# Laser Generated Broadband Rayleigh Waveform Evolution for Metal Additive Manufacturing Process Monitoring

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## Abstract

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## Featured Application

**Process monitoring of additive manufacturing of metals for material nonlinearity using finite amplitude ultrasonic Rayleigh waves.**

## Abstract

## 1. Introduction

#### 1.1. Laser Generated Finite Amlitude Rayleigh Waves

_{3}. In this article, without loss of generality, we take the Rayleigh waves to propagate in the x

_{1}direction and the outward normal to the surface to be in the negative x

_{3}direction. If the surface slope measurement is properly calibrated then v

_{3}has engineering units (e.g., m/s). A smooth surface is required for this detection method because the small diameter beam is reflected at an oblique angle from the surface to a photodetector. The in-plane particle velocity v

_{1}can be computed using the Hilbert transform and may have clearly defined shock fronts, which depend upon the algebraic sign of the nonlinearity parameters [11]. Experimental studies on fused quartz [9,11,18], fused silica [10,14], aluminum [14], stainless steel [12,15,16], and single-crystal silicon [9,13,17,18,19,20] are reported. Single-crystal silicon is anisotropic, therefore the waves are not Rayleigh waves, but rather are described simply as surface acoustic waves (SAWs).

_{1}Rayleigh waveform in a similar fashion to shock formation in fluids, depending upon the ‘sign of the nonlinearity’ as described below. Herein, we refer to the material parameter ${\epsilon}_{1}$ used in the Gusev et al model [21,22] for the sign of the nonlinearity, as it has been shown to dominate the waveform evolution [14]. Materials with positive ${\epsilon}_{1}$ nonlinearity parameter tend to have a v

_{1}waveform described by a large negative peak followed by a smaller positive peak as shown in Figure 1. The negative peak travels faster than the positive peak resulting in waveform compression, or steepening, leading to a higher peak frequency known as a frequency up-conversion. If the steepening is sufficiently high, it can cause shock formation. Materials with negative ${\epsilon}_{1}$ nonlinearity parameter tend to have a v

_{1}waveform described as an inverted N-shape as sketched in Figure 1, where the leading negative peak travels faster than the trailing positive peak. When this occurs, the peaks separate, resulting in a lower peak frequency known as a frequency down-conversion. In this case, shock fronts can form at the leading and trailing edges. We will see that nonlinearity in the v

_{3}Rayleigh waveform is evident by sharpening of the negative peak for material with positive nonlinearity and widening of the valley between the positive peaks for material with negative nonlinearity.

_{1}Rayleigh waveform from a sinusoid to sawtooth-like is described theoretically by two different models. The first model represents the wavefield as a Fourier series and uses Hamilton’s principle to determine the amplitudes of the harmonics [23,24,25,26,27,28]. The second model makes no a-priori assumption about the displacement profiles of the harmonics and uses the slowly varying wave profile method (described by Rudenko and Soluyan [29]) to handle the secular terms associated with shock front formation [21,22]. Both models have been shown to predict shock wave formation in good agreement with experimental results; i.e.,

- (1)
- for materials having a ‘positive nonlinearity’ the shock front in the v
_{1}waveform corresponds with a negative spike-like pulse in the v_{3}waveform that narrows with increasing amplitude with propagation, - (2)
- for materials having a ‘negative nonlinearity’ shock fronts in the v
_{1}waveform form at the leading and trailing edges, which correspond to two positive peaks in the v_{3}waveform that are separating as the valley between them expands with propagation.

_{3}waveform and towards shock formation in the v

_{1}waveform as in case (1) above. We consider the application of Rayleigh waveform evolution for process monitoring during additive manufacturing, therefore the use of an absorbent fluid on the surface is impractical, making shock formation unlikely.

_{3}particle velocity component, which is impractical in the additive manufacturing environment. Instead, an adaptive laser interferometer is used to measure the u

_{3}particle displacement component. Time differentiation of the time series u

_{3}data enables computation of v

_{3}, and the Hilbert transform can be used to compute the in-plane components u

_{1}and v

_{1}. To show what these four components look like for a metal (i.e., a polycrystalline aluminum alloy) having positive nonlinearity, we have digitized the v

_{3}waveform from Kolomenskii and Schuessler [14] and then computed the associated waveforms. The Kolomenskii and Schuessler [14] results are plotted in Figure 2 at the propagation distances of 13.9 and 26.7 mm.

^{3}, λ = 121 GPa, µ = 80 GPa, A = −484 GPa, B = −382 GPa, C = −174 GPa) determined by Gartsev and Köhler [30] is shown in Figure 3. The waveform evolution is from a sinusoid to a cusped sawtooth as the propagation distance increases. A shock front occurs in the v

_{1}waveform due to steepening, while the v

_{3}initial cosine-shape evolves into a negative spike with increasing amplitude. The displacement component waveform evolutions are much different, with u

_{1}steepening and its peak sharpening and u

_{3}exhibiting some sharpening, but retaining its overall character. The next section introduces process monitoring for additive manufacturing.

#### 1.2. Additive Manufacturing Process Monitoring

- the act of monitoring should not impede the manufacturing process;
- detection of both flaws and micro/mesostructure variations that affect mechanical properties are important;
- the surface of the deposited material is rough.

## 2. Materials and Methods

_{3}at a point on the surface. Its adaptability to variable surface roughness and reflectivity makes it a critical component in the system. The reception laser head is mounted on an XY stage to enable scanning along the centerline of the nominally planar wavefield. In addition to the benefits of the two-wave mixing approach, the interferometer has two output signals – AC (alternating current) and DC (direct current). The AC signal contains the time-varying voltage proportional to the surface displacements, while the DC level provides a measure of the light reflected from the surface. Thus, normalizing the AC signal by the DC level provides a means to compare the signals obtained from surfaces with varying roughness and reflectivity. Additionally, the wave propagation distance is kept low to minimize the attenuation and diffraction effects and improve the signal-to-noise ratio (SNR). When scanning across the hatches, the scan increment is a multiple of the hatch spacing, such that the reception laser beam is focused on the top of each track, thereby maximizing the light collected by the reception laser head.

_{3}waveform was received and processed, from which the u

_{1}waveform was computed using the Hilbert transform [14]

_{3}and v

_{1}waveforms as was described relative to Figure 2. Scanning experiments were conducted for the baseplate and the as-built deposition in our laser ultrasound testbed (i.e., not in the DED-AM chamber). Prior work documented that wrought baseplate Ti-6Al-4V has different nonlinearity than DED-AM as-built Ti-6Al-4V [60]. In addition, prior experiments [59] indicate that the surface roughness affects the nonlinearity, at least partially due its effect on attenuation. In addition, an experiment was conducted at low pulse energy to clarify linear from nonlinear behavior.

_{a}, S

_{q}, and S

_{z}, which are the arithmetic mean height, root mean square height, and maximum height respectively. The results provided in Table 3 show that the variations in process parameters had a more significant effect on roughness for IN-718 than for Ti-6Al-4V. The effect of process parameters on surface roughness (and microstructure) is analyzed in more detail by Dong et al. [63]. Clearly, the AM depositions are much rougher than their respective baseplates, but the effect that the variation in process parameters has on roughness is minor in comparison.

## 3. Results

#### 3.1. Detected Waveform Evolution

_{3}, with the laser interferometer detected AC signal normalized with respect to the mean DC level. Note that the variability in the DC level was approximately five times larger for tests on AM depositions than on the baseplate. The line-focused Nd:YAG laser beam generates a low-frequency airborne wave that is detected by the interferometer after the Rayleigh wave arrival. This wave is observed in the A-scan from 4 mm but is not of interest here.

_{3}waveforms in Figure 3. The Rayleigh waveform generated by low pulse energy is the most repeatable in Figure 6, both for the three trials and as a function of propagation distance. Thus, the V-shaped waveform represents a linear Rayleigh wave, as the nonlinearity is too small to notice. In contrast, the waveforms generated by high pulse energy, having much higher peak-to-peak amplitudes (note the amplitude scales are different for low and high pulse energy), have a different waveform shape and evolve with propagation distance. These two features could be invaluable for characterizing the material nonlinearity. For low pulse energy, the segments of the V-shaped pulse appear to have nominally the same steepness. However, for high pulse energy, the first segment is significantly steeper (and smoother) than the second segment. Thus, it may be possible to define a steepness ratio to characterize nonlinearity independent from propagation distance. These observations apply to high pulse energy for both the baseplate and the AM deposition.

_{3}waveforms in Figure 6 were differentiated with respect to time to derive the v

_{3}waveforms plotted in Figure 9. Since the u

_{3}waveforms were not calibrated to actual displacements in nm the v

_{3}waveforms have only arbitrary units (A.U.). The Hilbert transform is then used to compute the v

_{1}waveforms, which are also plotted in Figure 9. In general terms, the velocity waveforms agree with Figure 1, Figure 2 and Figure 3. The v

_{3}waveforms can be described as a negative spike-like pulse, while the v

_{1}waveforms have a negative peak followed by a positive peak. However, in many cases in Figure 9 the following positive peak is larger than the initial negative peak in the v

_{1}waveform.

#### 3.2. Effect of Off-Normal Processing Parameters

#### 3.2.1. Ti-6Al-4V

#### 3.2.2. IN-718

## 4. Discussion

_{3}waveforms in Figure 6 indicates that the peak-to-peak amplitude has substantial variability between trials, implying that it is not a good feature to quantify the nonlinearity. However, despite the amplitude variability normalized amplitudes as in Figure 7b are useful. In addition, the waveform shapes are self-similar and the change in steepness between the two legs of the V-shape could be a good way to quantify the nonlinearity. We note that this feature could be employed for waveforms acquired as a function of propagation distance as in Figure 6, or as a function of source amplitude at the same propagation distance. Quantifying the nonlinearity could be achieved by fitting nonlinearity parameters (e.g., third order elastic constants) to the waveform evolution through the evolution equations for finite amplitude Rayleigh waves.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Nonlinear Rayleigh particle velocity waveform sketches based on [14].

**Figure 2.**Particle velocity and displacement waveforms from aluminum substrate at (

**a**) 13.9 mm and (

**b**) 26.7 mm. v

_{3}was detected by Kolomenskii and Schuessler [14] and digitized by us, then v

_{1}was computed using the Hilbert transform, and finally u

_{3}and u

_{1}were computed by numerical integration. All waveforms are at the surface x

_{3}= 0.

**Figure 3.**Particle velocity and displacement waveform evolution predicted by Shull et al. model [24] for IN-718: v

_{1}, v

_{3}, u

_{1}, u

_{3}. The nondimensional abscissa is the product of the initial monochromatic frequency and the retarded time. The nondimensional ordinate is the waveform normalized with respect to the initial amplitude of the v

_{1}sinusoid. X is propagation distance normalized with respect to shock formation distance.

**Figure 6.**Sample u

_{3}displacement waveforms for Ti-6Al-4V received by laser interferometer after propagation distances of 4–24 mm for baseplate and AM deposition.

**Figure 7.**(

**a**) Schematic representatives of V-shaped waveforms in Figure 6 for low pulse energy and high pulse energy, (

**b**) Normalized peak-to-peak amplitude evolution with propagation distance for Ti-6Al-4V AM, with mean and standard deviation.

**Figure 8.**Steepness of Ti-6Al-4V AM waveforms in Figure 6 as a function of propagation distance, with mean and standard deviation.

**Figure 9.**Sample v

_{1}and v

_{3}velocity waveforms derived from the displacement waveforms in Figure 6.

**Figure 10.**Three different Ti-6Al-4V AM depositions for process parameter set A in Table 1 received at (

**a**) point 1 and (

**b**) point 2.

**Figure 11.**Ti-6Al-4V AM depositions for process parameter sets A, B, C in Table 1 received at (

**a**) point 1 and (

**b**) point 2.

**Figure 12.**Frequency spectra for signals received at point 1 (Figure 11a) for process parameter sets A, B, C.

**Figure 13.**IN-718 process parameter sets D, E, F where processing laser speed changes. Signals received at (

**a**) 23 mm, (

**b**) 39 mm.

**Figure 14.**IN-718, 28 mm propagation distance, process parameter sets D, G, H where hatch spacing changes given laser pulse energies of (

**a**) 30 mJ, (

**b**) 120 mJ.

Set | Material | Laser Power (W) | Scan Speed (mm/s) | Hatch Spacing (mm) |
---|---|---|---|---|

A ^{1} | Ti-6Al-4V | 450 | 10.6 | 0.8 |

B | Ti-6Al-4V | 380 | 10.6 | 0.8 |

C | Ti-6Al-4V | 450 | 10.6 | 0.9 |

D ^{1} | IN-718 | 400 | 10.6 | 0.6 |

E | IN-718 | 400 | 9.3 | 0.6 |

F | IN-718 | 400 | 11.8 | 0.6 |

G | IN-718 | 400 | 10.6 | 0.75 |

H | IN-718 | 400 | 10.6 | 0.85 |

^{1}Nominal processing parameters.

1 | 2 | 3 | 4 |
---|---|---|---|

Ti-6Al-4V | Ti-6Al-4V | IN-718 | IN-718 |

baseplate | baseplate | baseplate | baseplate |

4 layers Set A | 4 layers Set A | 4 layers Set D | 4 layers Set D |

LU test | LU test | LU test | LU test |

4 layers Set B | 4 layers Set C | 4 layers Set E | 4 layers Set G |

LU test | LU test | LU test | LU test |

4 layers Set F | 4 layers Set H | ||

LU test | LU test |

Material | S_{a} (µm) | S_{q} (µm) | S_{z} (μm) |
---|---|---|---|

Ti-6Al-4V baseplate | 1.14 | 1.42 | 10.25 |

Ti-6Al-4V Set A | 33.04 | 41.39 | 371.4 |

Ti-6Al-4V Set B | 33.09 | 42.26 | 385.7 |

Ti-6Al-4V Set C | 30.63 | 38.84 | 397.0 |

IN-718 baseplate | 3.72 | 4.64 | 33.94 |

IN-718 Set D | 19.59 | 25.23 | 264.7 |

IN-718 Set E | 18.27 | 22.65 | 318.5 |

IN-718 Set F | 17.52 | 21.76 | 352.1 |

IN-718 Set G | 13.89 | 18.16 | 237.8 |

IN-718 Set H | 25.60 | 31.82 | 293.3 |

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## Share and Cite

**MDPI and ACS Style**

Bakre, C.; Afzalimir, S.H.; Jamieson, C.; Nassar, A.; Reutzel, E.W.; Lissenden, C.J. Laser Generated Broadband Rayleigh Waveform Evolution for Metal Additive Manufacturing Process Monitoring. *Appl. Sci.* **2022**, *12*, 12208.
https://doi.org/10.3390/app122312208

**AMA Style**

Bakre C, Afzalimir SH, Jamieson C, Nassar A, Reutzel EW, Lissenden CJ. Laser Generated Broadband Rayleigh Waveform Evolution for Metal Additive Manufacturing Process Monitoring. *Applied Sciences*. 2022; 12(23):12208.
https://doi.org/10.3390/app122312208

**Chicago/Turabian Style**

Bakre, Chaitanya, Seyed Hamidreza Afzalimir, Cory Jamieson, Abdalla Nassar, Edward W. Reutzel, and Cliff J. Lissenden. 2022. "Laser Generated Broadband Rayleigh Waveform Evolution for Metal Additive Manufacturing Process Monitoring" *Applied Sciences* 12, no. 23: 12208.
https://doi.org/10.3390/app122312208