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

Transcription

1 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 Materials Syste Research Laboratory, Kanazawa Institute o Technology Hongneng Cai School o Materials Science and Engineering, Xi'an Jiaotong University October 8, 200 Sakai Meorial Hall, Kanazawa Institute o Technology Japan

2 Objective and Approach o Our Group -Objective: The accelerated testing ethodology (ATM or the atigue lie prediction o CFRP lainates proposed and veriied theoretically and experientally in the previous studies is expanded to the atigue lie prediction o the structures ade o CFRP lainates in this study. - Approach: :. MMF/ATM ethod cobined with our proposed ATM and the ioechanics o ailure (MMF developed by Proessor Sung-Kyu Ha and others is proposed or the atigue lie prediction o the structures ade o CFRP lainates (First presentation on this session. 2. The advanced accelerated testing ethodology (ATM-2 to be applied to the lie prediction o CFRP exposed to an actual loading having general stress and teperature history is proposed based on the viscoelasticity o atrix resin o CFRP (Second presentation on this session. 3. The applicability o odiied tie-teperature superposition principle (odiied TTSP is experientally conired to the viscoelasticity o therosetting resin used as the atrix resin o CFRP. The reliability o DMA test to evaluate easily the viscoelasticity o therosetting resin and the orulation o viscoelasticity are discussed (Third presentation on this session. 4. The sotware progra FLC o MMF/ATM ethod developed by Research Center o Coputational Mechanics, Inc. (RCCM is deonstrated at the poster sessions. 2

3 Prediction procedure by MMF/ATM ethod First step: Deterination o MMF/ATM paraeters Measuring ites Unidirectional CFRP (Orthotropic & linear viscoelastic MMF (Rule o ixture MMF/ATM paraeters o CFRP Carbon ibers (Orthotropic & linear elastic Static and atigue strengths T : Tensile Static and atigue strengths X : Longitudinal tensile X : Longitudinal copressive Y (=Z : Transverse tensile Y (=Z : Transverse copressive Mechanical and theral properties E : Longitudinal elastic odulus G : Transverse elastic odulus α : Theral expansion coeicient V : Volue raction o iber ATM (Tie-tepeature superposition principle The tie and teperature dependent MMF/ATM itical paraeters T, C, T and C, and others o carbon ibers and atrix resin are deterined by easuring the static and atigue strengths and other o unidirectional CFRP at various ties and teperatures based on MMF and ATM. C : Copressive Mechanical and theral properties E, G, α Matrix resin (Isotropic & linear viscoelastic Static and atigue strengths T : Tensile C : Copressive Mechanical and theral properties E, G, α 3

4 Prediction procedure by MMF/ATM ethod Second step: Lie deterination o CFRP structures Master curves o MMF/ATM itical paraeters o CFRP Strengths at tie t: Flow o structural analysis Structure CFRP lainates E, G,, α Stress ε Strain Histories T Tep. T C T C CFRP lainates UD CFRP layer E, G,, α UD CFRP layer Carbon iber and resin E, G,, α 0 0 0µ Stress ε Strain Histories T Tep. Stress and teperature history Carbon iber Resin Stress ε Strain Histories T Tep. The lie o CFRP structure, the ailure point in CFRP structure, the ailure layer in CFRP lainates and the ailure ode in ailed layer are deterined in this step. Equation or judgent - I k=ax,,, T C T C I : Failure index k < k = Stresses at tie t: t k c T C T C t c v : No ailure : Initial ailure : Maxiu tensile stress in carbon iber v : Von Misses stress in atrix resin : Maxiu copressive stress in carbon iber : First stress invariant in atrix resin 4

5 First step: Deterination o MMF/ATM paraeters Measuring ites Unidirectional CFRP (Orthotropic & linear viscoelastic MMF (Rule o ixture MMF/ATM paraeters o CFRP Carbon ibers (Orthotropic & linear elastic Static and atigue strengths T : Tensile Static and atigue strengths X : Longitudinal tensile X : Longitudinal copressive Y (=Z : Transverse tensile Y (=Z : Transverse copressive Mechanical and theral properties E : Longitudinal elastic odulus G : Transverse elastic odulus α : Theral expansion coeicient V : Volue raction o iber ATM (Tie-tepeature superposition principle The tie and teperature dependent MMF/ATM itical paraeters T, C, T and C, and others o carbon ibers and atrix resin are deterined by easuring the static and atigue strengths and other o unidirectional CFRP at various ties and teperatures based on MMF and ATM. C : Copressive Mechanical and theral properties E, G, α Matrix resin (Isotropic & linear viscoelastic Static and atigue strengths T : Tensile C : Copressive Mechanical and theral properties E, G, α 5

6 Mioechanics o ailure (MMF Mioechanics analysis o stresses = M + A T (i (i (i ech ech Mioechanics in iber and atrix Checked points in iber and atrix (i (i x M M2 M3 M4 M5 M6 (i A y M2 M22 M23 M24 M25 M 26 2 A 2 M M M M M M 3 A 3 = + τ T yz A 4 τ M M M M M M τ A 5 A 6 z τ yz M4 M42 M43 M44 M45 M46 xz xz τ M6 M62 M63 M64 M65 M xy 66 τ xy ech ech 6

7 Failure iterion or unidirectional CFRP Invalient Stress based Failure Criterion Stress based Fiber & Matrix Fiber Judgent o Failure Strengths at tie t: I = I 2 = I 3 = 2 3 VM ={0.5[( ( ( ]} 0.5 Strain based J = ε + ε 2 + ε 3 J 2 =ε ε 2 + ε ε 3 + ε 2 ε 3 J 3 = ε ε 2 ε 3 ε VM ={0.5[(ε - ε (ε - ε 3 2 +(ε 2 - ε 3 2 ]} 0.5 Couple Un-Couple Couple Un-Couple Ι Ι J J, Strain based, ε ε VM VM 2 2 VM VM 2 2 Ι VM + Ι VM J ε VM + J εvm Ι = t, Ι Ι = T = T VM Matrix Ι Ι, = Strengths Stresses = c, =C VM, T C T C t c v Ι VM VM = VM = C Equation or judgent - Ι k=ax,,, T C T C k : Failure index k < : No ailure k = Stresses at tie t: T C T C t c v : Initial ailure c t : Tensile strength o ibers : Copressive strength o ibers : Tensile strength o atrix : Copressive strength o atrix : Maxiu tensile stress in carbon iber : Maxiu copressive stress in carbon iber : Von Misses stress in atrix resin : First stress invariant in atrix resin Ι v 7

8 First step: Deterination o MMF/ATM paraeters Measuring ites Unidirectional CFRP (Orthotropic & linear viscoelastic MMF (Rule o ixture MMF/ATM paraeters o CFRP Carbon ibers (Orthotropic & linear elastic Static and atigue strengths T : Tensile Static and atigue strengths X : Longitudinal tensile X : Longitudinal copressive Y (=Z : Transverse tensile Y (=Z : Transverse copressive Mechanical and theral properties E : Longitudinal elastic odulus G : Transverse elastic odulus α : Theral expansion coeicient V : Volue raction o iber ATM (Tie-tepeature superposition principle The tie and teperature dependent MMF/ATM itical paraeters T, C, T and C, and others o carbon ibers and atrix resin are deterined by easuring the static and atigue strengths and other o unidirectional CFRP at various ties and teperatures based on MMF and ATM. C : Copressive Mechanical and theral properties E, G, α Matrix resin (Isotropic & linear viscoelastic Static and atigue strengths T : Tensile C : Copressive Mechanical and theral properties E, G, α 8

9 Mechanical and theral properties o unidirectional CFRP (MR60H/053 and carbon iber (MR60H CFRP MR60H/053 Carbon Fiber MR60H E XX 55[GPa] E XX 279[GPa] E YY 8.8[GPa] E YY 32.3[GPa] E ZZ E YY n XY n YX 0.08 E ZZ E YY ν XY 0.35 ν YZ Proper ties n YZ G XY 4.94[GPa] Proper ties ν XZ G XY ν XY 6.6[GPa] G XZ G XY G XZ G XY G YZ 2.62[GPa] G YZ 9.50[GPa] α XX -0.3x0-6 [/K] α XX x0-6 [/K] α YY 75.x0-6 [/K] α YY 87.5x0-6 [/K] α ZZ α YY α ZZ α YY V 55[%] Measured at roo teperature 9

10 Measuring o the storage odulus or the transverse direction o unidirectional CFRP (MR60H/053 Tie-teperature and teperature shit actors: ( H logat o T = H( Tg T 2.303G T To H H ( 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 ]( -H ( T -T 4 g 0 3 g 0 2 g 0 g 0 0 g G: gas constant H: activation energy T g : glass transition tep. T 0 25 [ o C] T g 62 [ o C] H 0 [kj/ol] H [kj/ol] b 0.3E-02 [-] b -9.85E-04 [-] b E-05 [-] b E-07 [-] b E-0 [-] 0

11 Creep copliance o atrix resin (MR60H053 Forulation o eep copliance g t' t' logdc = log Dc ( t' o, To + log + t' o t' g r where D c : eep copliance T o : reerence teperature t : reduced tie at T o t o : reerence reduced tie at T o t g : glassy reduced tie at T o Rule o ixture Creep copliance o atrix resin: Dc( t = / E( t Back-calculation o E using the rule o ixture :, 0.56 E V E V * + Vy * V = V * y = E y T T D c (t 0,T [/GPa] t o [in] t g 4.23 x 0 0 [in] g 0.06 [-] E : storage odulus o atrix rein V,V : volue ractions o iber and atrix r [-] E T, E T : storage oduli in the transverse direction o CFRP and carbon iber

12 Tensile strength or the longitudinal direction o unidirectional CFRP (MR60H/053 X ( t T N R P log,,,, = log ', o ( t T * D ( t, To D ( t', T o o o nr log c o o ( R n log 2N 2 kd + log ln α ( P ISO 527 (JIS K7073 Fitting paraeters o [MPa] 2924 n r 0.40 n 0.07 α s 25.7 α 7.7 2

13 Copressive strength or the longitudinal direction o unidirectional CFRP (MR60H/053 X ( t T N R P log,,,, = log ', o ( t T * D ( t, To D ( t', T o o o nr log c o o ( R n log 2N 2 kd + log ln α ( P ISO 425 (JIS K7074 (With cushion Fitting paraeters o [MPa] 2399 n r 0.58 n 0.04 α s 40.0 α 7.2 3

14 Tensile strength or the transverse direction o unidirectional CFRP (MR60H/053 Y ( t T N R P log,,,, = log ', o ( t T * D ( t, To D ( t', T o o o nr log c o o ( R n log 2N 2 kd + log ln α ( P ISO 425 (JIS K7074 Fitting paraeters o [MPa] 24 n r 3.05 n 0.08 α s 2.2 α 4.4 4

15 Copressive strength or the transverse direction o unidirectional CFRP (MR60H/053 Y ( t T N R P log,,,, = log ', o ( t T * D ( t, To D ( t', T o o o nr log c o o ( R n log 2N 2 kd + log ln α ( P Fitting paraeters o [MPa] 25 n r 3.2 n 0.05 α s 3.3 α 7.6 5

16 Master curves o MMF/ATM itical paraeters (MR60H/053 T (Tensile strength o iber T (Tensile strength o atrix C (Copressive strength o iber C (Copressive strength o iber 6

17 Second step: Lie deterination o CFRP structures Master curves o MMF/ATM itical paraeters o CFRP Strengths at tie t: Flow o structural analysis Structure CFRP lainates E, G,, α Stress ε Strain Histories T Tep. T C T C CFRP lainates UD CFRP layer E, G,, α UD CFRP layer Carbon iber and resin E, G,, α 0 0 0µ Stress ε Strain Histories T Tep. Stress and teperature history Carbon iber Resin Stress ε Strain Histories T Tep. The lie o CFRP structure, the ailure point in CFRP structure, the ailure layer in CFRP lainates and the ailure ode in ailed layer are deterined in this step. Equation or judgent - I k=ax,,, T C T C I : Failure index k < k = Stresses at tie t: t k c T C T C t c v : No ailure : Initial ailure : Maxiu tensile stress in carbon iber v : Von Misses stress in atrix resin : Maxiu copressive stress in carbon iber : First stress invariant in atrix resin 7

18 Prediction and observation o ailure position and ode in quasiisotropic CFRP lainates with a central hole under copressive load kt : Fiber tensile ailure index kc : Fiber copression ailure index kt : Matrix tensile ailure index kc : Matrix copression ailure index Static load condition T=25 V=0.0/in Stacking sequence [45/0/-45/90]2S The predicted results that the copressive ailure occurs in 0o layers at the edge o hole agree well with the results by observation. 8

19 Coparison o predicted and experiental results or OHC static and atigue strengths o quasi-isotropic CFRP lainates The open hole copression static and atigue strengths o quasi-isotropic CFRP lainates predicted by MMF/ATM ethod agree well with the experiental results. Thereore, it is cleared that MMF/ATM ethod has the possibility to be the strong tool to the atigue lie prediction o the structures ade o CFRP lainates. 9

20 Conclusions -Conclusion: : The accelerated testing ethodology (ATM or the atigue lie prediction o CFRP lainates proposed and veriied theoretically and experientally in the previous studies was expanded to the atigue lie prediction o the structures ade o CFRP lainates in this study. - Major Accoplishents:. MMF/ATM ethod cobined with our proposed ATM and the ioechanics o ailure (MMF developed by Proessor Sung-Kyu Ha and others was proposed or the atigue lie prediction o the structures ade o CFRP lainates. 2. The aster curves o MMF/ATM itical paraeters o CFRP were deterined by easuring the static and atigue strengths at elevated teperatures in the longitudinal and transverse, tension and copression directions o unidirectional CFRP. 3. The atigue strengths o quasi-isotropic CFRP lainates with a central hole under copression load as an exaple o CFRP structures were easured at elevated teperatures, and these experiental data agreed well with the predicted results by using the aster curves o MMF/ATM itical paraeters o CFRP based on MMF/ATM ethod. 4. It was cleared that MMF/ATM ethod has the possibility to be the strong tool to the atigue lie prediction o the structures ade o CFRP lainates. - Acknowledgents: Oice o Naval Research (ONR and Japan Aerospace Exploration Agency (JAXA 20