Mechanisms Based ModelingApproaches to Multiaxial Fatigue

of Wind Turbine Rotor Blades

Ramesh Talreja

Department of Aerospace Engineering

Texas A&M University, College Station, Texas

Marino Quaresimin

Department of Management and Engineering, University of Padova, Italy

Contents

• Introduction & Background

• The dismal state of multiaxial fatigue in composites

• A rational way forward – mechanisms based

• Results & Status

• Future direction

• Conclusion

Multiaxial Fatigue

Cruciform Tubular

Test samples

Stress Biaxiality Ratios

In material coordinates:

λ1=σ2/1 (normal)

λ2= σ6/1 (shear)

12= σ6/2 (shear)

x

q

y

1

z3

O

2

x

y

z

O

x

y

z

O

x

y

z

O

X

Y

Z=3

1

2

The dismal state of multiaxial fatigue

• Most current approaches are essentially modified “metal fatigue”, lacking THINK COMPOSITES content.

• Schemes, formulas, ad-hoc ideas with poor, uncertain predictive capability.

References:• Fatigue behaviour and life assessment of composite laminates under

multiaxial loadings, M. Quaresimin, L.Susmel, R. Talreja International Journal of Fatigue, 32 (2010) 2–16

• M. Quaresimin, R. Talreja “Fatigue of fiber reinforced composites under multiaxial loading” in Fatigue life prediction of composites and composite structures, A.Vassilopoulos Ed. , 2010 WoodheadPublishing Ltd,, 2010, p. 334-389.

Current approaches:Phenomenological failure criteria

• Tsai-Hill criterion

• Smith-Pascoe criterion

• Fewaz-Ellyin Criterion

Polynomial function based criterion

s s s

1 2 1 s 6

Nf Nf

1Õ 1Ó 2Õ

2Ó

Static

failure

envelope

s1=f1(Nf) s6=f6(Nf)

s1=f1(Nf) s2=f2(Nf)

Fatigue

failure

envelopes

- M. J. Owen, J. R. Griffiths, M.S. Found, I. C. C. M. (1975)

- M.J. Owen, J.R. Griffiths. Journal of Materials Science 1978

- M. J. Owen, J. R. Griffiths, M. S. Found 35th SPI (1980)

- D.F. Sims, V.H. Brogdon. ASTM STP 636 (1997)

Smith & Pascoe (1989)

0%

-200%

-400%

200%400%

100

1000

10000

100000

1000000

10000000

100 1000 10000 100000 1000000 10000000

Nf,e [cycles]

Nf

[cycle

s]

.

Aboul Wafa et al.[1]

Amijima et al.[2]

Kawakami et al.[3]

Kawai Taniguchi [16]

Smith Pascoe [4]

2

f6

2

fSE

2

21

12

21

1

12

1

2a,1

NfNf2

EEEE

1

1

s

Fawaz & Ellyin (1994)

0%

-200%

-400%

200%400%

10

100

1000

10000

100000

1000000

10000000

10 100 1000 10000 100000 1000000 1000000

0Nf,e [cycles]

Nf [

cycl

es]

Aboul Wafa et al.[1]

Amijima et al. [2]

Kawai Taniguchi [16]

Kawakami et al.[3]

Smith Pascoe [4]

external multiaxiality

s(T, C, q, R, N)=f(T, C, q[br+g(R) mr log(N) ]

Our Approach

Step 1. Develop mechanisms based Fatigue Life Diagrams to clarify:

• Effects of multiaxial loading• Conditions governing long fatigue life ( > 107 cycles)Step 2. Develop mechanics models guided by Step 1 to

quantitatively predict:• Effects of shear on tension-tension, tension-

compression and compression-compression fatigue• Effects of normal stresses on torsional fatigueStep 3. Develop failure criteria for long term fatigue life

under multiaxial loading.

The Team

Texas A&M University

• Aerospace Engineering (Talreja, Huang)

University of Padova – Vicenza, Italy

• Mechanical Engineering (Quaresimin, Carraro)

Technical University of Denmark

• Risø Laboratory for Sustainable Energy (Brøndsted, Sørensen)

Luleå University, Sweden

• Polymer Engineering (Varna)

Step 1. Mechanisms based Fatigue Life Diagram

Log N

max Noprogressive damage

Noevovig damage

Case 1: Unidirectional composites, on-axis loading

Fiber-bridged matrix cracking

On-axis fatigue life diagram modified by λ1 and λ2

Log N

1 > 0 2 > 0

max Noprogressive damage

Noevovig damage

Fiber-bridged matrix cracking

1 s 2, a

s1, a

2 s 6, a

s1, a

12 s 6, a

s 2, a

Off-axis fatigue life diagram modified by λ1, λ2 and λ12

λ1 , λ2

λ12

Experimental Programat University of Padova (Quaresimin)

• Start with cyclic transverse stress, σ2, and study the effect of λ12=σ6/σ2

• Specimen type: tubular

Fiber layups:

UD tubes: [904]

TU tubes [0F/90U,3]

TUT tubes: [0F/90U,3/0F]

Three fiber lay-ups

• UD tubes: [904]• Sudden failure, no damage evolution, damage

initiation from surface defects

• TU tubes [0F/90U,3] • Stable crack propagation and multiple cracking,

some influence of surface defects

• TUT tubes: [0F/90U,3/0F]• Stable crack propagation and multiple cracking,

negligible influence of surface defects

Specimen manufacturing

Samples produced by mandrel wrapping of glass/epoxy UD tapes and fabrics then cured in autoclave (1 hour at 140ºC and 6 bars) without

vacuum bag:some resin rich areas but no voids

Ext diameter 22 mmInt diameter 19 mmTab diameter 24 mm

5

50

100 1000 10000 100000 1000000 10000000

Tra

nsv

erse

str

ess

on

90°

pli

es [

MP

a]

Number of cycles, N

L

0L

1

λ12 = 0

λ12 = 1

λ12 = 2λ12

Fatigue curves (6 on 2 ) at R=0 [90]4 tubes

final failure ≈ crack initiation

WOHLER CURVES - tubes with one inner layer of fabric and three layer of 90 UD Tapes

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

10 100 1000 10000 100000 1000000 10000000

Log(Nf)

б2

[M

Pa

]

120

120.5

121

122

12

Fatigue testing (6 on 2 ) at R=0 [0F/903]

0.631.252.5

final failure fiber controlled

LED internal lighting of tubes damage observation

Fatigue curves (6 on 2 ) at R=0 – [0F/903]

5

50

10 100 1000 10000 100000 1000000 10000000

tran

sver

se s

tres

s s

2in

90°p

lies

[MP

a]

cycles for nucleation of cracks

l12=0

l12=0.63

λ12 = 0

λ12 = 0.63

λ12 = 1.25

λ12 = 2.5

12

Fatigue curves (6 on 2 ) at R=0 [0F/903/0F]

5

50

100 1000 10000 100000 1000000 10000000

Tran

sverse

str

ess

on

90

pli

es

[MP

a]

Number of cycles, N

l 1 2 = 0

l 1 2 = 1

l 1 2 = 2

λ12 = 0

λ12 = 1

λ12 = 212

Cycles for crack initiation

Comparison between [904] and [0F/903/0F]

5

50

100 1000 10000 100000 1000000 10000000

tra

nsv

erse

str

ess

on

90

pli

es [

MP

a]

number of cycles, N

: TUT tubes

dashed lines: UD tubes

λ12 = 0

λ12 = 1

λ12 = 2

Cycles for crack initiation

Crack propagation

0

20

40

60

80

100

0 50000 100000 150000

cycles of crack propagation, Np

λ12 = 0

λ12 = 0.5

λ12 = 1

λ12 = 1.5

cra

ck a

ng

le[d

egre

es]

2α

σ2 on 90º plies = 30 MPa

3-step Approach

Step 1. Develop mechanisms based Fatigue Life Diagrams to clarify:

• Effects of multiaxial loading• Conditions governing long fatigue life ( > 107 cycles)Step 2. Develop mechanics models guided by Step 1 to

quantitatively predict:• Effects of shear on tension-tension, tension-

compression and compression-compression fatigue• Effects of normal stresses on torsional fatigueStep 3. Develop failure criteria for long term fatigue life

under multiaxial loading.

Conclusion

• Grand plan for mechanisms based approach is in place

• Effects of combined transverse and shear stresses investigated

• Modeling efforts are ongoing, soon to be reported

• Phenomenological approaches not recommended