The development of ultrasonic signals that can at the same time detect both planar and surface defects is indeed an innovative idea in the field of Nondestructive Testing (NDT). Several studies in recent times have been performed on this topic, but using different methodologies to achieve this goal [1], [2]. In the current work, we introduce for the first time a multiple inspection simulation method which is able to detect both surface defects and internal cracks.

Simulation forms the first phase in Ultrasonic Testing (UT) modelling and helps in gaining insight into the testing process. Predictive models aid in determining the best parameter settings and create mathematical models of the physical system that react consistently to changes in input parameters. FE ultrasonic modelling was first introduced by Ludwig and Lord [3] and paved the way for further developments in this area. Simulation in phased array testing has proved especially useful in determining the favourable transducer properties and parameters.

There has been considerable interest in the Time-of-Flight Diffraction (ToFD) method due to its capability of precise characterization of flaws on planar surfaces. The accuracy of depth and length measurements in this method is much greater than that in conventional methods based on amplitude measurements. The finite element modeling of ToFD has been considered by Baskaran et al. [4] and Honarvar and Khorasani [5]. The recent developments in this field have allowed the usage of the ToFD technique for austenitic welds [6], as well as the analysis of ToFD for unequal thickness specimens [7], and the development of new curved-sole probes for improved inspection.

When it comes to surface crack testing, the best ultrasonic method is the application of Rayleigh waves. Silk [8] formulated the basics of using ultrasonic surface waves for determination of crack penetrations. These waves propagate close to the free surface of the material and have exponential decay with depth. The energy concentration in the thin surface layer makes them very sensitive to surface defects. Moreover, these waves can trace complicated curvatures, making it possible to examine hard-to-reach defects.

Date et al. [9] demonstrated the high accuracy of ultrasonic timing methods using Rayleigh waves for characterizing slots as shallow as 0.8 mm. Hévin et al. [10] determined surface crack depths in concrete with 15% accuracy using spectral analysis, while Scala and Bowles [11] achieved better than 50 μm accuracy for 0.5 mm deep slots using transmitted near-field measurements.

Date et al. [9] proved high precision of ultrasonic timing procedures with Rayleigh waves for detecting slots up to 0.8 mm depth. The surface crack depths in concrete were evaluated with 15% accuracy by Hévin et al. [10] with a spectral analysis procedure, whereas Scala and Bowles [11] provided detection precision better than 50 μm for slots of 0.5 mm depth with a transmitted near-field technique.

The recent research has greatly enhanced the applications of Rayleigh waves in NDT. Verma and Bélanger [12] have introduced a new pulse echo Rayleigh wave procedure for surface crack measurement with no usage of wedges and with sizing accuracy better than 5% error by means of signal averaging techniques. In addition to this, this technique solves the problem of loss of signal energy due to couplant, which had been limiting the Rayleigh wave applications for a long time. Liu et al. [13] have introduced an imaging technique based on leaky Rayleigh waves using an ultrasonic phased array with Total Focusing Method (TFM). Furthermore, the excitation of Rayleigh waves with phased array transducers and linear time delay law is now possible [14]. Application of such waves to characterizing surface-breaking cracks in tubular structures [15] and study of the interaction between the wave and rolling contact fatigue defect by numerical simulation [16] were also explored .

The use of finite element modeling in the simulation of ultrasonic phased arrays continues to be an active area of research. Kolkoori et al. [17] proposed a three-dimensional hybrid modeling technique that combines finite element analysis with semianalytical simulation in order to model the propagation of waves in heavy plates for porosity testing and showed good quantitative agreement with experimental results. Also, a recent review of sound field modeling techniques and imaging technology for ultrasonic phased arrays is presented [18]. Innovative techniques include multimodal image fusion [19], machine learning-enhanced characterization of surface defects based on Rayleigh wave [20], and principal component analysis for TFM imaging with Rayleigh wave [21]. In addition, novel techniques include laser-generated Rayleigh waves in coating/substrate structure [22] and guided wave phased array ultrasonic imaging for thin plate [23].

This research paper is an attempt to further consolidate these ideas through a multiple inspection technique which makes use of phased array beam steering along with the ToFD concept and Rayleigh waves to detect and characterize surface as well as subsurface defects.

The commercial FEM package ABAQUS6.11 is used for two-dimensional modelling of ultrasonic wave propagation. The physical properties of the block are as follows: E = 60 GPa, ρ= 2240 kg/m3, and υ= 0.244. The entire area of the sample is discretised into standard two-dimensional spatial Square Plane Strain Elements (CPE4R) with linear shape functions and four nodes, where each node has two degrees of freedom with respect to displacement. In order to get more accurate results, we can decrease element size, but there are limitations. These limitations occurred due to limited computer system capacity to calculate the enormous calculations needed for simulation. According to the previous work [24], mesh size (∆d) should satisfy Eq. (1):

∆d ≤ λ/15, (1)

where λmin is the shortest wavelength at the excitation frequency of the simulated waves, and Δd is the dimension of the element. Our trial and error studies showed that in order to have a low computation time and good convergence, a mesh size in the order of 5 × 10^-5 m should be chosen.

One of the most important parts of validation of the simulated model is the "convergence test" for FEM simulation. In order to discuss convergence results, different element sizes are considered. An amplitude diagram of the center node of the probe from the top crack tip is used to discuss the convergence results. Signal-to-noise ratio is obtained from received signals and plotted against element size in Fig. 1. For elements smaller than 50 µm, the SNR is stabilized and has a constant value approximately.

La t e r a l s h e a r

This study presents a comprehensive finite element investigation of a novel multiple inspection methodology for simultaneous surface and subsurface defect detection using ultrasonic phased array technology. The following conclusions are drawn:

I. Rayleigh wave superiority for surface inspection: Among surface wave modes, Rayleigh waves exhibit unique advantages for surface defect detection. They maintain constant amplitude with propagation distance, preserving energy even at extended ranges where other surface waves attenuate completely. Additionally, Rayleigh waves are the only surface wave mode unaffected by steering angle variations, maintaining consistent amplitude regardless of beam angle.

II. ToFD single-probe crack characterization: Error analysis of single-probe ToFD for cracks of constant length at various depths reveals that accurate crack sizing is achieved for depths from 1 cm to 6 cm. The critical depth range for reliable crack size evaluation is 6 cm to 8 cm, beyond which accuracy diminishes.

III. Multiple defect detection validation: Simulation of the multiple detection method, a novel approach combining surface and subsurface defect evaluation, has been successfully demonstrated. This method leverages the high capabilities of ultrasonic phased array systems to achieve comprehensive defect characterization in a single inspection procedure.

IV. Surface defect detection accuracy: Rayleigh wave-based surface defect detection achieves less than 10% error at distances up to 24 cm from the transducer, confirming the effectiveness of this approach for practical industrial applications.

The proposed multiple inspection method represents a significant advancement in ultrasonic nondestructive evaluation, offering the potential for reduced inspection time, enhanced detection capabilities, and more comprehensive material assessment.

The authors declare that they have no competing interests.

The data supporting the findings of this study are available within the article.

This research did not receive any external funding.