Microwave Dual-Crack Sensor with a High Q-Factor Using the TE20 Resonance of a Complementary Split-Ring Resonator on a Substrate-Integrated Waveguide

Microwave sensors have attracted interest as non-destructive metal crack detection (MCD) devices due to their low cost, simple fabrication, potential miniaturization, noncontact nature, and capability for remote detection. However, the development of multi-crack sensors of a suitable size and quality factor (Q-factor) remains a challenge. In the present study, we propose a multi-MCD sensor that combines a higher-mode substrate-integrated waveguide (SIW) and complementary split-ring resonators (CSRRs). In order to increase the Q-factor, the device is miniaturized; the MCD is facilitated; and two independent CSRRs are loaded onto the SIW, where the electromagnetic field is concentrated. The concentrated electromagnetic field of the SIW improves the Q-factor of the CSRRs, and each CSRR creates its own resonance and produces a miniaturizing effect by activating the sensor below the cut-off frequency of the SIW. The proposed multi-MCD sensor is numerically and experimentally demonstrated for cracks with different widths and depths. The fabricated sensor with a TE20-mode SIW and CSRRs is able to efficiently detect two sub-millimeter metal cracks simultaneously with a high Q-factor of 281.


Introduction
Surface cracks in the metal caused by fatigue and corrosion, which can lead to significant problems in both small metallic objects and large structures, are difficult to detect and repair. Recently, various metal crack detection (MCD) techniques have been developed, including destructive tests such as acid corrosion, sulfur printing, and pinhole tests. However, non-destructive testing (NDT) has received significant attention because destructive tests can cause undesired damage and are limited in detecting cracks under coatings, such as rust, paint, corrosion protection, and composite laminate [1][2][3]. NDT techniques include advanced ultrasound, acoustic emissions, eddy currents, and optical fiber techniques, all of which offer high-resolution crack detection. However, they have disadvantages such as high complexity, high cost, large-sized equipment, and manufacturing difficulties [4][5][6][7][8][9][10][11][12]. In contrast, microwave-based NDT employing microstrips, waveguides, meta-resonators, radio-frequency (RF) identification, and antennas are low-cost, have a smaller sensor size, and allow for easier fabrication [13][14][15][16][17][18][19][20]. Despite these advantages, microwave-based NDT is limited in its ability to detect a variety of crack shapes and multiple cracks simultaneously and generally requires an increase in sensitivity.
The quality factor (Q-factor) is a key parameter for sensitivity; thus, various RF sensor studies have sought to develop sensor systems with a high Q-factor [21][22][23]. High Q-factor RF sensors can be realized using active or passive feedback systems. Assisting an active feedback loop using an active microwave device can dynamically increase the Q-factor; however, DC adjustment and calibration are important issues for this setup that need to Figure 1 summarizes the principles underlying the proposed multi-crack detection sensor with a high Q-factor. First, we used a higher-mode SIW to form a separated E-field distribution, and the SIW subsequently enhanced the Q-factor of the CSRRs (Figure 1a) Next, independent CSRRs were positioned in the separated and concentrated E-fields on the TE20-mode SIW. Each CSRR produces an independent resonance, and the resonance frequency strengthens the E-field of the SIW (Figure 1b,c). As a result, changes in the meta surface, such as cracks or slots, sensitively affect the reflective coefficient due to the stronger external field for each CSRR (Figure 1d).

Figure 1.
Proposed multi-crack detecting sensor with a high Q-factor: (a) TE20 mode SIW only E field vector distribution. E-field vector distribution after the integration of the CSRRs (b) at 4.69 GHz and (c) 5.49 GHz. The E-field intensity range of (a-c) is the same. Concept illustration of (d) inde pendent multi-crack detection and (e) the reflective coefficients before and after CSRR loading.
For example, when a crack is near CSRR1, the field near this CSRR changes, affecting the reflective coefficient for its resonance frequency. On the other hand, when a crack is near CSRR2, the crack only affects the reflective coefficient for the resonance frequency o CSRR2. When cracks are near both CSRRs, the reflective coefficients both change. In par ticular, loading the CSRR onto a higher-mode SIW has some advantages. Firstly, a higher mode SIW enhances the Q-factor of the CSRR by strengthening the electromagnetic field thus, the proposed sensor has a sub-millimeter sensing resolution and can distinguish be tween various crack shapes. Secondly, the use of CSRRs reduces the physical size of the SIW while maintaining its advantages because the higher capacitance and inductance o the CSRR decrease the operating frequency of the SIW (Figure 1e). Table 1 compares the performance of the proposed crack sensor with that of conven tional multi-detection RF sensors and crack detection sensors using CSRRs. These ap proaches have received significant attention because multi-detection capability signifi cantly reduces the scanning time over wide areas and reduces power consumption. In [44], a power divider was used to produce independent frequencies and increase the Q factor, leading to the fabrication of a sensor with high accuracy for liquid material permit tivity measurements. In [16], a substrate highly sensitive to temperature was used to com bine temperature and crack sensing. In [18], metal crack and strain sensing were achieved using a dual-mode passive and active antenna. GHz. The E-field intensity range of (a-c) is the same. Concept illustration of (d) independent multi-crack detection and (e) the reflective coefficients before and after CSRR loading.
For example, when a crack is near CSRR1, the field near this CSRR changes, affecting the reflective coefficient for its resonance frequency. On the other hand, when a crack is near CSRR2, the crack only affects the reflective coefficient for the resonance frequency of CSRR2. When cracks are near both CSRRs, the reflective coefficients both change. In particular, loading the CSRR onto a higher-mode SIW has some advantages. Firstly, a higher-mode SIW enhances the Q-factor of the CSRR by strengthening the electromagnetic field; thus, the proposed sensor has a sub-millimeter sensing resolution and can distinguish between various crack shapes. Secondly, the use of CSRRs reduces the physical size of the SIW while maintaining its advantages because the higher capacitance and inductance of the CSRR decrease the operating frequency of the SIW (Figure 1e). Table 1 compares the performance of the proposed crack sensor with that of conventional multi-detection RF sensors and crack detection sensors using CSRRs. These approaches have received significant attention because multi-detection capability significantly reduces the scanning time over wide areas and reduces power consumption. In [44], a power divider was used to produce independent frequencies and increase the Q-factor, leading to the fabrication of a sensor with high accuracy for liquid material permittivity measurements. In [16], a substrate highly sensitive to temperature was used to combine temperature and crack sensing. In [18], metal crack and strain sensing were achieved using a dual-mode passive and active antenna.
For MCD, many researchers have focused on increasing the Q-factor or the number of cracks that can be detected, for which antennas and CSRRs are widely used. We previously demonstrated an increase in the Q-factor by integrating a CSRR with the dominant mode of a SIW [35]. In [36], four SRRs were used to increase the detectable number of cracks, exhibiting high sensitivity at 38 GHz. However, SRRs create E-fields on the surface, and some exhibit unstable detection performance with a sensing resolution that varies from 0.1 mm to 0.5 mm, depending on the crack position. In [14,41], higher-mode antennas were introduced to produce independent frequencies and detect the tilting angle of metal cracks. In [44], a spoof surface plasmon polariton sensor was used for multiple crack detection by incorporating liquid channels. The sensor had high accuracy, sensing resolution, and sensitivity, but liquid switches have a slow switching speed and require an additional system for movement and storage. Although the sensor in [13] had the capability to detect 12 cracks simultaneously and independently, it had a low Q-factor and resolution. In contrast, the highly sensitive sensor proposed in the present study has a high Q-factor and sensing resolution in terms of both width and depth. In particular, the sensor can detect crack depths at a resolution of 0.2 mm due to the stronger external E-field.  Figure 2 presents the proposed dual-crack sensor design. It consists of a three-layered bottom conductive element with a signal line, a top conductive layer with two etched CSRRs on the ground plane, and a substrate with a via that connects the top and bottom plane to produce SIW cavities. We used a 1.27 mm thick Rogers Duroid 6010 substrate with a dielectric constant (ε r ) of 10.2 and a loss tangent (tan δ) of 0.0023. Additionally, the final sensor design included an uncracked metal sheet ( Figure 1c). In this paper, aluminum with a thickness of 5 mm was used by a metal sheet.

Design of the Proposed Dual-Crack Detection Sensor
bottom conductive element with a signal line, a top conductive layer with two etched CSRRs on the ground plane, and a substrate with a via that connects the top and bottom plane to produce SIW cavities. We used a 1.27 mm thick Rogers Duroid 6010 substrate with a dielectric constant ( ) of 10.2 and a loss tangent (tan ) of 0.0023. Additionally, the final sensor design included an uncracked metal sheet (Figure 1c). In this paper, aluminum with a thickness of 5 mm was used by a metal sheet. The geometrical parameters for the SIW and CSRRs were determined using Equations (1)- (8). First, we designed the TE20-mode SIW structure using Equations (1)-(3). The resonance frequency of the TE20-mode SIW was calculated as where , , , , , and are the substrate permittivity, permeability, mode index, mode index, and effective width and length, respectively. The effective width and length were calculated as where and are the width and length of the SIW, respectively, from the center of the vias, and is the diameter of the vias [47,74]. Based on the SIW, the TE20-mode resonant frequency for the SIW loaded with CSRRs can be expressed as The geometrical parameters for the SIW and CSRRs were determined using Equations (1)- (8). First, we designed the TE 20 -mode SIW structure using Equations (1)-(3). The resonance frequency of the TE 20 -mode SIW was calculated as ( where ε, µ, m, n, W e f f , and L e f f are the substrate permittivity, permeability, mode m index, mode n index, and effective width and length, respectively. The effective width and length were calculated as where W c and L c are the width and length of the SIW, respectively, from the center of the vias, and D is the diameter of the vias [47,74]. Based on the SIW, the TE 20 -mode resonant frequency for the SIW loaded with CSRRs can be expressed as where L r and C r are the inductance and capacitance of the CSRR as shown in Figure 2b [74,75], which are determined by Equations (5) and (6), respectively: where ρ = c 4 +c 5 c 1 −c 4 −c 5 and C pul is the capacitance per unit length between the rings [76][77][78][79][80]. In addition, the proposed sensor employs CSRRs to reduce the evanescent wave effects and obtain a higher Q-factor compared with SIW-only approaches. The Q-factor at each resonant frequency can be expressed as where C r and L r are defined in Equations (5) and (6), respectively. A higher Q-factor increases the sensitivity, i.e., sharper resonance E-field concentrations and perturbations [77]. A large D and V p can occur due to E-field leakage in the SIW, thus we limit these to reduce radiation losses as follows: where λ g is the guided wavelength. Finally, the SIW cavities within the substrate have a width W of 25 mm, a length L of 11.1 mm, a via diameter D of 1 mm, and a center-to-center separation V p of 1. The cavity inserts were designed to match the impedance with the aluminum sheet used as the CSRR loading plane, with a width I W of 6 mm and a length I L of 2 mm. The total substrate size is SX = 36 mm and SY = 26 mm. Figure 3 presents simulated S11 results for the proposed crack sensor. The resonant frequency of the sensor changes from 4.626 and 5.436 GHz to 4.053 and 5.208 GHz after loading the Al sheet because the addition of material that has a different dielectric constant affects the resonant frequency ( Figure 3a). In this paper, we optimized the sensor via the loading material to increase its sensitivity for surface cracks. Figure 3b−d show that the proposed sensor can detect the position of multiple cracks with a width, depth, and length of 0.5 × 0.5 × 6.1 mm 3 . For example, when cracks are above both CSRRs, the resonance frequencies change from 4.053 and 5.208 GHz to 4.020 and 5.145 GHz for CSRR1 and CSRR2, respectively. On the other hand, when a crack is only above CSRR1, only the resonance frequency for CSRR1 changes, while the same is true for CSRR2. This is because the E-field near the CSRR is disturbed by the material, affecting the resonant frequency of the CSRR.

Sensing Method
In addition, when a crack is present in the CSRR region, the capacitance is affected. The concentrated E-field near the CSRR flows along the crack, which operates as a capacitor. The shorter side of the crack is considered the crack width, and it can be considered the distance between capacitors. The crack depth can be considered the area of the capacitor. When the crack width increases, the capacitance decreases, and the resonant frequency increases. In addition, as the crack depth increases, the capacitance rises, and the resonant frequency falls. The resonant frequency of a CSRR in the presence of a crack is represented by Equation (9): where C crack is the capacitance included by the crack. Thus, the proposed sensor detects a crack using the change in the resonant frequency. The proposed multi-crack sensor has a low fabrication cost and small waveguide cavities, and the independent sensing area can be extended because multi-E-fields in TEmn mode do not affect other sensing results [81][82][83].  In addition, when a crack is present in the CSRR region, the capacitance is affected The concentrated E-field near the CSRR flows along the crack, which operates as a capacitor. The shorter side of the crack is considered the crack width, and it can be considered the distance between capacitors. The crack depth can be considered the area of the capacitor. When the crack width increases, the capacitance decreases, and the resonant fre- Simulation results for the proposed crack sensor: (a) S11 without an Al sheet and with an uncracked Al sheet, (b) S11 for different crack numbers and positions (two cracks, single crack at CSRR1, single crack at CSRR2, no crack), S11 results (c) in the CSRR2 resonance frequency band, and (d) in the CSRR1 resonance frequency band (crack width, depth, and length of 0.5 × 0.5 × 6.1 mm). However, when the crack is outside the CSRR, there is little change in frequency from the y-axis movement of the crack.    (8,4); (f) S11 when the crack move y-axis from (4, −6) to (4, 6).
Next, Figure 6 shows the detection capability of the crack under the metal surface. Generally, non-destructive testing can be used for detecting cracks under the surfaces. In the simulation, the crack of 0.5 × 2 × 0.3 mm 3 is used, and the crack is positioned in the center of CSRR1, as shown in Figure 6a. Then, the crack is moved from the metal surface (Dud = 0 mm) to the interior of the metal (Dud = 2.5 mm). As a result, when Dud changes from 0.1 mm to 0.4 mm, the frequency is changed from 3.82 GHz to 3.88 GHz, and when Dud is bigger than 0.4 mm, the resonance frequency of the sensor generates at 3.94 GHz. In summary, the proposed sensor can detect whether a crack is on a metal surface or inside the metal, but it is difficult to distinguish how deep the crack penetrates accurately.  (8,4); (f) S11 when the crack move y-axis from (4, −6) to (4, 6). Figure 4a,b display the simulated frequency responses for various straight crack widths, with a consistent length of 6.1 mm for all cracks. Figure 4a presents the simulated S11 results as the width of a single straight crack above CSRR1 increases from 0.3 to 0.7 mm at intervals of 0.1 mm with a fixed depth of 0.5 mm. The resonant frequency for CSRR1 increases from 5.126 to 5.229 GHz as the crack width increases, and the average change in frequency is 257.5 MHz/mm (Figure 4a). On the other hand, when the width of a single straight crack above CSRR2 increases from 0.3 to 0.7 mm at intervals of 0.1 mm with a fixed depth of 0.5 mm, the resonant frequency for CSRR2 increases from 3.988 to 4.083 GHz and the average frequency shift is 237.5 MHz/mm. Figure 4d,e present the simulated S11 results when the depth of a single straight crack above CSRR1 and CSRR2 increases from 0.1 to 0.9 mm at intervals of 0.2 mm. The resonant frequency of CSRR1 decreases from 5.269 to 5.145 GHz, and the average change in frequency is 142.5 MHz/mm when the crack depth is changed above CSRR1. In contrast, when the crack depths above CSRR2 increase, the resonant frequency of CSRR2 decreases from 4.103 to 4.011 GHz, and the average change in frequency is 132.5 MHz/mm. The simulation results thus demonstrate the sensitivity of the proposed sensor for the detection of straight cracks, with the ability to distinguish differences of 0.1 and 0.2 mm in width and depth, respectively.
The proposed dual sensor can detect various shapes at each CSRR due to its high sensitivity. Figure 4f,g present the simulated S11 results for five crack shapes commonly found on metal surfaces: tilted, cross, zigzag, star, and pinhole. Figure 4f presents the S11 results for different tilting angles above CSRR1. A ±45 • rotation of the crack increases the resonant frequency to 5.228 GHz compared with a resonant frequency of 5.174 GHz at 0 • . Similarly, a 90 • horizontally oriented straight crack has a resonant frequency of 5.283 GHz. Figure 4g displays the S11 results for the straight, cross, zigzag, star, and pinhole cracks above CSRR2. Because the difference in the crack distribution affects Ccrack in Equation (9), and small differences can have a significant effect due to the concentrated Efield, the different crack patterns lead to differences in the change in the resonant frequency. Finally, Figure 7 shows the effect of the thickness of the Al sheet for the proposed sensor and the detection capability for the crack length. First, the thickness of the Al sheet has little effect on the RF sensor because the metal material reflects almost all the waves on the surface, as shown in Figure 7a. Next, the length of the crack has a different effect on the RF sensor depending on the direction of the crack. Figure 7b shows that a change in frequency occurs when the crack is lengthened toward the gap of the ring since the electric field is strongly formed in the center of the CSRR and near the gap of the ring. Conversely, little frequency change appears when the crack is lengthened in a direction unrelated to the ring's gap, as shown in Figure 7c.   Figure 5b, when the crack moves from (−1, 0) to (8, 0) around CSRR2, the further away from (4, 0), the center of the CSRR, the smaller the range of frequency variation. In the same way, in Figure 5c, when the crack moves from (−9, 0) to (−2, 0) around CSRR1, the further away from (−5, 0), the center of the CSRR, the smaller the range of frequency variation. However, when the crack positions outside the CSRR where the electric field is weak, there is little change in frequency from the x-axis movement of the crack, as shown in Figure 5d,e. In addition, we checked the effect of the y-direction position deviation of the crack (Figure 5f). Similar to the change in the x-axis, it was shown that the closer the center of the CSRR, the greater the frequency change in the position deviation of the y-axis. For example, when the crack is in (4, 0), the frequency moves from 4.82 GHz to 5.18 GHz; when the crack is in (4, −1) or (4, 1), the frequency moves from 4.82 GHz to 5.1 GHz; and when the crack is in (4, −3) or (4, 3), the frequencies move from 4.82 GHz to 5 GHz. However, when the crack is outside the CSRR, there is little change in frequency from the y-axis movement of the crack.

Fabrication and Sensor Measurement Results
We fabricated a prototype SIW-based dual-crack sensor with various Al sheets in accordance with the proposed design. Figure 8a,b show top and bottom views of the fabricated sensor, and Figure 8c shows a side view of the fabricated sensor with the Al sheet. We employed four representative Al sheets with different straight crack widths and depths ( Table 2); more complex shapes were not tested due to the difficulty of fabrication.  Next, Figure 6 shows the detection capability of the crack under the metal surface. Generally, non-destructive testing can be used for detecting cracks under the surfaces. In the simulation, the crack of 0.5 × 2 × 0.3 mm 3 is used, and the crack is positioned in the center of CSRR1, as shown in Figure 6a. Then, the crack is moved from the metal surface (D ud = 0 mm) to the interior of the metal (D ud = 2.5 mm). As a result, when D ud changes from 0.1 mm to 0.4 mm, the frequency is changed from 3.82 GHz to 3.88 GHz, and when D ud is bigger than 0.4 mm, the resonance frequency of the sensor generates at 3.94 GHz. In summary, the proposed sensor can detect whether a crack is on a metal surface or inside the metal, but it is difficult to distinguish how deep the crack penetrates accurately.
Finally, Figure 7 shows the effect of the thickness of the Al sheet for the proposed sensor and the detection capability for the crack length. First, the thickness of the Al sheet has little effect on the RF sensor because the metal material reflects almost all the waves on the surface, as shown in Figure 7a. Next, the length of the crack has a different effect on the RF sensor depending on the direction of the crack. Figure 7b shows that a change in frequency occurs when the crack is lengthened toward the gap of the ring since the electric field is strongly formed in the center of the CSRR and near the gap of the ring. Conversely, little frequency change appears when the crack is lengthened in a direction unrelated to the ring's gap, as shown in Figure 7c.

Fabrication and Sensor Measurement Results
We fabricated a prototype SIW-based dual-crack sensor with various Al sheets in accordance with the proposed design. Figure 8a,b show top and bottom views of the fabricated sensor, and Figure 8c shows a side view of the fabricated sensor with the Al sheet. We employed four representative Al sheets with different straight crack widths and depths ( Table 2); more complex shapes were not tested due to the difficulty of fabrication.
Micromachines 2023, 14, x FOR PEER REVIEW 13 of 19 sheet are consistent with the simulation results. However, although the sensor with an uncracked Al sheet exhibits a similar trend, there is some inconsistency with the simulation results, especially in terms of the magnitude of S11. This is ascribed to the presence of a small air gap between the prototype sensor and the Al sheet ( Figure 8e). When we employed a 0.025 mm air gap between the sensor and Al sheet in the simulation, the results became consistent.  Figure 9a presents the change in the resonant frequency due to the eight types of crack for each CSRR. In the absence of any cracks, the resonance frequency of the sensor is 5.20 GHz for CSRR1 and 4.12 GHz for CSRR2. In the presence of a crack with a width  The Al sheets were the same size as the detector (36 mm × 23 mm width and length) and were 5 mm thick. Because the cracks were positioned symmetrically, we measured eight situations using the four samples. The width and depth were changed, while the distance between the cracks was 10.8 mm, and the crack length was 6.1 mm. The fabricated cracks are located at the center of the CSRRs. Figure 8c,d compares the simulation and measured sensor results for the sensor only and for the sensor with an uncracked aluminum sheet. The S-parameter of the fabricated sample is measured using a Keysight N5227B (Keysight, Santa Rosa, CA, USA) vector network analyzer. Figure 8c shows that the measurement results for the sensor without an Al sheet are consistent with the simulation results. However, although the sensor with an uncracked Al sheet exhibits a similar trend, there is some inconsistency with the simulation results, especially in terms of the magnitude of S11. This is ascribed to the presence of a small air gap between the prototype sensor and the Al sheet ( Figure 8e). When we employed a 0.025 mm air gap between the sensor and Al sheet in the simulation, the results became consistent. Figure 9a presents the change in the resonant frequency due to the eight types of crack for each CSRR. In the absence of any cracks, the resonance frequency of the sensor is 5.20 GHz for CSRR1 and 4.12 GHz for CSRR2. In the presence of a crack with a width of 0.85 mm and a depth of 0.5 mm, the frequency increases to 4.32 GHz for CSRR2 and 5.34 GHz for CSRR1. In addition, as the width of the crack increases, the resonance frequency increases. On the other hand, when a crack has the same width, the resonance frequency increases as the depth of the crack reduces. Figure 9b,c present a more detailed plot of the measurement results for each CSRR, and the resonant frequency for each crack is summarized in Table 3.  Figure 9b displays the measured S11 plotted against the CSRR2 resonant frequency for the different cracks. The resonant frequency ranges from 4.320 GHz for the 0.85 × 0.5 mm crack to 4.527 GHz for the 1.05 × 0.1 mm 2 crack. This demonstrates that the proposed sensor can detect cracks above CSRR2 at a resolution of 0.1 mm for the crack width and 0.2 mm for the crack depth. Figure 9c presents the measured S11 plotted against the CSRR1 resonant frequency for the different cracks. The resonant frequency ranges from 5.340 GHz for the 0.85 × 0.5 mm 2 crack to 5.489 GHz for the 1.05 × 0.1 mm 2 crack; thus, CSRR1 has the same sending resolution as CSRR2. Figure 9d,e show the relationship between the resonant frequency and crack width and depth. Figure 9d presents the effect of the depth on the sensing of a crack with a fixed width of 0.95 and 1.05 mm at each CSRR. The average change in the resonant frequency is 20.7 and 18.3 MHz for CSRR1 and CSRR2, respectively, with a change of 0.1 mm in width. The fabricated sensor exhibits a linear reduction in the resonant frequency at both CSRRs with an increasing crack depth. Figure 6e presents the effect of the width on crack detection with a fixed depth of 0.3 and 0.5 mm at each CSRR. The average change in the resonant frequency is 28.0 and 33.7 MHz for CSRR1 and CSRR2, respectively, with a change of 0.2 mm in depth. The fabricated sensor thus exhibits a linear increase in the resonant frequency with an increase in the crack width.   The proposed sensor experiences a decrease in the resonant frequency of 30.8 MHz when the crack width increases by 0.1 mm and an increase of 19.5 MHz when the crack depth increases by 0.2 mm. Thus, the proposed crack sensor can detect differences in crack width down to 0.1 mm and crack depth down to 0.2 mm.

Crack Sensing Performance
The measured changes in the resonance due to changes in the crack dimension are generally linear, and the sensor can successfully simultaneously detect two different crack widths or depths, with each CSRR independent of the other. Cracks can thus be detected in situations where one crack is located near CSRR1, and another crack is located near CSRR2. In this respect, the measurement results exhibit the same trend as the simulation results and electromagnetic theory. The simulation results confirm that the effective capacitance falls with an increasing crack width; hence, the resonant frequency increases. In contrast, the effective capacitance increases with increasing crack depth, reducing the resonant frequency.

Conclusions
This study proposed a non-destructive multi-crack detection sensor consisting of differently sized CSRRs in a higher-mode SIW cavity to provide multi-resonant frequencies. Each CSRR on the SIW creates its own resonance, and the higher-mode SIW offers separated and concentrated E-fields for each CSRR. As a result, the proposed sensor has a high Q-factor and can simultaneously and independently detect multi-cracks. The reflective coefficient of the sensor is affected by the metal surface due to the strong external E-field from the CSRRs and SIW. When the metal has cracks, the efficient capacitance changes, which alters the resonant frequency of the nearby CSRR. Additionally, due to the high Q-factor, the proposed sensor can detect the metal crack at a high resolution. The effective capacitance of the sensor falls as the crack width increases, raising the resonant frequency, with the capacitance increasing as the crack depth becomes shallower, thus reducing the resonant frequency. The relationship between the resonance and the crack width or depth is almost linear. To demonstrate our proposed design, we designed and fabricated a dual-crack detection sensor using two independent CSRRs and a TE 20 -mode SIW. The fabricated crack sensor distinguishes crack width differences down to 0.1 mm and crack depth differences to 0.2 mm and is able to two detect two differently sized cracks independently and simultaneously with significantly lower power consumption and scanning time. The proposed dual-crack detection sensor also exhibits a higher Q-factor than previously reported multi-detection sensors.