Long-term Life Prediction of CFRP Structures Based …...MMF/ATM method combined with our proposed...

byYasushi Miyano and Masayuki Nakada

Materials System Research Laboratory, Kanazawa Institute of Technology

Hongneng CaiSchool of Materials Science and Engineering, Xi'an Jiaotong University

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

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

Objective and Approach of Our Group

:

- Objective:

The accelerated testing methodology (ATM) for the fatigue life prediction of CFRP laminates proposed and verified theoretically and experimentally in the previous studies is expanded to the fatigue life prediction of the structures made of CFRP laminates in this study.

- Approach:

1. MMF/ATM method combined with our proposed ATM and the micromechanics of failure (MMF) developed by Professor Sung-Kyu Ha and others is proposed for the fatigue life prediction of the structures made of CFRP laminates (First presentation on this session).

2. The advanced accelerated testing methodology (ATM-2) to be applied to the life prediction of CFRP exposed to an actual loading having general stress and temperature history is proposed based on the viscoelasticity of matrix resin of CFRP (Second presentation on this session).

3. The applicability of modified time-temperature superposition principle (modified TTSP) is experimentally confirmed to the viscoelasticity of thermosetting resin used as the matrix resin of CFRP. The reliability of DMA test to evaluate easily the viscoelasticity of thermosetting resin and the formulation of viscoelasticity are discussed (Third presentation on this session).

4. The software program “FLC” of MMF/ATM method developed by Research Center of Computational Mechanics, Inc. (RCCM) is demonstrated at the poster sessions.

3

Prediction procedure by MMF/ATM methodFirst step: Determination of MMF/ATM parameters

Unidirectional CFRP(Orthotropic & linear viscoelastic)

Static and fatigue strengthsX : Longitudinal tensile

Y (=Z) : Transverse tensileX’ : Longitudinal compressive

Y’ (=Z’) : Transverse compressive

Vf : Volume fraction of fiberVf : Volume fraction of fiber

Mechanical and thermal propertiesE : Longitudinal elastic modulusG : Transverse elastic modulusα : Thermal expansion coefficient

Measuring items

Matrix resin(Isotropic & linear viscoelastic)

MMF/ATM parameters of CFRP

TTmm : TensileCCmm : Compressive

Carbon fibers(Orthotropic & linear elastic)

TTff : TensileCCff : Compressive

EEff, , GGff, , ααff

Mechanical and thermal properties

Static and fatigue strengths


EEmm, , GGmm, , ααmm


ATM(Time-tempeature

superposition principle)

MMF(Rule of mixture)

The time and temperature dependent MMF/ATM critical parameters Tf, Cf, Tm and Cm, and others of carbon fibers and matrix resin are determined by measuring the static and fatigue strengths and other of unidirectional CFRP at various times and temperatures based on MMF and ATM.


4

Carbon fiber

Resin

UD CFRP layerCFRP laminatesStructure

: Failure index

Equation for judgment

Prediction procedure by MMF/ATM methodSecond step: Life determination of CFRP structures

EE,, GG, α, αCFRP laminates

EE,, GG, α, αUD CFRP layer

EE,, GG, α, αCarbon fiber and resin

Master curves of MMF/ATM critical parameters of CFRP Strengths at time t:

10m 10mm 10µm

Tf Cf Tm CmTTff CCff TTm m CCmm

f f m mt c 1 vm

f f m m

-=max , , ,IkT C T C

σ σ σ

m1I

mvmσ : Von Misses stress

in matrix resin

Stresses at time t:

The life of CFRP structure, the failure point in CFRP structure,the failure layer in CFRP laminates and the failure mode in failed layer are determined in this step.


Flow of structural analysis

: No failure1k <: Initial failure1k =

: Maximum tensile stress in carbon fiber

: Maximum compressive stressin carbon fiber

: First stress invariantin matrix resin

σ Stressε Strain HistoriesT Temp.

σσ StressStressε ε StrainStrain HistoriesHistoriesT T Temp.Temp.

Stress and temperature history






k

σtf

σcf

5

First step: Determination of MMF/ATM parameters







Measuring items












ATM(Time-tempeature





6

(i) (i) (i)mech mechM A Tσ σσ σ= + ∆

111 12 13 14 15 16

221 22 23 24 25 26

331 32 33 34 35 36

41 42 43 44 45 46

51 52 53 54 55 56

61 62 63 64 65 66mech

(i) (i)M M M M M MM M M M M MM M M M M MM M M M M MM M M M M MM M M M M M

x

y

z

yzyz

xzxz

xyxy

σ σσ σ

σσττττττ σ

=

1

2

3

4

5

6mech

(i)AAAAAA

T

σ

∆

+

Micromechanics in fiber and matrix

Checked points in fiber and matrix

Micromechanics of failure (MMF)Micromechanics analysis of stresses

7

Failure criterion for unidirectional CFRP

Invalient Failure Criterion

Stress based

Strain based

Cou

ple

Cou

ple

Un-

Cou

ple

Un-

Cou

ple

2 2

1

1

1 ε

+ ≤ ε VM

cr crVM

JJ

1

1

1≤cr

JJ

1ε≤

εVMcrVM,

1

1

1≤cr

ΙΙ

1σ≤

σVMcrVM,

2 2

1

1

1 σ

+ ≤ σ VM

cr crVM

ΙΙ

Fiber & Matrix Judgment of Failure

Fiber

Matrix

1 = σftΙ ,

fVM cσ = σ

1 =crfTΙ cr

VM fCσ =,

=crVM mCσ,1 =cr

mTΙ

= mVM VMσ σ1 1= mΙ Ι ,

σVM={0.5[(σ 1- σ 2)2

+ (σ 1- σ 3)2

+(σ 2- σ 3)2]}0.5

I1 = σ1 + σ 2 + σ3

I3 = σ1 σ2 σ 3

Stress based

Strain based

εVM={0.5[(ε 1- ε 2)2

+ (ε 1- ε 3)2

+(ε 2- ε 3)2]}0.5

J1 = ε1 + ε 2 + ε3

J2 =ε1 ε 2 + ε1 ε 3+ ε2 ε 3

J3 = ε1 ε2ε3

I2 = σ1 σ 2 + σ1 σ 3+ σ2 σ 3

Stresses

mvmσ : Von Misses stress in matrix resinm1Ι : First stress invariant in matrix resin

: Maximum tensile stress in carbon fiber ftσ

: Maximum compressive stress in carbon fiberσfc

Strengths at time t:

Equation for judgmentf f m mt c 1 vm

f f m m

-=max , , , σ σ σ

kT C T C

Ι

Stresses at time t:

: Failure index: No failure1k <: Initial failure1k =

k

TTff CCff TTm m CCmm

m1Ι m

vmσftσσf

c

TTff : Tensile strength of fibersCCff : Compressive strength of fibersTTm m : Tensile strength of matrix CCmm : Compressive strength of matrix

Strengths

8

First step: Determination of MMF/ATM parameters







Measuring items












ATM(Time-tempeature





9

Mechanical and thermal properties of unidirectional CFRP (MR60H/1053) and carbon fiber (MR60H)

CFRP MR60H/1053

Properties

EXX 155[GPa]EYY 8.18[GPa]

EZZ EYY

nXY 0.327nYX 0.018nYZ 0.559

GXY 4.94[GPa]GXZ GXY

GYZ 2.62[GPa]

αXX -0.3x10-6[1/K]

αYY 75.1x10-6[1/K]αZZ αYY

Vf 55[%]

9

Carbon Fiber MR60H

Properties

EfXX 279[GPa]EfYY 32.3[GPa]EfZZ EfYY

νfXY 0.315νfYZ 0.700νfXZ νfXY

GfXY 6.61[GPa]

GfXZ GfXY

GfYZ 9.50[GPa]αfXX -0.344x10-6 [1/K]αfYY 87.5x10-6 [1/K]αfZZ αfYY

Measured at room temperature

1010

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 ofunidirectional CFRP (MR60H/1053)

111111

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 temperaturet’: reduced time at To

t’o: reference reduced time at To

t’g: glassy reduced time at To

where

1212

Tensile strength for the longitudinal direction of unidirectional CFRP (MR60H/1053)

X

ISO 527（JIS K7073）

( )( )

( )( )

( )

f o f f

fo o o

*o

rc o o

ff

D

f

log , , , ,

log ' ,

, log

' ,

2(1 ) log2 1

1 log ln 1

t T N R P

t T

D t Tn

D t T

NR nk

P

′σ

= σ

′−

−

− −

+ − − α

Fitting parameters

σｆo [MPa] 2924nr 0.40nf 0.07

αs 25.7

αf 7.7

1313

X’

ISO 14125(JIS K7074)

(With cushion)

Compressive strength for the longitudinal direction of unidirectional CFRP (MR60H/1053)

( )( )

( )( )

( )

f o f f

fo o o

*o

rc o o

ff

D

f

log , , , ,

log ' ,

, log

' ,

2(1 ) log2 1

1 log ln 1

t T N R P

t T

D t Tn

D t T

NR nk

P

′σ

= σ

′−

−

− −

+ − − α

Fitting parameters

σｆo [MPa] 2399nr 0.58nf 0.04

αs 40.0

αf 17.2

1414

Y

ISO 14125(JIS K7074)

Tensile strength for the transverse direction of unidirectional CFRP (MR60H/1053)

( )( )

( )( )

( )

f o f f

fo o o

*o

rc o o

ff

D

f

log , , , ,

log ' ,

, log

' ,

2(1 ) log2 1

1 log ln 1

t T N R P

t T

D t Tn

D t T

NR nk

P

′σ

= σ

′−

−

− −

+ − − α

Fitting parameters

σｆo [MPa] 124nr 3.05nf 0.08

αs 12.2

αf 4.4

1515

Y’

Compressive strength for the transverse direction of unidirectional CFRP (MR60H/1053)

( )( )

( )( )

( )

f o f f

fo o o

*o

rc o o

ff

D

f

log , , , ,

log ' ,

, log

' ,

2(1 ) log2 1

1 log ln 1

t T N R P

t T

D t Tn

D t T

NR nk

P

′σ

= σ

′−

−

− −

+ − − α

Fitting parameters

σｆo [MPa] 215nr 3.21nf 0.05

αs 13.3

αf 7.6

16

TTff (Tensile strength of fiber) TTmm (Tensile strength of matrix)

16CCff (Compressive strength of fiber) CCmm (Compressive strength of fiber)

Master curves of MMF/ATM critical parameters(MR60H/1053)

17

Carbon fiber

Resin

UD CFRP layerCFRP laminatesStructure

: Failure index

Equation for judgment

Second step: Life determination of CFRP structures

EE,, GG, α, αCFRP laminates

EE,, GG, α, αUD CFRP layer

EE,, GG, α, αCarbon fiber and resin

Master curves of MMF/ATM critical parameters of CFRP Strengths at time t:

10m 10mm 10µm


f f m mt c 1 vm

f f m m

-=max , , ,IkT C T C

σ σ σ

m1I

mvmσ : Von Misses stress

in matrix resin

Stresses at time t:



Flow of structural analysis

: No failure1k <: Initial failure1k =

: Maximum tensile stress in carbon fiber

: Maximum compressive stressin carbon fiber

: First stress invariantin matrix resin



Stress and temperature history






k

σtf

σcf

1818

Prediction and observation of failure position and mode in quasi-isotropic CFRP laminates with a central hole under compressive load

The predicted results that the compressive failure occurs in 0o layers at the edge of hole agree well with the results by observation.

kTf : Fiber tensile failure indexkCf : Fiber compression failure indexkTm : Matrix tensile failure indexkCm : Matrix compression failure index

Static load conditionT=25℃V=0.01mm/min

Stacking sequence [45/0/-45/90]2S

1919

Comparison of predicted and experimental results for OHC static and fatigue strengths of quasi-isotropic CFRP laminates

The open hole compression static and fatigue strengths of quasi-isotropic CFRP laminates predicted by MMF/ATM method agree well with the experimental results. Therefore, it is cleared that MMF/ATM method has the possibility to be the strong tool to the fatigue life prediction of the structures made of CFRP laminates.

The open hole compression static and fatigue strengths of quasi-isotropic CFRP laminates predicted by MMF/ATM method agree well with the experimental results. Therefore, it is cleared that MMF/ATM method has the possibility to be the strong tool to the fatigue life prediction of the structures made of CFRP laminates.

20

Conclusions

:

-Conclusion:

The accelerated testing methodology (ATM) for the fatigue life prediction of CFRP laminates proposed and verified theoretically and experimentally in the previous studies was expanded to the fatigue life prediction of the structures made of CFRP laminates in this study.

- Major Accomplishments:

1. MMF/ATM method combined with our proposed ATM and the micromechanics of failure (MMF) developed by Professor Sung-Kyu Ha and others was proposed for the fatigue life prediction of the structures made of CFRP laminates.

2. The master curves of MMF/ATM critical parameters of CFRP were determined by measuring the static and fatigue strengths at elevated temperatures in the longitudinal and transverse, tension and compression directions of unidirectional CFRP.

3. The fatigue strengths of quasi-isotropic CFRP laminates with a central hole under compression load as an example of CFRP structures were measured at elevated temperatures, and these experimental data agreed well with the predicted results by using the master curves of MMF/ATM critical parameters of CFRP based on MMF/ATM method.

4. It was cleared that MMF/ATM method has the possibility to be the strong tool to the fatigue life prediction of the structures made of CFRP laminates.

- Acknowledgments:

Office of Naval Research (ONR) and Japan Aerospace Exploration Agency (JAXA)

Date post:	03-May-2020
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

Long-term Life Prediction of CFRP Structures Based …...MMF/ATM method combined with our proposed...

Documents