Experimentally monitoring the growth of surface-breaking cracks using digital image correlation technique integrated with permanently installed low-cost ultrasonic arrays in fatigue tests

Abstract

Monitoring crack growth is crucial for ensuring safety, assessing structural health, optimising maintenance strategies and advancing scientific knowledge in the field of structural engineering. It enables cost-effective asset management, proactive maintenance and the growth of innovative solutions for a safer and more sustainable built environment. In this paper, we explore various techniques to experimentally monitor the growth of surface-breaking cracks on a single edge notch Beam (SENB) specimen in four-point bending fatigue tests according to American Society for Testing and Materials (ASTM) standard E647-15. The notch was generated using electrical discharge machining (EDM). In the measurements, a 5 MHz low-cost ultrasonic array with 18 elements was permanently attached to the top surface of a structural steel (SS355) specimen. A clip gauge was installed around the EDM notch mouth to measure the crack mouth opening displacement (CMOD). Additionally, a digital camera was focused on the tip of the EDM notch to measure surface displacements using digital image correlation (DIC). During the four-point bending fatigue tests, experimental data sets were recorded from the ultrasonic array, the clip gauge and the digital camera at each loading cycle. We focused on the development of post-processing techniques for measuring crack length and CMOD using the acquired ultrasonic array datasets and the measured surface displacement and strain distributions from the DIC technique, as well as low-cost ultrasonic array design, fabrication and installation. The proposed post-processing techniques were validated by comparing the results obtained with calculations using the standard procedure in ASTM E1820 based on CMOD values acquired from clip gauge measurements. We demonstrated that both the low-cost ultrasonic array and DIC exhibit reasonable and reliable performance in detecting and monitoring crack growth. The developed post-processing techniques proved effective in accurately measuring key parameters of crack growth, such as crack length and CMOD. These findings validate the feasibility and applicability of using low-cost ultrasonic arrays and the associated post-processing techniques for crack monitoring and characterisation and for supporting structural integrity assessments.

Keywords

Ultrasonic arrays digital image correlation crack length defect characterisation

Introduction

In modern engineering practices, ensuring the safety, performance and longevity of critical components and infrastructure necessitates the reliable assessment of structural integrity and the early detection of potential defects. Structural health monitoring (SHM) is an interdisciplinary field that integrates various techniques and methods to assess the condition and performance of structures, such as buildings, bridges and infrastructure systems.^1–4 The primary goal of SHM is to detect, locate and quantify potential damage or deterioration in structures, enabling timely maintenance and repair actions.^5–8 SHM heavily relies on the deployment of various non-destructive testing (NDT) technologies to collect data from structures. Common sensors used include strain gauges, fibre optic sensors and ultrasound sensors.^9–11

Surface-breaking cracks, particularly fatigue cracks and stress corrosion cracks, emerge as significant challenges. These defects commonly result from cyclic loading and harsh operating conditions in safety-critical infrastructure, such as rail tracks, gears, vessels and pipelines, and their capacity to propagate can severely compromise structural integrity over time.¹² The ability to monitor the initiation and growth of these cracks is crucial for preventing catastrophic failures and minimising maintenance costs.

Assessing the size and type of defects is fundamental to structural integrity analysis as reaching a critical size could lead to structural failure.¹³ Non-destructive evaluation methods, including the use of surface waves^14–17 and guided waves,^18,19 play a key role in detecting these defects. These methods can identify defects along the wave propagation path, where the amplitude of reflected or transmitted signals may indicate defect size. Moreover, the application of ultrasonic bulk wave measurements often involves single-sided access, where a transducer or array placed on the structure’s front wall detects defects on the back wall.^20–24 Utilising ultrasonic arrays for this purpose is advantageous, as a single-array transducer can illuminate a defect from various angles and capture the full matrix capture (FMC) dataset,²⁵ which is then processed with an imaging algorithm such as the total focusing method (TFM)²⁵ and its variants,²⁶ providing effective defect detection, localisation and classification.^27–29 It is also worth mentioning that the traditional approach to ultrasonic testing, which involves handheld probes to deliver and analyse ultrasonic waves, falls short in continuous monitoring scenarios, such as fatigue tests, due to inefficiencies, cost implications and limitations in real-time data acquisition.²⁹ Existing cost-effective SHM solutions can provide an effective means of continuously monitoring corrosion by tracking wall thickness loss using piezoelectric sensors.^30–32 However, these sensors are not capable of detecting the subtle initiation and propagation of cracks. It is also worth noting that the traditional approach to ultrasonic testing – using handheld probes to deliver and analyse ultrasonic waves – is inadequate for continuous monitoring scenarios due to inefficiencies, cost implications and limitations in real-time data acquisition.

This paper explores the utilisation of permanently installed low-cost ultrasonic arrays³³ for continuous monitoring of crack mouth opening and growth. The technique’s validation involves a comparison with the established crack length measurement methods, including digital image correlation (DIC) and calculations based on crack mouth opening displacement (CMOD), to assess its accuracy, reliability and potential advantages. This study aims to evaluate the performance of low-cost ultrasonic arrays in continuous monitoring applications, covering theoretical foundations, experimental setups, data acquisition, processing methodology and validation results, thereby offering insights into enhancing SHM approaches and integrity assessments using the measurements from permanently installed low-cost ultrasonic arrays. The experimental measurement system is described in the second section; the third section introduces the methodology used to measure the CMOD and crack length, which comprises (1) the compliance method using a clip gauge, (2) the crack length measurements from the measured stress field by the DIC technique and (3) the TFM imaging algorithm based on the FMC array data sets; the fourth section shows and compares the results; and the discussions and conclusion are finally drawn in the fifth section.

Experimental setup

Figure 1(a) shows the schematic diagram of the four-point bending test and the geometry of a single edge notch beam (SENB) specimen. The test specimen was fabricated from SS355 structural steel according to ASTM E647-15 standard with an initial electrical discharge machining (EDM) notch with a length of $a_{0}$ = 6 mm, as illustrated in Figure 1(b). The sharp V-shape of the EDM notch ensures that crack initiation and growth will occur from the notch tip. Figure 2 shows the experimental setup used to monitor crack growth on the SENB specimen under a four-point bending fatigue test. The intention is to develop data post-processing techniques to monitor crack growth, denoted as $Δ a_{n,}$ as illustrated in Figure 1(b), from both FMC array datasets obtained from the low-cost ultrasonic array and the measured surface strain map measured by the DIC technique, as well as test the measurement performance of the low-cost ultrasonic array. This ultrasonic array was developed at the Bristol Ultrasonic and NDT group, and has 22 array elements, a central frequency of 5 MHz, an element width of 0.8 mm, an element pitch of 1.2 mm and an element elevation length of 10 mm. It should be noted that a centre frequency of 5 MHz was chosen for the ultrasonic array based on a trade-off between penetration depth and spatial resolution. This selection aligns with the recommendations in Sun’s prior work on permanently installed phased arrays for SHM, where 5 MHz demonstrated reliable imaging performance in similar steel specimens.³³ Given the importance of maintaining consistent coupling between the ultrasonic array and the specimen surface, potential de-bonding was carefully addressed. To mitigate this risk, a highly reliable adhesive – EpoThin epoxy resin (Buehler, Ltd., IL, USA)—was used to bond the array to the SENB specimen. During the curing process, a vacuum bag and vacuum pump were employed to ensure that the array was evenly and firmly pressed against the surface, promoting uniform adhesion by eliminating air pockets. Additionally, after bonding, the specimen was handled with particular care to avoid any mechanical stress that could compromise the integrity of the adhesive bond throughout the experiment. A single-camera setup was adopted for the DIC measurements in this study. This choice was based on the expectation of negligible out-of-plane strain in the region of interest, as the SENB specimen was subjected primarily to in-plane bending. Under such conditions, a monocular DIC system can provide sufficiently accurate displacement and strain fields while simplifying the experimental setup and reducing computational overhead. Similar assumptions and configurations have been successfully employed in previous DIC studies where out-of-plane motion was minimal and did not significantly affect measurement accuracy.³⁴

Figure 1.

(a) The schematic diagram of a four-point bending test and the geometry of an SENB specimen and (b) crack length definitions where $a_{0}$ is the length of the initial EDM notch, $Δ a_{n}$ and $a_{n}$ are the growth length and the total length of the crack after $n$ number of loading cycles, respectively. EDM: electrical discharge machining.

Figure 2.

Photos of the experimental setup used to monitor crack growth on an SENB specimen under a four-point bending test.

As shown in Figure 2, the experimental setup was adapted to fit the Instron hydraulic machine (1342 100 kN, Instron Co., Buckinghamshire, UK). The SENB specimen, fabricated from SS355, is subjected to a four-point bending fatigue test, with loading applied using an Instron hydraulic machine. The low-cost ultrasonic array was permanently attached to the top surface of the specimen and was connected with a commercial array controller (Micropulse MP5PA, Peak NDT, Ltd., Derby, UK) for acquiring FMC array datasets. The captured datasets were exported and processed using MATLAB (The MathWorks, Inc., Natick, MA, USA) to measure crack length. A clip gauge was installed around the EDM cut mouth to measure the CMOD. Additionally, a digital camera is focused on the tip of the EDM cut to measure surface displacement and strain through the DIC technique. During the four-point bending fatigue tests, the SS355 SENB specimen is supported by two lower points and loaded by two upper points, creating a bending moment within the specimen. The loading was applied cyclically. This loading configuration induces cyclic stresses at the EDM-cut notch tip, which initiate and propagate the crack over time. The objective of the test is to simulate real-world conditions where cyclic loading can lead to the initiation and growth of surface-breaking cracks. The experimental datasets were recorded from the ultrasonic array, the clip gauge and the digital camera at each loading cycle.

As shown in Figure 2, there is a clip gauge holder slot in the test specimen, with a height of $h$ = 2 mm, machined into the bottom of the specimen to hold the clip gauge used for directly measuring the CMOD. The use of a 9-mm long clip gauge for measuring the CMOD represents a precise method for evaluating the fracture mechanics of materials. As depicted in Figure 2, a clip gauge is directly attached to the specimen, enabling accurate monitoring of the crack opening as external forces are applied. The precision of clip gauge ensures reliable CMOD measurements, providing a solid reference for validating other crack monitoring approaches. In addition, a speckle pattern was applied with acrylic paint on the front face of the material, which was used by the DIC technique (DIC Nr. 5 and StrainMaster, LaVisionUK Ltd., Bicester, UK) to capture subtle movements on the surface of the specimen. Throughout the experimental measurements, it is assumed that the speckled surface has negligible out-of-plane strain. Therefore, a single-camera (AT-X M100 PRO D Macro (100 mm f/2.8; Tokina Co., Ltd., Tokyo, Japan) setup was used, as opposed to a dual-camera setup, which can calculate the out-of-plane strain. Figure 2 also shows a fine and uniformly distributed speckle pattern painted on the specimen surface. Through iterative testing, a subset size of approximately 90 μm was determined to provide optimal displacement and strain resolution for the DIC experiments.

The experimental setup was adapted to fit the Instron hydraulic machine (1342 100 kN, Instron Co.). The SENB specimen was subjected to a four-point bending fatigue test under load control, where minimum and maximum applied loads were $P_{\min} =$ 0.5 kN and $P_{\max} =$ 40 kN (R = $P_{\min} / P_{\max}$ = 0.0125), respectively. The loading frequency used was 10 Hz. This loading and geometric configuration induces the highest cyclic stresses and strains at the EDM notch tip, where crack initiation and propagation were expected to occur over cycles. For the first 2000 loading cycles, the bending rig was paused every 100 cycles to allow all three techniques take their respective measurements at various load conditions, from a relaxed state ( $P_{\min}$ = 0 kN) to maximum state ( $P_{\max}$ = 40 kN) with an increment of 5 kN. After 2000 loading cycles, same procedure was followed every 200 loading cycles instead.

Methodology used to measure CMOD and crack length

In this section, the different methods used for monitoring crack growth are introduced and described in detail.

CMOD-based crack length estimation

The reading on the clip gauge directly indicates the distance between the left and right ends of the clip gauge holder, which corresponds to the CMOD. From the clip gauge measurements, ASTM E1820 provides an equation to estimate the crack length, $a$ , based on the change in compliance of the specimen^35,36:

a = W (2.9184 μ_{CMOD}^{2} - 3.4508 μ_{CMOD} + 1.0581),

(1)

where

μ_{CMOD} = \frac{1}{1 + \sqrt{\frac{BEW Δ CMOD}{D Δ P}}},

(2)

where $μ_{CMOD}, B$ , $W$ and $D$ are the specimen compliance and geometry dimensions, respectively, as illustrated in Figure 1(a), $E$ is the Young’s modulus, $Δ CMOD$ is the change in CMOD after the loading $Δ P$ has been applied, which is kept at 39.5 kN in this paper.

As a way of cross-validation, the linear asymptotic superposition assumption (LASA) was also used to calculate the crack length, by³⁷:

a = \frac{EB W^{2} Δ CMOD}{3 PSf (α)},

(3)

where $S$ is a specimen geometry dimension, as marked in Figure 1(a), $f (α) = 0.8 - 1.7 α + 2.4 α^{2} + \frac{0.66}{{(1 - α)}^{2}}$ , $α = \frac{a + h}{W + h}$ and $h$ is the thickness of the clip gauge holder as shown in Figure 2.³⁷ The crack length is measured by iterating over the value of a.

It is worth noting that in the compliance method, the missing material in the test specimen due to the machining of the clip gauge holder is assumed to be effectively part of the crack length, whereas the LASA method accounts for the effect of the clip gauge holder slot.

DIC-based crack length estimation

DIC allows for the characterisation of in-plane deformation and displacement fields at the surface of specimens or components.³⁴ It begins with the application of a unique speckle pattern on the surface, as shown in Figure 2, which is then photographed in both loaded and unloaded configurations. The unloaded configuration serves as a reference against which the subsequent images are compared. Specialised software such as StrainMaster, analyses these images, tracking the movement of the speckle pattern across the surface. This analysis enables precise calculation of displacements and strains on the surface.³⁴ Since the displacement field on the surface of a specimen can be directly obtained from DIC, the CMOD can theoretically inferred from the displacement field at the specimen’s bottom edge. However, accurate displacement measurements along the edges of the specimen are challenging for the DIC technique due to discontinuities in the displacement field and the difficulty of establishing an even speckle pattern in that area.

In this paper, a procedure for measuring the CMOD is proposed by using the displacements along the crack surfaces, fitting them as two straight lines and finding their intersection points with the specimen’s bottom surface. The location of the intersection point of these two straight lines indicates the position of the crack tip. The location where displacements change sign at a specific crack depth can be determined by taking the derivatives of displacement with respect to their x-coordinates (see Figure 1 for coordinate definitions). This method is termed as the crack surface measurement (CSM). The detailed procedure for this process is introduced along with experimental data in “DIC-based crack length estimations” section.

It should be noted that the surface strains on both the $x$ axis and $y$ axis, that is, $ε_{xx}$ and $ε_{yy}$ , can be measured directly from the DIC technique. Using Hooke’s law under plane stress conditions, the stress field on the $x$ axis can be calculated by³⁸:

σ_{xx} = \frac{E}{1 - ν^{2}} (ε_{xx} + ν ε_{yy}),

(4)

where $ν$ is the Poisson’s ratio of the material. The resulting stress field is subsequently used to locate crack tips. Irwin³⁹ suggested that as the stress distribution ahead of the crack tip varies with the stress intensity factor (SIF), it can be expressed as:

σ_{xx} = \frac{Y σ \sqrt{π an}}{\sqrt{2 π (y - an)}},

(5)

where $Y$ is a factor related to the crack length. Equation (5) suggests that the stress ahead of the crack tip would increase as the crack length increases. At each loading cycle, $σ_{xx}$ can be calculated as a function of $y$ using the measured strain fields obtained from the DIC technique and Equation (4). Meanwhile, multiple hypothetical crack lengths, $a_{n}$ , can be proposed with an initial value of $a_{n - 1}$ , and varying within a defined region, to calculate $σ_{xx}$ using Equation (5). The measured crack length is the one among the proposed crack lengths that provides the best match of $σ_{xx}$ from Equations (4) and (5). We term this crack length measurement process as the SIF-based crack length estimation method.

UT-based crack length estimation

A main benefit of having a permanently installed ultrasonic arrays in the experimental tests is the ability to continuously acquire FMC array datasets under consistent conditions, both in terms of position and coupling. This enables the use of subtraction techniques to identify subtle changes in the ultrasonic array datasets, which can then be utilised to detect crack growth through an imaging algorithm such as the TFM. A subtracted signal can be written as:

g_{ij, km}^{(sub)} (t) = g_{ij, km}^{(ori)} (t) - g_{ij, k 0}^{(ori)} (t),

(6)

where the superscripts ‘sub’ and ‘ori’ denote the time-domain signal from subtraction and originally acquired, respectively, the subscripts $i$ , $j$ represent the indices of the transmitting element and receiving element, respectively, $k$ is the index of a loading cycle, and $0$ and $m$ are indices of originally acquired array datasets at the initial load ( $P_{0}$ = 0 kN) and the other loads in each loading cycle. The resulting TFM image in the $x$ – $z$ plane, defined in Figure 1(a), can be calculated by³³:

\begin{matrix} I_{km} (x, z) \\ = | \sum_{i, j} H [g_{ij, km}^{(sub)} (t = \frac{\sqrt{{(x_{i}^{(el)} - x)}^{2} + z^{2}} + \sqrt{{(x_{j}^{(el)} - x)}^{2} + z^{2}}}{v})] |, \end{matrix}

(7)

where $H$ is the Hilbert transform operator⁴⁰ applied to a time-domain signal, the superscript ‘el’ denotes array element and $v$ represents the wave speed.

The crack length is estimated from subtracted TFM images by first defining the region of interest where the crack is expected, and then locating the point of maximum image intensity within that region – this is identified as the crack tip. This method is related to the ultrasound scattering behaviour from the overall crack front and differs from the DIC measurement, which provides crack information on the surfaces.

Results

From the measurements using a clip gauge

Figure 3(a) illustrates the ΔCMOD measured by the clip gauge at each load cycle. These ΔCMOD values were then used to calculate crack length using both the compliance method (Equation (1)) and the LASA method (Equation (3)), shown in Figure 3(b). As expected, both ΔCMOD and the measured crack length increase monotonically with the number of load cycles. The root mean square difference between two methods is less than 0.007 mm, indicating excellent agreement between the two approaches.

Figure 3.

(a and b) Experimentally measured ΔCMOD and crack length at each loading cycle. In (a), the ΔCMOD was calculated from subtracting the clip gauge readings between maximum loaded ( $P_{m}$ = 40 kN) and relaxed ( $P_{0}$ = 0 kN) states. In (b), the crack length was calculated from the ΔCMOD values in (a) using both the compliance method (Equation (1)) and the LASA method (Equation (3)). CMOD: crack mouth opening displacement; LASA: linear asymptotic superposition assumption.

DIC-based crack length estimations

Figures 4 and 5 compare the displacements and strains at 0 and 18,000 loading cycles for a minimum and a maximum load level of 0.5 and 40 kN, respectively. From Figures 4 and 5, the crack surface can be identified as the locations with discontinuous displacement fields or ‘jumps’, that is, white region between the blue and red zones.

Figure 4.

Experimentally measured surface displacement from DIC technique, $P_{\min} = 0.5 kN$ and $P_{\max} = 40 kN$ on the: (a and b) $x$ axis; and (c and d) $y$ axis; (a and c) before fatigue testing and (b and d) after 18,000 cycles. DIC: digital image correlation.

Figure 5.

Experimentally measured surface strain using the DIC technique under loads of 0 and 40 kN on the: (a and b) $x$ axis and (c and d) $y$ axis. The loading cycles are (a and c) 0 and (b and d) 18k. DIC: digital image correlation.

The $Δ CMOD$ measurement procedure using the CSM described in “DIC-based crack length estimation” section is demonstrated here with the measured displacements from DIC. Figure 6(a) shows that the displacement vector directions are opposite with respect to the crack surfaces. Figure 6(b) shows the derivatives of each curve in Figure 6(a) with respect to x, $u_{x}^{'}$ and gives a clearer representation of the precise location of the crack surfaces.

Figure 6.

(a) $x$ -Displacements on different levels of $y$ , extracted from the displacement field in Figure 4(a); (b) the derivative of each curve in (a) with respect to $x$ ; (c) the calculated $e$ from (b) using Equation (8); (d) the measured $u_{x}$ on the crack surfaces; (e) the measured $Δ CMOD$ as a function of fitting range and (f) final measured $Δ CMOD$ at each loading cycle. Note that (a–e) were obtained from the measurement at a loading cycle of 13k. CMOD: crack mouth opening displacement.

To find the location of the crack surfaces from each curve in Figure 6(b), a parameter at each $X$ -position, $e$ , is defined as:

e (X) = {\begin{matrix} u_{x}^{'} (X) - \bar{u_{x}^{'}} (x < X) - 3 σ (x < X) if X \leq x_{p} \\ u_{x}^{'} (X) - \bar{u_{x}^{'}} (x > X) - 3 σ (x > X) if X < x_{p} \end{matrix}

(8)

where $x_{p}$ is the peak location of each curve in Figure 6(b), the bar denotes mean and $σ$ is the standard deviation of $u_{x}^{'}$ . Here, it is assumed that $u_{x}^{'}$ away from the crack surfaces should follow a statistical distribution, while its values at the crack surfaces provide ambiguity. Figure 6(c) shows the resulting $e$ from the three curves presented in Figure 6(b). The locations of the crack surfaces are defined at the farthest zero-crossing points at each side of $x_{p}$ , and their corresponding displacement, $u_{x}$ , can be found in Figure 6(a) and are illustrated in Figure 6(d). Also shown in Figure 6(d) are the examples of the fitted straight lines based on the data within a certain region, and the distance between the intersection points of these lines at $y$ = 0 is the measured $Δ CMOD$ . This fitting region was determined by the convergence of the resulting measured $Δ CMOD$ , as shown in Figure 6(e). By repeatedly applying this procedure to the data from each loading cycle, the measured $Δ CMOD$ is shown in Figure 6(d), differs by approximately 10 µm difference from the values measured using the clip gauge. This discrepancy is thought to be caused by the 2 mm difference ( $h$ = 2 mm as shown in Figure 1(b)) in their measurement locations in the $y$ axis. This will be considered in the final crack length measurements in the fourth section.

Using the values in Figure 5(a) to (d) and Equation (4), the surface stresses on $x$ axis were calculated, as shown in Figure 7(a) and (b). These calculated stresses were subsequently employed to determine the crack length using the SIF method described in “DIC-based crack length estimation” section. Figure 8(a) shows the measured stress, $σ_{xx}$ , along the crack surface using the DIC technique (shown as symbols) and Equation (5) (represented as lines). For each loading cycle case, multiple hypothetical crack lengths, $a_{n}$ , were proposed around an initial value of $a_{n - 1}$ and varying maximum range of ±0.2 mm. The measured crack length was determined by finding the best-matched line (shown as black lines) with symbols. Repeatedly processing data at each loading cycle, Figure 8(b) displays the measured crack lengths alongside those determined using a fixed stress threshold of 2200 MPa. This threshold was obtained from using Equation (4) for a crack length equal to the EDM notch length before the fatigue test with $Δ P = 39.5 kN$ . Figure 8(b) also shows the measured crack length from the measured crack surfaces shown in Figure 6(d). It is evident from Figure 8(b) that there is a generally good agreement with these measurements. The measured crack lengths using a fixed stress threshold are longer than those obtained from the SIF method. This discrepancy arises because the stress at the crack tip is higher for longer cracks. Consequently, if the threshold value is set based on an initial crack length, it will overestimate the crack length.

Figure 7.

The calculated surface stress under a load of 40 kN and at a loading cycle of (a) 0 and (b) 18k.

Figure 8.

(a) Measured stress distribution along the crack central line is compared with those predicted using Equation (5) with a few proposed crack lengths and (b) measured crack length from (a) using the SIF method, the fixed threshold (2.2 GPa) method and the measured crack surfaces (shown in Figure 6(d)). SIF: stress intensity factor.

Ultrasound-based crack length estimation

It should be noted that a digital filter with a central frequency of 5 MHz and a bandwidth of 10 MHz was applied to suppress noise before the subtraction of the FMC array datasets. Figure 9(a) to (d) compares the TFM images at different loads and loading cycles. As seen in Figure 9(a) to (d), the direct TFM images can clearly indicate the location of the back wall, the clip gauge holder and the notch, but the crack tip responses are vague. It is possible to detect the crack tips using the −6 dB drop and threshold techniques,²⁷ but this would involve additional parameters and require case-by-case calibrations. It is noticed that the geometry of the SENB specimen is supposed to be symmetrical, while the TFM images are asymmetrical. This is due to the imperfect adhesion between the array and the material surface, which caused de-bonding between the elements to the right of the images. The triangle-shaped feature in the top-right corner is an image artefact of the clip gauge holder, again; due to de-bonding, it is not present on the left side.

Figure 9.

The TFM images generated using the FMC array dataset acquired at a loading cycle of (a, c and e) $n$ = 0 and (b, d and f) $n$ = 9.1k. The used load, $P$ =: (a and b) 0 kN and (c and d) 40 kN. (e) and (f) are TFMs from subtracted FMC between $P$ = 0 kN and $P$ = 40 kN. FMC: full matrix capture; TFM: total focusing method.

Figure 9(e) and (f) shows that the subtracted TFM images are capable of detecting crack tip responses, as there are local peaks within the region of interest. The use of the tip response enables the detection algorithm can be generally applied to other cases with similar geometries (i.e. surface-breaking crack from the other side of the material) without the need for calibration.

We also tried to measure the $Δ CMOD$ from the TFM images. Figure 10(a) and (b) illustrates how it is done: it starts by plotting the image intensity of the two dashed lines in Figure 9(a) and (c). The bottom of the trough in the centre is supposedly the notch opening, while the peaks on either side are where the corners of the crack mouth are, as shown in Figure 10(a). Theoretically, the sum of the spatial difference between these peaks at different loads should be the $Δ CMOD$ being measured, and the results are shown in Figure 10(b). Compared to the measurements from the clip gauge, significant differences are observed, where maximum differences are of one order of magnitude. This means using ultrasound images to measure $Δ CMOD$ directly is not possible due to the limitation in resolution of the method (displacements are around a quarter of the ultrasound’s wavelength).

Figure 10.

(a) Back wall image intensity along the dashed line shown in Figure 9(a) and (c) and (b) the measured $Δ CMOD$ as a function of loading cycle. CMOD: crack mouth opening displacement.

Results comparison

After the experiment was completed, the specimen was submerged in liquid nitrogen and broken open using three-point bending to reveal the crack growth pattern during the fatigue cycles. At liquid nitrogen temperature, SS355 is significantly more brittle and ensuring that brittle fracture process does not affect the shape of the fatigue crack. As a result, the shape and boundaries of the relatively smooth fatigue crack are clearly visible in Figure 11(a), which shows a slightly shorter crack length on the surface ( $y_{edge}$ = 6.46 mm) than that at the centre ( $y_{\max}$ = 7.15 mm), due to the different triaxial stress state conditions. Lower stress triaxility levels at the specimen surface result in higher levels of plastic deformation, allowing more deformation before fracture occurs compared to the specimen centre, where plastic deformation is inhibited by higher constraint conditions.

Figure 11.

(a) Photo of crack shape after specimen was broken open, (b) comparison of the measured crack lengths from various methods and (c) the pulse-echo ultrasonic signals acquired at a load of 40 kN in a loading cycle of 13k.

Figure 11(b) compares the measured crack lengths using various methods. It should be noted that, combined with the compliance method, the measured $Δ$ CMOD shown in Figure 6(f) from the CSM on the DIC results was used to calculate $y_{n}$ and the resulting measured $a_{n} = y_{n} + h$ is also shown in Figure 11(b). As shown in Figure 11(b), both DIC measurements agree very well with each other but overestimate the crack length. Ultrasound measurements show close results to the reference values provided by the compliance method up until 10k cycles, and stopped yielding good results afterwards. This was thought to be caused by the de-bonding problem between the sensor and the surface of the material, as evidenced by the lack of signals received from the first array elements, as shown in Figure 11(c).

Table 1 compares and summarises the considered methods. Regarding the overestimation of the measured crack lengths by the DIC methods, it could be caused by geometric changes in the deformed specimen and slight shifts in its position on the supporting bars. These factors may cause the crack initiation point to appear higher in pixel coordinates. However, the crack length measurement was still taken relative to the initial initiation point. It should be noted that identifying the exact crack initiation point in DIC images is challenging. Regarding the divergence of UT results after 10k cycles, it could be attributed to inconsistent de-bonding, which introduces significant errors and noise into the subtracted FMC array datasets used to form the ultrasound images.

Table 1.

Comparison of the used methods for crack length measurements.

Method		Description and used equations	Pro	Con
CMOD-based	Compliance	Following ASTM E1820 guidelines (Equations (1) and (2)).	High reliability; serves as the reference method; excellent agreement between compliance and LASA methods (root mean square difference less than 0.007 mm).	Requires access to a crack opening and a clip gauge holder feature.
CMOD-based	LASA	Estimation based on LASA (Equation (3)).
DIC-based	SIF	Estimation derived from SIF (Equations (4) and (5)).	Generally agrees with the compliance measurement.	Overestimation is observed when trying to measure crack length directly; measurement accuracy is sensitive to any relative movement between the camera and the specimen during loading.
DIC-based	CSM for crack length	Locates the crack tip and crack mouth by analysing measured displacement discontinuities (Equation (8)).	Generally agrees with the compliance measurement.
	CSM for CMOD	Locates the crack mouth by analysing measured displacement discontinuities.	Agrees very well with the compliance method using clip gauge data.
UT-based		Using the TFM imaging algorithm on subtracted FMC ultrasonic array datasets (Equations (6) and (7)).	Good agreement with compliance method up to approximately 10k cycles.	Performance degrades after 10k cycles due to de-bonding between the array and specimen; imaged resolution limits affect measurement accuracy at higher cycles.

CMOD: crack mouth opening displacement; LASA: linear asymptotic superposition assumption; DIC: digital image correlation; FMC: full matrix capture; TFM: total focusing method; CSM: crack surface measurement; SIF: stress intensity factor.

Conclusion

Correlative post-processing techniques were used for measuring CMODs and crack length during fatigue testing. Results obtained from the DIC-based (SIF and CSM approaches) and the UT-based approaches were compared. The proposed techniques were validated by comparing the results with those obtained using the compliance method in ASTM E1820, which uses the ΔCMOD measured by the clip gauge measurements. We demonstrated that both the low-cost ultrasonic arrays and DIC exhibit reasonable and reliable performance in detecting and monitoring crack growth in four-point bending fatigue tests. The developed post-processing techniques proved effective in accurately measuring important parameters of crack growth, such as crack length and CMOD. These findings validate the feasibility and applicability of using low-cost ultrasonic arrays and the associated post-processing techniques for crack monitoring and characterisation. Our results provide confidence in the practical use of these methods for assessing crack growth and structural integrity in various applications. Future work should consider improving the bonding quality between the ultrasonic array and the specimen. Potential solutions include selecting a more robust epoxy resin and incorporating additional mechanical fixtures, such as clamping. More practical trials are also needed to advance the developed techniques towards final industrial applications.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the EPSRC Centre for Doctoral Training in Future Innovation in Non-Destructive Evaluation (FIND) (grant number EP/S023275/1) and the UK EPSRC under grant number EP/X527257/1 through the Henry Royce Institute MCAP Award. Nicolas O Larrosa acknowledges funding from the UK EPSRC under grant number EP/S012362/1 and RCNDE for the project ‘Quantitative Sizing of Short Fatigue Cracks and Assessment of Crack Driving Force Using Ultrasonic Arrays: A Feasibility Study’. Jie Zhang also acknowledges funding from the UK EPSRC under grant number EP/Y016661/1.

ORCID iDs

Junlei An

Xiaoyu Sun

Jie Zhang

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