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byHongneng Cai
School of Materials Science and Engineering, Xi'an Jiaotong University
Yasushi Miyano and Masayuki NakadaMaterials System Research Laboratory, Kanazawa Institute of Technology
Modified Time-temperature Superposition Principle for Viscoelasticity of Thermosetting Resins
The 15th Composites Durability Workshop (CDW-15), October 17 to 20, 2010, Kanazawa Institute of Technology
October 18, 2010Sakai Memorial Hall, Kanazawa Institute of Technology
Japan
2
Background and Objectives
Background
The most important hypothesis used in our accelerated testing for the prediction of long-term life of CFRP is the time-temperature superposition principle (TTSP).
The time-temperature shift factor for the visceoelasticity of matrix resin, that is the accelerating rate, should be determined accurately based on TTSP.
The modified time-temperature superposition was proposed, in which the master curves of viscoelastic models are constructed by shifting vertically as well as horizontallyviscoelastic modulus at various temperatures.
ObjectivesThe reliability of time-temperature shift factor determined for the creep compliance of the thermosetting resin by applying the modified TTSP is experimentally confirmed. The applicability of simplified method using the dynamic mechanical analysis (DMA) testto get the reliable time-temperature shift factor is discussed and confirmed experimentally.The formulation of master curve of creep compliance for matrix resin is introduced, and automatic determination of formulation parameters is introduced.
3
The modified TTSP
The master curve is constructed by shifting vertically as well as horizontallythe creep compliances measured at various temperatures T to superimposesmoothly to that at the reference temperature To.
Modified TTSP
Auto shifting principle
Adjust a and b, the data plots at T2 moves horizontally and vertically until a smoothest curve is got with the data plots at T1. The maximal 6th order polynomialis used to fit the master curve.
5
Auto shifting method for creep compliance master curve
( )
( )
1o g
o
1 2g
g o g
1 1log H( )2.303
1 1 1 1 1 H( )2.303 2.303
THa T T T
G T T
H H T TG T T G T T
∆= − −
∆ ∆ + − + − − −
Time-temperature and temperature shift factors:
G: gas constant ∆H: activation energy Tg: glass transition temp.
( ) ( ) ( ) ( ) ( ) ( )
[ ( ) ( ) ( ) ( ) ]( ( ) )
= − + − + − + − +
+ − + − + − + − + +
－
－ －
o
4 3 24 0 3 0 2 0 1 0 0 g
4 3 2 g4 g 0 3 g 0 2 g 0 1 g 0 0 g
log H
log 1 H
Tb T b T T b T T b T T b T T b T T
Tb T T b T T b T T b T T b T T
T
Tg is determined by TMA test , ∆H1, ∆H2, bi(i=0,4)are determined by auto shifting method.
Parameter determination:
6
Composition and curing condition of creep specimen
Composition and curing condition
Test type Test period t Temperature T ( °C)Short term 10s.~3hr 50,60,70,80,90,100,110
Medium term 10s.~24hr 50,60,70,80,90,100,110Long term 10s.~1000hr 50,80,100
7
Creep compliances measured in the long term
Only horizontal shift Vertical and horizontal shifts
The smooth master curve is obtained by vertical and horizontal shifting.
8
Creep compliances measured in the medium term and short term
Only horizontal shift Vertical and horizontal shifts
The master curves coincide with the creep compliance measured in the long term at T=50oC by vertical and horizontal shifting.
Only horizontal shiftc Vertical and horizontal shifts
Medium term
Short term
9
Comparison of shift amount obtained from master curvesby both methods
Same horizontal shift amounts and vertical shift amounts can be obtained by vertical and horizontal shifting regardless of test period.
Vertical shift amount
TTSP Modified TTSP
Horizontal shift amountHorizontal shift amount
10
Measurement of creep compliance of epoxy resin using DMA test
Comparison of test periods
If same time-temperature shift factor can be obtained by the creep test as DMA test, the long-term creep compliance can be predicted by DMA test.
11
Master curve of storage modulus by DMA test
Same horizontal shift amounts and vertical shift amounts can be obtained by vertical and horizontal shifting regardless of test period and test methods.
Vertical shift amount
Modified TTSP Shift factors
Horizontal shift amountMaster curve of storage modulus by DMA tests
Test conditions for DMA test
Frequency f(Hz)
Strain(%)
Temperature T ( °C)
0.01～10 0.06 25～140
12
The master curves of compliance obtained from the creep test andDMA test agree well with each other.
Modified TTSP
Comparison of master curves of creep compliances from creep and DMA tests
13
T0 25 [oC]Tg 162 [oC]
∆H1 101 [kJ/mol]
∆H2 760 [kJ/mol]
b0 1.13E-02 [-]
b1 -9.85E-04 [-]
b2 2.43E-05 [-]
b3 -2.23E-07 [-]
b4 6.98E-10 [-]
( )
( )
1o g
o
1 2g
g o g
1 1log H( )2.303
1 1 1 1 1 H( )2.303 2.303
THa T T T
G T T
H H T TG T T G T T
∆= − −
∆ ∆ + − + − − −
Time-temperature and temperature shift factors:
G: gas constant ∆H: activation energy Tg: glass transition temp.
( ) ( ) ( ) ( ) ( ) ( )
[ ( ) ( ) ( ) ( ) ]( ( ) )
= − + − + − + − +
+ − + − + − + − + +
－
－ －
o
4 3 24 0 3 0 2 0 1 0 0 g
4 3 2 g4 g 0 3 g 0 2 g 0 1 g 0 0 g
log H
log 1 H
Tb T b T T b T T b T T b T T b T T
Tb T T b T T b T T b T T b T T
T
Measuring of the storage modulus for the transverse direction of unidirectional CFRP (MR60H/1053)
14
Creep compliance of matrix resin (MR60H1053)
Dc(t’0,T0) 0.347 [1/GPa]
t’o 1 [min]
t’g 4.23 x 1010 [min]
mg 0.0116 [-]
mr 0.2876 [-]
( )g r
c c o oo g
' 'log log ' , log' '
mmt tD D t Tt t
= + +
Creep compliance of matrix resin: c m( ) 1/ ( )D t E t′ ′=
Back-calculation of Emusing the rule of mixture :
*y * m
y*Tm y fT f
11 1 1 , 0.516V VV
EE V E V
+= − =
Em: storage modulus of matrix rein Vf ,Vm: volume fractions of fiber and matrix
ET, EfT : storage moduli in the transverse direction of CFRP and carbon fiber
Rule of mixture
Formulation of creep compliance
Dc: creep complianceTo: reference temperature
t’: reduced time at To
t’o: reference reduced time at To
t’g: glassy reduced time at To
where
Formulation of creep compliance
15
Conclusion
Thank you for your attention!
The reliability of time-temperature shift factor determined for the creep compliance of the thermosetting resin by applying the modified TTSP was experimentally confirmed.
The applicability of simplified method using the dynamic mechanical analysis (DMA) test to get the reliable time-temperature shift factor was confirmed experimentally.
The autoshift method is applicable to get smooth master curve of creep compliance and reliable time-temperature dependent shift factor master curve.
The master curve of creep compliance for matrix resin was formulated, and formulation parameters were determined automatically.
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