fatigue crack localization using laser nonlinear...

<Original Paper>Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 419-427, 2014

ISSN 1225-7842 / eISSN 2287-402X http://dx.doi.org/10.7779/JKSNT.2014.34.6.419

1. Introduction

Structures with inhomogeneities or defects

exhibit nonlinear behavior. In particular, strong

nonlinear responses can be observed in structures

with fatigue cracks. Nonlinear parameters are

often more sensitive to fatigue cracks than their

linear counterparts [1-3]. Nonlinearity due to

crack formation manifests itself as distortion,

accompanying wave harmonics, and in sum and

difference frequency generation (sidebands). For

linear intact structures, these nonlinear responses

are weak, but they become remarkably strong for

damaged structures [4-8].

Nonlinear wave modulation spectroscopy

(NWMS) is one of the nonlinear ultrasonic

techniques based on nonlinear mixing of two

distinct input signals [4]. Normally, a low-

frequency pumping input and a high-frequency

probing input are used in NWMS for creating

modulation. Here, the amplitude of modulation

heavily depends on the choice of the probing

and pumping frequencies, and the optimal

combination of these two input frequencies is

also affected by environmental and operational

conditions (e.g., temperature and loading) of the

target structure and even by defect configurtions

[7, 9-11]. Therefore, finding the optimal combin-

ation of the probing and pumping frequencies,

which can maximize the modulation level,

becomes a moving target. To find an optimal

combination of the probing and pumping

frequencies that can maximize the modulation

level, frequency-swept probing signals and a

Fatigue Crack Localization Using Laser Nonlinear Wave Modulation

Spectroscopy (LNWMS)

Peipei Liu*, Hoon Sohn* and Tribikram Kundu**

Abstract Nonlinear features of ultrasonic waves are more sensitive to the presence of a fatigue crack than their

linear counterparts are. For this reason, the use of nonlinear ultrasonic techniques to detect a fatigue crack at its

early stage has been widely investigated. Of the different proposed techniques, laser nonlinear wave modulation

spectroscopy (LNWMS) is unique because a pulse laser is used to exert a single broadband input and a noncontact

measurement can be performed. Broadband excitation causes a nonlinear source to exhibits modulation at multiple

spectral peaks owing to interactions among various input frequency components. A feature called maximum

sideband peak count difference (MSPCD), which is extracted from the spectral plot, measures the degree of crack-

induced material nonlinearity. First, the ratios of spectral peaks whose amplitudes are above a moving threshold to

the total number of peaks are computed for spectral signals obtained from the pristine and the current state of a

target structure. Then, the difference of these ratios are computed as a function of the moving threshold. Finally,

the MSPCD is defined as the maximum difference between these ratios. The basic premise is that the MSPCD

will increase as the nonlinearity of the material increases. This technique has been used successfully for localizing

fatigue cracks in metallic plates.

Keywords: Fatigue Crack Localization, Nonlinear Wave Modulation Spectroscopy, Noncontact Laser Ultrasonics,

Sideband Peak Count

[Received: November 3, 2014, Revised: December 15, 2014, Accepted: December 16, 2014] *Deptment of Civil and

Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea,

**Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Az 85721, USA

Corresponding Author: [email protected]

2014, Korean Society for Nondestructive Testing

420 Peipei Liu, Hoon Sohn and Tribikram Kundu

frequency-fixed pumping signal are used [11].

Similarly, a first sideband spectrogram is created

by sweeping both pumping and probing signals

over specified frequency ranges to study the

effect of pumping and probing frequencies [7].

On the other hand, a laser nonlinear wave

modulation spectroscopy (LNWMS) utilizes a

laser pulse as an input signal, instead of using

two distinct frequency inputs, to excite multiple

frequency components simultaneously into the

target structure [12]. However, because of the

broadband nature of the laser pulse input, no

clear modulation frequency can be identified.

Instead, a fatigue crack is detected by counting

the number of spectral peaks (Sideband Peak

Count, SPC) above a moving threshold based on

the premise that a spectral signal obtained from

a nonlinear system would have more spectral

peaks compared to a linear system [5]. Experi-

mental test results obtained from simple plates

and aircraft fitting-lugs demonstrate that an

increased number of spectral peaks appear with

fatigue crack formation.

This study advances SPC to localize a fatigue

crack using LNWMS. The proposed damage

localization technique offers the following advan-

tages: (1) A pulse excitation input is used instead

of two distinct sinusoidal inputs for the extrac-

tion of nonlinear modulation responses; (2) A

complete noncontact laser ultrasonic system is

adopted for LNWMS measurement by inte-

grating and synchronizing a Q-switched Nd:YAG

laser for ultrasonic wave generation and a laser

Doppler vibrometer for ultrasonic wave detec-

tion; (3) SPC technique is improved for fatigue

crack localization.

This paper is organized as follows. In section

2, the working principle of nonlinear wave mod-

ulation was briefly reviewed and the proposed

damage-sensitive feature, maximum sideband peak

count difference (MSPCD) was described. Then,

the experimental test is described in Section 3,

and the proposed damage detection technique is

applied for localizing of actual fatigue cracks in

aluminum plates in Section 4. Finally, the conclu-

sion is provided in Section 5.

2. Theoretical Background

2.1 Laser Nonlinear Wave Modulation Spectro-

scopy (LNWMS)

It is known that, when two waves having

two different frequencies and (<)

propagate through a nonlinear region of a plate-

like structure in the z-direction, the solution for

the total particle displacement can be written

as the summation of the linear response,

harmonics and modulations (Fig. 1) as follows

[9,10]:

(1)

where c.c stands for complex conjugate, and

are the amplitudes of the linear waves at

and , and are the amplitudes of the

nonlinear harmonics at 2 and 2, and ±

is the amplitude of the modulation responses at

±. , and , are the wavenumbers

and phases corresponding to waves a and b,

respectively. For simplicity, the higher-order

harmonics and modulations are omitted.

In general, two binding conditions must be

satisfied for creation of modulated waves [9,10]:

(1) Synchronism condition - Both the phase and

group velocities of the linear waves must match

with those of the modulated waves; and (2)

Non-zero power flux condition - The mode

shapes of the linear waves should be matched

with those of the modulated ones, ensuring

non-zero power transfer from the linear waves

to the modulated waves. These conditions can

Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 419-427 2014 421

be applied to nonlinear harmonics when

and .

In practice, it is challenging to find the

optimal combination of two input frequencies,

which satisfies all binding conditions. In order

to tackle this issue, a broadband excitation was

used instead of two distinct input frequencies as

an input signal [5,12]. When a broadband pulse

signal is used as the input signal, nonlinear

wave modulation can occur among various

frequency components of the input signal and

multiple frequency peaks are generated as shown

in Fig. 2. In addition, some of the frequency

peaks in Fig. 2 could have been the results

of higher-order nonlinear modulations (cascade

cross modulations) in presence of cracks [13]. In

this paper, since the pulse signal will be

provided by a noncontact laser ultrasonic system,

this modified nonlinear wave modulation tech-

nique is called laser nonlinear wave modulation

spectroscopy (LNWMS).

2.2 Maximum Sideband Peak Count Difference

(MSPCD)

To quantify the level of nonlinearity

generated by a single pulse excitation, a side-

band peak count (SPC) technique was proposed

[5,12]. This technique does not count the

dominant peaks but keeps track of the relatively

weak peaks in the neighborhood of the strong

peaks generated by the material nonlinearity

and/or the anomalies in the material. Eiras et

al. [5] discussed the variation of the sideband

energy and sideband peak count for monitoring

the aging process of Glass Fiber Reinforced

Cement (GRC) using two PZT transducers for

excitation and sensing. Liu et al. [12] extended

the SPC technique for fatigue crack detection in

metallic structures, including aircraft fitting-lugs

with complex geometries. They all observed that

a greater number of relatively stronger minor

peaks appear as the degree of material non-

linearity increases.

The SPC is defined as the ratio of the

number of frequency peaks () over a

moving threshold () to the total peak number

() in the normalized frequency domain:

(2)

where all peaks are counted as shown in Fig.

3(a), including the dominant peaks as well as

Fig. 1 Illustration of nonlinear wave modulation

using two distinct sinusoidal inputs, intact

(top), damage (bottom)

Fig. 2 Illustration of nonlinear wave modulation

using a pulse input, intact (top), damage

(bottom)


the sideband peaks above the threshold. It is not

necessary to separate the dominant peaks from

the sideband peaks since the number of dom-

inant peaks is negligible in comparison to the

sideband peaks. Due to the nonlinearity induced

by defects, more sideband peaks show up in the

spectrum and consequently the sideband energy

grows. Therefore, the SPC value for the

damaged case should be larger than that for the

intact case, especially when the threshold value

is relatively low. Fig. 3(b) shows a representa-

tive plot of SPC difference obtained from the

later experiment presented in this study. Here,

the SPC difference is defined as the difference

between the SPC values obtained from the

current and baseline base statuses.

The SPC difference is positive when there is a

fatigue crack in the target specimen, and the

maximum SPC difference (MSPCD) is obtained

when the threshold value is relatively low. In

this study, the MSPCD defined below is

selected as the damage feature and used to

localize a fatigue crack:

(3)

3. Experimental Setup

3.1 Description of Specimen and Fatigue

Testing

Two identical aluminum plate specimens were

fabricated using 6061-T6 aluminum alloy, and a

notch was introduced in the middle of one side of

the specimen as shown in Fig. 4. A fatigue crack

was introduced to each specimen using an

INSTRON 8801 fatigue testing system. The

specimens were tested under tension-tension

cycling of a maximum load of 25 kN and a

minimum load of 2.5 kN at a frequency of

10 Hz. 15 mm long cracks were produced to

two specimens after 18793 and 20209 loading

cycles, respectively. The widths of the fatigue

cracks are less than 10 m and even below 5μ mμ

near the crack tips, as shown in Fig. 5. These

cracks are hardly detectable using conventional

linear ultrasonic techniques.

Fig. 4 Specimen dimensions, crack location, and

laser excitation and sensing arrangement

(a)

(b)

Fig. 3 Description of sideband peak count(SPC)

and SPC difference: (a) SPC is defined as

the ratio of the number of frequency peaks

over a moving threshold to the total number

of peaks in the frequency domain, (b) the

SPC difference, which is defined as the

difference between the SPC values obtained

from the current and initial intact stages,

increases as more spectral peaks show up

for the damaged specimen especially when

the threshold is relatively low


(a)

(b)

Fig. 5 Microscopic images of fatigue cracks in

aluminum specimens: (a) specimen I, (b)

specimen II

3.2 Description of a Noncontact Laser Ultrasonic

System

A complete noncontact laser ultrasonic

system is used in this study for generation and

sensing of ultrasonic waves [14]. As shown in

Fig. 6, the excitation unit comprises a

Q-switched Nd:YAG pulse laser, a galvanometer

and a focal lens. The Nd:YAG laser has a

wavelength of 1064 nm and a maximum peak

power of 3.7 MW, and generates a pulse input

with 8 ns pulse duration at a repetition rate of

20 Hz. Note that, although the available

maximum peak power is 3.7 MW, a peak power

of around 0.2 MW is used for the experiment

in this study. Ultrasonic waves are created by

the thermal expansion of an infinitesimal area

heated by the laser. Using the galvanometer, the

laser pulse can be aimed at the desired target

excitation points.

For the sensing unit, a commercial scanning

LDV (Polytec PSV-400-M4) with a built-in

galvanometer and an auto-focal lens is used. The

laser source used for this LDV is a helium neon

(He-Ne) laser with a wavelength of 633 nm.

This one-dimensional (1D) LDV measures the

out-of-plane velocity in the range of 0.01 um/s

to 10 m/s over a target surface based on the

Doppler frequency-shift effect of light. In this

experiment, each ultrasonic response is measured

with a sampling frequency of 2.56 MHz for

25.6 ms, achieving frequency resolution close to

40 Hz.

The control unit consists of a personal

computer(PC), controller, velocity decoder with a

maximum velocity sensitivity of 1 mm/s/V and

a 14-bit digitizer with a maximum sampling

frequency of 5.12 MHz. The controller generates

control signals to aim the excitation and sensing

laser beams at the desired target positions. In

addition, the controller sends out trigger signals

to launch the excitation laser beam and to start

the data collection simultaneously.

Fig. 7 shows the actual hardware compon-

ents used in this experiment. The distances

between the Nd:YAG laser head and the target

specimen and between LDV and the target

specimen are set to 1 m. To improve the signal

to noise ratio, the responses are measured 100

times and averaged in the time domain.

Fig. 6 Schematic diagram of the noncontact laser

ultrasonic system


As shown in Fig. 4, six pairs of excitation

and sensing laser beam points are selected to

examine the localization capability of the

proposed crack detection technique. For the

intact condition of each specimen, ultrasonic

responses were recorded three times from every

path. One of them was used as the reference sig

nal, and the other two as the test signals

acquired from the intact case. To take into

account variations caused by resetting of the

measurement system and the specimen after

fatigue test, the whole measurement system was

reconfigured even for the intact case. After

crack formation, ultrasonic signals were collected

again following the same measurement procedure

as the intact case.

4. Experimental Results

Representative ultrasonic responses obtained

from path 2 of specimen I in both time and

frequency domains are displayed in Fig. 8(a)

and (b). The frequency content of the response

signal spans up to 400 kHz. A close-up view of

the frequency spectra is shown in Fig. 8(c) and

it displays that more sideband peaks appear

when the specimen is damaged. A frequency

band of 20 kHz to 400 kHz is selected for

calculating the MSPCD values. Fig. 9 shows the

SPC value and its difference from the reference

case obtained for the intact and damage cases of

specimen I. Fig. 9(a) shows the SPC and its

difference from path 2, which passes through

the crack tip. The maximum SPC difference

(MSPCD) reaches above 0.15 for the damage

case when the threshold is quite low (around

0.4% of the largest peak value in the frequency

Fig. 7 Experimental setup using noncontact laser

ultrasonic system(a)

(b)

(c)

Fig. 8 Representative response signals from path

2 in specimen I: (a) time histories, (b)

normalized frequency spectra, (c) close-up

view of the frequency spectra


domain). Fig. 9(b) shows the SPC and its diffe

rence for path 3, which does not directly pass

through the crack. Therefore, it can be seen that

the MSPCD obtained from the damage case

shows a much higher value compared to the

intact cases when the propagating ultrasonic

waves pass directly through the crack tip.

Therefore, a fatigue crack can be located based

on this finding.

Fig. 10 shows the MSPCD values obtained

from all six paths in specimens I and II. It can

be clearly seen that the MSPCD value whose

path passes through the crack, especially at the

crack tip, is much higher than the others mainly

caused by the measurement noises and the

measurement system reconfiguration after each

fatigue test. Note that, in Liu et al. [12], the

MSPCD value significantly increased even when

the path did not pass through the crack. That is

(a)

(b)

Fig. 9 SPC and SPC difference values obtained

from the intact and damaged cases for

specimen I: (a) path 2 passing through the

crack tip, (b) path 3 not passing through the

crack

(a)

(b)

Fig. 10 MSPCD obtained using 0.2 MW peak

power laser pulse excitation: (a) specimen

I, (b) specimen II


because the power level of the laser excitation

was much higher (0.4 MW peak power). On the

other hand, the power level of the excitation

laser beam was kept below 0.2 MW in this

study so that the laser excitation can well

‘activate’ crack opening and closing only when

the propagating waves directly pass through the

crack. Furthermore, this crack opening and

closing is most prominent near the crack tip

where the crack width is minimum as shown in

Fig. 5.

In order to clarify the difference better, the

same experiment is repeated with a higher

power laser excitation (0.4 MW peak power)

and the results are shown in Fig. 11. For all six

paths, the MSPCD values for the damaged case

are much higher than the corresponding values

from the intact case, failing for crack

localization. Therefore, ideally, a higher power

laser excitation can be used initially to identify

the presence of a fatigue crack, and then a

lower power laser can be applied for the crack

localization.

5. Conclusions

This study demonstrates that laser nonlinear

wave modulation spectroscopy (LNWMS) can be

successfully applied for fatigue crack localization

in metallic structures. Different from most of the

conventional nonlinear wave modulation tests,

the LNWMS uses a single pulse excitation. A

complete noncontact laser ultrasonic system is

used for LNWMS measurement. A damage

feature called maximum sideband peak count

difference (MSPCD) is proposed to keep track

of the relatively weak peaks in the

neighborhood of the strong spectral peaks

generated by the anomalies in the material. By

controlling the energy level for laser excitation,

this feature can be used to identify the presence

of a fatigue crack and localize it. However,

there still remain a number of challenges

associated with laser ultrasonic techniques. For

example, eye-safety issue, material ablation and

surface treatment. A follow-up study with the

proposed LNWMS will focus on fatigue crack

visualization by laser scanning.

Acknowledgment

This work was supported by the National

Research Laboratory (NRL) Program (NRF-2010-

0017456) of National Research Foundation of

Korea (NRF) funded by the Ministry of

Education, Science and Technology (MEST),

and a grant (13SCIPA01) from Smart Civil

Infrastructure Research Program funded by

Ministry of Land, Infrastructure and Transport

(MOLIT) of Korea government and Korea

Agency for Infrastructure Technology Advance-

ment (KAIA).

(a)

(b)

Fig. 11 MSPCD obtained using 0.4 MW peak

power laser pulse excitation: (a) specimen

I, (b) specimen II


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