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

Outline Introduction Theoretical Background Algorithm Development Experimental Validation Conclusion

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

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

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.

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.

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.

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

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

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).

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 )

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.

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

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

∴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

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.

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

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

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

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)

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

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 (181-183 kHz) The AWGs and DIG are synchronized and controlled by LabVIEW

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

Experimental Results: 6061-t6, 6mm thickness Loading 3.5-35kN (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

Experimental Results: 6061-t6, 8mm thickness Loading 4.8-48kN (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

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

Experimental Results: 7075-t6, 6mm thickness Loading 3.5-35kN (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

Experimental Results: 7075-t6, 8.3mm thickness Loading 4.8-48kN (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

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

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

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

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

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

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)

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 0.752+2.02 𝑎 𝑊 +0.37 (1− sin 𝜋𝑎 2𝑊 ) 3 cos 𝜋𝑎 2𝑊 Width (W) Loading (P)

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

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 1,972.29 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

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

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

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

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

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

Experimental Results: 6061-t6, 6mm thickness 06t_#1 specimen: Loading 3.5-35kN (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

Experimental Results: 6061-t6, 6mm thickness 06t_#2 specimen: Loading 3.5-35kN (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

Experimental Results: 6061-t6, 8mm thickness 08t_#1 specimen: Loading 4.8-48kN (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

Experimental Results: 6061-t6, 8mm thickness 08t_#3 specimen: Loading 4.8-48kN (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