Mechanisms Based Modeling Approaches to Multiaxial Fatigue ...
Transcript of Mechanisms Based Modeling Approaches to Multiaxial Fatigue ...
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%
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10000000
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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)
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200%400%
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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
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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
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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]
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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]
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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]
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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
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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