1. Development of a Fatigue Crack Growth Monitoring and Failure Stage Detection Technique Based on Nonlinear Ultrasonic Modulation
Yongtak Kim
Department of Civil and Environmental Engineering
Korea Advanced Institute of Science and Technology (KAIST)
Committee Members
Prof. Hoon Sohn, KAIST (Chair) Prof. Jungju Lee, KAIST Prof. Seyoung Im, KAIST

2. Outline Introduction Theoretical Background Algorithm Development
Experimental Validation
Conclusion

3. Outline Introduction Theoretical Background Algorithm Development
Motivations
Fatigue crack propagation
Objective & Uniqueness
Theoretical Background
Algorithm Development
Experimental Validation
Conclusion

4. Motivation Eschde train disaster, 1998, Germany
(101 people died and 100 were injured)
Seongsu bridge collapse, 1994, South Korea
(32 people died and 17 were injured)
Monitoring of fatigue cracks in inaccessible locations
Automatic failure stage alarming for machines in use

5. Fatigue Crack Propagation and Detection
Failure
Crack width
Damage
Conventional
NDT
~ mm
Non-damage
No. of cycles
~80%
The conventional techniques can detect fatigue cracks only after the cracks reach about 80% of the total fatigue life for most metallic materials. Thus, the time for failure preparation is limited.
The nonlinear ultrasonic technique can detect much smaller fatigue cracks. However, the portion of remaining life cycle is too large, and the technique cannot say when it will fail.
In this study, a new technique is developed that can monitor the fatigue crack growth and alarm the failure stage by monitoring the nonlinearity changes of a structure.

6. Fatigue Crack Propagation and Detection
Failure
Crack width
Damage
Nonlinear
ultrasonic
~ μm
Non-damage
No. of cycles
~10%
The conventional techniques can detect fatigue cracks only after the cracks reach about 80% of the total fatigue life for most metallic materials. Thus, the time for failure preparation is limited.
The nonlinear ultrasonic technique can detect much smaller fatigue cracks. However, the portion of remaining life cycle is too large, and the technique cannot say when it will fail.
In this study, a new technique is developed that can monitor the fatigue crack growth and alarm the failure stage by monitoring the nonlinearity changes of a structure.

7. Crack growth monitoring
Fatigue Crack Propagation and Detection
Failure
Crack growth monitoring
Crack width
Failure
stage
No. of cycles
~10%
~80%
~90%
The conventional techniques can detect fatigue cracks only after the cracks reach about 80% of the total fatigue life for most metallic materials. Thus, the time for failure preparation is limited.
The nonlinear ultrasonic technique can detect much smaller fatigue cracks. However, the portion of remaining life cycle is too large, and the technique cannot say when it will fail.
In this study, a new technique is developed that can monitor the fatigue crack growth and alarm the failure stage by monitoring the nonlinearity changes of a structure.

8. Fatigue crack growth monitoring Determination of failure stage
Objectives & Uniqueness
1. Objective
Development of a fatigue crack growth monitoring and failure stage determination technique using nonlinear ultrasonic modulation
2. Uniqueness
A fatigue crack growth monitoring technique based on nonlinear ultrasonic modulation.
Autonomous detection of failure stage of a structure under fatigue loadings.
Applicability to welded structures (Not affected by initial nonlinearities of a structure).
Fatigue crack growth monitoring
Determination of failure stage
Butt welded plate

9. Outline Introduction Theoretical Background Algorithm Development
Concept of nonlinear ultrasonic modulation
Working principle of nonlinear ultrasonic modulation
Fracture toughness
Relationship between a crack length and nonlinear ultrasonic modulation
Algorithm Development
Experimental Validation
Conclusion

10. Concept of Nonlinear Ultrasonic Modulation
Compression
phase
Dilation
phase
compression
compression LF
time
Crack width
Crack width
dilation
dilation HF
time
Crack closing and opening by LF (vibration signal)
Amplitude modulation of HF (probe signal)
LF signal changes the width of the crack depending on the phase of the vibration
HF signal is simultaneously applied to the crack
During the dilation phase of the LF cycle, the HF signal is partially decoupled by the open crack. This reduces the amplitude of the HF signal passing through the crack
Fourier transformation of this signal reveals sideband frequencies that are the sum and difference of the frequencies of the ultrasonic probe (HF) and vibration signals (LF).

11. Working Principle of Nonlinear Ultrasonic Modulation
𝝎 𝒂 < 𝝎 𝒃
LF ( 𝝎 𝒂 )
HF ( 𝝎 𝒃 ) A B
Magnitude
Intact (Linear)
Structure
PZT
LF( 𝝎 𝒂 )
HF( 𝝎 𝒃 )
Frequency
Modulations
LF ( 𝝎 𝒂 )
HF ( 𝝎 𝒃 ) A B MD
Magnitude MS
Damage (Nonlinear)
Structure
Fatigue Crack
LF( 𝝎 𝒂 )
HF( 𝝎 𝒃 )
Frequency
βD ( 𝝎 𝒃 − 𝝎 𝒂 )
βS ( 𝝎 𝒃 + 𝝎 𝒂 )

12. Fracture Toughness (KIC)
Stage Ⅰ
Near-threshold region
Stage Ⅱ
Stable propagation region
Stage Ⅲ
Unstable crack growth region
Kmax = KIC (Fracture toughness )
Crack growth rate ( 𝒅𝒂 𝒅𝑵 ), log scale
Crack length
SIF
KIC
Critical
crack length ac
Threshold ΔKth
ΔKth
Stress intensity factor range (ΔK), log scale
The fatigue crack is initiated when the ΔK is larger than the threshold ΔKth. After the initiation, the crack propagation is stable (Stage Ⅱ).
As length of the fatigue crack becomes the critical crack length, the maximum stress intensity factor reaches the fracture toughness value. Then the crack rapidly grows and then soon meets the failure.
Therefore, the time when the fatigue crack length equals to the critical crack length can represent the failure stage.

13. Relationship Between a Fatigue Crack Length and Nonlinear
Ultrasonic Modulation
Crack initiation ( 0 < a )
Crack growth ( 0 < a < ac )
Unstable fracture ( ac < a )
Width ac ac a a a
The structure has nonlinearity due to the crack
Crack opening/closing happens
Modulation occurs
The structure’s nonlinearity increases
Effects of crack opening/closing increases
Modulation increases
The crack width increases due to unstable fracture
Crack opening/closing does not happen
Modulation decreases

14. Outline Introduction Theoretical Background Algorithm Development
How to measure nonlinearity of a structure: Conventional way
Problem of the conventional nonlinearity index calculation
Nonlinearity index (β) calculation using multiple combinations of dual frequency
Failure stage determination algorithm: Outlier analysis
Experimental Validation
Conclusion

15. ∴𝑵𝒐𝒏𝒍𝒊𝒏𝒆𝒂𝒓𝒊𝒕𝒚 𝒐𝒇 𝒂 𝑺𝒕𝒓𝒖𝒄𝒕𝒖𝒓𝒆∝ 𝑴 𝑫 + 𝑴 𝑺 𝑨×𝑩
How to Measure Nonlinearity of a Structure: Conventional Way A B
Amplitude MD MS
LF( 𝝎 𝒂 )
βD ( 𝝎 𝒃 − 𝝎 𝒂 )
HF( 𝝎 𝒃 )
βS ( 𝝎 𝒃 + 𝝎 𝒂 )
Frequency
The nonlinearity of a structure has a proportional relationship with a fatigue crack length.
As the crack length increases, the amplitudes of βD and βS (MD and MS, respectively) increase.
The modulation amplitudes MD and MS are also increased when the amplitudes of input signals LF and HF (A and B, respectively) increase.
Therefore, to measure nonlinearity of a structure, the sum of modulation amplitudes should be normalized by input signals’ amplitudes.
∴𝑵𝒐𝒏𝒍𝒊𝒏𝒆𝒂𝒓𝒊𝒕𝒚 𝒐𝒇 𝒂 𝑺𝒕𝒓𝒖𝒄𝒕𝒖𝒓𝒆∝ 𝑴 𝑫 + 𝑴 𝑺 𝑨×𝑩

16. Problem of the Conventional Nonlinearity Index Calculation
Frequency
Amplitude
When FRF matches with input frequencies
Amplitude LF HF LF HF
noise
noise
Frequency
Amplitude
Frequency
When FRF does not match with input frequencies
Amplitude
Negligible
(≈𝟎) LF HF LF HF
noise
noise
Frequency
When the frequencies of input signals are matched with frequency response function (FRF) of a structure, modulation components can be extracted from the noise.
However, when the frequencies of input signals are not matched with FRF of a structure, modulation components are buried in the noise.
Since the nonlinearity of a structure should be normalized by input amplitudes, if any of input signals are almost zero value, the noise can be extracted as large nonlinearity.

17. Nonlinearity Index (β) Calculation using Multiple Combinations of
Dual Frequency
Summation A
Summation MD
Summation B
Summation MS 𝑨1 𝑩1
Combination #1
𝑴 𝑫𝟏
𝑴 𝑺𝟏
Amplitude
𝝎 𝒂1
𝝎 𝒃1 − 𝝎 𝒂1
𝝎 𝒃1
𝝎 𝒃1 + 𝝎 𝒂1
Frequency 𝑨2
Combination #2
Amplitude
𝑴 𝑫𝟐 𝑩2
𝑴 𝑺𝟐
𝝎 𝒂2
𝝎 𝒃2 − 𝝎 𝒂2
𝝎 𝒃2
𝝎 𝒃2 + 𝝎 𝒂2
Frequency … … 𝑨n 𝑩n
Combination #n
𝑴 𝑫𝒏
𝑴 𝑺𝒏
Amplitude … …
𝝎 𝒂𝑛
𝝎 𝒃𝑛 − 𝝎 𝒂𝑛
𝝎 𝒃𝑛
𝝎 𝒃𝑛 + 𝝎 𝒂𝑛
Frequency
𝜷= 𝒊=𝟏 𝒊=𝒏 ( 𝑴 𝑫𝒊 + 𝑴 𝑺𝒊 ) 𝒊=𝟏 𝒊=𝒏 𝑨 𝒊 𝒊=𝟏 𝒊=𝒏 𝑩 𝒊
Stable and reliable nonlinearity index
The reliability increases as the number of combination increases

18. Failure Stage Determination Algorithm: Outlier Analysis
+3σ
Abrupt
decrease
Standard deviation (σ)
calculation
-3σ
Failure stage is reached
The crack length just pass
the critical crack length (ac)
Every time when another data is acquired, the change rate of β value is calculated.
The outlier level is determined by dividing the change rate of β with the standard deviation of previous data.
In this study, 3σ method is used. That means, when the outlier level is less than ±3σ, the data considered as usual/normal data.
When the outlier level is less than -3σ, it is considered that the critical crack length is just passed

19. Outline Introduction Theoretical Background Algorithm Development
Experimental Validation
Experiment procedure
Types of specimens
Hardware configuration
Experimental results
Conclusion

20. Experiment Procedure Perform a fatigue test for a specimen
Input signals (LF and HF) are applied at appropriate intervals and the output signal is acquired. At the same time, the length of fatigue crack is measured (up to 0.01mm)
From the acquired signal, the nonlinearity index (β) is calculated
Monitor the fatigue crack growth by observing increases in β value
The abrupt decrease in β value is automatically detected by outlier analysis
The fatigue crack length at the abrupt decrease is compared with the empirically calculated critical crack length (ac)

21. Schematic diagram of the specimen design
Types of Specimens
Schematic diagram of the specimen design
KS B ISO 12108:2004
Metallic materials –
Fatigue testing –
Fatigue crack growth method
Aluminum 6061-t6
Aluminum 7075-t6
Thickness
KIC
Loading ac
3mm
33.5
2-20kN
21.5mm
6mm
3.5-35kN
24.2mm
8mm
4.8-48kN
23.6mm
Thickness
KIC
Loading ac
3.3mm 29
2-20kN
20.5mm
6mm
3.5-35kN
21.3mm
8.3mm 25
4.8-48kN
18.4mm

22. Hardware schematic configuration Hardware picture & Details
Hardware Configuration
Hardware schematic configuration
Hardware picture & Details
DIG
AWGs
Controller
Controller (NI PXIe-8840)
AWGs (NI PXI-5421), DIG (NI PXIe-5122)
LF signal: Sine wave (30-40 kHz)
HF signal: Sine wave ( kHz)
The AWGs and DIG are synchronized and controlled by LabVIEW

23. Experimental Results: 6061-t6, 3mm thickness
Loading 2-20kN (10Hz), Critical crack length 21.5mm, Failure at 55k cycles
Critical crack length
Standard deviation (σ)
calculation
+3σ
Crack growth
monitoring
21.0mm
-3σ
-35.64σ
21.5mm
89% of life
cycle
Number of cycle
25k
28k
33k
38k
41k
44k
47k
49k
β (10-3)
0.08
0.12
0.37
0.77
1.15
1.59
0.86
∆β σ
0.00
0.21
1.34
8.04
18.73
12.89
21.82
-35.64
Crack
length
(mm)
8.36
9.08
10.95
12.95
14.60
17.04
18.94
21.00

24. Experimental Results: 6061-t6, 6mm thickness
Loading kN (10Hz), Critical crack length 24.2mm, Failure at 47k cycles
Critical crack length
Standard deviation (σ)
calculation
+3σ
-3σ
Crack growth
monitoring
24.3mm
-19.72σ
24.2mm
89% of life
cycle
Number of cycle
35k
36k
37k
38k
39k
40k
41k
42k
β (10-3)
0.78
0.81
0.73
0.85
1.13
2.23
3.30
∆β σ
-0.22
-0.28
-0.15
0.59
2.40
5.72
4.44
-19.72
Crack
length
(mm)
16.60
17.51
18.50
19.48
20.30
21.63
23.30
24.30

25. Experimental Results: 6061-t6, 8mm thickness
Loading kN (10Hz), Critical crack length 23.6mm, Failure at 41k cycles
Critical crack length
Standard deviation (σ)
calculation
+3σ
Crack growth
monitoring
-3σ
23.41mm
-160.4σ
23.6mm
93% of life
cycle
Number of cycle
25k
27k
29k
31k
35k
36k
37k
38k
β (10-3)
0.08
0.11
0.44
0.84
1.47
1.48
0.68
∆β σ
1.82
5.28
78.13
72.43
40.29
2.30
-0.64
-160.4
Crack
length
(mm)
10.52
11.60
12.71
14.36
19.51
20.53
22.34
23.41

26. Experimental Results: 7075-t6, 3.3mm thickness
Loading 2-20kN (10Hz), Critical crack length 20.5mm, Failure at 29k cycles
Critical crack length
Standard deviation (σ)
calculation
+3σ
21.14mm
Crack growth
monitoring
-3σ
-12.51σ
20.5mm
97% of life
cycle
Number of cycle
21k
23k
25k
26k
26.5k
27k
27.5k
28k
β (10-3)
0.15
0.35
0.34
0.32
0.40
0.51
0.58
0.45
∆β σ
-0.22
11.29
0.01
-1.37
7.32
6.12
8.76
-12.51
Crack
length
(mm)
12.20
13.35
16.33
17.58
18.33
19.67
20.30
21.14

27. Experimental Results: 7075-t6, 6mm thickness
Loading kN (10Hz), Critical crack length 21.3mm, Failure at 36k cycles
Critical crack length
Standard deviation (σ)
calculation
+3σ
21.85mm
Crack growth
monitoring
-5.40σ
-3σ
21.3mm
94% of life
cycle
Number of cycle
28k
29k
30k
31k
32k
33k
33.5k
34k
β (10-3)
0.83
0.56
0.60
0.79
2.56
3.66
3.15
∆β σ
-0.13
-0.91
-0.05
0.92
4.45
7.70
-5.40
Crack
length
(mm)
14.03
14.98
17.07
17.86
19.05
20.74
21.4
21.85

28. Experimental Results: 7075-t6, 8.3mm thickness
Loading kN (10Hz), Critical crack length 18.4mm, Failure at 31k cycles
+3σ
Standard deviation (σ)
calculation
Critical crack length
Crack growth
monitoring
19.00mm
-3σ
-4.83σ
18.4mm
97% of life
cycle
Number of cycle
23k
24k
25k
26k
27k
28k
29k
30k
β (10-3)
0.32
0.43
0.46
0.67
0.81
0.90
1.11
0.73
∆β σ
0.00
-1.32
1.87
-0.05
1.08
-0.46
-4.83
Crack
length
(mm)
9.61
10.50
11.64
12.98
14.55
15.17
17.90
19.00

29. Experimental Results: Overall results and errors
Result: Aluminum 6061-t6
Specimen
Thickness
(mm)
Loading
(Loading ratio = 0.1)
Critical crack
length, ac
number
Real crack
Length, a
Difference,
ac - a
Error rate
(%) 3
20kN
21.5 #1
21.00
0.50
2.3 #2
21.80
-0.30
-1.4 #3
21.70
-0.20
-0.9 6
35kN
24.2 #4
24.92
-0.72
-3.0 #5
26.95
-2.75
-11.4 #6
24.30
-0.10
-0.4 8
48kN
23.6 #7
22.18
1.42
6.0 #8
23.41
0.19
0.8 #9
23.64
-0.04
-0.2
Result: Aluminum 7075-t6
Specimen
Thickness
(mm)
Loading
(Loading ratio = 0.1)
Critical crack
length, ac
number
Real crack
Length, a
Difference,
ac - a
Error rate
(%)
3.3
20kN
20.5
#10
21.14
-0.64
-3.1 6
35kN
21.3
#11
21.85
-0.55
-2.6
8.3
48kN
18.4
#12
19.00
-0.6
-3.3
RMSE
0.98mm

30. Outline Introduction Theoretical Background Algorithm Development
Experimental Validation
Conclusion
Executive summary & Future work

31. Executive Summary & Future Works
A new technique that can monitor the fatigue crack growth and detect the failure stage is developed
Nonlinearity of a structure increases as a fatigue crack grows
When the length of crack reaches the critical crack length that SIF equals to Fracture toughness, the nonlinearity abruptly decreases
The more stable and reliable nonlinearity index (β) can be calculated by using multiple combinations of dual frequency input signals
The developed crack growth monitoring and failure alarming technique is verified by different types of aluminum specimens
2. Future Works
Verify the developed technique for other materials with other geometrical specimens
Apply to welded structure
Prediction of the remaining fatigue life of a structure

32. Thank you for your attention Smart Structures and Systems Lab at KAIST

34. According to Boeing Company’s regulation Boeing 747 under inspection
Example: Fatigue Life of Airplanes (Boeing 747 model)
According to Boeing Company’s regulation
Design Service Objective (DSO):
Minimum period of service during which primary structure is designed to be essentially free of detectable fatigue cracks, with high degree of reliability and confidence
# of Landings
Ages
Time of flight
20,000
20 years
60,000 hours
Boeing 747 under inspection
Limit Of Validity (LOV):
The period of time up to which it has been demonstrated by test evidence, analysis and, if available, service experience and teardown inspections, that widespread fatigue damage will no occur in the airplane structure.
# of landings: 1,050
Age: 12.6 months
Time of flight: 4,050 hours
# of Landings
Ages
Time of flight
35,000
35 years
135,000 hours
3% of life

35. Metallurgical Direction of Aluminum Alloy
In Aluminum 6061-T6 alloy,
The fracture toughness value (KIC),
33.5MPa-m1/2 for T-L direction
48.7MPa-m1/2 for L-T direction
T-L
L-T
Rolling direction (L)
Width (T)
In Aluminum 7075-T6 alloy,
The fracture toughness value (KIC),
25MPa-m1/2 for T-L direction
29MPa-m1/2 for L-T direction
Thickness(S)

36. Stress Intensity Factor Calculation for Single Edge Notch Specimens
Loading (P)
The stress intensity factor (SIF) describes the stress stage at a crack tip.
The SIF is a function of a loading, a crack length, and structural geometry.
There are empirical SIF equations for general geometry of specimens.
In this study, the single edge notch test specimens without eccentric load, were used, and the empirical equation for them is following:
Thickness (B)
Crack length (𝒂)
𝐾= 𝑃 𝐵𝑊 𝜋𝑎 𝐹( 𝑎 𝑊 )
Where
𝐹( 𝑎 𝑊 ) = 2𝑊 𝜋𝑎 tan 𝜋𝑎 2𝑊 𝑎 𝑊 (1− sin 𝜋𝑎 2𝑊 ) 3 cos 𝜋𝑎 2𝑊
Width (W)
Loading (P)

37. Fatigue Test Configuration
Install on fatigue machine
Schematic diagram of the specimen design
notch
Pictures of the specimen
Loading (P)
Specimen
notch

38. Application to a Welded Steel Specimens: Setting
Welded specimen
Specimen details
Material
SS400
Welding type
Single V butt welding
Loading type
Tensile fatigue
Load
+5 ~ 50kN (10Hz)
No. of cycles
200,000 cycles
PZT sensor size
Φ25mm x 0.5mm
High frequency
193 ~ 195kHz (1kHz increment)
Low frequency
40 ~ 50kHz (1kHz increment)
Sample rating
1MHz
Crack width
~50μm
120
PZT A
(LF)
PZT B
(HF) 60
weldment 30 15
250
Photomicrograph
Fatigue crack 55
500μm
500μm
1, μm
PZT C
(SEN)
46.05 μm
33.46 μm
33.47 μm
35.95 μm
50.87 μm
24.24 μm 80
(Thickness: 6mm) (Unit : mm)
Back view
Side view

39. The crack length and SIF should be defined in welding joint
Application to a Welded Steel Specimens: Result
Welded specimen: Loading 5-50kN (10Hz)
23.64mm
-4.45σ
Number of cycle
85k
100k
115k
130k
139k
154k
169k
180k
β (10-5)
1.94
2.18
2.24
3.59
3.84
3.92
4.79
3.71 σ
-0.03
0.59
0.11
4.01
1.27
0.05
2.68
-3.63
Crack
length
(mm)
The crack length and SIF should be defined in welding joint

40. Application to a Mock-up Welded Structure: Specimen Design
Supported by Hyundai Heavy Industry
Loading
Fixed by bolts
100
250
1000
Unit: mm

41. Application to a Mock-up Welded Structure: Result
Supported by Hyundai Heavy Industry
-31.62σ
Minus outlier algorithm should be modified
-4.81σ
-4.27σ

42. Experimental Results: 6061-t6, 3mm thickness
03t_#2 specimen: Loading 2-20kN (10Hz), Critical crack length 21.5mm
21.80mm
-5.85σ
Number of cycle 0k
10k
17k
20k
23k
25k
28.5k
30.5k
β (10-3)
0.12
0.38
0.56
0.84
1.39
1.47
2.63
1.71 σ
0.00
1.19
4.15
-2.61
5.28
-5.85
Crack
length
(mm)
5.00
6.97
9.02
10.97
13.26
14.60
18.60
21.80

43. Experimental Results: 6061-t6, 3mm thickness
03t_#3 specimen: Loading 2-20kN (10Hz), Critical crack length 21.5mm
21.70mm
-14.75σ
Number of cycle 0k
20k
30k
38k
40k
42k
43k
44k
β (10-3)
0.18
0.13
0.29
1.02
1.20
2.68
3.57
1.53 σ
0.00
2.37
1.98
4.77
3.46
-14.75
Crack
length
(mm)
5.00
6.64
9.80
14.97
15.74
18.12
20.20
21.70

44. Experimental Results: 6061-t6, 6mm thickness
06t_#1 specimen: Loading kN (10Hz), Critical crack length 24.2mm
24.92mm
-17.09σ
Number of cycle
34k
35k
36k
37k
38k
39k
40k
41k
β (10-3)
0.30
0.41
0.45
0.46
1.51
3.17
2.93
1.11 σ
0.14
1.37
0.00
-0.29
19.79
28.35
-2.72
-17.09
Crack
length
(mm)
15.76
16.91
18.30
19.73
20.71
21.84
23.32
24.92

45. Experimental Results: 6061-t6, 6mm thickness
06t_#2 specimen: Loading kN (10Hz), Critical crack length 24.2mm
26.95mm
-19.90σ
Number of cycle
37k
38k
39k
40k
41k
42k
43k
44k
β (10-3)
0.91
2.24
2.83
2.75
2.63
4.70
6.26
1.43 σ
3.57
16.55
4.76
-0.59
-1.12
11.86
12.78
-19.90
Crack
length
(mm)
15.78
16.62
17.95
19.34
20.57
22.56
24.00
26.95

46. Experimental Results: 6061-t6, 8mm thickness
08t_#1 specimen: Loading kN (10Hz), Critical crack length 23.6mm
22.18mm
-5.70σ
Number of cycle
34k
36k
37k
38k
39k
40k
40.5k
41k
β (10-3)
1.38
1.37
1.02
1.25
1.05
3.91
3.49
2.43 σ
0.75
1.60
-1.50
0.95
-0.18
5.19
-1.33
-5.70
Crack
length
(mm)
12.91
14.62
15.65
16.44
17.82
20.20
21.40
22.18

47. Experimental Results: 6061-t6, 8mm thickness
08t_#3 specimen: Loading kN (10Hz), Critical crack length 23.6mm
23.64mm
-4.45σ
Number of cycle
34.5k
36.5k
38.5k
40k
41k
42k
44k
45k
β (10-3)
0.13
0.20
0.65
1.10
1.26
1.28
1.22
0.99 σ
0.26
2.48
5.00
11.07
6.02
0.09
-0.47
-4.45
Crack
length
(mm)
11.22
12.48
14.90
16.14
17.02
18.92
21.65
23.64