Modified Time-temperature Superposition Principle for Viscoelasticity of Thermosetting Resins

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1 The 15 th Composites Durability Workshop (CDW-15), October 17 to 20, 2010, Kanazawa Institute of Technology Modified Time-temperature Superposition Principle for Viscoelasticity of Thermosetting Resins by Hongneng Cai School of Materials Science and Engineering, Xi'an Jiaotong University Yasushi Miyano and Masayuki Nakada Materials System Research Laboratory, Kanazawa Institute of Technology October 18, 2010 Sakai 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 longterm 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 horizontally viscoelastic modulus at various temperatures. Objectives The 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) test to 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. 2

3 The modified TTSP Modified TTSP The master curve is constructed by shifting vertically as well as horizontally the creep compliances measured at various temperatures T to superimpose smoothly to that at the reference temperature T o. 3

4 Auto shifting principle Adjust a and b, the data plots at T 2 moves horizontally and vertically until a smoothest curve is got with the data plots at T 1. The maximal 6th order polynomial is used to fit the master curve.

5 Auto shifting method for creep compliance master curve Time-temperature and temperature shift factors: ( ) H logat o T = H( Tg T) 2.303G T To H 1 1 H 1 1 ( 1 H( Tg T) ) G Tg T o 2.303G T T g ( ) = ( ) + ( ) + ( ) + ( ) H( g- ) logbt T b T T b T T b T T b T T b T T o T T g [ b ( T T ) b ( T T ) b ( T T ) b ( T T ) b log ]( 1-H ( T -T ) ) 4 g 0 3 g 0 2 g 0 1 g 0 0 g G: gas constant H: activation energy T g : glass transition temp. Parameter determination: T g is determined by TMA test, H1, H2, b i(i=0,4) are determined by auto shifting method. 5

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 50,60,70,80,90,100,110 Long term 10s.~1000hr 50,80,100 6

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. 7

8 Creep compliances measured in the medium term and short term Medium term Only horizontal shift Vertical and horizontal shifts Short term Only horizontal shiftc Vertical and horizontal shifts The master curves coincide with the creep compliance measured in the long term at T=50 o C by vertical and horizontal shifting. 8

9 Comparison of shift amount obtained from master curves by both methods TTSP Horizontal shift amount Horizontal shift amount Modified TTSP Vertical shift amount Same horizontal shift amounts and vertical shift amounts can be obtained by vertical and horizontal shifting regardless of test period. 9

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. 10

Master curve of storage modulus by DMA test Modified TTSP Master curve of storage modulus by DMA tests Shift factors Horizontal shift amount Vertical shift amount Test conditions for DMA test

11 Master curve of storage modulus by DMA test Modified TTSP Master curve of storage modulus by DMA tests Shift factors Horizontal shift amount Vertical shift amount Test conditions for DMA test Frequency f Strain Temperature (Hz) (%) T ( C) 0.01~ ~140 Same horizontal shift amounts and vertical shift amounts can be obtained by vertical and horizontal shifting regardless of test period and test methods. 11

12 Comparison of master curves of creep compliances from creep and DMA tests Modified TTSP The master curves of compliance obtained from the creep test and DMA test agree well with each other. 12

Measuring of the storage modulus for the transverse direction of unidirectional CFRP (MR60H/1053) Time-temperature and temperature shift factors: ( ) H 1 1 1 logat o T = H( Tg T) 2.

13 Measuring of the storage modulus for the transverse direction of unidirectional CFRP (MR60H/1053) Time-temperature and temperature shift factors: ( ) H logat o T = H( Tg T) 2.303G T To H 1 1 H 1 1 ( 1 H( Tg T) ) G Tg T o 2.303G T T g ( ) = ( ) + ( ) + ( ) + ( ) H( g- ) logbt T b T T b T T b T T b T T b T T o T T g [ b ( T T ) b ( T T ) b ( T T ) b ( T T ) b log ]( 1-H ( T -T ) ) 4 g 0 3 g 0 2 g 0 1 g 0 0 g G: gas constant H: activation energy T g : glass transition temp. T 0 25 [ o C] T g 162 [ o C] H [kj/mol] H [kj/mol] b E-02 [-] b E-04 [-] b E-05 [-] b E-07 [-] b E-10 [-] 13

14 Creep compliance of matrix resin (MR60H1053) Formulation of creep compliance mg t' t' logdc = log Dc ( t' o, To) + log + t' o t' g where D c : creep compliance T o : reference temperature m r t : reduced time at T o t o : reference reduced time at T o t g : glassy reduced time at T o Rule of mixture Creep compliance of matrix resin: Dc( t ) = 1/ Em( t ) Back-calculation of E m using the rule of mixture : E m : storage modulus of matrix rein 1 1 1, E V E V * 1+ Vy * Vm = V * y = m y ET ft f V f,v m : volume fractions of fiber and matrix E T, E ft : storage moduli in the transverse direction of CFRP and carbon fiber D c (t 0,T 0 ) [1/GPa] t o 1 [min] t g 4.23 x [min] m g [-] m r [-] 14

15 Conclusion 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. Thank you for your attention! 15

Long-term Life Prediction of CFRP Structures Based on MMF/ATM Method

Long-term Life Prediction of CFRP Structures Based on MMF/ATM Method The 5 th Coposites Durability Workshop (CDW-5, October 7 to 20, 200, Kanazawa Institute o Technology Long-ter Lie Prediction o CFRP Structures Based on MMF/ATM Method by Yasushi Miyano and Masayuki Nakada