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Material Characterization for Processing:Hexcel 8552
Material Model DevelopmentFinal Project Wrap-Up
Prepared by: A. ShahkaramiReviewed by: D. Van EeApproved: A.PoursartipDate: November 15th, 2009Version: 1.0
2
Project Definition
Modeling performed for:
• Cure Kinetics
• Heat Capacity (Cp)
• Viscosity
Material: Hexcel 8552
3
Material Description• HEXPLY 8552
• Material forms received from Hexcel are as follows:- Neat Resin: HS-AD-693 (received Oct 18, 2006)- Resin Film: 74#CCA1030/B430, 35G, 45.75 (received Oct 18, 2006)- Fabric Prepreg: AGP193P/8552S, 38%, 193AW, 60” (received Oct 18,
2006)
• Cure cycle suggested by Manufacturer (US version) is as follows:- Heat at 3-5ºF/min to 225ºF- Hold at 225ºF for 30-60 min- Heat to 350ºF at 3-5ºF/min- Hold at 350ºF for 120±10 min- Cool at 2-5ºF/min 150ºF
• The tests were done on resin and comparison drawn with other forms
4
Cure Kinetics Model
5
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
6
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 +=
7
HR Definition
-20ºC
Handling &Storage
Making Samples
DSC Test
Hold
Ramp
Time
preTestHR TestHR
HoldHR RampHR
TotalHR
8
Summary
• Differential Scanning Calorimetry (DSC) tests were performed to characterize the cure kinetics of Hexcel 8552. A Q1000 TA Instrument DSC was used for this purpose.
• Normal pans were used to perform the DSC tests on neat resin.
• Characterisation was performed on the resin. Other forms of this resin (film and fabric prepreg) were also tested and compared to the neat resin.
9
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).
10
DSC Tests Performed
The DSC tests were performed are summarized below:
• Dynamic tests: 18 tests @ 1 to 10ºCpm• Isothermal tests: 11 tests 100ºC to 190ºC• Interrupted Isothermal tests: 2 tests at 160ºC• Other: 4 cure cycle tests, 4 dynamic on other forms
After careful examination of the results and investigation of the consistency of the data, the complete temperature range (100ºC to 190ºC) was consistent. However, a number of tests were dismissed dueto anomalies and the remaining isothermal and dynamic tests (see table on next slide) were considered in the analysis.
11
DSC Tests Used in Model FittingMass Rate Tempmax
(mg) (ºC/min) (ºC)8552-MDYN-01cpm-01 4.99 1 3008552-MDYN-02cpm-01 4.19 2 3008552-MDYN-02cpm-02 5.3 2 2808552-MDYN-03cpm-01 5.59 3 3008552-MDYN-04cpm-01 5.59 4 3008552-MDYN-05cpm-01 4.79 5 3008552-MDYN-06cpm-01 4.79 6 3008552-MDYN-07cpm-01 5.89 7 3008552-MDYN-08cpm-01 4.09 8 3308552-MDYN-09cpm-01 5.19 9 3308552-MDYN-10cpm-01 3.39 10 330
Test
Mass(mg)
8552-CC-S1-02 4.68552-CC-S3-00-01 58552-CC-S3-60-01 4.7
8552-CC-S4-01 4.9
Test
Mass Temp Time(mg) (ºC) (min)
8552-MISO-100C-01 5.3 100 7208552-MISO-110C-01 5.7 110 5408552-MISO-120C-01 4.7 120 4808552-MISO-130C-01 4.4 130 4208552-MISO-140C-01 5.2 140 3608552-MISO-150C-01 5.6 150 3608552-MISO-160C-01 5.4 160 3008552-MISO-170C-01 3.6 170 1808552-MISO-180C-01 5.59 180 1808552-MISO-180C-02 5.4 180 1808552-MISO-190C-01 4.49 190 180
8552-160C-INT15 5 160 158552-160C-INT30 0 160 30
TestHold
12
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.
Consistently positioned at 230±1ºC for dynamic tests
13
Cure Rate vs. DoC – Dyns
14
Cure Rate vs. DoC – Isos
15
Heat Flow Response – 1cpm
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
10000 13000 16000 19000 22000
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 Dynamic TestHRRamp = 558.9 J/g
16
DoC and Cure Rate – 1cpm
0.00
0.20
0.40
0.60
0.80
1.00
10000 13000 16000 19000 22000
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)
1ºCpm Dynamic Test
17
Heat Flow Response – 2cpm-1
-0.10
0.00
0.10
0.20
0.30
0.40
6000 7000 8000 9000 10000 11000 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-1 Dynamic TestHRRamp = 575.4 J/g
18
DoC and Cure Rate – 2cpm-1
0.00
0.20
0.40
0.60
0.80
1.00
6000 7000 8000 9000 10000 11000 12000
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
7.0E-04
Cur
e ra
te (1
/s)
2ºCpm-1 Dynamic Test
19
Heat Flow Response – 2cpm-2
-0.10
0.00
0.10
0.20
0.30
0.40
6000 7000 8000 9000 10000 11000 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-2 Dynamic TestHRRamp = 601.7 J/g
20
DoC and Cure Rate – 2cpm-2
0.00
0.20
0.40
0.60
0.80
1.00
6000 7000 8000 9000 10000 11000 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-2 Dynamic Test
21
Heat Flow Response – 3cpm
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
4000 5000 6000 7000 8000 9000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
2.0E-04
4.0E-04
6.0E-04
8.0E-04
1.0E-03
Cur
e ra
te (1
/s)
3ºCpm Dynamic TestHRRamp = 594.9 J/g
22
DoC and Cure Rate – 3cpm
0.00
0.20
0.40
0.60
0.80
1.00
4000 5000 6000 7000 8000 9000
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)
3ºCpm Dynamic Test
23
Heat Flow Response – 4cpm
-0.20
0.00
0.20
0.40
0.60
0.80
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 = 621.8 J/g
24
DoC and Cure Rate – 4cpm
0.00
0.20
0.40
0.60
0.80
1.00
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
25
Heat Flow Response – 5cpm
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
2000 3000 4000 5000 6000
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)
5ºCpm Dynamic TestHRRamp = 597 J/g
26
DoC and Cure Rate – 5cpm
0.00
0.20
0.40
0.60
0.80
1.00
3000 4000 5000 6000
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)
5ºCpm Dynamic Test
27
Heat Flow Response – 6cpm
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
2000 3000 4000 5000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
4.0E-04
8.0E-04
1.2E-03
1.6E-03
2.0E-03
Cur
e ra
te (1
/s)
6ºCpm Dynamic TestHRRamp = 616.4 J/g
28
DoC and Cure Rate – 6cpm
0.00
0.20
0.40
0.60
0.80
1.00
2000 3000 4000 5000
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)
6ºCpm Dynamic Test
29
Heat Flow Response – 7cpm
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1000 2000 3000 4000 5000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
4.0E-04
8.0E-04
1.2E-03
1.6E-03
2.0E-03
Cur
e ra
te (1
/s)
7ºCpm Dynamic TestHRRamp = 583 J/g
30
DoC and Cure Rate – 7cpm
0.00
0.20
0.40
0.60
0.80
1.00
1000 2000 3000 4000 5000
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)
7ºCpm Dynamic Test
31
Heat Flow Response – 8cpm
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1000 1500 2000 2500 3000 3500 4000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
8ºCpm Dynamic TestHRRamp = 630.1 J/g
32
DoC and Cure Rate – 8cpm
0.00
0.20
0.40
0.60
0.80
1.00
1000 1500 2000 2500 3000 3500 4000
Time (s)
Deg
ree
of c
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
8ºCpm Dynamic Test
33
Heat Flow Response – 9cpm
-0.40
0.00
0.40
0.80
1.20
1.60
1000 1500 2000 2500 3000 3500
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
9ºCpm Dynamic TestHRRamp = 614.1 J/g
34
DoC and Cure Rate – 9cpm
0.00
0.20
0.40
0.60
0.80
1.00
1000 1500 2000 2500 3000 3500
Time (s)
Deg
ree
of c
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
9ºCpm Dynamic Test
35
Heat Flow Response – 10cpm
-0.40
0.00
0.40
0.80
1.20
1.60
2.00
1500 2000 2500 3000 3500
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
Cur
e ra
te (1
/s)
10ºCpm Dynamic TestHRRamp = 583.6 J/g
36
DoC and Cure Rate – 10cpm
0.00
0.20
0.40
0.60
0.80
1.00
1500 2000 2500 3000 3500
Time (s)
Deg
ree
of c
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
Cur
e ra
te (1
/s)
10ºCpm Dynamic Test
37
Heat Flow Response – 100ºC
0.00
0.01
0.02
0.03
0.04
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
Cur
e ra
te (1
/s)
100ºC Isothermal TestHRHold = 296.0 J/g
38
DoC and Cure Rate – 100ºC
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-06
1.0E-05
1.5E-05
2.0E-05
2.5E-05
Cur
e ra
te (1
/s)
100ºC Isothermal TestDoCHold = 0.524
39
Heat Flow Response – 110ºC
0.00
0.01
0.02
0.03
0.04
0 5000 10000 15000 20000 25000 30000 35000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
1.0E-05
2.0E-05
3.0E-05
4.0E-05
Cur
e ra
te (1
/s)
110ºC Isothermal TestHRHold = 334.9 J/g
40
DoC and Cure Rate – 110ºC
0.0
0.2
0.4
0.6
0.8
1.0
0 5000 10000 15000 20000 25000 30000 35000
Time (s)
Deg
ree
of c
ure
0.0E+00
1.0E-05
2.0E-05
3.0E-05
4.0E-05
Cur
e ra
te (1
/s)
110ºC Isothermal TestDoCHold = 0.589
41
Heat Flow Response – 120ºC
0.00
0.02
0.04
0.06
0 5000 10000 15000 20000 25000 30000
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
6.0E-05
Cur
e ra
te (1
/s)
120ºC Isothermal TestHRHold = 357.4 J/g
42
DoC and Cure Rate – 120ºC
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-05
2.0E-05
3.0E-05
4.0E-05
5.0E-05
6.0E-05
Cur
e ra
te (1
/s)
120ºC Isothermal TestDoCHold = 0.636
43
Heat Flow Response – 130ºC
0.00
0.02
0.04
0.06
0.08
0 5000 10000 15000 20000 25000 30000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
Cur
e ra
te (1
/s)
130ºC Isothermal TestHRHold = 403.4 J/g
44
DoC and Cure Rate – 130ºC
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
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
Cur
e ra
te (1
/s)
130ºC Isothermal TestDoCHold = 0.704
45
Heat Flow Response – 140ºC
0.00
0.02
0.04
0.06
0.08
0.10
0 5000 10000 15000 20000 25000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
4.0E-05
8.0E-05
1.2E-04
1.6E-04
Cur
e ra
te (1
/s)
140ºC Isothermal TestHRHold = 413.4 J/g
46
DoC and Cure Rate – 140ºC
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
4.0E-05
8.0E-05
1.2E-04
1.6E-04
Cur
e ra
te (1
/s)
140ºC Isothermal TestDoCHold = 0.740
47
Heat Flow Response – 150ºC
0.00
0.04
0.08
0.12
0.16
0.20
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
Cur
e ra
te (1
/s)
150ºC Isothermal TestHRHold = 432.6 J/g
48
DoC and Cure Rate – 150ºC
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
Cur
e ra
te (1
/s)
150ºC Isothermal TestDoCHold = 0.788
49
Heat Flow Response – 160ºC
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 5000 10000 15000 20000 25000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
Cur
e ra
te (1
/s)
160ºC Isothermal TestHRHold = 466.0 J/g
50
DoC and Cure Rate – 160ºC
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)
160ºC Isothermal TestDoCHold = 0.833
51
Heat Flow Response – 170ºC
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 2000 4000 6000 8000 10000 12000 14000
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 = 479.8 J/g
52
DoC and Cure Rate – 170ºC
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
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 TestDoCHold = 0.862
53
Heat Flow Response – 180ºC-1
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0 2000 4000 6000 8000 10000 12000 14000
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)
180ºC-1 Isothermal TestHRHold = 473.1 J/g
54
DoC and Cure Rate – 180ºC-1
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
2.0E-04
4.0E-04
6.0E-04
8.0E-04
Cur
e ra
te (1
/s)
180ºC-1 Isothermal TestDoCHold = 0.898
55
Heat Flow Response – 180ºC-2
-0.1
0.1
0.3
0.5
0.7
0 3000 6000 9000 12000 15000
Time (s)
Spec
ific
heat
flow
(W/g
)
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-2 Isothermal TestHRHold = 486.5 J/g
56
DoC and Cure Rate – 180ºC-2
0.0
0.2
0.4
0.6
0.8
1.0
0 3000 6000 9000 12000 15000
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-2 Isothermal TestDoCHold = 0.904
57
Heat Flow Response – 190ºC
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 3000 6000 9000 12000 15000
Time (s)
Spec
ific
heat
flow
(W/g
)
0.0E+00
2.0E-04
4.0E-04
6.0E-04
8.0E-04
1.0E-03
1.2E-03
Cur
e ra
te (1
/s)
190ºC Isothermal TestHRHold = 502.8 J/g
58
DoC and Cure Rate – 190ºC
0.0
0.2
0.4
0.6
0.8
1.0
0 3000 6000 9000 12000 15000
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
1.2E-03
Cur
e ra
te (1
/s)
190ºC Isothermal TestDoCHold = 0.937
59
Heat of Reaction Tables
Pre-Test Ramp Total8552-MDYN-01cpm-01 0.00 558.91 558.918552-MDYN-02cpm-01 0.00 575.43 575.438552-MDYN-02cpm-02 0.00 601.65 601.658552-MDYN-03cpm-01 0.00 594.88 594.888552-MDYN-04cpm-01 0.00 621.82 621.828552-MDYN-05cpm-01 0.00 596.98 596.988552-MDYN-06cpm-01 0.00 616.41 616.418552-MDYN-07cpm-01 0.00 582.98 582.988552-MDYN-08cpm-01 0.00 630.07 630.078552-MDYN-09cpm-01 0.00 614.07 614.078552-MDYN-10cpm-01 0.00 583.62 583.62
Heat of Reaction (J/g)Test Iso-Ramp Hold Ramp Total8552-MISO-100C-01 2.00 295.95 270.47 568.428552-MISO-110C-01 2.00 334.88 235.30 572.188552-MISO-120C-01 3.00 357.40 206.01 566.418552-MISO-130C-01 3.50 403.40 171.32 578.218552-MISO-140C-01 4.50 413.43 147.17 565.108552-MISO-150C-01 6.50 432.63 118.29 557.428552-MISO-160C-01 10.00 466.01 95.26 571.278552-MISO-170C-01 12.00 479.84 79.00 570.848552-MISO-180C-01 16.50 473.10 55.43 545.038552-MISO-180C-02 15.00 486.49 53.05 554.548552-MISO-190C-01 19.00 502.82 34.88 556.70
8552-160C-INT15 8.50 99.40 445.77 553.668552-160C-INT30 8.50 274.09 275.24 557.83
Heat of Reaction (J/g)Test
60
Total Heat of Reaction - Dyns
0
100
200
300
400
500
600
700
8552
-01c
pm-0
1
8552
-02c
pm-0
1
8552
-02c
pm-0
2
8552
-03c
pm-0
1
8552
-04c
pm-0
1
8552
-05c
pm-0
1
8552
-06c
pm-0
1
8552
-07c
pm-0
1
8552
-08c
pm-0
1
8552
-09c
pm-0
1
8552
-10c
pm-0
1
HR
(J/g
) J/g 598=avgDynHR
J/g 600=ModelHR
61
Total Heat of Reaction - Isos
0
100
200
300
400
500
600
700
8552
-100
C-0
1
8552
-110
C-0
1
8552
-120
C-0
1
8552
-130
C-0
1
8552
-140
C-0
1
8552
-150
C-0
1
8552
-160
C-0
1
8552
-170
C-0
1
8552
-180
C-0
1
8552
-180
C-0
2
8552
-190
C-0
1
8552
-160
C-IN
T15
8552
-160
C-IN
T30
HR
(J/g
)
Isothermal - Residual
Isothermal - Hold
Isothermal - PreHold
J/g 564=avgIsoHR
J/g 600=ModelHR
62
Tg TablesDoC Tg (ºC) DoC Tg (ºC)
8552-MDYN-01cpm-01 0.00 -8.84 1.00 197.268552-MDYN-02cpm-01 0.00 -8.15 1.00 205.798552-MDYN-02cpm-02 0.00 -10.09 1.00 217.288552-MDYN-03cpm-01 0.00 -7.36 1.00 204.158552-MDYN-04cpm-01 0.00 -6.66 1.00 203.678552-MDYN-05cpm-01 0.00 -7.68 1.00 203.588552-MDYN-06cpm-01 0.00 -7.28 1.00 203.488552-MDYN-07cpm-01 0.00 -2.70 1.00 203.058552-MDYN-08cpm-01 0.00 -7.08 1.00 162.638552-MDYN-09cpm-01 0.00 -5.78 1.00 162.288552-MDYN-10cpm-01 0.00 -2.99 1.00 167.96
Test Initial Final
DoC Tg (ºC) DoC Tg (ºC)8552-MISO-100C-01 0.00 -12.57 0.52 108.218552-MISO-110C-01 0.00 -14.36 0.59 126.058552-MISO-120C-01 0.00 -13.94 0.64 142.728552-MISO-130C-01 0.00 -13.48 0.70 165.858552-MISO-140C-01 0.00 -12.55 0.74 169.278552-MISO-150C-01 0.00 -12.71 0.79 182.658552-MISO-160C-01 0.00 -14.44 0.83 195.998552-MISO-170C-01 0.00 -14.31 0.86 204.918552-MISO-180C-01 0.00 - 0.90 226.658552-MISO-180C-02 0.00 -13.53 0.90 218.098552-MISO-190C-01 0.00 - 0.94 217.58
8552-160C-INT15 0.00 -14.28 0.19 33.478552-160C-INT30 0.00 -14.58 0.51 91.53
Test Initial Post-Hold
63
-50
0
50
100
150
200
250
300
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 hold
Isothermal-final
Dynamic-final
Dynamic-initial
DB Equation
Glass Transition Temperature
CTg °−= 70
CTg °=∞
250
78.0=λ
Drop in Tg due to degradation
64
Cure Kinetics ModelChemical Reaction:
where
21 kkk xxx &&& +=
( ) ( ) 413.1347.25.929,64
1 1594.015.900,153 +−×=−
xxex RTk&
( ) 586.5029.13.168,133
112 110963.3 xxex RT
k −××=−
&
65
Cure Kinetics ModelDiffusion Component:
( )xFeKx dfB
dd
−
= 0&
( ) bTTaf g +−=
with
and
fd ex
21.0
0.4−
×=&
4108.4 −×=a
⎪⎩
⎪⎨
⎧
°>°<<°
°<=
CTCTC
CTb
g
g
g
195195120
120
031.00.031 and 0.021 bwLinear
021.0
where1
1If f<small then f=small (=1E-30 see CMT_vars2.f90)
66
Cure Kinetics Model
111
−
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
dk xxx
&&&
C-70 °=gT 0.78=λC052 °=∞gT
Total Heat of Reaction:
Glass Transition (Tg) Model (DeBenedetto):
J/g 600=HR
67
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg x = 0.02
68
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg x = 0.1
69
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModel x = 0.2
70
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModel x = 0.3
71
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.003
1/T (1/s)
Ln(x
dot)
Test Data-Isos
Test Data-Dyns
Model-Kinetic
Model
Tg x = 0.4
72
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg x = 0.5
73
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg
x = 0.6
74
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg x = 0.7
75
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticTgModel
x = 0.8
76
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg
x = 0.9
77
Ln(xdot)-1/T
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-40.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003
1/T (1/s)
Ln(x
dot)
Test Data-IsosTest Data-DynsModel-KineticModelTg
x = 0.98
78
Model Parameters
1.413
0.15941.000.001.002.347
64,929.5153,900.5
Reaction 1
0.001.000.00
5.586
1.001.029
133,168.3(J/mol)3.963E+11(1/s)
Reaction 2Parameter
195 (ºC)120 (ºC)
0.021100 (ºC)0 (ºC)
0.031
4.8E-04 (1/ºC)4.8E-04 (1/ºC)
0.214.0 (1/s)
Value (unit)Parameter
0.78250 (ºC)-7 (ºC)
Value (unit)Parameter
aE
l
r
m
2n
b
n
0dk
B
1a
2a
1agT
2agT
1b2b
1bgT
2bgT0gT
∞gT
λ
0k
Model’s range of validity100ºC < Iso Temperature < 190ºC-90ºC < Dyn Temperature < 275ºC
79
Dynamic Tests – 1cpm
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
1ºCpm Dynamic Test
80
Dynamic Tests – 2cpm-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
2.0E-04
4.0E-04
6.0E-04
8.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
2ºCpm-1 Dynamic Test
81
Dynamic Tests – 2cpm-2
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
2ºCpm-2 Dynamic Test
82
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
3ºCpm Dynamic Test
83
Dynamic Tests – 4cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
4ºCpm Dynamic Test
84
Dynamic Tests – 5cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
4.0E-04
8.0E-04
1.2E-03
1.6E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
5ºCpm Dynamic Test
85
Dynamic Tests – 6cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
6ºCpm Dynamic Test
86
Dynamic Tests – 7cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
7ºCpm Dynamic Test
87
Dynamic Tests – 8cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
8ºCpm Dynamic Test
88
Dynamic Tests – 9cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
9ºCpm Dynamic Test
89
Dynamic Tests – 10cpm
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
Temperature (°C)
Deg
ree
of C
ure
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
10ºCpm Dynamic Test
90
Isothermal Tests - 100ºC
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-06
1.0E-05
1.5E-05
2.0E-05
2.5E-05
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
100ºC Isothermal TestDoCHold = 0.524
91
Isothermal Tests - 110ºC
0.0
0.2
0.4
0.6
0.8
1.0
0 5000 10000 15000 20000 25000 30000 35000
Time (s)
Deg
ree
of c
ure
0.0E+00
1.0E-05
2.0E-05
3.0E-05
4.0E-05
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
110ºC Isothermal TestDoCHold = 0.589
92
Isothermal Tests - 120ºC
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-05
2.0E-05
3.0E-05
4.0E-05
5.0E-05
6.0E-05
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
120ºC Isothermal TestDoCHold = 0.636
93
Isothermal Tests - 130ºC
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
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
130ºC Isothermal TestDoCHold = 0.704
94
Isothermal Tests - 140ºC
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
140ºC Isothermal TestDoCHold = 0.740
95
Isothermal Tests - 150ºC
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
150ºC Isothermal TestDoCHold = 0.788
96
Isothermal Tests - 160ºC
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
1.0E-04
2.0E-04
3.0E-04
4.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
160ºC Isothermal TestDoCHold = 0.833
97
Isothermal Tests - 170ºC
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
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
6.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
170ºC Isothermal TestDoCHold = 0.862
98
Isothermal Tests - 180ºC-1
0.0
0.2
0.4
0.6
0.8
1.0
0 4000 8000 12000 16000
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
180ºC-1 Isothermal TestDoCHold = 0.898
99
Isothermal Tests - 180ºC-2
0.0
0.2
0.4
0.6
0.8
1.0
0 3000 6000 9000 12000 15000
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
180ºC-2 Isothermal TestDoCHold = 0.904
100
Isothermal Tests - 190ºC
0.0
0.2
0.4
0.6
0.8
1.0
0 3000 6000 9000 12000 15000
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
1.2E-03
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
190ºC Isothermal TestDoCHold = 0.937
101
0.0
0.2
0.4
0.6
0.8
1.0
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)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 100ºC
100ºC Isothermal TestResidual Ramp
102
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 110ºC
110ºC Isothermal TestResidual Ramp
103
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 120ºC
120ºC Isothermal TestResidual Ramp
104
0.0
0.2
0.4
0.6
0.8
1.0
100 150 200 250 300
Temperature (C)
Deg
ree
of c
ure
0.0E+00
4.0E-05
8.0E-05
1.2E-04
1.6E-04
2.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 130ºC
130ºC Isothermal TestResidual Ramp
105
0.0
0.2
0.4
0.6
0.8
1.0
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
Isothermal Tests - 140ºC
140ºC Isothermal TestResidual Ramp
106
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 150ºC
150ºC Isothermal TestResidual Ramp
107
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)Degree of cure
Degree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 160ºC
160ºC Isothermal TestResidual Ramp
108
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 170ºC
170ºC Isothermal TestResidual Ramp
109
0.0
0.2
0.4
0.6
0.8
1.0
100 150 200 250 300
Temperature (C)
Deg
ree
of c
ure
0.0E+00
1.0E-04
2.0E-04
3.0E-04
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 180ºC-1
180ºC-1 Isothermal TestResidual Ramp
110
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 180ºC-2
180ºC-2 Isothermal TestResidual Ramp
111
0.0
0.2
0.4
0.6
0.8
1.0
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
Cur
e ra
te (1
/s)
Degree of cureDegree of cure - ModelCure Rate (1/s)Cure Rate (1/s) - Model
Isothermal Tests - 190ºC
190ºC Isothermal TestResidual Ramp
112
Dynamic Tests – All
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 50 100 150 200 250 300
Temperature (°C)
Deg
ree
of C
ure
DOC (10cpm, expt)
DOC (10cpm, model)
DOC (9cpm, expt)
DOC (9cpm, model)
DOC (8cpm, expt)
DOC (8cpm, model)
DOC (7cpm, expt)
DOC (7cpm, model)
DOC (6cpm, expt)
DOC (6cpm, model)
DOC (5cpm, expt)
DOC (5cpm, model)
DOC (4cpm, expt)
DOC (4cpm, model)
DOC (3cpm, expt)
DOC (3cpm, model)
DOC (2cpm-2, expt)
DOC (2cpm-2,model)DOC (2cpm-1, expt)
113
Dynamic Tests – All
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
0 50 100 150 200 250 300
Temperature (°C)
Cur
e ra
te (1
/s)
Cure rate (10cpm, expt)
Cure rate (10cpm, model)
Cure rate (9cpm, expt)
Cure rate (9cpm, model)
Cure rate (8cpm, expt)
Cure rate (8cpm, model)
Cure rate (7cpm, expt)
Cure rate (7cpm, model)
Cure rate (6cpm, expt)
Cure rate (6cpm, model)
Cure rate (5cpm, expt)
Cure rate (5cpm, model)
Cure rate (4cpm, expt)
Cure rate (4cpm, model)
Cure rate (3cpm, expt)
Cure rate (3cpm, model)
Cure rate (2cpm-2, expt)
Cure rate (2cpm-2,model)Cure rate (2cpm-1, expt)
114
Isothermal Tests – All
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 10000 20000 30000 40000 50000
Time (s)
Deg
ree
of C
ure
DOC 190C (expt) DOC 190C (model)DOC 180C-2 (expt) DOC 180C-2 (model)DOC 180C-1 (expt) DOC 180C-1 (model)DOC 170C (expt) DOC 170C (model)DOC 160C (expt) DOC 160C (model)DOC 150C (expt) DOC 150C (model)DOC 140C (expt) DOC 140C (model)DOC 130C (expt) DOC 130C (model)DOC 120C (expt) DOC 120C (model)DOC 110C (expt) DOC 110C (model)DOC 100C (expt) DOC 100C (model)
115
Isothermal Tests – All
0.0E+00
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
6.0E-04
7.0E-04
8.0E-04
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Time (s)
Cur
e ra
te (1
/s)
Cure rate (190C, expt)
Cure rate (190C, model)
Cure rate (180C-2, expt)
Cure rate (180C-2,model)Cure rate (180C-1, expt)
Cure rate (180C-1,model)Cure rate (170C, expt)
Cure rate (170C, model)
Cure rate (160C, expt)
Cure rate (160C, model)
Cure rate (150C, expt)
Cure rate (150C, model)
Cure rate (140C, expt)
Cure rate (140C, model)
Cure rate (130C, expt)
Cure rate (130C, model)
Cure rate (120C, expt)
Cure rate (120C, model)
Cure rate (110C expt)
116
Post-Hold TgTg 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 Model8552-MISO-100C-01 108.2 114.88552-MISO-110C-01 126.1 126.48552-MISO-120C-01 142.7 141.28552-MISO-130C-01 165.9 155.38552-MISO-140C-01 169.3 169.18552-MISO-150C-01 182.7 183.48552-MISO-160C-01 196.0 196.68552-MISO-170C-01 204.9 205.68552-MISO-180C-01 226.7 215.98552-MISO-180C-02 218.1 215.98552-MISO-190C-01 217.6 226.0
8552-160C-INT15 33.5 33.48552-160C-INT30 91.5 98.8
Test Post-Hold Tg (ºC)
0
50
100
150
200
250
8552
-100
C-0
1
8552
-110
C-0
1
8552
-120
C-0
1
8552
-130
C-0
1
8552
-140
C-0
1
8552
-150
C-0
1
8552
-160
C-0
1
8552
-170
C-0
1
8552
-180
C-0
1
8552
-180
C-0
2
8552
-190
C-0
1
8552
-160
C-
INT1
5
8552
-160
C-
INT3
0
Tg (C
)
TestModel
117
S1
S3-00 S3-60 S4
Post-Hold TgTg values at various points along the MRCC were measured and then compared to the predictions of the cure kinetics model. Good agreement was observed.
0
50
100
150
200
250
8552-CC-S1-02 8552-CC-S3-00-01 8552-CC-S3-60-01 8552-CC-S4-01
Tg (C
)
Test Tg
Model Tg
Test Model8552-CC-S1-02 4.2 9.3
8552-CC-S3-00-01 96.8 97.48552-CC-S3-60-01 208.5 211.4
8552-CC-S4-01 214.3 214.8
Test Tg (ºC)
118
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.
119
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
120
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
121
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
122
Goodness of Fit – Iso Timing
-1200
-900
-600
-300
0
300
600
900
1200
8552
-MIS
O-1
00C
-01
8552
-MIS
O-1
10C
-01
8552
-MIS
O-1
20C
-01
8552
-MIS
O-1
30C
-01
8552
-MIS
O-1
40C
-01
8552
-MIS
O-1
50C
-01
8552
-MIS
O-1
60C
-01
8552
-MIS
O-1
70C
-01
8552
-MIS
O-1
80C
-01
8552
-MIS
O-1
80C
-02
8552
-MIS
O-1
90C
-01
Tim
e Er
ror (
sec)
Timing - StartTiming - KickoffTiming - PeakTiming - SlowTiming - End
123
Goodness of Fit – Iso DOC
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
8552
-MIS
O-1
00C
-01
8552
-MIS
O-1
10C
-01
8552
-MIS
O-1
20C
-01
8552
-MIS
O-1
30C
-01
8552
-MIS
O-1
40C
-01
8552
-MIS
O-1
50C
-01
8552
-MIS
O-1
60C
-01
8552
-MIS
O-1
70C
-01
8552
-MIS
O-1
80C
-01
8552
-MIS
O-1
80C
-02
8552
-MIS
O-1
90C
-01
DO
C E
rror
DOC - StartDOC - KickoffDOC - PeakDOC - SlowDOC - End
124
Goodness of Fit – Dyn Timing
0
30
60
9085
52-M
DY
N-0
1cpm
-01
8552
-MD
YN
-02c
pm-
01
8552
-MD
YN
-02c
pm-
02
8552
-MD
YN
-03c
pm-
01
8552
-MD
YN
-04c
pm-
01
8552
-MD
YN
-05c
pm-
01
8552
-MD
YN
-06c
pm-
01
8552
-MD
YN
-07c
pm-
01
8552
-MD
YN
-08c
pm-
01
8552
-MD
YN
-09c
pm-
01
8552
-MD
YN
-10c
pm-
01
Tim
e Er
ror (
sec)
Timing - Peak
125
Goodness of Fit – Dyn DOC
0
0.02
0.04
0.06
0.08
0.1
0.12
8552
-MD
YN
-01c
pm-
01
8552
-MD
YN
-02c
pm-
01
8552
-MD
YN
-02c
pm-
02
8552
-MD
YN
-03c
pm-
01
8552
-MD
YN
-04c
pm-
01
8552
-MD
YN
-05c
pm-
01
8552
-MD
YN
-06c
pm-
01
8552
-MD
YN
-07c
pm-
01
8552
-MD
YN
-08c
pm-
01
8552
-MD
YN
-09c
pm-
01
8552
-MD
YN
-10c
pm-
01
DO
C E
rror
Timing - Peak
126
Other Forms - Fabric
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Non
rev
Hea
t Flo
w (W
/g)
8552-FABRIC-MDYN-2cpm-01-HeatUp
8552-MDYN-02cpm-01-HeatUp
8552-MDYN-02cpm-02-HeatUp
127
Other Forms - Fabric
0
0.2
0.4
0.6
0.8
1
50 100 150 200 250 300Temperature (C)
DoC
8552-FABRIC-MDYN-2cpm-01-HeatUp
8552-MDYN-02cpm-01-HeatUp
8552-MDYN-02cpm-02-HeatUp
128
Other Forms - Fabric
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-50 0 50 100 150 200 250 300
Temperature (C)
Non
rev
Hea
t Flo
w (W
/g)
8552-FABRIC-MDYN-4cpm-01-HeatUp
8552-MDYN-04cpm-01-HeatUp
129
Other Forms - Fabric
0
0.2
0.4
0.6
0.8
1
50 100 150 200 250 300Temperature (C)
DoC
8552-FABRIC-MDYN-4cpm-01-HeatUp
8552-MDYN-04cpm-01-HeatUp
130
Other Forms - Film
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Non
rev
Hea
t Flo
w (W
/g)
8552-FILM-MDYN-2cpm-01-HeatUp-0%
8552-MDYN-02cpm-02-HeatUp
8552-MDYN-02cpm-01-HeatUp
Smaller peak is observed in the response of the film sample.
Reaction dies faster in the film sample.
131
Other Forms - Film
0
0.2
0.4
0.6
0.8
1
50 100 150 200 250 300Temperature (C)
DoC
8552-FILM-MDYN-2cpm-01-HeatUp-0%
8552-MDYN-02cpm-02-HeatUp
8552-MDYN-02cpm-01-HeatUp
The curing behaviour is very similar to neat resin up to 220C.
132
Other Forms - Film
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Non
rev
Hea
t Flo
w (W
/g)
8552-FILM-MDYN-4cpm-01-HeatUp-0%
8552-MDYN-04cpm-01-HeatUp
Smaller peak is observed in the response of the film sample.
Reaction dies faster in the film sample.
133
Other Forms - Film
0
0.2
0.4
0.6
0.8
1
50 100 150 200 250 300Temperature (C)
DoC
8552-FILM-MDYN-4cpm-01-HeatUp-0%
8552-MDYN-04cpm-01-HeatUp
The curing behaviour is very similar to neat resin up to 220C.
134
Other Forms – HR Values
More tests on fabric are done but not analysed yet.
0
100
200
300
400
500
600
700
8552-MDYN-02cpm-
01-HeatUp
8552-MDYN-02cpm-
02-HeatUp
8552-FABRIC-MDYN-
2cpm-01-HeatUp
8552-FILM-
MDYN-2cpm-01-HeatUp
8552-MDYN-04cpm-
01-HeatUp
8552-FABRIC-MDYN-
4cpm-01-HeatUp
8552-FILM-
MDYN-4cpm-01-HeatUp
Hea
t of R
eact
ion
(J/g
)
Raw Adjustedinitial Final HR HR(C) (C) (J/G) (J/G)
8552-MDYN-02cpm-01-HeatUp -8.15 202.95 575.43 1 575.438552-MDYN-02cpm-02-HeatUp -10.09 217.28 601.65 1 601.65
8552-FABRIC-MDYN-2cpm-01-HeatUp -7.88 200.78 225.22 0.38 592.688552-FILM-MDYN-2cpm-01-HeatUp -5.07 209.67 537.95 1 537.95
8552-MDYN-04cpm-01-HeatUp -6.66 203.1 621.82 1 621.828552-FABRIC-MDYN-4cpm-01-HeatUp -8.11 195.81 243.50 0.38 640.80
8552-FILM-MDYN-4cpm-01-HeatUp -4.43 206.03 543.48 1 543.48
Test Adjustment Ratio
Tg
Lower total heat of reaction is measured for the film compared to the neat resin. Considering the similarities between the responses of neat resin and film up to 220C, the model (developed based on neat resin) is considered valid for resin film. The error in the total HR of the film results in conservative estimation of exhothermic events.
The fabric response is similar to the neat resin. The heat flow measured for the fabric samples was divided by the resin content (0.38), based on the material datasheet. The total HF resulted was in agreement with neat resin.
Assuming a mass resin content of 0.38, the fibre volume fraction is calculated to be 54.5%, which compares to the MDS reported laminate fraction of 58%.
135
Material Model Verification – 100C
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700 800
Time (min)
DoC
RavenTestCKA Model
100C-01
136
Material Model Verification – 190C
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200 250 300
Time (min)
DoC
RavenTestCKA Model
190C-01
137
Material Model Verification – 1Cpm
0
0.2
0.4
0.6
0.8
1
1.2
0 50 100 150 200 250 300 350 400 450
Time (min)
DoC
RavenTestCKA Model
1Cpm-01
138
Material Model Verification – 1Cpm
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60 70
Time (min)
DoC
RavenTestCKA Model
10Cpm-01
139
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
Model Not Validated in This Zone.
140
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
1°C/min
Model Not Validated in This Zone.
141
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
2°C/min
Model Not Validated in This Zone.
142
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
3°C/min
Model Not Validated in This Zone.
143
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
4°C/min
Model Not Validated in This Zone.
144
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
5°C/min
Model Not Validated in This Zone.
145
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Green: 1’-9’ at 1’Red: 10’-50’ at 10’Cyan: 60’-330’ at 30’Magenta: 360’-1080’ at 60’Yellow: Tg line
1-10°C/min Uncured
Model Not Validated in This Zone.
146
HEXPLY 8552 – Version 1.0
Model Not Validated in This Zone.
Cure Rate
Green: 1E-06 to 1E-05 (at 1E-4)Red: 1E-05 to 1E-04 (at 1E-05)Cyan: 1E-04 to 1E-03 (at 1E-04)Magenta: 1E-03 to 1E-02 (at 1E-03)Yellow: Tg line
Model Not Validated in This Zone.
147
Viscosity Model
148
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
149
Viscosity Tests
• Material viscosity was measured using an 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 8 tests at 1, 2, 3, and 4 C/min (two at each rate) were performed.
• Disposable aluminum plates of diameter 25mm were used at a gap of 1mm (sample thickness). Frequency of oscillation was chosen to be 1Hz.
150
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.
151
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 fluid1. In other words:
'ημ =
The viscosity model developed here is based on the measured η’, i.e. the dynamic viscosity response of the material.
152
Raw Data
1
10
100
1000
10000
100000
1000000
0 50 100 150 200 250
Temperature (C)
Visc
osity
n' (
Pa.s
)
4°Cpm-1 4°Cpm-2
3°Cpm-1 3°Cpm-2
2°Cpm-1 2°Cpm-2
1°Cpm-1 1°Cpm-2
Start End1ºCpm-01 25.1 171.41ºCpm-02 24.9 171.82ºCpm-01 23.3 187.92ºCpm-02 25 188.13ºCpm-01 23.2 199.33ºCpm-02 23.4 201.14ºCpm-01 25 205.74ºCpm-02 24.5 207.3
Test Temperature (ºC)
153
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 the degree of cure at gelation
154
Mathematical ModelThe parameters of the viscosity model are determined by fitting to the experimental results.
908,811 =E
545.0=gx
0=C
Model’s range of validity25ºC < Temperature < 250ºC
1 < η’ < 106
Frequency: ω = 1 Hz
( )2
21
0201
CxBxA
g
gRTE
RTE
xxx
ee++
⎟⎟⎠
⎞⎜⎜⎝
⎛
−+= μμμ
0=B
466.2=A228,132 =E
1101 105.7 −×=μ
0481.001 =μ
155
Dynamic Tests – 1cpm-1
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
1cpm-01
156
Dynamic Tests – 1cpm-2
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
1cpm-02
157
Dynamic Tests – 2cpm-1
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
2cpm-01
158
Dynamic Tests – 2cpm-2
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
2cpm-02
159
Dynamic Tests – 3cpm-1
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
3cpm-01
160
Dynamic Tests – 3cpm-2
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
3cpm-02
161
Dynamic Tests – 4cpm-1
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
4cpm-01
162
Dynamic Tests – 4cpm-2
1
10
100
1000
10000
100000
1000000
0 50 100 150 200
Temperature (ºC)
Visc
osity
n' (
Pa.s
)
Test Data
Total Viscosity
4cpm-02
163
Material Model Verification – 1Cpm-1
1
10
100
1000
10000
100000
1000000
0 20 40 60 80 100 120 140 160
Time (min)
DoC
RavenTestCKA Model
1Cpm-01
164
Material Model Verification – 4Cpm-2
1
10
100
1000
10000
100000
1000000
0 5 10 15 20 25 30 35 40 45 50
Time (min)
DoC
RavenTestCKA Model
4Cpm-02
165
HEXPLY 8552 – Version 1.0
Resin Viscosity
Blue: 1-9 at 1 (Pa.s)Green: 10-90 at 10 (Pa.s)Red: 100-900 at 100 (Pa.s)Cyan: 1000-10000 at 1000 (Pa.s)
166
Heat Capacity (Cp) Model
167
NomenclatureCp Heat Capacity (J/gC)
168
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).
169
Raw Data
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300Temperature (C)
Cp
1cpm 2cpm2cpm 3cpm4cpm 5cpm6cpm 7cpm8cpm 9cpm10cpm
170
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300Temperature (C)
Cp
1cpm 2-01cpm2-02cpm 4cpm4cpm 5cpm6cpm 7cpm8cpm 9cpm10cpm GlassyRubbery
Raw Data – Shifted
Shifted to match the glassy response
171
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
0.0
0.5
1.0
1.5
2.0
2.5
-50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
1 cpm - 01
T-Tg
Test
Glassy
RubberyTotal Cp
172
Cp Model
278.0=k
The parameters of the Cp model are determined by fitting to the experimental results. The model is formulated as shown below:
003775.00 =gs
Valid for temperature values between -70ºC to 275ºC.
Glassy Rubbery
( )[ ]cg TTTkrpgp
rpp e
CCCC Δ−−+
−+=
1
5.1−=Δ cT
Other parameters
( )∞==+= ,0 and , jgricTsC ijijijp
( )∞
+−=ipipp xCCxC
i 01
Virgin and cured responses:
Glassy or rubbery at x:
Total Cp response:
73.00 =gc0034.0=∞gs83.0=∞gc
00327.00 =rs088.10 =rc
002.0=∞gs35.1=∞gc
173
Dynamic Tests – 1cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
1 cpm - 01
174
Dynamic Tests – 2cpm-1
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
2 cpm - 01
175
Dynamic Tests – 2cpm-2
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
2 cpm - 02
176
Dynamic Tests – 3cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
3 cpm - 01
177
Dynamic Tests – 4cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
4 cpm - 01
178
Dynamic Tests – 5cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
5 cpm - 01
179
Dynamic Tests – 6cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
6 cpm - 01
180
Dynamic Tests – 7cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
7 cpm - 01
181
Dynamic Tests – 8cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
8 cpm - 01
182
Dynamic Tests – 9cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
9 cpm - 01
183
Dynamic Tests – 10cpm
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (C)
Cp
-50
0
50
100
150
200
250
T-Tg
10 cpm - 01
184
Isothermal Tests – 100C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
100C - 01
185
Isothermal Tests – 110C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000 35000 40000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
110C - 01
186
Isothermal Tests – 120C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000 35000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
120C - 01
187
Isothermal Tests – 130C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
130C - 01
188
Isothermal Tests – 140C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
140C - 01
189
Isothermal Tests – 150C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
150C - 01
190
Isothermal Tests – 160C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
160C - 01
191
Isothermal Tests – 170C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
170C - 01
192
Isothermal Tests – 180C-1
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
180C - 01
193
Isothermal Tests – 180C-2
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
180C - 02
194
Isothermal Tests – 190C
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000
Time (s)
Cp
-50
0
50
100
150
200
250
T-Tg
190C - 01
195
Dynamic Tests – 1Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
1 cpm - Test1 cpm - Model
196
Dynamic Tests – 1Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
1 cpm - Test1 cpm - Model
197
Dynamic Tests – 2Cpm-1
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
2 cpm-1 - Test2 cpm-1 - Model
198
Dynamic Tests – 2Cpm-1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
2 cpm-1 - Test2 cpm-1 - Model
199
Dynamic Tests – 2Cpm-1
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
2 cpm-2 - Test2 cpm-2 - Model
200
Dynamic Tests – 2Cpm-1
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
2 cpm-2 - Test2 cpm-2 - Model
201
Dynamic Tests – 3Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
3 cpm - Test3 cpm - Model
202
Dynamic Tests – 3Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
3 cpm - Test3 cpm - Model
203
Dynamic Tests – 4Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
4 cpm - Test4 cpm - Model
204
Dynamic Tests – 4Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
4 cpm - Test4 cpm - Model
205
Dynamic Tests – 5Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
5 cpm - Test5 cpm - Model
206
Dynamic Tests – 5Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
5 cpm - Test5 cpm - Model
207
Dynamic Tests – 6Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 -50 0 50 100 150 200 250 300
Temperature (ºC)
Cp
(J/g
ºC)
6 cpm - Test6 cpm - Model
208
Dynamic Tests – 6Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
6 cpm - Test6 cpm - Model
209
Dynamic Tests – 7Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300 400
Temperature (ºC)
Cp
(J/g
ºC)
7 cpm - Test7 cpm - Model
210
Dynamic Tests – 7Cpm
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
7 cpm - Test7 cpm - Model
211
Dynamic Tests – 8Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300 400
Temperature (ºC)
Cp
(J/g
ºC)
8 cpm - Test8 cpm - Model
212
Dynamic Tests – 8Cpm
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
8 cpm - Test8 cpm - Model
213
Dynamic Tests – 9Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300 400
Temperature (ºC)
Cp
(J/g
ºC)
9 cpm - Test9 cpm - Model
214
Dynamic Tests – 9Cpm
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
9 cpm - Test9 cpm - Model
215
Dynamic Tests – 10Cpm
0.0
0.5
1.0
1.5
2.0
2.5
-100 0 100 200 300 400
Temperature (ºC)
Cp
(J/g
ºC)
10 cpm - Test10 cpm - Model
216
Dynamic Tests – 10Cpm
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
10 cpm - Test10 cpm - Model
217
Isothermal Tests – 100C
0.0
0.5
1.0
1.5
2.0
2.5
0 10000 20000 30000 40000 50000Time (s)
Cp
100C - 01
218
Isothermal Tests – 100C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
100C - 01
219
Isothermal Tests – 110C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000 35000 40000
Time (s)
Cp
110C - 01
220
Isothermal Tests – 110C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
110C - 01
221
Isothermal Tests – 120C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000 35000
Time (s)
Cp
120C - 01
222
Isothermal Tests – 120C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
120C - 01
223
Isothermal Tests – 130C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000
Time (s)
Cp
130C - 01
224
Isothermal Tests – 130C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
130C - 01
225
Isothermal Tests – 140C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000
Time (s)
Cp
140C - 01
226
Isothermal Tests – 140C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
140C - 01
227
Isothermal Tests – 150C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000
Time (s)
Cp
150C - 01
228
Isothermal Tests – 150C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
150C - 01
229
Isothermal Tests – 160C
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000
Time (s)
Cp
160C - 01
230
Isothermal Tests – 160C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
160C - 01
231
Isothermal Tests – 170C
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Time (s)
Cp
170C - 01
232
Isothermal Tests – 170C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
170C - 01
233
Isothermal Tests – 180C-1
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000
Time (s)
Cp
180C - 01
234
Isothermal Tests – 180C-1
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
180C - 01
235
Isothermal Tests – 180C-2
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000 16000
Time (s)
Cp
180C - 02
236
Isothermal Tests – 180C-2
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
180C - 02
237
Isothermal Tests – 190C
0.0
0.5
1.0
1.5
2.0
2.5
0 2000 4000 6000 8000 10000 12000 14000
Time (s)
Cp
190C - 01
238
Isothermal Tests – 190C
0.0
0.5
1.0
1.5
2.0
2.5
0 0.2 0.4 0.6 0.8 1
Degree of Cure
Cp
(J/g
ºC)
190C - 01
239
Material Model Verification – 100C
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0 100 200 300 400 500 600 700 800
Time (min)
Cp
RavenCKA Model
100C-01
240
Material Model Verification – 190C
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 50 100 150 200 250 300
Time (min)
Cp
RavenCKA Model
190C-01
241
Material Model Verification – 1Cpm
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250 300 350 400 450
Time (min)
Cp
RavenCKA Model
1Cpm-01
242
Material Model Verification – 10Cpm
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60 70
Time (min)
Cp
RavenCKA Model
10Cpm-01