-100

-02

MTM

45-M

ISO

-110

-03

MTM

45-M

ISO

-120

-02

MTM

45-M

ISO

-130

-02

MTM

45-M

ISO

-140

-01

MTM

45-M

ISO

-150

-03

MTM

45-M

ISO

-155

-03

MTM

45-M

ISO

-160

-03

MTM

45-M

ISO

-170

-01

MTM

45-M

ISO

-175

-02

MTM

45-M

ISO

-180

-01

MTM

45-M

ISO

-180

-04

MTM

45-M

ISO

-190

-03

MTM

45-M

ISO

-200

-02

Tim

e Er

ror (

sec)

Timing - StartTiming - KickoffTiming - PeakTiming - SlowTiming - End

149

Goodness of Fit – Iso DOC

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

MTM

45-M

ISO

-100

-02

MTM

45-M

ISO

-110

-03

MTM

45-M

ISO

-120

-02

MTM

45-M

ISO

-130

-02

MTM

45-M

ISO

-140

-01

MTM

45-M

ISO

-150

-03

MTM

45-M

ISO

-155

-03

MTM

45-M

ISO

-160

-03

MTM

45-M

ISO

-170

-01

MTM

45-M

ISO

-175

-02

MTM

45-M

ISO

-180

-01

MTM

45-M

ISO

-180

-04

MTM

45-M

ISO

-190

-03

MTM

45-M

ISO

-200

-02

DO

C E

rror

DOC - StartDOC - KickoffDOC - PeakDOC - SlowDOC - End

150

Goodness of Fit – Dyn Timing

-300

-240

-180

-120

-60

0

60

120

180

MTM

45-M

DYN

-02

5cpm

-02

MTM

45-M

DYN

-05

cpm

-02

MTM

45-M

DYN

-075

-02

MTM

45-M

DYN

-1_

5cpm

-01

MTM

45-M

DYN

-1_

5cpm

-02

MTM

45-M

DYN

-1_

5cpm

-03

MTM

45-M

DYN

-1cp

m-

01

MTM

45-M

DYN

-1cp

m-

02

MTM

45-M

DYN

-2cp

m-

01

MTM

45-M

DYN

-2cp

m-

02

MTM

45-M

DYN

-3cp

m-

02

MTM

45-M

DYN

-4cp

m-

02

Tim

e Er

ror (

sec)

Timing - Peak

151

Goodness of Fit – Dyn DOC

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

MTM

45-M

DYN

-02

5cpm

-02

MTM

45-M

DYN

-05

cpm

-02

MTM

45-M

DYN

-075

-02

MTM

45-M

DYN

-1_

5cpm

-01

MTM

45-M

DYN

-1_

5cpm

-02

MTM

45-M

DYN

-1_

5cpm

-03

MTM

45-M

DYN

-1cp

m-

01

MTM

45-M

DYN

-1cp

m-

02

MTM

45-M

DYN

-2cp

m-

01

MTM

45-M

DYN

-2cp

m-

02

MTM

45-M

DYN

-3cp

m-

02

MTM

45-M

DYN

-4cp

m-

02

DO

C E

rror

Timing - Peak

152

Other Forms – Fabric

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

-100 -50 0 50 100 150 200 250 300

Temperature (C)

Non

rev

Hea

t Flo

w (W

/g)

MTM45-FABRIC-MDYN-2cpm-01-HeatUp

MTM45-MDYN-2cpm-02-HeatUp

153


0

0.2

0.4

0.6

0.8

1

50 100 150 200 250 300Temperature (C)

Deg

ree

of C

ure



154


-0.05

0

0.05

0.1

0.15

0.2

-50 0 50 100 150 200 250 300

Temperature (C)

Non

rev

Hea

t Flo

w (W

/g)



155


0

0.2

0.4

0.6

0.8

1

50 100 150 200 250 300Temperature (C)

Deg

ree

of C

ure



156


0

100

200

300

400

500

MTM45-2cpm-02 MTM45-FABRIC-MDYN-2cpm-01

MTM45-4cpm-02 MTM45-FABRIC-MDYN-4cpm-01

Hea

t of R

eact

ion

(J/g

)

Raw Adjustedinitial Final HR HR(C) (C) (J/G) (J/G)

MTM45-2cpm-02 2.34 205.65 144.75 0.32 452.33MTM45-FABRIC-MDYN-2cpm-01 -0.53 171.37 127.039 0.36 352.89

MTM45-4cpm-02 2.23 - 147.99 0.32 462.46MTM45-FABRIC-MDYN-4cpm-01 0.18 179.94 144.19 0.36 400.53

Test Adjustment Ratio

Tg

Lower total heat of reaction is measured for the fabric compared to the uni prepreg. The curing behaviour of the two forms, however, was found to be very similar. The error in the total HR of the fabric results in conservative estimation of exhothermic events.

157

Process Maps - IsothermalBlue: 0.1’-0.9’ at 0.1’Green: 1’-9’ at 1’Red: 10’-55’ at 5’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line

Model Not Validated in This Zone.

Model Not Valid in This Zone.

158

Process Maps – 0.5cpmBlue: 0.1’-0.9’ at 0.1’Green: 1’-9’ at 1’Red: 10’-55’ at 5’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line



159




160




161




162




163




164




165




166

Process Maps – All Dynamic RatesBlue: 0.1’-0.9’ at 0.1’Green: 1’-9’ at 1’Red: 10’-55’ at 5’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line



167

Viscosity Model

168

Nomenclatureη′

η ′′

*η

μ

Dynamic viscosity or the real part of the complex viscosity

Elastic complex part of the complex viscosity

Complex viscosity

Material viscosity calculated by the viscosity model

169

Viscosity Tests

• Material viscosity was measured using a AR2000 Rheometer with parallel plate geometry.

• Dynamic tests at different ramp rates were performed to capture the changes in material viscosity as a function of temperature and degree of cure. A total of 5 tests at 1, 2, 3, 4, and 5 cpm were performed.

• Ramp-Hold tests at 2 cpm were also performed with holds at 125, 130, 135, 140 and 145C.

• Disposable aluminum plates of diameter 25mm were used at a gap of 1mm (sample thickness). Frequency of oscillation was chosen to be 1Hz.

170

Viscosity MeasureRheometry tests are performed under sinusoidal oscillatory loads. The classical solution of the viscoelastic behaviour of materials in such circumstances is usually expressed in terms of storage and loss moduli. Considering the following strain function, the resulting stress would be:

Strain applied:

Resulting stress:

tωγγ sin0=

( )δωσσ += tsin0

( )tGtG ωωγσ cos"sin'0 +=

where δ is the phase angle between the strain and the stress. Decomposing the stress into in-phase and out-of-phase components, we get:

where G’ is the in-phase (elastic or storage) modulus and G” is the out-of-phase (viscous or loss) modulus.

171

Viscosity MeasureAlternatively, a complex viscosity η* can be defined with “dynamic viscosity”(η’) as its real part and an elastic complex part (η”), defined as:

ωη "' G=

ωη '" G

=where"'* ηηη i+= and

For low shear rates, the dynamic viscosity corresponds mainly to the real part of the complex viscosity and can be considered the steady state viscosity of the fluid. In other words:

'ημ =

The viscosity model developed here is based on the measured η’, i.e. the dynamic viscosity response of the material.

172

Viscosity Tests SummaryDynamics vs Temperature

1

10

100

1000

10000

100000

0 50 100 150 200 250Temperature (°C)

Visc

osity

n' (

Pa.s

)

Test Data - 5cpmTest Data - 4cpmTest Data - 3cpmTest Data - 2cpmTest Data - 1cpm

173

Viscosity Tests SummaryDynamics vs Time

1

10

100

1000

10000

100000

0 20 40 60 80 100 120 140 160Time (min)

Visc

osity

n' (

Pa.s

)

Test Data - 5cpmTest Data - 4cpmTest Data - 3cpmTest Data - 2cpmTest Data - 1cpm

174

Viscosity Tests SummaryIsothermals vs Time

1

10

100

1000

10000

100000

0 20 40 60 80 100 120 140 160Time (min)

Visc

osity

n' (

Pa.s

)

Test Data - 125CTest Data - 130CTest Data - 135CTest Data - 145CTest Data - 140C

175

Mathematical Model

( ) ( )( )2

21

CxBxA

g

g

xxx

TT++

⎟⎟⎠

⎞⎜⎜⎝

⎛

−+= μμμ

( ) RTE

ii

i

eT 0μμ =

The viscosity model chosen is in the following form1:

where

1Khoun and Hubert, Processing Characterization of a RTM Carbon Epoxy System for Aeronautical Applications.

2or 1=i

gx is a critical degree of cure

176

Mathematical Model

maxmax then if μμμμ =>

The parameters of the viscosity model are determined by fitting to the experimental results.

000,851 =E

6.0=gx

0=C

( )2

21

0201

CxBxA

g

gRTE

RTE

xxx

ee++

⎟⎟⎠

⎞⎜⎜⎝

⎛

−+= μμμ

0=B

9=A

000,82 =E

1101 100.3 −×=μ

3.001 =μ

6max 10=μ

177


1

10

100

1000

10000

100000

1000000

20 40 60 80 100 120 140 160 180Temperature (°C)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure

Test DataTotal ViscosityDegree of Cure

1cpm test

178


1

10

100

1000

10000

100000

1000000

20 40 60 80 100 120 140 160 180 200Temperature (°C)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


2cpm test

179


1

10

100

1000

10000

100000

1000000

20 40 60 80 100 120 140 160 180 200Temperature (°C)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


3cpm test

180


1

10

100

1000

10000

100000

1000000

20 40 60 80 100 120 140 160 180 200 220Temperature (°C)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


4cpm test

181


1

10

100

1000

10000

100000

1000000

20 40 60 80 100 120 140 160 180 200 220Temperature (°C)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


5cpm test

182

Isothermal Tests – 125C 2cpm

1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100 120 140 160Time (min)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


125C test

183


1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100 120 140Time (min)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


130C test

184


1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100 120Time (min)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


135C test

185


1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100 120Time (min)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


140C test

186


1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100 120Time (min)

Visc

osity

n' (

Pa.s

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Deg

ree

of C

ure


145C test

187

Gel Degree of Cure Model

125

0.3

0.5

0.0028

0.285

ValueParameter

( )0TTTxx fgelgel nom−+=

The gel degree of cure model chosen is in the following form:

gelx

fT

0Tmingelx

maxgelx

188

Gel Degree of Cure

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

100 120 140 160 180 200 220

Temperature (°C)

Gel

Deg

ree

of C

ure

DynamicsIsothermalsModel

189

Gel Time Predictions

0

20

40

60

80

100

120

140

1cpm 2cpm 3cpm 4cpm 5cpm 125C 130C 135C 140C 145C

Gel

Tim

e (m

in)

TestModel

190

Process Maps – ViscosityBlue: 1-9 at 1 (Pa.s)Green: 10-90 at 10 (Pa.s)Red: 100-900 at 100 (Pa.s)Cyan: 1000-9000 at 1000 (Pa.s)Magenta: 10000-100000 at 10000 (Pa.s)



191

Heat Capacity (Cp) Model

192

Cp Measurement

• The DSC tests were temperature modulated to obtain a measure of the material’s heat capacity, Cp.

• Due to the variability associated with the measured values, some scatter was observed in the Cp response of various tests.

• The Cp responses were modified to match that of a fully cured specimen (identified as reheat tests).

193

Raw Data

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300Temperature (C)

Cp

0.25cpm0.5cpm0.75cpm1.5cpm1cpm2cpm3cpm

194

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300Temperature (C)

Cp

0.25cpm

0.5cpm

0.75cpm

1.5cpm

1cpm

2cpm

3cpm

Raw Data – Anchored to Reheat Test

Shifted to match the rubbery response

195

Raw Data – 0.25Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

0.25 cpm - Test

196

Raw Data – 0.5Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

0.5 cpm - Test

197

Raw Data – 0.75Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

0.75 cpm - Test

198

Raw Data – 1Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

1 cpm - Test

199

Raw Data – 1.5Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

1.5 cpm - Test

200

Raw Data – 2Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

2 cpm - Test

201

Raw Data – 3Cpm

0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

3 cpm - Test

202

Cp Model Basics• Glassy and rubbery Cp were assumed to be functions of temperature and DoC• Cp was assumed to transition between the glassy and rubbery responses with changes in T-Tg

0.5

1.0

1.5

2.0

2.5

-50 0 50 100 150 200 250 300Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

T-Tg

(ºC

)

Rubbery

GlassyTotal Cp

T-Tg

203

Cp Model

20.0=k

The parameters of the Cp model are determined by fitting to the experimental results. The model is formulated as shown below:

0037.00 =gs

Valid for temperature values between -20ºC to 200ºC.

Glassy Rubbery

( )[ ]cg TTTkrpgp

rpp e

CCCC Δ−−+

−+=

1

2=Δ cT

Other parameters

( )∞==+= ,0 and , jgricTsC ijijijp

( )∞

+−=ipipp xCCxC

i 01

Virgin and cured responses:

Glassy or rubbery at x:

Total Cp response:

95.00 =gc0024.0=∞gs04.1=∞gc

0028.00 =rs13.10 =rc

002.0=∞gs2.1=∞gc

204


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-20

0

20

40

60

80

100

120

T-Tg

(ºC

)

0.25cpm test

Cp (Model)

Cp (Test)

T-Tg

205


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

0.5cpm test

Cp (Model)

Cp (Test)

T-Tg

206


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

0.75cpm test

Cp (Model)

Cp (Test)

T-Tg

207


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

1.5cpm test

Cp (Model)

Cp (Test)

T-Tg

208


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

1cpm test

Cp (Model)

Cp (Test)

T-Tg

209


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

2cpm test

Cp (Model)

Cp (Test)

T-Tg

210


-0.5

0

0.5

1

1.5

2

2.5

3

-50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

-50

0

50

100

150

200

250

300

T-Tg

(ºC

)

3cpm test

Cp (Model)

Cp (Test)

T-Tg

211


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

0.25 cpm - Test0.25 cpm - Model

212


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


213


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)


214


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


215


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)


216


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


217


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)

1 cpm - Test1 cpm - Model

218


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


219


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)


220


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


221


0.5

1

1.5

2

2.5

-100 -50 0 50 100 150 200 250 300

Temperature (ºC)

Cp

(J/g

ºC)


222


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


223


0.5

1

1.5

2

2.5

-100 0 100 200 300 400

Temperature (ºC)

Cp

(J/g

ºC)


224


0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


225

Isothermal Tests – 110C

0

0.5

1

1.5

2

2.5

3

3.5

0 10000 20000 30000 40000 50000

Time (s)

Cp

(J/g

ºC)

110C - Test110C - Model

226


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


227


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000 25000 30000 35000

Time (s)

Cp

(J/g

ºC)


228


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


229


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000 25000 30000

Time (s)

Cp

(J/g

ºC)


230


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


231


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000 25000 30000

Time (s)

Cp

(J/g

ºC)


232


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


233


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000 25000 30000

Time (s)

Cp

(J/g

ºC)


234


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


235


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000

Time (s)

Cp

(J/g

ºC)


236


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


237


0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000

Time (s)

Cp

(J/g

ºC)


238


0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Degree of Cure

Cp

(J/g

ºC)


Material Characterization for Processing: ACG MTM45-1 MTM45-1... · 2009-11-15 · Degree of Cure...

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Transcript of Material Characterization for Processing: ACG MTM45-1 MTM45-1... · 2009-11-15 · Degree of Cure...