M. Kawai Institute of Engineering Mechanics and Systems,
description
Transcript of M. Kawai Institute of Engineering Mechanics and Systems,
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A New Strength Parameter and a Damage Mechanics Model for Off-Axis Fatigue of Unidirectional
Composites Under Different Stress Ratios
M. Kawai
Institute of Engineering Mechanics and Systems,
University of Tsukuba, Tsukuba 305-8573, JAPAN
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Background
Objectives
Experimental Results
Modeling & Verification
Conclusions
Strength Measures
Outline
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UD Lamina:
Fatigue Failure Analysis of Composites
MD Laminate:
Fiber
Matrix
Local off-axis loading of inclined plies
Matrix-Dominated Behavior
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Loading Mode Dependence of Fatigue
time
Service Loading of Structural Laminates
(in general)
・ Alternating stress (Amplitude)
・ Mean stress
・ Waveshape
・ Frequency
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Effects of Mean Stress on Off-Axis Fatigue Behavior of PMCs
—Experimental Data—
Unidirectional Carbon/Epoxy
(Kawai, M., Suda, H. and Koizumi, M., 2002)
Unidirectional Glass/Epoxy
(El Kadi, H. and Ellyin, F., 1994)
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Fatigue Model Considering Mean Stress Effects
Mean Stress Effects on Off-Axis Fatigue Behavior of UD PMCs
for the range –1 ≤ R ≤ 1
Objectives
Fatigue Strength Measure
Stress Ratio:Stress Ratio:
time
max
min
Mean
R min
max
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Effects of Mean Stress on Off-Axis Fatigue Behavior of PMCs
—Experimental Data—
Unidirectional Carbon/Epoxy
(Kawai, M., Suda, H. and Koizumi, M., 2002)
Unidirectional Glass/Epoxy
(El-Kadi, H. and Ellyin, F., 1994)
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10
50 100 50
21
(unit:mm)
50 100 50
2120
(unit:mm)
= 0°
= 10 , 15 , 30 , 45 , 90°
Carbon/Epoxy (T800H/2500)
Specimens:
Material System
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Comparison Between Tensile and Compressive Strengths
0
0.5
1
1.5
2
0 10 15 30 45 90
T800H/2500
TensionCompression
Fra
ctur
e st
ress
x
f , M
Pa
Fra
ctur
e st
ress
x
f , M
Pa
Fra
ctur
e st
ress
x
f , M
Pa
Fra
ctur
e st
ress
x
f , M
Pa
xU
TS /
xU
TS ,
xU
CS /
xU
TS
Off-axis angle , degree
R = - 0.3R = - 1.0
Experimental (RT)
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Off-Axis Fatigue Testing
・ Load control
R = 0.5 R = 0.1
・ Frequency 10 Hz
・ Temperature RT
・ Stress ratio R = 0.5, 0.1, –0.3 ( = 0°) R = 0.5, 0.1, –1.0 ( > 0°)
Fatigue Testing on CFRP
time
max
min
R = –0.3, –1.0
time
max
min
time
max
min
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Antibuckling Guide Fixtures
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Effects of Stress Ratio on Off-Axis Fatigue (CFRP)
Nf
0
50
100
150
200
100 101 102 103 104 105 106 107
Fatigue = 30 (UD) RT 10Hz L/w=5
max ,
MPa
● R = 0.5● R = 0.1● R = -1.0
0
20
40
60
80
100
100 101 102 103 104 105 106 107
Fatigue = 45 (UD) RT 10Hz L/w=5
Nf
max ,
MPa
● R = 0.5● R = 0.1● R = -1.0
0
20
40
60
80
100
100 101 102 103 104 105 106 107
Fatigue = 90 (UD) RT 10Hz L/w=5
Nf
max ,
MPa
● R = 0.5● R = 0.1● R = -1.0
Nf
0
100
200
300
400
500
100 101 102 103 104 105 106 107
Fatigue = 15 (UD) RT 10Hz L/w=5
max ,
MPa
● R = 0.5● R = 0.1● R = -1.0
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T-T Fatigue Failure Morphology (CFRP)
R = 0.5 R = 0.1
0°
10°
15°
30°
45°
90°
Failure along fibers
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T-C Fatigue Failure Morphology (CFRP)
( R = -0.3 )
0° 30°
10° 45°
15° 90°
Failure along fibersOut-of-plane shear, Microbuckling
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0
50
100
150
200
250
300
350
400
100 101 102 103 104 105 106
m
ax,
MP
a
Nf
E-Glass/Epoxy (RT)
Experimental (Kadi & Ellyin, 1994)(3.3 Hz)
▲ R = 0.5○ R = 0× R = -1
= 19°
0
20
40
60
80
100
100 101 102 103 104 105 106 107
m
ax,
MP
a
Nf
E-Glass/Epoxy (RT)
Experimental (Kadi & Ellyin, 1994)(3.3 Hz)
▲ R = 0.5○ R = 0× R = -1
= 45°
0
20
40
60
80
100
100 101 102 103 104 105 106 107
m
ax,
MP
a
Nf
E-Glass/Epoxy (RT)
Experimental (Kadi & Ellyin, 1994)(3.3 Hz)
▲ R = 0.5○ R = 0× R = -1
=71°
0
20
40
60
80
100
100 101 102 103 104 105 106 107
m
ax,
MP
a
Nf
E-Glass/Epoxy (RT)
Experimental (Kadi & Ellyin, 1994)(3.3 Hz)
▲ R = 0.5○ R = 0× R = -1
= 90°
Effects of Stress Ratio on Off-Axis Fatigue (GFRP)
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Non-Dimensional Fatigue Strength Measure
Strength Ratio:
s* max
B
max
B
Maximum fatigue stress
Static strength
where
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Off-Axis S-N Relationship Using Strength Ratio
Unidirectional T800H/Epoxy (R = 0.1)
101
102
103
104
105
100 101 102 103 104 105 106 107
Nf
m
ax,
MP
a
Experimental (Kawai & Suda)(RT, f = 10 Hz, R = 0.1)
T800H/2500
○ 0°▲ 10°◇ 15°
● 30°▽ 45°■ 90°
s* max
B
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
○ 0° ▲ 10° ◇ 15° ● 30° ▽ 45° ■ 90°
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz, R = 0.1)
m
ax/
B(e
xp)
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Effect of Stress Ratio on Off-Axis S-N Relationship
Unidirectional T800H/Epoxy
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
m
ax/
B(e
xp)
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
+ R = -0.3
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Modified Strength Ratio:
S* a
B m
Non-Dimensional Fatigue Strength Measure
a 12
(1 R)max
m 12
(1 R)max
where
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S*
12
(1 R)s*
1 12
(1 R)s*
S*
max
B
1
S*
R 1s*
Master S-N RelationshipR = –1
Modified Strength Ratio
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Unidirectional T800H/Epoxy
Off-Axis S-N Relationship Using
Modified Strength Ratio
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
m
ax/
B(e
xp)
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
+ R = -0.3
S* a
B m
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
S*
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
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Unidirectional Glass/Epoxy (R = 0)
101
102
103
104
105
100 101 102 103 104 105 106 107
E-Glass/Epoxy Experimental (Kadi & Ellyin) (RT, f = 3.3 Hz, R = 0)
m
ax
Nf
○ 0° ▽ 71° ▲ 19° ■ 90° ◇ 45°
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
m
ax/
B(e
xp)
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz, R = 0)
○ 0° ▲ 19° ◇ 45° ▽ 71° ■ 90°
s* max
B
Off-Axis S-N Relationship Using Strength Ratio
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Off-Axis S-N Relationship Using
Modified Strength Ratio
Unidirectional Glass/Epoxy
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
m
ax/
B(e
xp)
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
S*
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
S* a
B m
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A Unified Fatigue Strength Measure
—Experimental—
Modified Strength Ratio:
S* a
B m
Stress ratio effect
Fiber orientation effect
(for the tested range of R)
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Tsai-Hill Static Failure Criterion:
11
X
2
11 22
X 2 22
Y
2
12
S
2
1
Non-Dimensional Effective Stress
Y
2
1
X
X: Longitudinal strength
Y: Transverse strength
S: Shear strength
Non-Dimensional Effective Stress:
* 11
X
2
11 22
X 2 22
Y
2
12
S
2
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Theoretical Strength Ratio
Off-Axis Fatigue Loading of UD Composites
* x 1
Non-Dimensional Effective Stress
* x Static Failure Condition:
B ( pred ) 1
max
* max max
1
max
B ( pred )
Maximum Non-Dimensional Effective Stress
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Off-Axis S-N Relationship Using Theoretical Strength Ratio
10-1
100
101
100 101 102 103 104 105 106 107
Nf
T800H/2500
* m
ax
R = 0.5 n = 64.8
R = -1.0 n = 11.9R = -0.3 n = 12.0R = 0.1 n = 23.1
R = 0.1
R = 0.5
R = -0.3
R = -1.0
(*
max)nN
f=1Experimental (RT, 10 Hz)
● R = 0.5 ○ R = 0.1 ▲ R = -0.3 × R = -1.0
Unidirectional T800H/Epoxy
s* vs N f
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10-1
100
101
100 101 102 103 104 105 106 107
*m
ax
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
Off-Axis S-N Relationship Using Theoretical Strength Ratio
Unidirectional Glass/Epoxy
s* vs N f
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Modified Non-Dimensional Effective Stress:
* a
*
1 m*
a
* 12
(1 R)max
*
m
* 12
(1 R)max
*
where
Non-Dimensional Effective Stress for Fatigue
R [ 1, 1]
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*
12
(1 R) max
*
1 12
(1 R) max*
*
R 1 max
*
Theoretical Modified Strength Ratio
Master S-N RelationshipR = –1
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10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
*
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
+ R = -0.3
Off-Axis S-N Relationship Using Theoretical Modified Strength Ratio
Unidirectional T800H/Epoxy
S* vs N f
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Off-Axis S-N Relationship Using Theoretical Modified Strength Ratio
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
*
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
Unidirectional Glass/Epoxy
S* vs N f
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Damage Mechanics Modeling of Composite Fatigue
ddN
Kn 11
k
: Fatigue strength parameter
Fatigue Damage Growth Law:
N f 1
(k 1)Kn
Fatigue Life Equation:
1
N f 1
N f 1
n
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Off-Axis Fatigue Model
ddN
K * n* 11
k
N f 1
* n*
*
*-Based Fatigue Damage Model:
Master S-N Relationship:
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Unidirectional T800H/Epoxy
Master S-N Relationship
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
S*
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
s* =
m
ax/
B(e
xp
),
*m
ax
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz)
○ R = 0.5△ R = 0.1● R = -1
N f 1
* n
N f 1
* n*
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max 2*
( ) (1 R) (1 R)*
max
* 2*
(1 R) (1 R)*
Transformation of Master S-N Relationship
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101
102
103
104
105
100
101
102
103
104
105
106
107
m
ax, M
Pa
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz, R = -1)
○ 0° (R = -0.3)
▲ 10°◇ 15°
Predicted
● 30°▽ 45°■ 90°
101
102
103
104
105
100
101
102
103
104
105
106
107
m
ax, M
Pa
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz, R = 0.1)
○ 0°▲ 10° ◇ 15°
Predicted
● 30°▽ 45°■ 90°
101
102
103
104
105
100
101
102
103
104
105
106
107
m
ax, M
Pa
Nf
T800H/2500 Experimental (Kawai & Suda)(RT, f = 10 Hz, R = 0.5)
Predicted
○ 0°▲ 10° ◇ 15°
● 30°▽ 45°■ 90°
Comparisons With Experimental Results
Unidirectional T800H/Epoxy
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Unidirectional Glass/Epoxy
Master S-N Relationship
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
S*
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
10-2
10-1
100
101
102
100 101 102 103 104 105 106 107
Sm
ax =
m
ax/
B(e
xp
),
*m
ax
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz)
○ R = 0.5△ R = 0● R = -1
N f 1
* n
N f 1
* n*
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100
101
102
103
104
105
100
101
102
103
104
105
106
107
m
ax, M
Pa
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz, R= -1)
○ 0° ▽ 71°
▲ 19° ■ 90°
◇ 45°
Predicted
101
102
103
104
105
100 101 102 103 104 105 106 107
m
ax, M
Pa
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz, R= 0) ○ 0° ▽ 71°
▲ 19° ■ 90° ◇ 45°
Predicted10
1
102
103
104
105
100
101
102
103
104
105
106
107
m
ax, M
Pa
Nf
E-Glass/Epoxy Experimental (Kadi & Ellyin)(RT, f = 3.3 Hz, R = 0.5)
○ 0° ▽ 71°
▲ 19° ■ 90°
◇ 45°
Predicted
Unidirectional Glass/Epoxy
Comparisons With Experimental Results
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Constant Fatigue Life Diagram (CFLD)
N f 1
* n* ( R 1)
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
R = -1.0
a/B
(ex
p)
R = 0.5
R = 0.1
m/
B(exp)
Experimental (RT, 10Hz)
● Nf=104
○ Nf=105
× Nf=106
T800H/2500 = 45
a
* 1N f
1
n*
1 m
*
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A non-dimensional strength measure * that considers the mean stress as well as fiber orientation effects on the off-axis fatigue behavior of unidirectional polymer matrix composites was proposed.
Validity of the fatigue model based on the non-dimensional strength measure * was evaluated by comparing with experimental results.
Conclusions
For ” ,
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Using the modified strength ratio S*, we can substantially remove the fiber orientation as well as stress ratio dependence of the off-axis fatigue data to obtain an experimental master S-N relationship.
A general expression * of the modified fatigue strength ratio is obtained as a natural extension of the non-dimensional effective stress based on the Tsai-Hill static failure criterion.
A fatigue damage mechanics model that considers the fiber orientation as well as stress ratio effects is formulated using the modified non-dimensional effective stress *.
The proposed fatigue model can adequately describe the off-axis S-N relationships of unidirectional glass/epoxy and carbon/epoxy laminates under constant-amplitude cyclic loading with non-negative mean stresses.
ConclusionsFor ” ,
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Summary Chart
Experimental Theoretical
s* max
B
S* a
B m
max
*
*
Application to Fatigue
Metals UD-PMCs
Basquin
(1910)
Awerbuch-Hahn
(1981)
Landgraf
(1970)?
(* )n*N f 1
(R [ 1,1])
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Thank you for your kind attention !
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