# An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

^{*}

## Abstract

**:**

## Featured Application

**The proposed models’ validation will enable the proper use of ultrasonic simulation for designing NDT methods for embedded crack detection and characterization.**

## Abstract

## 1. Introduction

## 2. Simulation Methods

## 3. Numerical Validations of 3D Embedded Flaws Simulations

^{3}. All the input data for simulation are exactly the same for all the used models. These data describe the inspection configuration [1]: the characteristics of the component, the used probes, the inspection scanning, the inspected flaws and the simulation settings.

#### 3.1. Longitudinal Waves

#### 3.2. Shear Waves

#### 3.2.1. Immersion Pulse Echo Mode: S45° Waves—Various Incidences on the Flaw

#### 3.2.2. Contact Pulse Echo Mode: S45° Waves—Vertical Flaw

_{1}) is generated. It propagates along each crack face towards the opposite tip. Upon reaching the bottom tip, R

_{1}sheds the bulk S

_{5}wave. The path of this Rayleigh wave then diffracted in the bulk corresponds to that of the so-called S

_{5}wave, which is due to a secondary diffraction (see its path drawn in Figure 6 of Ref. [26]).

_{inc}= 45° whereas θ

_{c}= 33° for steel). The third echo corresponds to the secondary Rayleigh wave diffraction S

_{5.}PTD predicts correctly the amplitudes of the primary bulk waves diffracted by the two edges but the PTD model does not simulate the secondary Rayleigh wave diffraction S

_{5}. It is this latter wave which leads to the more important amplitude in the 3D FEM Ascan.

## 4. Experimental Validations

#### 4.1. Inspection of Large Flaws

#### 4.2. Inspection of Small Flaws Compared to the Wavelength

- -
- Four electro-eroded notches (5 mm height × 30 mm extension) and four side-drilled holes (2 mm diameter × 40 mm extension) which are embedded with respective bottom ligaments (distance between notch extremity and backwall) of 5, 10, 15 and 20 mm;
- -
- One backwall breaking notch (not considered in the following validation study);
- -
- Four flat bottom holes on the right side.

#### 4.2.1. Inspections with Compressional (P) Waves

#### 4.2.2. Inspections with Shear (S) Waves

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Hybrid Method Description

**Figure A1.**The two different states for reciprocity application. For state R, the dashed red line mimics the absence of the flaw.

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**Figure 1.**Different coupling strategies used in the CIVA hybrid FEM model for (

**a**) embedded and (

**b**) breaking cracks.

**Figure 2.**(

**a**) Inspection of a 5 mm high (height represented by a red segment) and varied extent rectangular crack inspected using P45 waves in TOFD mode at 2.25 MHz; Echo magnitude versus the flaw extension (

**b**) for the 0.5 mm high crack and (

**c**) for the 5 mm high crack.

**Figure 3.**Inspection of a 25 mm extent rectangular crack inspected using P45 waves in TOFD mode at 2.25 MHz: (

**a**) Echo magnitude versus the flaw height; (

**b**) Ascans simulated both by the 3D FEM and PTD models for the 5 mm high crack.

**Figure 4.**(

**a**) Inspection of a 25 mm extent rectangular crack of varying height using P60 waves in TOFD mode at 2.25 MHz. (

**b**) Superimposition of Ascans simulated both by the 3D FEM and PTD for the echoes generated for the 5 mm high crack. (

**c**) Echo magnitude versus the flaw height.

**Figure 5.**Inspection of a 25 mm extent rectangular crack of varied height inspected using P60 waves in TOFD mode at 2.25 MHz: Ascan versus the flaw height.

**Figure 6.**(

**a**) pulse echo configuration with the SV45° wave at 5 MHz of a rectangular defect of varying height (5 mm here—red segment), 0.5 mm extent and various tilts; (

**b**) α = −45°, specular reflection configuration; (

**c**) α = 0°, classical configuration of a vertical flaw.

**Figure 7.**A planar component containing an embedded rectangular flaw of 0.5 mm extent and of height: (

**a**) 5, (

**b**) 1 and (

**c**) 0.5 mm. Comparison of FEM and PTD (standard or with smoothing around the critical angle) models.

**Figure 8.**(

**a**) Inspection of rectangular crack using SV45 waves in Pulse Echo mode at 2.25 MHz (circular planar probe of 6.35 mm diameter), (

**b**) of 5 mm height and varying extension and (

**c**) of a 34 mm extension and varying height.

**Figure 9.**Inspection of a 40 mm extent and 5 mm high rectangular crack inspected using SV45 waves in Pulse Echo mode (circular plane probe of 6.35 mm diameter); Ascans simulated by 3D FEM and 3D PTD: (

**a**) at 2.25 MHz (

**b**) at 5 MHz with also the normalized Ascan modelled by 2D FEM Civa/Athena. (

**c**) S head waves diffracted from a crack (in blue) under 45° incidence: the S wave shed by the bottom tip irradiated by the P creeping wave coming back to the probe at 45° direction and the S head wave radiated during the propagation of the P creeping wave along the crack surface.

**Figure 10.**(

**a**) A planar component containing disoriented backwall breaking flaws and a 2 mm diameter SDH; the TOFD configuration with the 11° probes’ skew: (

**b**) top view and (

**c**) side view showing the flaw used for simulating the top edge of the 30° disoriented notch.

**Figure 11.**(

**a**) Experimental B-scan obtained when scanning the side drilled hole (SDH) and the three defects (with vertical misorientation of 10° to 30° for the top edge); (

**b**) validation of the 2.5D GTD, 3D PTD and the hybrid 3D FEM models against the measured echoes from the top tip of misoriented backwall breaking flaws.

**Figure 12.**(

**a**) TOFD configuration on a skewed backwall breaking crack; (

**b**) top edge diffraction echoes amplitudes versus skew angle for measure, 2.5D GTD and 3D PTD and FEM simulations.

**Figure 14.**(

**a**) Photograph of the setup; (

**b**) TOFD inspection configuration using immersion probes: study of P45 echoes scattered by the flaw surrounded in blue.

**Figure 15.**For the TOFD P45° waves inspection at 1 MHz: (

**a**) experimental Bscan; (

**b**) Bscan simulated using the 3D hybrid FEM model in simulation.

**Figure 16.**(

**a**) Configuration of ultrasonic pulse echo NDT of the embedded planar electro-eroded slots (depicted in Figure 13); (

**b**) experimental True BScan using the immersion probe at 0.5 MHz. The entry surface and backwall of the component are indicated in grey. The slot utilized for validation is shown thanks to the blue arrow, whereas the yellow ellipse indicates the component right corners and the flat bottom holes.

**Figure 17.**(

**a**) Disagreements with measurements obtained with the 3D FEM and PTD simulations; (

**b**) Predicted and measured signals with the 0.5 MHz probe; (

**c**) the same as (

**b**) with normalization on the maximal amplitude.

**Figure 18.**(

**a**) S45° TOFD immersion inspection of several embedded planar electro eroded slots; (

**b**) experimental BScan obtained when scanning the notches and the flat bottom holes at 0.5 MHz.

**Figure 19.**(

**a**) Gap between simulation and experience for the 3D hybrid FEM model and for the 3D PTD model; (

**b**) Superimposition of the normalized experimental and simulated AScans at 0.5 MHz.

**Table 1.**Analysis of Ascans simulated by 3D FEM and 3D PTD of the inspection of a 40 mm extent and 5 mm high rectangular crack using SV45 waves in Pulse Echo mode (circular planar probe of 6.35 mm diameter) at 5 MHz: time of flight of the different waves theoretically calculated using ray theory or obtained after 3D FEM simulation; PTD amplitude versus 3D FEM (dB).

Top Edge Diffraction | Head Wave | Bottom Edge Diffraction | Secondary Rayleigh Wave Diffraction | |
---|---|---|---|---|

Theoretical time of flight (µs) | 0 | 1.94 | 2.19 | 2.81 |

FEM simulated time of flight (µs) | 0 | Lost in the bottom edge echo | 2.12 | 2.70 |

PTD amplitude versus 3D FEM (dB) | −0.9 | Not calculated by the PTD model | −1.0 | Not calculated by the PTD model |

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**MDPI and ACS Style**

Darmon, M.; Toullelan, G.; Dorval, V.
An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks. *Appl. Sci.* **2022**, *12*, 5078.
https://doi.org/10.3390/app12105078

**AMA Style**

Darmon M, Toullelan G, Dorval V.
An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks. *Applied Sciences*. 2022; 12(10):5078.
https://doi.org/10.3390/app12105078

**Chicago/Turabian Style**

Darmon, Michel, Gwenael Toullelan, and Vincent Dorval.
2022. "An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks" *Applied Sciences* 12, no. 10: 5078.
https://doi.org/10.3390/app12105078