# Effect of Surface Roughness on Ultrasonic Testing of Back-Surface Micro-Cracks

^{*}

## Abstract

**:**

## Featured Application

**Effect of surface roughness on ultrasonic detection capacity of microcracks was investigated by simulation and experiment, this evaluated method provided a valuable reference for obtaining detection limits of micro-cracks under different rough surfaces.**

## Abstract

**R**). The signal amplitude ratio factor (SARF) is defined to assess the ultrasonic detection capacity for micro-cracks. Both finite element analysis and experimental results show that signal amplitude decreases with an increase in

_{a}**R**, resulting in signal-to-noise ratio loss. Amplitude attenuation caused by the rough back surface is less than that caused by the rough front surface. It is difficult to identify the signal of micro-cracks with a depth less than 400 μm when the

_{a}**R**of the front surface is larger than 15 μm. Cracks with depths of more than 200 μm can be distinguished when the back-surface roughness is less than 24 μm. Furthermore, the amplitude of the micro-crack signal increases slightly with variation in the horizontal parameter (

_{a}**R**). This study provides a valuable reference for the precision evaluation of micro-cracks using ultrasonic inspection.

_{sm}## 1. Introduction

**R**and

_{a}**R**are analyzed significantly. In Section 4, a number of experiments are designed to verify the effect of rough front surface and rough back surface. The results from experimental measurements are compared to theoretical analyses and simulations. An accurate description of the detection capacity of micro-cracks is obtained. Section 5 contains a brief conclusion.

_{sm}## 2. Background

#### 2.1. Surface Roughness

**R**corresponds to vertical deviation of the surface from the mean plane and reflects the arithmetic average height parameter [32,33]. The two-dimensional model used to represent the rough surface is spatially discretized and the discretized equivalent is given by:

_{a}_{i}represents the height of a single discrete point on the surface, as shown in Figure 1. The second parameter,

**R**, is used to describe the characteristics along the surface in the horizontal direction (x-axis). A series of normally distributed discretized intervals is used to define

_{sm}**R**[34]:

_{sm}_{j}is the spacing length of a profile element. It can be seen that

**R**represents the spacing length between two points on the mean plane, and it is set as an isotropic correlation length. The parameters

_{sm}**R**and

_{a}**R**are widely used in the machining process for general quality control and other fields for surface quality assessment. The statistical characteristics described in this manner can be related to the wave scattering behavior.

_{sm}#### 2.2. Scattering from Rough Surface

#### 2.3. Detection of Back-Surface Crack with Rough Surface

_{1}and T

_{2}are modified by surface roughness [12]. The reflection coefficient R

_{1}reflects the interaction of transmitted shear wave with the micro-crack and rough back surface. Considering absorption attenuation and scattering attenuation caused by the backscatter of microstructures inside the solid, the relationship between I

_{0}and I

_{5}can be simply given by:

**R**according to the phase-screen approximation. To further confirm the results of theoretical analysis, simulation and experimental studies are described in the following sections.

_{a}## 3. Simulation and Analyses

#### 3.1. Two-Dimensional Rough Surface Model Setup

**R**and

_{a}**R**) and time-domain signal of micro-crack. The model consists of a virtual focused transducer, coupled water, and a 9 mm thick steel plate with a back-surface micro-crack. The depth of the micro-crack is normally less than five percent of the wall thickness of the workpiece. The focused transducer, formed by a piezoelectric wafer and arc lens, has chord length of 8 mm and curvature radius 25 mm. It is at a stand-off distance of 20 mm from the front surface of the steel plate. The material properties used in the model are obtained from the material library of the software. The longitude wave velocity in water is 1480 m/s and shear wave velocity in steel is 3230 m/s. The excitation signal applied to the external circuit is a broadband modulated pulse, which can be modeled as a Gabor function [35]:

_{sm}**R**and

_{a}**R**. The mathematical expression corresponding to the roughness parameters in the model can be described as:

_{sm}**R**. Half of the amplitude B of the sinusoid is chosen to be of similar extent to

_{sm}**R**. In addition, W represents the width of the crack and D represents the crack depth.

_{a}#### 3.2. Verification of the Micro-Crack Signal on the Rough Surface

**R**is 25 μm and

_{a}**R**400 μm. Figure 5 shows the propagation of the acoustic wave for ultrasonic detection of micro-crack. The coherent and incoherent waves caused by the interaction of the incident wave with the rough interface are shown in Figure 5a–c. It can be seen clearly that the reflected wave beam from the rough coupled interface inside water is no longer focused. The incoherent wave inside the solid is scattered in all directions. Figure 5d shows that the energy intensity of the reflected wave from the crack reduces significantly. The pulse-echo of the crack transmits from the rough solid-water interface. The energy intensity further weakens because of multiple scattering, as shown in Figure 5e,f. The phenomenon agrees with the previous analysis.

_{sm}**R**on the front surface are set to 3.2 μm, 12.5 μm, and 25 μm, respectively. The signals at the center correspond to the micro-crack, as shown in Figure 6a. The noise signals occurring elsewhere are attributed to scattering from the rough surface. Figure 6b,c show the echo received from rougher surfaces; the amplitude of the crack signal decreases with increase in

_{a}**R**. When the front surface roughness

_{a}**R**is 25 μm, the signal of the crack becomes nearly indistinguishable from the noise (Figure 6a). The reflected wave signals obtained from the front surface get wider with increase in

_{a}**R**due to scattering in different directions. Figure 6d presents the reference signal when no micro-crack is on the rough back surface, and there is no apparent micro-crack signal (Figure 6c). The results correspond to previous analyses that the energy intensity of transmitted wave reduces because of multiple scattering. Furthermore, the amplitude of the noise signal increases slightly. Therefore, the signal-to-noise of the micro-crack signal degrades significantly with rougher surface.

_{a}#### 3.3. Micro-Crack Signal Assessment under the Effect of Front-Surface R_{a}

**R**of the rough surface was set to 300 μm, width of the crack was 250 μm, and

_{sm}**R**changed from 0 to 25 μm. For the surface with determined

_{a}**R**and

_{a}**R**, multiple simulations were performed and amplitudes of micro-cracks were averaged. Figure 7a shows that the mean amplitudes of crack signals decrease with an increase in

_{sm}**R**for micro-cracks with different depths. It can be seen that the mean amplitudes increase obviously when the crack depth changes from 100 μm to 200 μm. The trend remains almost unchanged as the depth increases from 200 μm to 400 μm. Meanwhile, the mean amplitudes of crack signals tend to be the same when

_{a}**R**is larger than 15 μm.

_{a}**R**increases. The significant decrease of SARF from

_{a}**R**12.5 µm is mainly caused by two aspects. On one hand, the amplitude of the echo signal drops significantly for cracks with different depths, as shown in Figure 7a. On the other hand, the mean amplitude of noise signal is nearly doubled compared to that of

_{a}**R**6.3 µm. The SARF tends to be less than the critical value when

_{a}**R**is larger than 15 μm, which means that it is difficult to distinguish useful crack signals. Additionally, the smaller depth of micro-crack corresponds to a smaller SARF critical value because the depth of the micro-crack is close to the order of magnitude of the height of the rough surface and the scattering attenuation becomes more serious, as described in the previous section.

_{a}#### 3.4. Micro-Crack Signal Assessment under the Effect of Back-Surface R_{a}

**R**with a rough back surface.

_{a}**R**and size of crack parameters are the same as in Section 3.3 while the front surface is smooth. Compared to the influence of a rough front surface, the mean amplitudes of cracks drop more slowly with a rough back surface. According to the analysis in Section 2.2, there is only reflected attenuation caused by back-surface roughness for corner reflection wave of the crack while both reflected and transmitted attenuations exist when the ultrasound wave passes through the rough front surface. The relationship between SARF and

_{sm}**R**is displayed in Figure 8b, and the procedure for calculation is the same as that in Section 3.3. It can be seen that the SARF critical values corresponding to micro-cracks with depths 100 μm, 150 μm, and 200 μm, are 8.5 μm, 15.8 μm, and 24 μm, respectively. This means that it can be accurately identified when the depth of the micro-crack on the rough back surface is larger than 200 μm. On the other hand, the smaller the size of the micro-crack on the rough surface, the greater the effect of

_{a}**R**becomes on ultrasonic detection.

_{a}#### 3.5. Micro-Crack Signal Assessment under the Effect of Roughness R_{sm}

**R**and normalized mean amplitude of the micro-crack signal, further simulations are performed and the results are shown in Figure 9. The width W and depth D of the crack are simultaneously set to be 250 μm, and

_{sm}**R**is set as 200 μm, 300 μm, 500 μm, or 700 μm. It can be seen from Figure 9a that the change trends are similar when

_{sm}**R**changes from 6.3 μm to 25 μm. The mean amplitudes of micro-crack signals grow slowly with an increase in

_{a}**R**with rough front surface due to weaker wave scattering. On the other hand, the influence of back-surface

_{sm}**R**on the mean amplitude of the crack signal is slighter than that with front surface, according to Figure 9b. The variation in surface roughness parameter in the horizontal direction has a slight effect on acoustic attenuation. The fluctuation of microstructure height has greater influence on acoustic wave scattering, resulting in more serious distortion of the crack signal.

_{sm}## 4. Experiments and Discussion

#### 4.1. Experimental Equipment

**R**and

_{a}**R**was machined by vertical CNC milling and CNC turning, respectively. The opposite sides of all test samples were ground to make their surfaces smooth. To validate surface variations of the test samples, a Comprehensive Measurement System (Form Talysurf PG1830, Taylor Hobson Limited, Leicester, UK) was used to measure roughness profiles across the surfaces of each sample. There was good agreement with the set roughness values. Different rectangular notches on the rough and smooth surfaces of each sample were machined by a laser cutting machine. The notches were used as reference defects for studying the ultrasonic detection capacity of micro-cracks. The notches were at the bottom of the surface texture.

_{sm}#### 4.2. The Effect of Front-Surface Roughness on Notch Detection

**R**. It can be seen that the mean amplitudes of notch signals dropped rapidly and the average signal shapes changed with an increase in

_{a}**R**. In addition, the noise signals caused by the rough surface grew slightly with larger

_{a}**R**. There is good agreement with the simulation results.

_{a}**R**of front surface. The results indicated that the mean amplitude of notch signal was sensitive to notch depth. It can also be seen that larger

_{a}**R**corresponds to weaker $\overline{A{s}_{max}}$ of notch signal; the mean amplitude of the deeper notch signal reduced rapidly with an increase in

_{a}**R**, and was the same when

_{a}**R**was larger than 17 µm. It indicated that the attenuation of energy intensity of pulse-echo increased with enhancement of multiple scattering caused by surface roughness

_{a}**R**. Considering the experimental uncertainties of the attenuation measurement, the agreement between simulation results and measured data was deemed satisfactory.

_{a}**R**is presented in Figure 13b. It can be seen that the SARF value decreased with

_{a}**R**because of decrease in ${As}_{max}$ of the notch signal and increase in noise signal. When the roughness

_{a}**R**was lower than 12.5 µm, the impact of a decrease in notch size on mean amplitude of notch signal was obvious. The SARF value of notch 3 was larger than those of notches 2 and 1 for the same

_{a}**R**and processing method. On the other hand, the SARF critical solid line that represented the critical value 3.16 is given in Figure 13b. The deeper notch corresponded to larger critical

_{a}**R**. When the roughness was larger than approximately 15 µm, the SARF value was lower than the critical value for these notches. The weaker notch signals were almost immersed in the noise signal and could not be distinguished easily.

_{a}**R**. The horizontal direction parameter

_{sm}**R**of the test samples obtained from different processing methods were not the same, as shown in Table 1. Comparing the ${As}_{max}$ of sample numbers 1–5 and sample numbers 6–10, the mean amplitudes of notch signals changed slightly with an increase in

_{sm}**R**at the same

_{sm}**R**and notch depth. The decreasing trend in SARF value was similar to the mean amplitudes of notch signals for different

_{a}**R**, as can be seen in Figure 13b.

_{sm}#### 4.3. The Effect of Back-Surface Roughness on Notch Detection

**R**. The mean amplitude of the notch signal was directly proportional to the notch depth. As can be seen in Figure 14b, the signal amplitude ratio factor (SARF) also decreased with increase in

_{a}**R**. The degree of attenuation caused by back surface roughness was slighter than that caused by front-surface roughness, observed from the relationship between variations in the mean amplitude of notch signal and

_{a}**R**. The SARF critical value corresponding to notches with different depths in this experiment was larger than that of the rough front surface. The SARF critical value of M-notch3 was 22.5 µm in Figure 14b while the value was 15 µm corresponding to a rough front surface. This was due to the fact that the attenuation of energy intensity of the pulse-echo of the notch caused by reflection on the rough back surface was less than that caused by transmission on the rough front surface.

_{a}## 5. Conclusions

**R**. The horizontal direction parameter

_{a}**R**had a negligible effect on change in crack signal. On the other hand, the mean amplitude of the noise signal caused by multiple scattering nearly in all directions on rough surface increased slightly with an increase in

_{sm}**R**.

_{a}**R**exceeded 15 μm. Compared to the rough front surface, attenuation of the energy intensity of micro-crack pulse-echo caused by the rough back surface was slighter. The micro-crack with depth over 200 μm was accurately identified when the

_{a}**R**of back surface was less than 24 μm. The surface roughness leads to substantial changes in the results of ultrasonic inspection for micro-cracks. This research provides a valuable reference for obtaining detection limits of micro-cracks under different rough surfaces, which is beneficial for improving detection reliability and accuracy for micro-cracks. Further work will focus on the effect of surface roughness on the detection of front-surface micro-cracks.

_{a}## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**(

**a**) Schematic diagram of ultrasonic detection of micro-crack with rough surface; (

**b**) changes in energy intensity of acoustic wave for micro-crack detection. I

_{0}~I

_{5}represent the changes in energy intensity from incident wave to crack echo. T

_{1}represents the transmission coefficient of incident acoustic wave, R

_{1}represents the reflection coefficient of transmitted shear wave, and T

_{2}represents the retransmission coefficient of the reflected wave of back-surface crack.

**Figure 5.**Scattering diagram of acoustic wave during ultrasonic detection process of micro-crack when the front surface is rough and back surface is smooth. (

**a**) t = 13.5 μs; (

**b**) t = 15 μs; (

**c**) t = 16.5 μs; (

**d**) t = 19.4 μs; (

**e**) t = 21.9 μs; (

**f**) t = 24 μs.

**Figure 6.**Ultrasonic time-domain signal when front-surface roughness

**R**is (

_{a}**a**) 3.2 μm, (

**b**) 12.5 μm, and (

**c**) 25 μm and there is a micro-crack on the smooth back surface. Reference signal in (

**d**) while front-surface roughness

**R**is 25 μm and there is no micro-crack on the smooth back surface.

_{a}**Figure 7.**(

**a**) Normalized mean signal amplitudes of different cracks reduce as front-surface roughness

**R**increases. (

_{a}**b**) The signal amplitude ratio factor (SARF) reduces as front-surface roughness

**R**increases.

_{a}**Figure 8.**(

**a**) Normalized mean signal amplitudes of different cracks reduce as back-surface roughness

**R**increases. (

_{a}**b**) The signal amplitude ratio factor (SARF) reduces as back-surface roughness

**R**increases.

_{a}**Figure 9.**(

**a**) Normalized mean signal amplitude of the same crack reduces as front-surface roughness

**R**increases. (

_{sm}**b**) Normalized mean signal amplitude of the same crack reduces as back-surface roughness

**R**increases.

_{sm}**Figure 11.**(

**a**) The distribution of notches 1–3 on rough surface and smooth surface of test sample plate; (

**b**) test samples 1–10; all steel plates are of the same size (240 mm × 50 mm × 90 mm).

**Figure 12.**Ultrasonic time-domain mean signals of notch 3 on different experimental samples with front-surface roughness

**R**= 3.2 μm, 6.3 μm, and 12.5 μm.

_{a}**Figure 13.**(

**a**) Normalized mean signal amplitudes of notches reduce as front-surface roughness

**R**increases; ‘T’ represents CNC turning, ‘M’ represents vertical CNC milling. (

_{a}**b**) The signal amplitude ratio factor (SARF) reduces as front-surface roughness

**R**increases.

_{a}**Figure 14.**(

**a**) Normalized mean signal amplitudes of notches reduce as back-surface roughness

**R**increases; ‘T’ represents CNC turning, ‘M’ represents vertical CNC milling. (

_{a}**b**) The signal amplitude ratio factor (SARF) reduces as back-surface roughness

**R**increases.

_{a}**Table 1.**Parameters of test samples with rough and smooth surfaces. CNC: Computerized Numerical Control.

**R**: the arithmetic average heights of rough surface.

_{a}**R**: the horizontal parameter of rough surface.

_{sm}Processing Method | Sample No. | R_{a} (µm) | R_{sm} (µm) | Notch Depth D (µm) | Notch Width W (µm) | Material | ||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | ||||||

CNC turning (Rough surface) | 1 | 3.2 | 1320 | 250 | 150 | 100 | 100 | Q235A Steel |

2 | 6.3 | |||||||

3 | 12.5 | |||||||

4 | 17.0 | |||||||

5 | 23.0 | |||||||

Vertical CNC milling (Rough surface) | 6 | 3.2 | 900 | 250 | 150 | 100 | ||

7 | 6.3 | |||||||

8 | 12.5 | |||||||

9 | 17.0 | |||||||

10 | 23.0 | |||||||

Grinding (Smooth surface) | All samples | 1.6 | 85 | 250 | 150 | 100 |

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**MDPI and ACS Style**

Wang, Z.; Cui, X.; Ma, H.; Kang, Y.; Deng, Z.
Effect of Surface Roughness on Ultrasonic Testing of Back-Surface Micro-Cracks. *Appl. Sci.* **2018**, *8*, 1233.
https://doi.org/10.3390/app8081233

**AMA Style**

Wang Z, Cui X, Ma H, Kang Y, Deng Z.
Effect of Surface Roughness on Ultrasonic Testing of Back-Surface Micro-Cracks. *Applied Sciences*. 2018; 8(8):1233.
https://doi.org/10.3390/app8081233

**Chicago/Turabian Style**

Wang, Zhe, Ximing Cui, Hongbao Ma, Yihua Kang, and Zhiyang Deng.
2018. "Effect of Surface Roughness on Ultrasonic Testing of Back-Surface Micro-Cracks" *Applied Sciences* 8, no. 8: 1233.
https://doi.org/10.3390/app8081233