Damage assessment in Q690 high strength structural steel using nonlinear Lamb waves

Construction and Building Materials 234 (2020) 117384

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Damage assessment in Q690 high strength structural steel using nonlinear Lamb waves Xiao Wang a,1,⇑, Yanxun Xiang b,1,⇑, Wu-Jun Zhu b,1, Tao-Tao Ding b, Hua-Ying Li c a

Department of Engineering Physics, Tsinghua University, Beijing 100084, China Key Laboratory of Safety Science of Pressurized System of MOE, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China c College of Literature and Communication, Hebei Normal University for Nationalities, Chengde 067000, China b

h i g h l i g h t s
Mechanical properties of the Q690 High strength structural steel was investigated.
Evolution of void and dislocation in Q690 steel under plastic damage was revealed.
Nonlinear Lamb wave technique was employed to characterize the damage in Q690 steel.
Effect of plastic damage on the nonlinear effect of Q690 steel was investigated.

a r t i c l e

i n f o

Article history: Received 28 April 2019 Received in revised form 22 October 2019 Accepted 24 October 2019

Keywords: Nonlinear ultrasonic technique Lamb wave Q690 high strength steel Plastic damage

a b s t r a c t The nonlinear ultrasonic technique has been used to assess the plastic damage in High strength Q690 steel. The Q690 steel was stretched to different levels of plastic strain so as to obtain the specimen with different degrees of plastic damage. When strain was increased from 1% to 9%, the nonlinear parameter shows a general upward trend, and in the subsequent strain process, the nonlinear response drop off instead of going up. Meanwhile, metallographic examination indicates that, within the strain 9%, the growth of the void as well as the variation of dislocation structure and density are the main damage characteristic in Q690 steel. Many dislocation structures such as the dislocation cell and dislocation wall have formed in the tensile specimen, which is contribute to raise of the nonlinear effect. The results indicate that the nonlinear ultrasonic technique can be utilized to characterize the plastic damage in Q690 structural steel at the early stage. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction High strength structural (HSS) steels, typically refers to steels with yield strength exceed 460 MPa, are widely employed in many engineering machineries and infrastructures such as harbor crane, bridges, dams and roadways. The utilization of HSS steels could reduce the dimension of work piece as well as decrease the weight of structure, so as to obtain the environmental and economic benefits [1–3]. Due to the widespread use of this steel, it is of increasing important to carry out the nondestructive evaluation (NDE) on

⇑ Corresponding authors at: Room1117, building Liu Qing, shuangqing road, Tsinghua University, Beijing 100084, China. E-mail addresses: [email protected] (X. Wang), [email protected] (Y. Xiang). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.conbuildmat.2019.117384 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

the state of structural material damages [4], so that the follow-up maintenance and repair work can be taken in a timely manner. Nondestructive assessment of materials degradation based on the ultrasonic technology has received increasingly attention in the recent year, because the propagation characteristics of ultrasonic wave could reflect the intrinsic property of material [5–7]. Nevertheless, most of the conventional ultrasonic techniques (i.e. wave velocity, attenuation, transmission and reflection coefficients) are only effective for gross defects detection, but relatively insensitive to the micro-damage (e.g. micro-void and micro-crack) that happened at the early stages [8]. The nonlinear ultrasonic technique is an emerging alternative approach, which underwent a rapid development in recent years [9–12]. And now it has been considered as a promising method to evaluate the micro-structural damage in metals. The nonlinear ultrasonic technique and the conventional ultrasonic technique have apparent distinction, i.e., the former could reflect the

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

wave and longitudinal wave, respectively. cL is the velocity of

frequency change of input signal while the latter could not [10– 13]. Thus, the material degradation can be assessed by monitoring the higher order harmonic wave of the damaged specimen. Compared with the longitudinal wave method that could realize the localized damage assessment, the ultrasonic Lamb waves can focus on the overall damage within the measurable ranges, and it possess some advantages, which include the one-side ultrasonic launching and receiving, and the capability of long-range inspection. Therefore, the nonlinear Lamb waves can be used and promoted in the actual detection of large plate- and shell-like structural components on the construction site [13,14]. To date, many studies based on the nonlinear ultrasonic evaluation have been conducted, and the potential of nonlinear ultrasonic techniques have been realized [15–18]. However, there is still less information available about the relationship between the nonlinear ultrasonic responses with damage evolution in high strength structural steels. Considering that the failure of HSS steel components in a machine or construction can have disastrous consequences, in this paper, we selected the Q690 steel as the research object. Q690 steel is a Chinese grade of structural steel with nominal yield strength of 690 MPa, and internationally, a number of codes cover the steel grades up to 690 N/mm2, such as the S700 steel in EN 1993-1-12, and the ASTM A514 steel and A709 steel in ANSI/AISC 360–16. In this experiment, through tracking and measuring for the different degrees of plastic damage by using nonlinear Lamb waves, we tried to systematically investigate the nonlinear response vary with the damage evolution in Q690 High strength steel.

ðf ;lÞ

longitudinal wave, U Lq is the component of primary Lamb wave (l-mode). hL is the angle between the oy axis and the KLq , hT is the ^ Lq andK ^ Tq are the unit vectors angle between the oy axis and theKTq . K of theKLq and KTq , respectively. ^x denotes the unit vector along the ox ðFCÞ

2

bLamb ¼ A2f =A21f

¼

3. Experiments 3.1. Material specification and tensile tests

h io 2 n  P ðDLÞ  ðFCÞ U Lq sinhL z þ ð1Þq coshL y þ U Lq coshL z þ ð1Þq1 sinhL y

Table 1 shows the chemical composition of this HSS Q690 steel. The Q690 steel were processed into the plate-like shape specimen with dimension of length-266 mm, width-42 mm, and thickness5 mm (see Fig. 1(a)). The machinery performance of this steel was shown in Table 2. The tensile experiment was carried out on a MTS-C45 stretch tester, and an extensometer was used in the process of experiment. To prepare the specimens with different degrees of plastic damage, the Q690 steel specimens were stretched to the different levels of strain, which can be recognized in Fig. 1(b). The specific information of the stress-strain value was given in Table 3.

q¼1

^ Tq exp½2jKTq r þ jDu ½coshT z þ ð1Þq1 sinhT yð1Þq ½^x  K 2 sinð ^ Lq exp½2jKLq r þ jDu þ DuÞ P U ðFCÞ K Tq Du q¼1

ð1Þ

whereDuis the phase matching degree (in radians), and can be written as:

Du ¼

2pfZ dis ðcð2f ;nÞ  cðf ;lÞ Þ cð2f ;nÞ  cðf ;lÞ

ð2Þ

wheref is the primary Lamb wave frequency, Z dis is the wave propagation distance, cð2f ;nÞ and cðf ;lÞ are the phase velocity of double frequency Lamb wave (n-mode) and primary Lamb wave (l-mode), ðDLÞ

respectively. And the U Lq ðDLÞ U Lq

3.2. Nonlinear ultrasonic Lamb wave measurement A Ritec-snap RAM-5000 high power ultrasonic system was used for nonlinear Lamb wave measurement. The RITEC system is composed of a high power 50 X termination (RT-50), a high power 6 dB attenuator (RA-6), and two diplexers (FDK-X). Simultaneously, this system incorporates a high power gated amplifier for producing (RF) bursts, three accurate direct digital synthesizers (DDS) for high-resolution frequency control. Fig. 2 shows the phase and

can be given as:

 2 ðf ;lÞ 2 ½U Lq  ½3j þ 4l þ 2A þ 6B þ 2C 2pf ¼ d ½j þ 4l=3 cL d

ð5Þ

Due to the inherent dispersion and multimode characteristics, nonlinear effects of Lamb waves are generally weak. A series of second harmonic modes can be generated by the primary Lamb wave. Second harmonics can only accumulate with the propagation distance under certain conditions. Phase-velocity matching and non-zero energy flux are validated to be necessary for cumulative second harmonic generation, while group-velocity matching is not. Several studies [21–23] presented that the group-velocity matching is independent of the cumulative second-harmonic generation. From the condition of non-zero energy flux, only symmetric second harmonics can be generated by either the symmetric or antisymmetric Lamb waves.

of second order harmonic wave Uð2f Þ during the Lamb wave propagation can be given as: U

ð4Þ

where A1f is the fundamental wave amplitude, and A2f is the second-order harmonic wave amplitude. E2 ,E3 are the second and third-order elastic constants, respectively. Since the FðhT ; hL ; KLq ; KTq ; r; E2 ; E3 Þ, k, and Z dis were kept as consistent during the ultrasonic measurements, so the normalized nonlinear parameter can be written as:

If we set the coordinates origin of a solid plate was in its midplane, the direction of the wave travel is along the z axis, and the thickness direction of this plate was in y axis. Then, the cumulation

sinðDuÞ Du

ðDLÞ

bLamb ¼ FðhT ; hL ; KLq ; KTq ; r; E2 ; E3 ÞA2f =ðk Z dis A21f Þ

2. Nonlinear Lamb waves propagation in an elastic plate

ð2f Þ

ðFCÞ

axis. U Lq and U Tq are proportional to U Lq . ris the position vector, j is the unit vector. Based on the formulas above, the nonlinear parameter of Lamb waves can be expressed as [19,20]:

ð3Þ

wherej,l, A, B, C are second and third order elastic constants, d is one-half of the plate thickness. T and L represent the transverse

Table 1 The chemical composition of Q690 steel (wt.%). Element

C

Cr

Si

Ni

Mn

Nb

V

Al

Cu

Ti

Q690

0.123

0.067

0.264

0.018

2.245

0.049

0.004

0.047

0.009

0.198

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

(c)

(a)

Tensile stress (MPa)

800

(b)

5

4

1 2 3

6

7

8 9

600

400

200 tensile rate: 1 mm/min

0

0

2

4

6

8

10

12

14

16

strain (%) Fig. 1. Schematic diagram of experimental scheme. (a) The plate-like shaped Q690 HSS steel. (b) The Stretch Curve of the Q690 HSS steel specimen. (c) The MTS-C45 stretch tester machine.

Table 2 The mechanical properties of the HSS Q690 steel. Mechanical properties

yield strength

tensile strength

Percentage elongation after fracture

reduction of area

Q690 steel

690 MPa

734 MPa

15.4%

50.4%

Table 3 The specific stress–strain value of each tensile point. Point

1

2

3

4

5

6

7

8

9

Strain (%) Stress (MPa)

1.0 697.35

2.0 711.81

3.0 725.91

5.0 733.34

7.0 733.85

9.0 734.45

11.0 732.95

13.0 706.23

– –

group velocity dispersion curves for Q690 steel. Symmetric Lamb mode pair S1-s2 has been selected for nonlinear Lamb wave measurements, which satisfy the conditions of phase and group velocity matching. The fundamental frequency was calculated to be 0.82 MHz. A pair of commercial piezoelectric transducers was used in this experiment. The 1.0 MHz transducers acted as a transmitter (T) for

sending pulse signal, and the 2.25 MHz transducer was selected as the receiver (R) so that the second order harmonic wave signal (A2f ) can be received (see Fig. 3). The wedge angle of the transducers was adjusted to 27°. The tone-burst duration (s) and propagation distance (Zdis) are kept as 8 ms and 50 mm in every measurement. For observation of an obvious cumulative secondharmonic signal of Lamb wave propagation, the primary Lamb

Fig. 2. Dispersion curves for Lamb waves in a Q690 plate (a) phase and (b) group velocities.

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4. Results and discussion 4.1. Results of nonlinear Lamb wave measurement Fig. 4(a) shows the time-domain signal of the original Q690 sample, the time-domain signal contains the excitation signal and the receipt signal. To perform the Fast Fourier transform (FFT) of the receipt signal, the frequency-Amplitude function can be obtained. Fig. 4(b) shows the frequency spectra of the original Q690 steel, this curve contains the frequency signal of 0.82 MHz and 1.64 MHz, which corresponding to the fundamental wave (A1) and second harmonic wave (A2), respectively. Generally, the variation of the A2 can be used to characterize the material damage, however, the amplitude of the A2 was relatively small by comparison with the A1, and thus, it is difficult to observe the A2 change at this spectra range. To identify the amplitude variation of second harmonic wave (A2) more clearly, the frequency spectra that range from 1.5 MHz to 1.75 MHz was focused, which is marked in Fig. 4(b). The instrumentation nonlinearity was firstly calibrated before the nonlinear Lamb wave measurements of plastic damaged specimens. The calibration method was same as that described in our previous work [4]. The second harmonic (A2) of the Q690 HSS steel varies with plastic strain are shown in Fig. 5. The A2 value shows a trend of increase from the Strain 1% to the Strain 9%, and then come down in the subsequent stress–strain process. Further, it can be seen that the A2 increases less within range of Strain 1% ~2%, but increases obviously when the strain was up to 5%. Meanwhile, a tooth-like oscillation can be observed around the 1.64 MHz, which makes it difficult to determine the accurate value of A2. In this case, the frequency components that ranged from 1.635 MHz to 1.645 MHz were selected for signal processing. We took the average of these eleven points, and this value could better reflect the overall level of nonlinearity in each tensile specimen. A similar upward trend was also observed in the change of nonlinear parameter (bLamb ). Fig. 6 shows the bLamb of Q690 steel specimens under different tensile strain, and the bLamb was calculated from the Eq. (5). Compared with the original specimen, it can be observed that the bLamb shows a noticeable rise when strain was up to 2% (i.e. specimen went into the full plastic stage, see Fig. 1 (b)). As the strain increases, the bLamb changes little when strain was below the 3%, but increases significantly when strain was up to 5%. In the subsequent process, the bLamb increase progressively

Fig. 3. The schematic diagram of the nonlinear ultrasonic measurement.

wave mode (7-th, cðf ;7Þ ) and the double frequency Lamb mode (15th, cð2f ;15Þ ) are selected in this experiment, which could meet the condition of the phase velocity matching between the cðf ;lÞ and cð2f ;nÞ . The transducers are coupled to the steel specimen with light lubrication oil. The scanning frequency was set from 0 MHz to 2.4 MHz. Through the fast Fourier transfer (FFT), the frequency domain signal can be obtained. 3.3. Observation of microstructures To study the plastic damage accumulation in Q690 HSS steel, the specimens were cut from the green dotted line (see Fig. 1(a)) for metallographic observation. After grinding, polishing, and etching, each Q690 sample was observed by using SEM (MIRA3-LMH) and TEM (JEM-2100F). The void area fraction was counted by using the image analysis software (Image-Pro Plus 6.0). Besides, dislocation density of each sample was also counted by using the X-ray diffraction (XRD) method (Bruker-D8AdvanceX, Cu-Ka radiation, 40 kV, 40 mA). Note that before XRD measurements, electrolytic polishing was conducted in each Q690 sample. The scan range was set from 10 to 90°, with the scan rate of 2°/min.

0.0040

0.20 0.15

(a)

(b)

excitation signals receipt signal

0.0032

0.10

A1 Amplitude (V)

Amplitude (V)

Original Q690 steel

0.05 0.00 -0.05 -0.10

0.0024 0.0016 0.0008

A2

-0.15 Original Q690 steel

-0.20 -5.0x10-5

0.0

5.0x10-5

time (s)

1.0x10-4

1.5x10-4

0.0000 0.0

8.0x105

1.6x106

Frequency (Hz)

Fig. 4. The schematic diagram of the time-domain signal and frequency spectra of the original Q690 steel.

2.4x106

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

7x10-5 6x10-5

7x10-5

Origin

(a)

6x10-5 5x10-5

Amplitude (V)

Amplitude (V)

5x10-5 4x10-5 3x10-5 2x10-5

4x10-5 3x10-5 2x10-5

1x10-5

1x10-5

0

0

1.50E+06 1.55E+06 1.60E+06 1.65E+06 1.70E+06 1.75E+06

1.50E+06 1.55E+06 1.60E+06 1.65E+06 1.70E+06 1.75E+06

Frequency (Hz)

7x10-5 6x10-5

Strain 2%

(c)

6x10-5

Amplitude (V)

Amplitude (V)

Strain 5%

(d)

5x10-5

4x10-5 3x10-5 2x10-5

4x10-5 3x10-5 2x10-5

1x10-5

1x10-5

0

0

1.50E+06

1.55E+06

1.60E+06

1.65E+06

1.70E+06

1.75E+06

1.50E+06 1.55E+06 1.60E+06 1.65E+06 1.70E+06 1.75E+06

Frequency (Hz)

7x10-5

Strain 9%

(e)

Frequency (Hz)

7x10-5 6x10-5

5x10-5

Strain 13%

(f)

5x10-5

Amplitude (V)

Amplitude (V)

Frequency (Hz)

7x10-5

5x10-5

6x10-5

Strain 1%

(b)

4x10-5 3x10-5 2x10-5 1x10-5

4x10-5 3x10-5 2x10-5 1x10-5

0

0

1.50E+06 1.55E+06 1.60E+06 1.65E+06 1.70E+06 1.75E+06

1.50E+06 1.55E+06 1.60E+06 1.65E+06 1.70E+06 1.75E+06

Frequency (Hz)

Frequency (Hz)

Fig. 5. The variation of A2 in Q690 steel specimen with different tensile strain.

with the strain, and reach the maximum value when strain was rise to 9%. After this point, the bLamb starts to decline instead of keeping rise, which indicates that the nonlinearity effect was no longer accumulated on the verge of the fracture of Q690 steel. In general, the continued rise of nonlinear parameter during the plastic deformation indicates that the nonlinearity effect is cumulative in the material. Recent researches [8–13] indicate that there are three determining factors that can lead to the increase of the nonlinear parameter, which include the micro-void formation,

the growth of precipitates, and the increase of dislocation density. To investigate the reason for the increase of bLamb , the microstructural changes of the Q690 HSS steel were studied. 4.2. Microscopic structures observation under optical microscope (OM) Fig. 7 shows the OM images of Q690 HSS steel with different tensile strain. In original Q690 steel, the grain was very fine and equiaxed, which can be recognized in Fig. 7(a). The mean grain size

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

Nonlinear parameter (1/V)

0.007 0.006 0.005 0.004 0.003 0.002

0

2

4

6

8

10

12

14

Strain (%) Fig. 6. The variation of the nonlinear parameter with different tensile strain in Q690 steel.

(dm) of the original Q690 steel was nearly 6.6 lm, which was much smaller than that of the carbon structural steel (davg 13.64 lm, and its yield strength was about 310 MPa) [8]. Besides, fine grain strengthening is the main reinforcing mechanism for the high strength of this Q690 steel, and this will be discussed in more detail in the next section. With the increase of the applied stress, the tensile form void damage can be clearly observed (see Fig. 7(c)). The variation of the void area fraction as well as the void number density of Q690 steel can be seen in Fig. 8. It can be seen that the plastic damage gets worse with increasing tensile strain, as the area and quantity of the void increased steadily (see Fig. 7(d)–(f)). In the meantime, the size of the equiaxed grain shows an elongated trend when strain continuously rises. The extension of grain was along the tensile direction, which can be identified in Fig. 7(e). Besides, the OM image of the Q690 steel was going to be blurry as the strain increase (see Fig. 7(f)), which may be due to the sliding of grain boundary during the plastic deformation.

tensile direction Origin (b)

(a)

Strain 1%

Strain 2% (d)

(c)

Strain 5%

void void void void void

Strain 9% (f)

(e)

Strain 13% void

Grain deformation

void void

void

void

Fig. 7. The OM images of Q690 HSS steel with different tensile strain.

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

0.6

(b) Void number density (µm-2)

Void fraction area (%)

0.5

0.0016

(a)

0.4 0.3 0.2 0.1 0.0

0

1

2

5

9

13

Strain (%)

0.0012

0.0008

0.0004

0.0000

0

1

2 5 Strain (%)

9

13

Fig. 8. The variation of void area fraction and void number density of Q690 steels with different tensile strain. (a) void area fraction; (b) void number density.

4.3. Microscopic structures observation under scanning electron microscope (SEM) Fig. 9 shows the SEM images of Q690 HSS steels with different tensile strain, and the specimens were observed under two magnification times (1000 and 5000). The Q690 steel was consist of the mixture structure of granular bainite (GB) and bainitic ferrite (BF). The (GB) possess different morphology, which includes the island pattern (bainite-I, see Fig. 9(b)), acicular pattern (bainite-II, see Fig. 9(d)) and stripe-like pattern (bainite-III, see Fig. 9(f)). Figs. 10 and 11 show the EDS results of the (GB-test 1) and (BFtest 2), both of two structures contain the element of Fe, Mn, Si, but the Ti element was also presented in the (GB) structure (see Tables 4 and 5). It has been recognized that the addition of Ti facilitates the forming of precipitates such as TiN and TiC. These fine particles precipitated at the grain interior and grain boundary, which could retard the growth of austenite grain as well as limit the migration of grain boundary (i.e. the pinning effect). Therefore, the prior austenite grains were significantly refined, consequently achieved the fine structure of bainite. Meanwhile, the TiC precipitates possess high hardness, which could also realize the dispersion strengthening and secondary hardening. Fig. 9(j) shows the SEM image of Q690 steel that was stretched to the strain of 13%, a certain number of voids can be observed in this specimen. A noteworthy phenomenon is that there were precipitates existed inside the void. The EDS result of test 3 (see Fig. 12) reveals that the precipitates were TiN particles, which have a high content of Ti and N (see Table 6). As the TiN particle has a higher modulus than the (GB) or (BF) structures, when the latter was stretched into yield, the TiN particles undergo less deformation than the (GB) and (BF). Thus, the large difference in stress– strain characteristics of them result in deformation incompatibility, which cause the voids form around the TiN particles. Besides, there was no distinct micro-crack formation in the Strain-13% specimen. Thus, the fracture mechanism of this Q690 steel during the plastic tensile can be inferred as localized plastic flow prior to the micro-crack propagation. 4.4. Microscopic structures observation under Transmission electron microscope (TEM) The TEM images of the Q690 steel specimen with different levels of strain were shown in Fig. 13. The initial dislocation morphology can be recognized in the original specimen (see Fig. 13(a)), which manifests as long straight and discrete. The distribution of

the dislocation lines in this situation was sparse, and the dislocation density was relatively low in the initial state; when stress was applied to this material, the dislocation structure changed under the influence of the alternating stress. The dislocation lines appear to begin flexing when the strain was to reach 1% (within the extent of elasticity), and tending to form a cellular structure in the following deformation process. Fig. 13(c) shows the Q690 steel that was stretched to the strain of 2%, great changes have occurred in the dislocation structure of this specimen (Note that the plastic deformation has occurred). The zig-zag dislocation segments formed, while the long straight of dislocation lines disappeared. Besides, the phenomenon of dislocation jog and kink can be also observed in this state. When the strain was up to 5%, the dislocation density of the Q690 steel increased significantly, meanwhile, the dislocation interactions become more complex, since the dislocation loop structure has developed (see Fig. 13(d)); With the increasing degree of the strain, the dislocation walls and dislocation cells structure have also developed and can be seen in the Strain 9% specimen (see Fig. 13(e)), the dislocation cells were composed of high-density dislocation tangles, which possess lower area but larger groups compared with the dislocation loops structure in the Strain 5% specimen. Meanwhile, the dislocation density is so high in the dislocation wall structure, which indicates that the subgrain movement and dislocation pile-ups were severe in this region. In the latter stage of the plastic deformation, the wall/channel structure has formed, which can be recognized in Fig. 13(f). The channel structure possesses low dislocation density, and this could be due to the annihilation of the edge dislocations during the dislocation climb and cross-slip [13]. Besides, the dislocation network can also be seen, which contains bundles of intermixed dislocations. 4.5. The relationship between nonlinear parameter and plastic damage evolution In this study, it can be recognized that the main microstructural changes of Q690 steel during the plastic deformation are the initiation and growth of micro-voids, as well as the variations of dislocation structure and density. These factors could contribute to the distortion of ultrasonic wave propagation, and induce the variation of high order harmonic wave. Previous studies [24,25] indicate that the nonlinearity generation resulting from the dislocation pinned can be given as:

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

1000× (a)

5000× Strain 1% (b)

Strain 1%

2

(GB)-I

1

(c)

(BF)

Strain 2% (d)

Strain 2%

(GB)-II

(BF)

(e)

Strain 5% (f)

Strain 5%

(GB)-III

(GB)-III

Fig. 9. The SEM images of Q690 HSS steel with different tensile strain.

Db 24 XKL4 R3 E22 ¼ jrj b0 5 b0 l3 b2

ð6Þ

whereb0 is the initial value of nonlinear parameter. Db is the change of nonlinearity parameter. Kis the dislocation density, L is the length of the pinned dislocation segment, E2 is the second-order elastic constant, l is the shear modulus of the matrix, b is the Burgers vector, R is the resolving shear factor, and Xis the conversion factor from shear strain to longitudinal strain. r is a longitudinal stress [24]. From Eq. (6), it can be seen that the nonlinearity change is proportional to the parameters of Kand L4 if the parameters of X, R,l, b, E2 was assumed as constant. The parameters could be given as: X ¼ R ¼ 0:33, l ¼ 76 GPa, b ¼ 0:25 nm, E2 = 196 GPa, referring to the literature [25]. The dislocation density K was measured by referring the modified Williamson-Hall (WH) method [4], and the

average dislocation length L was figured out by analyzing the TEM micrograph. Specific parameters of the Q690 steel specimens with different plastic strain was given in Table 7. The model calculation results as well as the measurement data were shown in Fig. 14, it can be seen that there is a good agreement between the change trend of actual measured data and theoretical data. The rise of the nonlinear effect between the 0 and 9% strain is probably due to the increase of the dislocation density, while the decrease of nonlinear parameter after the 9% strain may come from many complicated factors, such as the occurrence of gross defects, local annihilation of the edge dislocations, and the formation of the channel structure. In our previous study, we found that the amplitude of the second harmonic and nonlinear parameter did not show a further rise in mild steel when the applied stress exceeds its tensile strength [8], in the Q690 high strength steel, a similar

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

Strain 9% (h)

(g)

Strain 9%

(GB)-I

Strain 13% (j)

(i)

Strain 13%

3

Fig. 9 (continued)

Test 1

Test 2

Fig. 11. EDS spectrum of the test 2.

Fig. 10. EDS spectrum of the test 1.

Table 4 EDS result of the test 1.

Table 5 EDS result of the test 2.

Element

Weight percentage

Atomic percentage

Element

Weight percentage

Atomic percentage

C O Si Fe Ti Mn Total

20.66 2.29 0.19 74.99 0.23 1.69 100.00

52.97 4.41 0.21 41.35 0.12 0.95 .

C Si Mn Fe O Total

13.41 0.17 2.31 81.85 2.26 100.00

40.29 0.22 1.52 52.88 5.10 .

phenomenon has been recognized, since there is a downward tendency of the nonlinear response when specimen was close to the breaking point. In fact, it should be noted that the dominant use of the nonlinear ultrasonic technique is to characterize the material damage at the early stages, instead of examining the presence of gross defects. With respect to those gross defects, the traditional ultrasonic tech-

nology (e.g. attenuation coefficient and wave velocity measurement) may be more effective [8]. In this experiment, the nonlinear ultrasonic effect shows a general upward trend when Q690 steel was stretched from the original state to strain 9%. The result indicates that the nonlinear ultrasonic technique is an alternative method to assess the plastic damage in HSS Q690 steel at the early stage.

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X. Wang et al. / Construction and Building Materials 234 (2020) 117384

Test 3

Table 6 EDS result of the test 3. Element

Weight percentage

Atomic percentage

C N O Fe Ti Nb Total

11.97 21.89 3.72 4.22 56.73 1.48 100.00

24.50 38.42 5.72 1.86 29.12 0.39 .

Fig. 12. EDS spectrum of the test 3.

(a)

Origin

(b)

Strain 1%

dislocation flexing

grain boundary

dislocation line

(c)

Strain 2%

(d)

Strain 5%

dislocation loop

Zig-zag dislocation segment

(e)

Strain 9%

(f)

Strain 13%

dislocation network dislocation cell

(e) dislocation cell

dislocation wall dislocation wall

Channel structures

Fig. 13. The TEM images of Q690 HSS steel with different tensile strain.

11

X. Wang et al. / Construction and Building Materials 234 (2020) 117384 Table 7 Microstructure parameters of the Q690 steel specimens with different plastic strain. origin Dislocation density Pinning dislocation length

Strain 1% 15

2

0.646✕10 m 0.11239 ± 0.037 lm

Strain 2% 15

2

0.781✕10 m 0.10881 ± 0.033 lm

Nomalized Nonlinear parameter (1/V)

2

1.389✕10 m 0.09572 ± 0.042 lm

2.4

Strain 9% 15

2

1.829✕10 m 0.09421 ± 0.030 lm

Strain 13% 15

2

2.105✕10 m 0.09672 ± 0.032 lm

2.1474✕1015 m2 0.09415 ± 0.040 lm

would also like to express their gratitude for projects supported by the Beijing Key 646 Laboratory of city integrated Emergency response science.

Measurement data

2.2

Strain 5% 15

Model calculation of Eq.(6) References

2.0 1.8 1.6 1.4 1.2 1.0 0

2

4

6

8

10

12

14

Strain (%) Fig. 14. The TEM images of Q690 HSS steel with different tensile strain.

5. Conclusions In summary, the application of nonlinear ultrasonic technique to characterize the plastic damage in the HSS Q690 steel was investigated in this work. The conclusions can be drawn as follows: (1) Compared with the original Q690 steel specimen, the nonlinear parameter shows a general upward trend when the strain was increased from 1% to 9%. Then, the nonlinear effect comes down in the subsequent stress–strain process until the specimen fracture. (2) Both of the void area fraction and the void number density increased with the increasing strain in Q690 steel. There was still no distinct micro-crack formation when the Q690 specimen was stretched to 13% strain. This manifests that the fracture mechanism of Q690 steel is localized plastic flow prior to the micro-crack propagation. (3) The dislocation structure and dislocation density significantly changed with the increasing of the plastic strain, the dislocation cell and dislocation wall structure can be clearly observed in the Strain 9% specimen. (4) The high sensitivity of the nonlinear measurement can be recognized in this experiment, which indicates that the nonlinear ultrasonic technique is a useful way to evaluate the plastic damage in HSS Q690 steel at the early stage.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Acknowledgements This research was funded by the National Natural Science Foundation of China (11622430; 11774090; 51835003). The authors

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