Microwave and millimetre wave sensors for crack detection

Fatigue & Fracture of Engineering Materials & Structures doi:10.1111/j.1460-2695.2008.01255.x Microwave and millimetre wave sensors for crack detection R. ZOUGHI and S. KHARKOVSKY Applied Microwave Nondestructive Testing Laboratory (amntl), Electrical and Computer Engineering Department, Missouri University of Science and Technology (Missouri S&T) (formerly University of Missouri-Rolla), Rolla, MO, 65409, USA Received in final form 4 June 2008 ABSTRACT Non-destructive detection and evaluation of stress-induced fatigue cracks in metals is an important practical issue in several critical environments including surface transportation (steel bridges, railroad tracks, railroad car wheels, etc.), aerospace transportation (aircraft fuselage, landing gears, etc.) and power plants (steam generator tubings, etc.). Although there are several standard non-destructive evaluation techniques, near-field microwave and millimetre wave techniques have shown tremendous potential for significantly adding to the available non-destructive toolbox for this purpose. This paper serves as a review of recent advances made in this area and the capabilities of these techniques for detecting cracks and evaluating their various dimensional properties including determining a crack tip location accurately. These techniques include using open-ended rectangular probes (in two distinct modes) and open-ended coaxial probes. Keywords crack; microwaves; millimetre waves; open-ended probes. NOMENCLATURE a = broad dimension of the open-ended rectangular waveguide aperture b = narrow dimension of the open-ended rectangular waveguide aperture D = crack depth dc = direct current DM = dominant mode GHz = gigahertz h = distance between the crack and the coaxial centre HOM = higher order mode k = ratio of the distance between the probe and the waveguide wall and narrow dimension (height) of the open-ended rectangular waveguide aperture l = distance between a detector and a waveguide aperture NDE = non-destructive evaluation TE = transverse electrical TEM = transverse electric and magnetic TM = transverse magnetic 2D = two dimensional r i = radius of an internal conductor of a coaxial probe r o = radius of an external conductor of a coaxial probe W = crack width T = the distance between the probe and the waveguide wall δ = location of the crack within waveguide aperture INTRODUCTION Metal fatigue or failure usually begins from the surface. Aircraft fuselage, nuclear power plant steam generator tubings and steel bridges are examples of environments in which this type of metal failure occurs. Hence, fatigue and Correspondence: R. Zoughi. E-mail: zoughir@mst.edu stress crack detection on metallic structures is of utmost importance to the on-line and in-service inspections of critical metallic components. Currently, there are several prominent non-destructive evaluation (NDE) techniques for detecting surface cracks in metals. Acoustic emission testing, dye penetrant testing, eddy current testing, ultrasonic testing, radiographic testing and magnetic particle testing are examples of the techniques. 1 However, each 695

696 R. ZOUGHI and S. KHARKOVSKY method possesses certain limitations and disadvantages. For instance, cracks under coatings such as paint, rust, composite laminates and corrosion protective substances are not always reliably detected using these methods. The same applies to cracks filled with dielectric materials such as rust, dirt, paint and other substances. Identification of the exact location of crack tips is another important practical issue (for prevention of crack propagation) that is not fully addressed by conventional NDE techniques. Environmental concerns must also be addressed when using an NDE technique (e.g. concerns associated with the dye penetrant method). Removal of surface coating, to facilitate crack detection, is an undesirable procedure. Furthermore, remote crack detection (i.e. a standoff distance between the surface under test and the detection probe) is very desirable from a practical standpoint. Until 1992, microwave NDE techniques had been proposed for detecting surface cracks in metals but with limited success. 2 5 Since 1992, near-field microwave crack detection approaches and techniques that use open-ended rectangular waveguide probes have been developed. 6 18 The investigation and applications of these techniques for detecting and evaluating fatigue surface cracks have shown several advantageous features, such as: The probe may or may not be in contact with the surface under examination. They are applicable in high-temperature environments. Crack may be filled with dielectric materials such as dirt, paint or rust. The surface of the metal may be covered with paint or a similar compound and the crack may still be detected because microwaves penetrate dielectric materials. They are applicable to non-ferromagnetic as well as ferromagnetic metals or alloys and coarse-grained materials, because microwaves do not penetrate in metal and depend on perturbations in surface current. The dimensions of a crack can be closely estimated. Polarization properties of microwaves can provide information regarding relative crack orientation. Crack tip location can be determined. A comprehensive description of the near-field microwave approaches and techniques utilizing open-ended waveguide probes developed in the past, up to the end of the 1990s, for detection and evaluation of cracks are presented in Ref.[18]. Recently, these approaches and techniques have been expanded and investigated for detecting V-shaped 19 and tilted 20 cracks. In addition, a statistical analysis was developed to associate a statistical quantitative measure on the ability of several probes to repeatedly detect a crack and distinguish it from other anomalies such as changes in standoff distance. 21 22 A near-field approach utilizing open-ended coaxial probes has also been developed. 23 26 This approach offers several distinct advantages including the ability to inspect for cracks near rivets and panel edges, tight places and corners and inside bore holes because the coaxial probe can be made of semirigid coaxial lines that can be readily shaped into curves and bends. Recently, imaging of real cracked metal panels for enhanced crack detection sensitivity has also been performed at millimetre wave frequencies (up to 100 GHz). This paper presents an overview of these unique techniques for crack detection and evaluation that have been developed at the Applied Microwave Nondestructive Testing Laboratory (amntl) currently at the University of Missouri-Rolla, United States. Clearly not all can be discussed in this article in some reasonable detail. Consequently, this paper focuses on design of these near-field microwave and millimetre wave probes and presents the basic results obtained utilizing these probes. BACKGROUND The well-established microwave spectrum is 300 MHz 30 GHz, while the frequency span of 30 GHz 300 GHz is associated with the millimetre wave spectrum with the corresponding wavelength ranges of 1000 10 mm and 10 1 mm, respectively. 27 Microwaves and millimetre wave signals do not penetrate through metals but are sensitive to the presence of metal surface discontinuities such as cracks. However, these signals penetrate through dielectric materials, such as paint, and therefore can interrogate paint-covered metal surfaces for crack detection. For imaging purposes and when operating in the nearfield region of open-ended probes, the spatial resolution is determined by the probe aperture dimensions, which are relatively small at these frequency ranges. Figure 1 shows the front view of flanges and apertures of standard open-ended rectangular waveguides for several different frequency bands, namely (from left to right) K-band (18 26.5 GHz) with an aperture dimension of 10.7 mm by 4.3 mm, Ka-band (26.5 40 GHz) with an aperture dimension of 7.11 mm by 3.56 mm, V-band (50 75 GHz) with an aperture dimension of 3.8 mm by 1.9 mm and W-band (75 110 GHz) with an aperture dimension of 2.54 mm by 1.27 mm. Open-ended coaxial probes can operate in a much wider frequency band for a given probe dimension. Crack detection with the near-field open-ended waveguide or coaxial probes is based on surface current perturbation. When using these probes for detecting surface cracks, the perturbation caused to the induced surface current density on the metal plate by the presence of a crack renders its detection and provides information about its dimensions. This is a very sensitive interaction and is function of crack dimensions and placement within

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 697 Fig. 1 The front view of the flanges and apertures of standard rectangular waveguides at (from left to right) K-, Ka-, V- and W- band. the probe aperture. Consequently, for the purpose of surface crack detection, very tight cracks can be detected at relatively low frequencies (e.g. cracks with 5 μm opening have been detected at frequencies around 10 GHz, a crack opening to wavelength ratio of 0.00016 24,26 ). When using an open-ended waveguide probe, a surface current is generated on the metal surface under investigation creating a reflected wave and subsequently a standing wave inside the probing waveguide. The presence of a crack inside the waveguide aperture disturbs the surface current density and causes the properties of the reflected wave (and subsequently the standing wave) to change. It should be noted that the surface current density negligibly depends on the type of metals for crack detection application because metals are considered to be very good conductors. 27 Therefore, strategic probing of the standing wave pattern inside the waveguide, as a cracked surface is scanned, renders information about the presence of the crack. In addition, the ability of these signals to penetrate inside dielectric materials makes them an excellent candidate for non-destructively detecting surface cracks covered with dielectric coatings such as paint, composite laminates and corrosion protecting substances and/or filled with dielectric materials such as dirt, rust or paint. Finally, the characteristics of the change in the standing wave give information about various dimensional properties of the crack and its relative location within the openended probe. OPEN-ENDED RECTANGULAR WAVEGUIDE PROBE The primary operational mode of the rectangular waveguide is the transverse electric (TE) mode in which the electric field polarization vector is perpendicular to the broad dimension of the waveguide aperture (referred to as TE 10 mode). 27 Thus, the dominant mode electric field induces a surface current density on a metal plate that is in the same direction as that of the electric field vector direction. Subsequently, in the presence of a crack the surface current density on the metal plate is disturbed if the crack and the electric field polarization vector are perpendicular to each other (or there is some perpendicular component of the current density interacting with the crack). 7 This perturbation results in a crack being detected and the properties of the perturbation give information about various properties of the crack (i.e. width, depth, etc.). In addition, this interaction creates higher order modes in the vicinity of the crack. Therefore, the crack can be detected by using either: (1) the effect of the perturbation of dominant mode (DM) or (2) the effect of the generated higher order modes (HOM). These effects are used in DM and HOM open-ended rectangular waveguide probes, as described in the following sections. Dominant-mode approach In the early 1990s several preliminary yet important experiments were conducted to investigate the feasibility of using open-ended rectangular waveguide probes for detecting long surface cracks in metals. 7 In this context, long refers to a crack whose length is greater than or equal to the broad dimension of a waveguide. Various long cracks of different widths and depths were milled in several metal (aluminium, steel and brass) plates. The experiments were conducted by moving (using a computercontrolled stepping motor) the cracked metal surface over the aperture of the open-ended waveguide while monitoring the standing-wave characteristics inside the waveguide. Subsequently, it was observed that when the crack axis (length) is parallel to the broad dimension of the waveguide (orthogonal to the electric field polarization vector of the dominant mode) the standing wave experiences a pronounced shift in location when the crack is exposed to the aperture of the waveguide compared to when the crack is outside the aperture (the short-circuit condition). This shift indicates changes in the reflection

698 R. ZOUGHI and S. KHARKOVSKY Fig. 4 Laboratory apparatus for surface crack evaluation. Fig. 2 Side-view of a surface crack and an open-ended rectangular waveguide aperture (Yeh, C. and R. Zoughi, A novel microwave method for detection of long surface cracks in metals, IEEE Transactions on Instrumentation and Measurement, vol. 43, no. 5, pp. 719 725, 1994 c 1994 IEEE). coefficient properties (primarily phase) of the metal surface perturbed by the crack. It was observed that this shift is highly dependent on the relative location of the crack within the waveguide aperture (i.e. whether the crack is at the edge or at the centre of the aperture). This shift is also dependent on the probing location on the standing wave pattern. Figures 2 and 3 show the side- and plan-views of a crack with a width of W, a depth of D and a length of L and a waveguide aperture with dimensions of a and b, when the crack length is parallel to the broad dimension of the waveguide, and δ is a dimension indicating the location of the crack relative to an arbitrary location on the small dimension of the waveguide aperture. Figure 4 shows a simple measurement apparatus used for the dominant-mode (DM) crack detection technique. An oscillator feeds a waveguide terminated by a metal plate in which there is a crack. Placing the diode detector a distance l away from the waveguide aperture, the metal plate can be scanned by the waveguide aperture and the standing wave voltage recorded. Different detector locations, l, influence the difference between the measured signals for the short-circuit case (i.e. when the waveguide is terminated by the metal plate with no crack) and when the crack is in the middle of the aperture. 18 If l is chosen such that the detector is located between a maximum and a minimum on the standing-wave pattern, this difference is substantial. Figure 5 shows a typical dependency of the detector output voltage versus location of the crack relative to the waveguide aperture obtained when a long crack with L > 10.7 mm, W = 0.84 mm and D = 1.03 mm 2 1.6 Detector voltage (mv) 1.2 0.8 0.4 Crack Outside Aperture Crack Inside Aperture Crack Outside Aperture 0 0 2 4 6 8 10 δ (mm) Fig. 3 Plan-view of a surface crack and an open-ended rectangular waveguide aperture (Yeh, C. and R. Zoughi, A novel microwave method for detection of long surface cracks in metals, IEEE Transactions on Instrumentation and Measurement, vol.43,no.5, pp. 719 725, 1994 c 1994 IEEE). Fig. 5 Experimental crack characteristic signal for a long crack with width W = 0.84 mm and depth D = 1.03 mm at a frequency of 24 GHz (Yeh, C. and R. Zoughi, A novel microwave method for detection of long surface cracks in metals, IEEE Transactions on Instrumentation and Measurement, vol. 43, no. 5, pp. 719 725, 1994 c 1994 IEEE).

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 699 was scanned over the aperture of a K-band waveguide (a = 10.67 mm and b = 4.32 mm). The results indicate that while the crack is outside the waveguide aperture the diode registers very little voltage variation due to the fact that the waveguide is terminated by a short circuit. The noise-like feature associated with the signal is due to the quantization resolution of the analog/digital converter and the internal noise of the voltmeter. As the crack begins to appear within the waveguide aperture the voltage experiences a rapid magnitude change, which is an indication of rapid phase change in the reflection coefficient at the aperture. The same phenomenon occurs when the crack leaves the waveguide aperture. The voltage value does not change very much while the crack is inside the aperture; however, its value is still different to that of a short-circuit case. The diode output voltage as a function of δ (hereon referred to as the crack characteristics signal)is clearly an indication of the presence of a crack (detection), because the absence of a crack results in a fairly constant voltage. Theoretical approaches for exposed cracks Two different electromagnetic approaches have been developed for modelling the interaction of a crack and a waveguide aperture. 6,7,13 15 In both approaches long surface cracks are assumed to be narrow slots cut out of a metal plate, and because it has been shown that long cracks and cracks with a length equal to the broad dimension of the probing waveguide produce very similar crack characteristic signals, in both approaches it was assumed that a long surface crack has a length equal to the broad dimension of the probing waveguide. 7 In this way the problem reduces to the larger probing waveguide interacting with a smaller waveguide (e.g. the crack) with the same broad dimension. Because the crack opening or width is assumed to be small, given the incident dominant TE 10 mode at the waveguide aperture, in the first approach it was assumed that the presence of the crack within the aperture only produces higher order-reflected TM modes. 7 This assumption is valid for tight cracks whose lengths are equal to or larger than the broad dimension of the probe s waveguide aperture. 8 For long cracks this assumption reduces the analytical complexity of this electromagnetic model considerably. In addition, this model relies on a mode-matching approach to analyze the electromagnetic properties of a system formed by the probing waveguide and the crack as a function of crack location within the waveguide aperture. The inherent drawback of this approach is evident when the crack is at the edge of the waveguide aperture in which case many modes are needed to replicate the sharp transitions. Hence, this model, which in effect is a brute force approach of setting up the boundary conditions and solving for the unknown coefficients, becomes increasingly computer resource intensive and inefficient. This problem is more severe for finite cracks in which both the TM and TE higher order reflected modes need to be considered. 8 In addition, the solution is crack location dependent. Finally, this model is not general and may be only applied to finite cracks after substantial modification. Nevertheless, this first approach significantly aided the understanding of the interaction of a surface crack modelled as a small waveguide fed by a larger probing waveguide aperture. 6,7 The second approach evaluates the change in the reflection coefficient for a generalized system encompassing empty, filled, covered and finite cracks, located at an arbitrary position inside the probing waveguide aperture. 13 15 A general representation of the system formed by the three waveguides (for the general case of a covered crack) is obtained by assuming arbitrary incident electric and magnetic fields in the probing waveguide. The incident and reflected fields in the waveguide, the dielectric coating layer and the crack are expressed in terms of their discrete orthonormal eigenfunctions with unknown complex coefficients. Applying the equivalence principle allows the system to be separated into three waveguide sections (two waveguide junctions) representing the probing waveguide, the dielectric coating layer and the crack. According to the equivalence principle the field in the probing waveguide is identical to the exciting field plus the field produced by an equivalent magnetic current density, M, when the aperture is replaced by a perfect conductor. 28 29 The equivalent magnetic current density, M, is introduced over the common aperture of the system formed by the waveguide and the crack, as shown in Figs 6 and 7. A numerical solution employing the method of moments is obtained, and the reflection coefficient at the waveguide aperture is expressed in terms of a generalized scattering matrix. 30 The convergence behaviour was then studied to determine an optimized set of basis functions and the optimal number of higher order modes required for a fast and accurate solution. This modelling approach is more versatile and provides for a more convenient convergence analysis for examining the appropriateness of the incorporated number of HOMs. 14,15 As the width of a crack approaches zero or in practice a (closed) fatigue crack, the numerical computational resources become significant and prohibitive. However, both of these methods show that their foundations for detecting and evaluating cracks are sound, and computer resource availability (at the time of their development) notwithstanding, the formulations would perform properly and accordingly for any crack width and depth.

700 R. ZOUGHI and S. KHARKOVSKY Fig. 6 Side-view of the relative geometry of a surface crack and a waveguide aperture (Huber, C., H. Abiri, S. Ganchev and R. Zoughi, Analysis of the crack characteristic signal using a generalized scattering matrix representation, IEEE Transactions on Microwave Theory and Technique, vol. 45, no. 4, pp. 477 484, 1997 c 1997 IEEE). to the crack width (opening) and the waveguide narrow dimension, b. 7 The error associated with estimating the crack width and depth using this method is shown to be less than ±20%. For applications in which this is considered to be an excessive error a swept frequency technique may be used rendering much higher depth estimation accuracy. The swept frequency method relies on using the estimated crack depth from the crack characteristic signal for choosing the proper probing waveguide size. In this technique, by sweeping the operating frequency and by measuring the phase of the reflection coefficient at the waveguide aperture, the crack length and depth can be estimated accurately. 6,10,18 Crack width or opening may not be a particularly important parameter for fracture analysis or repair considerations. For these purposes, crack length and particularly depth information are sufficient for determining whether a specimen should be rejected. 10 Extensive theoretical and experimental efforts were undertaken to study the features of the microwave crack detection and evaluation as a function of many parameters such as the crack width and depth, the frequency of operation, the incident power level and for empty, filled and covered cracks. 11 Some typical results for filled and covered cracks as well as for crack tip location determination are presented below. Filled cracks Fig. 7 Plan-view of the relative geometry of a surface crack, a waveguide aperture and the coordinate system where z-axis is out of the page (Huber, C., H. Abiri, S. Ganchev and R. Zoughi, Analysis of the crack characteristic signal using a generalized scattering matrix representation, IEEE Transactions on Microwave Theory and Technique, vol. 45, no. 4, pp. 477 484, 1997 c 1997 IEEE). Crack sizing The above models developed for surface crack detection and their associated numerical codes are used to establish a practical and useful crack sizing techniques. 6,7,10 Subsequent to detecting a surface crack using the near-field open-ended waveguide probe, sizing becomes the natural next step because sizing is very important for fracture analysis and repair considerations. The sizing method first estimates the crack width and depth from the dominant mode crack characteristic signal. Extensive experiments showed that the relative signal level when the crack is inside the waveguide aperture and when outside of the aperture is a strong function of crack depth, while the distance between the two peaks in the signal is strongly correlated Rust, dirt, chemical and other substances may fill a crack at any time particularly if the crack is old (e.g. steel bridges). Additionally, any potential distinction between a filled and non-filled (empty) crack may render information about when the crack may have been generated (i.e. recent or old). Figures 8 and 9 show the normalized calculated and measured crack characteristic signals, recorded at a frequency of 24 GHz, for empty and filled with rust powder cracks/slots, with a width of W = 0.85 mm and a depth of D = 1.25 mm, respectively. The calculated results were obtained using a generalized scattering matrix representation described in the previous sections. 14 Filled crack experiments were conducted using rust powder (Fe 2 O 3 ) as the crack filler. A reduction in the width of the crack characteristic signal (i.e. distance between the two sharp transitions) and the change in the middle level of the crack characteristic signal are evident from Figs 8 and 9. These changes are considered to be a result of the fact that a filled crack is electrically deeper than the same crack when empty (i.e. larger electrical depth). As mentioned earlier, a change in the depth of a crack significantly influences this middle signal level and to a lesser extent influences the distance between the two sharp transitions. 7 For instance, Fig. 10 shows the normalized crack characteristic signals, recorded at 24 GHz, for empty and filled with rust powder cracks/slots with a width of 0.51 mm and depths of

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 701 Fig. 8 Normalized calculated crack characteristic signals for an empty and filled (with rust powder) crack with width W = 0.85 mm and depth D = 1.25 mm at a frequency of 24 GHz (Huber, C., H. Abiri, S. Ganchev and R. Zoughi, Analysis of the crack characteristic signal using a generalized scattering matrix representation, IEEE Transactions on Microwave Theory and Technique, vol. 45, no. 4, pp. 477 484, 1997 c 1997 IEEE). Fig. 10 Normalized crack characteristic signals for an empty and a filled crack (with Fe 2 O 3 ) with width W = 0.51 mm and depth D = 2.5mmat24GHz(Zoughiet al., Report, 1995). variation in the operating frequency or the use of multiple detector diodes, positioned at several locations on the standing wave pattern, will result in the detection of the crack. 18 The same may be accomplished by placing a thin layer of dielectric sheet in front of the waveguide aperture (i.e. covered crack as will be discussed later). In addition, the use of HOM detection in tandem with the dominant mode detection will render all cracks detectable. Dominant mode and HOM detection can be simultaneously accomplished with one sensor. 22 Covered cracks Fig. 9 Normalized measured crack characteristic signals for an empty and filled (with rust powder) crack with width W = 0.85 mm and depth D = 1.25 mm at a frequency of 24 GHz (Huber, C., H. Abiri, S. Ganchev and R. Zoughi, Analysis of the crack characteristic signal using a generalized scattering matrix representation, IEEE Transactions on Microwave Theory and Technique, vol. 45, no. 4, pp. 477 484, 1997 c 1997 IEEE). 2.5 mm. This result primarily shows a significant change in the middle signal level, as expected. The results shown in this section are very important as they indicate the utility of this microwave crack detection method in a complementary fashion with the dye penetrant method, because the dye filling a crack is a dielectric material. In all cases, when a crack characteristic signal does not render the crack detectable, a slight One of the most important advantages of this microwave methodology is evident when it is used for detecting surface cracks under dielectric coatings. Because microwave signals easily penetrate inside dielectric materials, this methodology is expected to detect cracks under dielectric coatings of various thicknesses. It must be noted that dielectric coatings such as paint, corrosion preventative substances, etc., may have varied thicknesses although they are generally not very thick and are commonly known as the family of low-loss dielectric materials. Therefore, it was important to establish the potentials and limitations of this microwave approach as a function of the dielectric coating thickness covering a crack. Extensive measurements, at 24 GHz, on cracks covered with thin sheets of wrapping paper (simulating paint with different thicknesses) were conducted. Wrapping paper has similar dielectric properties as common paint. Furthermore, wrapping paper (with uniform thickness of 0.04 mm) may easily be stacked on top of each other to provide various thicknesses. Additionally, the effect of increased input power on detecting cracks under thicker coatings was also investigated. 16

702 R. ZOUGHI and S. KHARKOVSKY A crack with a width of W = 0.51 mm and a depth of D = 2 mm was covered with up to 12 sheets of wrapping paper (coating thickness of 0 0.5 mm) and their crack characteristic signals were recorded, as shown in Fig. 11. It should be noted that the recorded crack characteristic signals are shown and not their normalized versions because in the case of covered cracks, the short-circuit level (when the crack is outside of the waveguide aperture) changes as a function of the coating thickness. It can be seen from Fig. 11 that the coating thickness increases as the overall level of the recorded signal decreases. This is primarily due to the fact that the standing wave pattern inside the waveguide is different when it is terminated by a conductor (i.e. short circuit) and when it is terminated by a dielectric covered conductor. The difference between the maximum and the minimum levels of the standing wave decreases (i.e. decreasing standing wave ratio). The signal level in the middle of the crack characteristic signal decreases as a function of increasing coating thickness, however, so does the signal level when the crack is outside of the waveguide aperture. The results of these experiments indicated that the crack may be covered with additional sheets (more than 25) before it becomes undetectable 11 (not shown here). The dynamic range of the detected voltage for these crack characteristic signals is quite large indicating that many more layers may cover this crack, and it will still be detectable. Coating thicknesses of greater than a couple of millimetres are considered unusually thick for paint and corrosion preventative substances, although not for metals covered with special coatings. However, the results indicate that cracks under such thick coatings may also be detected using this microwave method. Furthermore, it was shown that the input power may be used as an additional optimizing parameter to probe surfaces with a few millimetres of dielectric coatings. 16 Crack tip location determination Fig. 11 Crack characteristic signals for a crack with width W = 0.51 mm and depth D = 2 mm at flush and when covered with four different layers of wrapping paper (coating thickness range of 0.24 0.48 mm) at 24 GHz (Zoughi et al., Report, 1995). For repair purposes, it is often necessary to know the exact location of the tip of a propagating crack along the length on the surface. One practice for preventing crack propagation is to drill a hole at the crack tip. Assuming a crack has been found, there are two methods to determine its crack tip location. The first method involves producing the image of a crack by scanning it in two directions and generating two-dimensional (2D) crack characteristic signal 13 as will be seen later. The second method requires scanning the crack only in one direction (crack tip characteristic signal). The latter approach is more useful for practical applications because only scanning in one direction is necessary to identify crack tip location. However, the former approach is useful for understanding the process of tip location identification as well as obtaining general information about the crack. 11 The former approach will be demonstrated later. Although a 2D crack characteristic signal may be useful and interesting because it shows the impression of a crack as it appears on a metal surface, practically its production is time consuming and somewhat cumbersome. Consequently, an alternative simple and fast approach for identifying crack tips was developed. Once a crack has been detected, the waveguide aperture may be placed on it as shown in the left illustration in the top of Fig. 12. For this case, it is sufficient that the crack be aligned somewhere in the middle of the narrow dimension of the waveguide. Fig. 12 Calculated and measured crack tip characteristic signals for a long crack with width W = 0.51 mm and depth D = 1.5 mm at 24 GHz (From Materials Evaluation, vol. 54, no 5. Reprinted with permission of The American Society for Nondestructive Testing, Inc.).

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 703 Now if the waveguide only moves along the x-direction (as depicted sequentially in the illustrations in Fig. 12), first the crack is totally inside the aperture, then its tip enters the aperture where a significant change in the detected signal should occur, then it continues to move further inside the aperture where the change in the detected signal becomes gradual, and finally the crack tip leaves the aperture. Figure 12 shows the crack tip characteristic signal, obtained in this manner, for a machined slot with a width of W = 0.51 mm and a depth of D = 1.5 mm at 24 GHz. Here, the per cent absolute difference between the measured voltage, at any point in the scan, and when the crack is totally outside the aperture (short-circuit case) is plotted as a function of the scanning distance. Here, scanning distance refers to movement of the waveguide aperture along the x-direction. The three distinct regions in this figure show the location of the slot, with respect to the waveguide aperture, along the x-direction. The two vertical lines indicate the relative location of the slot tip once at one edge of the waveguide and once at the other, respectively. Thus, the distance between these two lines is equal to the broad dimension of the waveguide aperture, a. The results show that when the crack is fully within the waveguide aperture the detected-voltage-change is relatively constant, as expected. However, as soon as the crack tip enters the aperture (indicated as crack tip in the figure) this detected-voltage-change abruptly decreases and continues to decrease while the crack tip moves along inside the aperture. This is due to the fact that the HOM structure changes significantly when the crack tip enters inside the waveguide aperture (e.g. from primarily TM to TE and TM modes). 7 8 When the crack comes to the vicinity of the other side of the waveguide ( 3 mm away, which is about a third of the broad dimension of the waveguide) there is hardly any variation in the detectedvoltage-change, also as expected. The theoretical model, describing the interaction of a crack with an open-ended rectangular waveguide 14 was used to theoretically obtain the results of this experiment (also depicted in Fig. 12). Clearly, there is excellent agreement between the theoretical and the experimental results. The influence of different crack dimensions, on the crack tip characteristic signals, was also investigated. 12 Crack depth and width variations cause expected changes in the level of the detected signal when the crack is totally within the waveguide. The crack tip characteristic signal for a filled crack (compared to an empty crack) is similar to a deeper crack. The accuracy of the crack tip location for empty and filled cracks is estimated to be within 0.25 mm of the actual tip location. If necessary, the accuracy may be improved by changing the operating frequency or the detector diode position. The crack tip characteristic signal for covered cracks was also investigated. For this purpose the crack was covered with 2 sheets (0.08 mm), 6 sheets (0.24 mm), 12 sheets (0.48 mm), 16 sheets (0.64 mm) and 20 sheets (0.8 mm) of wrapping paper. It was shown that the accuracy by which the tip of a crack may be located is estimated to be within 2 mm of its actual position. 12 As explained earlier, the accuracy of determining covered crack tip locations may also be improved by optimizing the operating frequency and the detector diode position. 18 However, for all investigated cases, the accuracy by which the tip position of a crack may be located is very good. It must be noted that the results presented here are raw data without the application of any post-processing. Simple processing algorithms such as forward difference method for gradient approximation (i.e. calculating forward slope for every data point) may be another way to analyze these data. 12 It may be suggested that, using this approach, the crack tip is identified when the slope begins to change substantially. Substantially will then depend on the particular application, level of accuracy required and whether the crack is covered or filled. HOM approach Referring to Figs 2 and 3 and as mentioned earlier, in the absence of a crack only the dominant TE 10 mode exists in the waveguide. However, the presence of a crack generates an infinite number of reflected higher order transverse magnetic (TM) modes in addition to the dominant mode. For modelling long cracks, it is assumed that only the higher order TM modes are generated because no mechanism for generating higher order TE modes exist. However, for finite cracks this will no longer be true and the contribution of all higher order modes must be taken into account. 7,8,14,15 The reason for exploring the characteristics of these higher order modes for fatigue/surface crack detection is that in the absence of a crack there are no higher order modes present, hence theoretically the magnitude of the measured signal associated with the higher order modes is zero. 9 However, the presence of a crack generates HOMs, and hence a finite amount of signal is measured. Therefore, theoretically a signal-to-noise ratio equal to infinity is achieved, which results in very sensitive (to the presence of a crack) measurements. In practice, however, the noise characteristics of the measurement system dictate the noise level. Nevertheless, high measurement sensitivity associated with the higher order probe renders small fatigue/surface cracks (i.e. at their early stages of development) easily detectable. Moreover, it implies that for a given range of crack widths or opening lower microwave frequencies may be used with relatively high detection sensitivity. A novel HOM probe was designed, built and tested for the purpose of crack detection. 9 Figure 13 shows a closeup geometry of the relative location of the probe and the

704 R. ZOUGHI and S. KHARKOVSKY Fig. 13 The close-up geometry of the HOM probe showing the relative location of the probe tip and the waveguide aperture (From Materials Evaluation, vol. 52, no 6. Reprinted with permission of The American Society for Nondestructive Testing, Inc.). Fig. 14 Experimental results for a crack with width W = 0.144 mm, depth D = 1.2mmandlengthL = 22.86 mm at 12.4 GHz for k = 0.5 (From Materials Evaluation, vol. 52, no 6. Reprinted with permission of The American Society for Nondestructive Testing, Inc). waveguide aperture. Here, T is the distance between the probe and the waveguide wall, and the proper choice of this parameter can substantially increase detection capability of this technique. The probe must be placed near the aperture (l must be small) due to evanescence nature of higher order modes. Figure 14 shows the experimental result, for a crack with width W = 0.144 mm, depth D = 1.2 mm and length L = 22.86 mm at 12.4 GHz for k = 0.5 and l = 0.2 mm (k = T/b). The results closely match, both in shape and relative magnitude, those obtained through theoretical modelling. 9 To demonstrate the capability of this technique to detect real fatigue cracks, a standard fatigue specimen was subjected to cyclical loading until a fatigue crack was generated, as shown in Fig. 15. The width of this crack was measured, by a microscope, and varied between 1.9 and 4.9 μm. The depth of this crack could not be measured with the equipment available in the laboratory. This crack Fig. 15 Schematic of a standard fatigue specimen (From Materials Evaluation, vol. 52, no 6. Reprinted with permission of The American Society for Nondestructive Testing, Inc). was scanned by a HOM probe operating at 38 GHz in such a way as to ensure that the notch associated with the fatigue specimen was not exposed to the waveguide aperture during the scanning. 9 Figure 16 shows the results of this experiment. The indication of the fatigue crack is clearly seen in Fig. 16. There are several issues to be considered regarding the HOM approach. Although the higher order TM modes are assumed to be the significant set of modes for long cracks, depending on the width or opening of the crack other modes and field components (not just x-component of the electric fields associated with the higher order TM modes) with lesser influence may also contribute to the process. From a practical point of view, the effect of the probe in disturbing the fields at the waveguide aperture may be a significant issue. The probe should be long enough to pick up high enough HOM signal amplitude necessary for detecting the crack. However, it should be short and thin enough so as to not to perturb the aperture fields significantly. This is similar to the design criterion for a slotted waveguide probe. Extensive

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 705 Fig. 16 Experimental result for the fatigue crack shown in Fig. 15 at 38 GHz for k = 0.2 (From Materials Evaluation, vol. 52, no 6. Reprinted with permission of The American Society for Nondestructive Testing, Inc). measurements were conduced to show the influence of the probe characteristics and the frequency of operation on a crack detection using the dominant and the HOM probes in tandem. 11 APPLICATION TO REAL STRESS-INDUCED FATIGUE CRACK DETECTION To demonstrate the practical utility of the microwave crack detection approach, an A-36 steel specimen with a thickness of 12.7 mm and with the dimensions shown in Fig. 17a was used in which a small hole was drilled through the specimen and a saw-cut starter notch was introduced on both sides of the hole as shown in Fig. 17b. 17 The specimen was then fatigued at 8 Hz, using a closed loop servo-hydraulic fatigue machine, at a maximum stress of 103 Mpa (15 ksi) and a stress ratio of 0.05. Consequently, a tight fatigue crack was generated at the end of the notch whose width varied as a function of the distance away from the notch tip, as shown in Fig. 17c. The dominant mode measurements were made at a point half-way between the tip of the machined starter notch and the final crack tip. As the crack tip advances during fatigue, the surface of the specimen (at the crack tip) is in a state of plane stress, which influences the size of the plastic zone. The crack front typically tunnels along its path, with the specimen surface crack trailing the inner portion of the crack front. The uncracked ligament between the inner portion of the crack front and the specimen surface yields as the crack advances, creating a slight indentation along the crack length. The indentation depth varies with the size of the plastic zone. When the plastic zone is large, the indentation can be large, (analogous to necking in a tensile specimen). But when the plastic zone is small, as in fatigue of bridge structures, the indentation can be quite small. The indentation on this A-36 steel sample was small, and could not be accurately measured without destroying the sample. An estimate of the indentation, using a replication technique, showed the depth to be less than 0.040 mm. Two DM probes were used for this investigation, one operating at 24.125 GHz (K-band) and the other at 33.6 GHz (Ka-band). The specimen was monotonically loaded at various load levels, resulting in different crack openings. The crack was then scanned while under various static loads. 17 Figure 18 shows the shifted detector output voltage, as a function of scanning distance, for 12 different crack openings (i.e. load levels) at 33.6 GHz (Ka-band). Shifted detector output voltage (or shifted crack characteristic signal) refers to the recorded amplified detector voltage, under various loads, to which a constant dc voltage has been added so that, once plotted, each scan stands distinguished from the others. In this way, one may see the progression of the changes in the crack characteristics signal as a function of crack opening. The results show that for the specimen under no load (0 mm crack opening), there is very little signal variation detected as the crack is scanned. The crack characteristic signal begins to appear at around a crack opening of 0.0032 mm. The results clearly indicate that the crack is detected even at low load values, and the dynamic range of the detected signal increases as the loading increases. The increase in loading causes the crack opening to increase (and to some extent its depth). Thus, the respective crack characteristics signals become more pronounced. It should be noted that not only does there exist indications due to the presence of the crack at the waveguide aperture, but also there are perturbations in these shifted crack characteristic signals that are due to the interaction between the crack and electromagnetic field generated under the flange (flange effect). The arrows denoting Flange and Aperture in Fig. 18 correspond well with the dimension of the flange and the aperture (the flange dimension at this band, in the scanning direction, is 19 mm and the narrow dimension of the probing waveguide aperture is 3.56 mm). When there is a certain standoff distance between the specimen and the waveguide aperture, some microwave signal is trapped between the specimen and the flange. Once this signal reaches the flange edge, a portion of it is reflected back and the combination of these two signals forms a standing wave between the flange and the specimen surface. When the waveguide flange passes over the crack, the properties of this standing wave change and subsequently the signal detected by the detector changes. At higher frequencies the flange effect may result in interference pattern in the image of the crack as will be discussed later.

706 R. ZOUGHI and S. KHARKOVSKY Fig. 17 (a) The A-36 steel specimen used in the experiments, (b) geometry of the hole and the starter notch and (c) close-up geometry of the stress-induced fatigue crack (Research in Nondestructive Evaluation, vol. 12, 2000, pp. 87 103, Microwave detection of stress-induced fatigue cracks in steel and potential for crack opening determination Qaddoumi, N., E. Ranu, J.D. McColskey, R. Mirshahi and R. Zoughi, Fig. 2, c 2000 Springer-Verlag New York, Inc., with kind permission of Springer Science and Business Media.). STATISTICAL ANALYSIS OF THE DOMINANT AND HOM PROBES CRACK DETECTION CAPABILITIES The choice of the best (optimal) probe is an important issue in crack detection using microwaves and millimetre waves. An optimal probe must produce a relatively distinctive crack characteristic signal with an adequate dynamic range, be relatively unaffected by noise due to random surface roughness, and most important, it must easily detect a crack repeatedly. The ability to detect and locate a crack repeatedly has thus far been treated as a qualitative factor. While a probe may work well for one scan, it may not work well when examining four scans or even 12 scans. In a test where four crack scans were made, there existed the possibility of one or more of the crack characteristic signals being masked by an unwanted lift-off. Therefore, it was necessary to place some quantitative measure on the ability of the probes to repeatedly detect a crack and distinguish it from other anomalies. A statistical analysis was developed to determine such a quantitative measure. 21,22 The goal of this investigation was to eliminate detection

MICROWAVE AND MILLIMETRE WAVE SENSORS FOR CRACK DETECTION 707 Fig. 18 Shifted detector output voltage at 33.6 GHz (Ka-band) as a function of scanning distance at different crack openings (load levels) (Research in Nondestructive Evaluation, vol. 12, 2000, pp. 87 103, Microwave detection of stress-induced fatigue cracks in steel and potential for crack opening determination Qaddoumi, N., E. Ranu, J.D. McColskey, R. Mirshahi and R. Zoughi, Fig. 2, c 2000 Springer-Verlag New York, Inc., with kind permission of Springer Science and Business Media.). ambiguities due to the presence of lift-off and its variation while scanning a crack. Description of the statistical experiment The statistical experiment was conducted to evaluate the reliability of many probes. The probe reliability, as defined above as a best probe, was determined by four possible scenarios regarding the output of the microwave probes: 1 A crack is detected when there is a crack. 2 A crack is not detected when there is a crack. 3 A crack is detected when there is not a crack. 4 A crack is not detected when there is not a crack. Several different DM and HOM probes were designed and tested, each varying in some aspect of its hardware design. 21 22 A section of an A-36 steel sample was examined because this provided tight closed cracks, generated by cyclical loading, with moderate surface conditions (i.e. corrosion and abrasions). This sample had two through cracks on each side of a circular hole cut out of the sample. Only one side of the sample was examined and scans were continuous over crack and non-crack regions, simulating, for example, scanning a bridge member while looking for a crack. Although the output of the probes was a continuous voltage signal, a qualitative response such as crack or no crack was only of interest. Therefore, the output of the microwave probes was converted from a signal to a success/fail type of an output. These data labels, rather than values, had no implied ordering and were considered to be nominal categorical data during analysis. Each experiment consisted of a single scan of a small region of the sample either with or without a crack. However, we can assume that when a crack is scanned it can be considered as a discrete scan, while the scanning of non-crack regions is a continuous process and we cannot say we passed over a non-crack region in the same manner that we could say we passed over a crack. This will be an issue when determining the probability of detecting a crack given there is actually no crack present. The probability of detecting a crack was calculated as the number of times a crack was actually detected divided by the number of scans conducted. However, there is no quantity of scans of No Crack. Therefore, we cannot simply say the probability of detecting a crack given there is not a crack is the number of times a Crack is detected divided by the number of times a No Crack was passed over. To implement this statistical approach, three people were involved: one person scanned the sample; one person watched the voltage output (i.e. crack characteristic signal); and one person recorded the data. Three trials were performed with the following characteristics: 1 First trial involved no scan repeats. 2 Second trail required at least two scans of a suspect region.

708 R. ZOUGHI and S. KHARKOVSKY dominant mode probe still detected the crack more than 90% of the time, but the HOM probe required the ability to see and touch the sample. This result further encourages a combination probe using both a dominant and a HOM detector. 22 24 MILLIMETRE WAVE IMAGING OF CRACKS Fig. 19 (a) Picture of the fatigue crack obtained with a microscope and (b) the 90-GHz image (dimensions are in mm) of the crack obtained at standoff distance of 0.8 mm. Solid arrows show the indication of crack non-uniformities and dash arrow shows the indication of pitting. 3 Final trial included a bridge web sample (more realistic sample with surface anomalies), and a dual probe. In addition, relative frequency approach was employed, requiring at least 100 scans per trial. The idea was primarily that a lift-off cannot produce identically repeatable signals, where a crack or other permanent anomalies will. Results of statistical experiment The results of the statistical analysis were invaluable in comparing the probes. These results placed a quantitative measure on the previous qualitative results. It was seen that the dominant mode probe results of this statistical analysis and previous qualitative analyses agreed, but there were some differences in the HOM probe results. A higher level of confidence is placed upon this investigation and its results than those of the previous analyses. 22 The probes that were determined to be the optimal probes were indeed the probes, which produced a signal with a distinctive crack characteristic signal, had an adequately large dynamic range for the crack characteristic signal, were relatively unaffected by noise due to random surface roughness, were able to minimize liftoff issues through scanning repetition, and easily located the crack repeatedly. The dominant and HOM probes at Ka-band were tested with the tight crack in the A-36 steel sample, as shown in Fig. 19a, which is a fatigue crack under static (no load) condition, and produced excellent results, exceeding 90% detection rate. When examining a more difficult sample, such as a bridge web, the results were not as clear. The As mentioned earlier, producing a 2D image of a crack by scanning it in two directions is useful for understanding the process of tip location identification as well as obtaining general information about the crack. 11,13 Based on previous experience with inspecting of different types of composite structures including crack, corrosion 18,31,32 and corrosion precursor pitting 33 34 detection under paint several sensors with open-ended rectangular waveguide DM probes at millimetre wave frequencies (up to 100 GHz) were assembled and used to produce 2D images of real fatigue cracks in steel samples. It was expected that the spatial resolution of the system (associated with an image) would be higher at these high frequencies. The sample was placed on a computer-controlled 2D scanning table and the inspection system was held at a certain distance above it. The measured output voltages were normalized and assigned different greyscale levels producing greyscale 2D images. One of the tested samples was on A-36 steel panel with two tight closed through cracks on each side of a circular hole cut out of the sample. Figure 19a shows the picture of one of the cracks obtained using a microscope. This panel was slightly corroded and its surface was not smooth. Several measurements were conducted using this panel to investigate the ability of the millimetre wave imaging approach to detect and evaluate cracks, and accurately identify crack tip location. The 90 GHz image of the crack, whose picture is shown in Fig. 19a, obtained at standoff distance of 0.8 mm is shown in Fig. 19b. This image shows that the probe produced an indication of the crack with a unique set of features. A vertical dark line in the middle of the images corresponds to the crack. The image also clearly shows a set of vertical bright and dark lines (interference lines) on both sides of the crack as a result of the interaction of the crack and standing wave generated between the waveguide flange and the steel plate ( flange effect ). As mentioned earlier, this type of interaction has also been observed when scanning a crack at lower frequencies (Ka-band), 17 however, at these frequencies only a couple of dark (bright) lines were produced at each side of the crack due to relatively short electrical length (ratio of geometrical length and wavelength) of the flange. At higher frequencies there are more interference lines (pattern) due to the significantly higher frequency used. Thus, the presence of the crack is depicted by these characteristic