Fatigue Behavior of Impact-Damaged CarbonFatigue Behavior of Impact Damaged Carbon Fiber / Toughened Epoxy Composites under

Compressive loadingCompressive loading

Toshio Ogasawara, Hisaya Katoh, Sunao Sugimoto, g , y , g ,and Takashi Ishikawa

Ad d C it T h l C t (ACE T C)Advanced Composite Technology Center (ACE-TeC)Japan Aerospace Exploration Agency (JAXA)

Tokyo Japan

CDW-15 (15th Composites Durability Workshop)CDW 15 (15th Composites Durability Workshop) October 17-19, 2010, Kanazawa, Japan

Outline

IntroductionExperimental procedureExperimental procedure

MaterialsCompression after impact (CAI) and fatigue testingCompression after impact (CAI) and fatigue testing

Results and discussionStatic strengthStatic strengthFatigue life (S-N curves)R h ti ti f f ti lif ti di t ib ti fRough estimation of fatigue lifetime distribution of an impact-damaged specimenCAI fatigue lifetime predictionCAI fatigue lifetime prediction

Conclusion

Backgroundg

Fatigue behavior of impact-damaged carbon fiber composite (CFRP) laminates has been studied since thecomposite (CFRP) laminates has been studied since the late 1970s. The fatigue data of early CFRP materials were published in ASTM-STP, NASA reports, and other reports of the literature.

Fatigue behaviors of impact-damaged carbon fiber composites (CMH-17-3G, Vol. 3, Chapter 12.7)p

The endurance limit at 106 cycles turned out as between 50 and 75% of the initial strength.

Damage growth starts very close to the end of the specimen lifetime

S-N curves for the IM7/977-2 and the T800H/F 655 2 material

Damage growth as measured using C-SCAN, versus fatigue cycles for the T800H/ F655 2 material

The ratio between the endurance limit at 106 cycles, and the initial static strength turned out as between 0.50 and 0.75.

Unrealistic fatigue stress (greater than 75% of the static strength) was necessary to produce such measurements.

the T800H/F-655-2 material fatigue cycles for the T800H/ F655-2 material

Therefore, sizing a structure (with these materials) using Ultimate Loads is expected to push fatigue loads down to a level that is likely to limit fatigue problems with low energy impact damage.

This figure shows that, despite the log axis, damage growth starts very close to the end of the specimen lifetime (between 85% and 95% for all cases investigated in this program), with a very high slope.

Backgroundg

Damage growth under cyclic compressive loading is extremely sensitive to stress and it starts very close to theextremely sensitive to stress, and it starts very close to the end of the specimen lifetime.A conventional damage tolerance methodology for g gyaluminum alloys is not applicable for CFRP.“No damage growth” (allowable stress design) is becoming g g ( g ) gthe most common concept for designing composite structures.For this methodology, fatigue strength of composite laminates which have barely visible impact damage (BVID) is important to determine the allowable stressis important to determine the allowable stress.

BVID: The minimum impact damage surely detectable by scheduled inspection

Objectivesj

Experimental results that clarify the fatigue lifetime distribution of impact-damaged CFRP laminates have notdistribution of impact damaged CFRP laminates have not been published because they are sensitive for material suppliers as well as aircraft companies.Statistical methods for predicting CAI fatigue lifetime have not been understood sufficiently.

The objective of this study is to obtain the fatigue lifetime d f i d d b fib i ddata of impact-damaged carbon fiber composites under compressive loading to elucidate the lifetime prediction methodology based on statistical approachesmethodology based on statistical approaches.

Experimental proceduresp p

MaterialsCarbon fiber / toughened epoxy compositesCarbon fiber / toughened epoxy compositesToray T800S/3900-2BQuasi-isotropic laminates [45/0/-45/90]4s (32 ply)(Elastic modulus 49.2 GPa)

Low-speed Impact loading (in accordance with ASTM D7136)

Drop weight type impact testerSpecimen geometrySpecimen geometry100 mm width, 150 mm length6 mm thicknessDrop weightWeight 5.5 kg, Radius 5/8 inchImpact energy 6.7 J/mm

Low speed Impact

Experimental procedurep p

Compression after impact (CAI) testing (ASTM D7137)Test fixture ASTM D7137Test fixture ASTM D7137Electromechanical testing system (250 kN, 5885; Instron Corp.)Number of samples: 9

CAI fatigue testing Servo-hydraulic testing system (500 kN, 8804; Instron Corp.)Test fixture ASTM D7137Side: simple supportSide: simple supportTop & bottom: fixed supportStress ratio R = σmim / σmax=10mim max

Frequency f = 3 HzSinusoidal waveRun-out 107

Number of samples > 36

CAI strength distribution (Weibull plot)g ( p )

1CAI

CAI strength (ASTM D7137)

0

-F))

CAI(m=17.5) Average 272MPa (0.55%）

CV 5.4%m=17.5

2

-1

ln (-

ln (1 NHC

(m=53.2) NHC strength (ASTM D6144)Average 583 MPa (1 18%）

-3

-2 Average 583 MPa (1.18%）CV 1.8 %m=53.2

200 300 400 500 600700

3

))/(exp(1)( 0m

fff SSSF −−=

The Weibull shape parameter (m) for CAI strength is much lower than that for NHC t th

Strength (MPa)

NHC strengths. This result seems to derive from the variation in impact damage size.

S-N curves (peak compressive stress vs. fatigue life)(p p g )

300CAI strength (average 272 MPa)

73% of CAI strength (200 MPa)200

300

s (M

Pa)

73% of CAI strength (200 MPa)200

ak s

tress

100

Pea

Impact 6.7 J/mR = 10f = 3 Hz

Specimen failed at 1 23 × 106 cycles

100 101 102 103 104 105 106 107

CAI fatigue lifetime exhibits relatively flat S-N curves and considerable tt i

Specimen failed at 1.23 × 106 cycles( σmin = 220 MPa )Number of cycles to failure

scattering. Fatigue failures occurred at the 73% of CAI strength, which agrees with the data found in some literatures.

Fatigue life distribution (Weibull plot)g ( p )

1

M = 0.6 Weibull parameters

0

1

F)) 230 MPa

220 MPa Stress(MPa) M N0

Number of samples

200 0.52 2.1 ×106 6

-1

n (-l

n (1

-F 210 0.60 6.6 ×105 8

220 0.60 1.6 ×105 9

230 0 45 2 8 ×104 6

-3

-2

ln

I t 6 7 J/

210 MPa230 0.45 2.8 ×104 6

102 103 104 105 106 107

-3 Impact 6.7 J/m

))/(exp(1)( 0M

fff NNNF −−=

Number of cycles to failure

Weibull plots showing fatigue lifetime distribution for 210, 220, and 230 MPa are h hshown here.

The Weibull shape parameters (M) are apparently independent of the stress.

Evaluation of damage growth using ultrasonic C-scan

CAI-B-04 (σmin = 220 MPa, R=10, f= 3 Hz, fatigue life 1.23 × 106)

34.034.034.0

0 l 105 l 106 l0 cycle 105 cycles 106 cycles

Damage growth is not clearly visible until 106 cycles, even though the lifetime was 1.23 × 106. However, the pulse-echo intensity from damage increases with the number of cycles.

Observations of damage growth using digital video recordingg g

CAI-A-04 (σmin = 200 MPa, R=10, f= 3 Hz, fatigue life 1.67 × 106)

Final failure– 3 cycles– 1000 cycles– 1500 cycles(1.67×106 Cycles)(no growth)

Damage growth to transverse direction was observed very close to the end of the specimen lifetime (1000-1500 cycles before the final failure (1.67 × 106)).Until then, no visible damage growth was observed.

Rough estimation of fatigue lifetime distribution of an impact-damaged specimen (1)p g p ( )

We made two assumptionsThe mode-ratio (GII/GI, GIII/GI) at the critical point of a damage is independent of damage growth during a fatigue test.Stress redistribution attributable to damage growth is ignored.

Based on dimensional analysis, the energy release rate G is roughly approximated by the following relation.

S C i t ( P/A)

Then strength of the impact-damaged specimen, Sf , is given as

02aSG ∝ S : Compressive stress (=P/A)

a0 : Representative damage size(1)

S

Gc is a mixed mode fracture toughness (see appendix).

0/ aGS cf ∝ (2)a0Gc is a mixed mode fracture toughness (see appendix).

S

Rough estimation of fatigue lifetime distribution of an impact-damaged specimen (2)

Paris’ law is applied for damage growth under cyclic compressive loading.nn aSGdNda )()(/ 2/ Δ=Δ∝ (3)SRS )/11( −=Δ

p g p ( )

Integrating Eq. (3) from the initial damage size a0 to the final size af, the fatigue life Nf under a constant stress amplitude ΔS is given as

aSGdNda )()(/ Δ=Δ∝ (3)SRS )/11( −=Δ

life Nf under a constant stress amplitude ΔS is given as

F th l l ti i d b 10

nnff SQSN )/(2 Δ= − (4)

For these calculations, af-n <<a0

-n is assumed because n > 10. Q is a fatigue parameter which depends on the material properties, damage geometries, damage size, specimen geometries, loading constraint, etc. CAI strength (Sf) distribution is given as,

))/(exp(1)( 0m

fff SSSF −−= (5)

Substituting Eq.(4) into Eq. (5) yields the fatigue life distribution function.

))/(exp(1)( 0M

fff NNNF −−= (6)nn SQSN )/()( 2

00 Δ= −)2/( −= nmM0fff ( )

Rough estimation of fatigue lifetime distribution of an impact-damaged specimen (3)

This equation shows that two methods can be used to determine the damage

th t ( )nn SSN )/()( 2

00 Δ= −α

p g p ( )Method B

growth exponent (n).A) Weibull shape parameters m ( CAI

strength) and M (CAI fatigue)

SRS )/11( −=Δ

B) Weibull scale parameters (N0) and compressive stress (S) 300

MP

a) n=31

(6)))/(exp(1)( 0M

fff NNNF −−=

)2/( −= nmM

200

ak s

tress

(M

nn SQSN )/()( 200 Δ= −

100

Pe

)2/( −= nmMMethod A

m = 17.5M = 0.60 n=31

103 104 105 106 107

Weibull scale parameter, N 0

)2/(nmM

(S=210, 220 MPa)

Typical exponent value in delamination growth rate reported in literaturesg p

Detailed investigations using DCB and ENF methods in literatures revealed delamination growth behaviors of carbon fiber composites. Exponent values in d l i ti th t t dl b t 20 d 50delamination growth rate are reportedly between 20 and 50.

n = 20n = 32

J. Schön et al., Comp. Sci. Technol., 60 (2000), 173-184

M. Hojo et al., Comp. Sci. Technol., 29 (1987), 273-92

CAI fatigue lifetime prediction g p

300 F=0.9Mean

Fatigue strength

Static strength 272 MPa

200

300

s (M

Pa)

Lifetime F=10% B-value*1 X 106 183 MPa

(67 %)167 MPa(61 %)

200

ak s

tress

F=0.1

(67 %) (61 %)1 X 107 170 MPa

(63 %)155 MPa(57 %)100

Pea

Impact 6.7 J/mR = 10f = 3 Hz

B-basis value

* Number of samples 9

100 101 102 103 104 105 106 107

f 3 Hz

Fatigue lifetime is predicted for failure probability (F) of 10 %, 50 %,

B-Basis valueAt least 90% of the population of material values is expected to equal or exceed this

Number of cycles to failure

and 90%. Numerical results agree with the experimental data. The ratio between the endurance limit (B-value) at 106 cycles and the initial static strength was estimated as 61%.

qtolerance bound with 95% confidence.

Conclusion

Fatigue lifetime data of impact-damaged carbon fiber / epoxy composites (Impact energy 6 7 J/mm) wereepoxy composites (Impact energy 6.7 J/mm) were obtained. The CAI strength and fatigue lifetime exhibit considerable g gscattering. A simple statistical model was proposed for predicting the p p p p glifetime of impact-damaged CFRP laminates. In spite of rough approximation, the estimates agreed with the

i t l ltexperimental results.The ratio between the endurance limit (B-value) at 106

cycles and the initial static strength was estimated as 61%cycles and the initial static strength was estimated as 61%.

In future the effect of stress ratio on CAI fatigue behaviorsIn future, the effect of stress ratio on CAI fatigue behaviors will be investigated.

AppendixMixed mode fracture toughness Gcg

A mixed mode failure criterion is assumed as follows.

1≥++ IIIIII GGG (1)

S

The energy release rate of each mode (i = I, II, II) is given as

1≥++IIICIICIC GGG

2

(1)a0

02aSG ii κ= (2)

κi : constant (i = 0, I, II, III)

Failure stress Sf is assumed to be given as the following equation.

GS ≥2

S

Substituting Eq.(2) into Eq. (1), a mixed mode fracture toughness Gc is obtained as

cf GaS ≥02

0κ (3)

obtained as1

0

−

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

IIIC

III

IIC

II

IC

Ic GGG

Gκκκ

κ (4)⎠⎝ IIICIICIC GGG