The correlation between the nonlinear acousto-ultrasonic response and the progressive accumulation of fatigue damage is investigated for an additively manufactured aluminum alloy AlSi7Mg and compared with the behavior of a conventional wrought aluminum alloy 6060-T5. A dual transducer and wedge setup is employed to excite a 30-cycle Hann-windowed tone burst at a center frequency of 500 kHz in plate-like specimens that are 7.2 mm thick. This choice of frequency-thickness is designed to excite the symmetric Lamb mode s1, which, in turn, generates a second-harmonic s2 mode in the presence of distributed material nonlinearity. This s1-s2 mode pair satisfies the conditions for internal resonance, thereby leading to a cumulative build-up of amplitude for the second-harmonic s2 mode with increasing propagation distance. Measurements of a nonlinearity parameter β derived from the second-harmonic amplitude are plotted against propagation distance at various fractions of fatigue life under constant amplitude loading, for three different stress levels corresponding to low-cycle fatigue (LCF), high-cycle fatigue (HCF), and an intermediate case. The results show both qualitative and quantitative differences between LCF and HCF, and between the additively manufactured specimens and the wrought alloy. The potential use of this nonlinearity parameter for monitoring the early stages of fatigue damage accumulation, and hence for predicting the residual fatigue life, is discussed, as well as the potential for quality control of the additive manufacturing (AM) process.

## Introduction

In the past decade, several studies have investigated the use of nonlinear guided waves to potentially detect and quantify microstructural changes prior to microcrack initiation, whereas conventional linear methods are only sensitive to macroscale damage such as fatigue cracks [15]. While most previous studies have considered higher-harmonic generation in bulk and Rayleigh waves [3,615], more recently, studies have focused on using nonlinear Lamb waves due to their highly advantageous properties of long propagation with minimal attenuation, which makes them suitable for wide-area inspection in structural health monitoring [1,1626]. However, difficulties can arise because Lamb waves are generally dispersive, and multiple modes are excited at higher frequency-thickness, thereby presenting a technical challenge to distinguish each individual mode. Additionally, solving Lamb wave applications involving complex shape geometry, composite structures, and manufacturing process require the aid of experimental and computational investigations, since solving them theoretically are known to be very difficult.

Microstructural features, such as voids, dislocations, persistent slip bands, etc., are the cause of material nonlinearity and contribute to the generation of second-order harmonics [2729]. A theoretical analysis for higher-order harmonic Lamb wave generation in isotropic materials was reported by de Lima and Hamilton [30]. Several studies on second-harmonic generation have been experimentally and computationally validated for inspecting microstructural damage, dislocations and persistent slips bands, as a function of plastic strain, fatigue life/cycle and propagating distance in metallic materials [8,1417,2023,3133]. More recent studies have investigated second-harmonic generations in composite structures [3436] and cumulative third- and higher-order harmonics [6,7,37]. Furthermore, comprehensive reviews by Matlack et al. [38] and Chillara and Lissenden [39] have summarized previous decades of work on the theoretical, experimental, and computational studies on nonlinear cumulative higher-order waves for nondestructive evaluation (NDE). Many studies have been conducted on damage inspection and quantification in commercially available aluminum alloys; however, there is a lack of research on specifically three-dimensional (3D)-printed or additively manufactured materials for NDE [40].

Additive manufacturing (AM), in particular via selective laser melting (SLM), provides an attractive alternative manufacturing method for complex customized metallic components that are too time-consuming or impossible for conventional manufacturing methods. AM is also more environmentally friendly and cost effective as it minimizes material waste and eliminates the need for multiple manufacturing processes [41]. Although AM methods will promote more innovative and complex parts in engineering applications, they also pose a significant challenge for nondestructive inspection. There is, thus, a requirement for novel inspection techniques to complement the advance in engineering technology and manufacturing.

Additive manufactured aluminum processed by SLM is known to have high levels of porosity, which limits its use in high-value engineering industries. A quantitative characterization of this porosity is a crucial quality control objective, which presents a challenge for conventional NDE [42]. Previous studies have investigated in detail the microstructure imperfections of aluminum alloy manufactured by SLM and procedures to minimize its microstructural flaws as they adversely affect the material performance [4346]. It is crucial to assess the quality of an AM process and products before they can be applied in high-value industries such as aerospace applications [40,47]. Recent studies have discussed implementable nondestructive techniques, such as eddy current, ultrasonic, and acoustic, to assess AM process and structural integrity of the additively manufactured parts to ensure the quality of production and process [4852]. Although similar engineering properties of a commercially available aluminum alloy can be achieved in additively manufactured aluminum, the microstructural change while under fatigue loading is significantly different from those formed in a commercial aluminum alloy [43]. Hence, it is of particular interest to investigate the material nonlinearity of an additively manufactured material and whether the second- or higher-harmonic generation may become of potential use for quality assurance in an AM process.

This study experimentally investigates the potential use of the second-harmonic symmetric Lamb wave (s2) to evaluate microstructural damage in additively manufactured aluminum AlSi7Mg and to monitor fatigue damage accumulation. A comparative study using a wrought aluminum alloy 6060-T5 is also undertaken. First, the stress–strain curves and dispersion curves for both alloys are presented. Next, specimens are fatigued at different loads and the material nonlinearity parameter is reported as a function of normalized propagating distance, fatigue load, and fraction of fatigue life. The relevance of the results as a potential NDE technique for additively manufactured metallic materials is then discussed.

## Background: Second-Harmonic Lamb Wave Generation

The second-harmonic Lamb wave accumulates when specific “internal resonance” conditions are satisfied [16,17,30]. The first condition is synchronicity, which requires the phase velocity of the primary wave mode to match that of the second harmonic. The second condition is a non-zero power flux between the primary wave mode and the second harmonic. These two conditions allow the transfer of energy from the primary to the second-harmonic mode, thereby resulting in a linear increase in the amplitude of the second harmonic with increasing propagation distance. Liu et al. [24] have shown experimentally that these conditions for internal resonance can only be achieved for symmetric modes, which is consistent with earlier work [16,17,20]. Some authors [1,18] have suggested that it is also necessary to match the group velocity to ensure the cumulative build-up of amplitude for the second-harmonic Lamb mode. However, this view is disputed in more recent work [39], where the matching of phase velocity is considered to be sufficient to ensure the cumulative increase in amplitude.

Theoretically, there are infinitely many pairs that satisfy these conditions for internal resonance in an elastic plate. Possible pairs for cumulative harmonic generation are reported in detail [19,20]. It is ideal to select well-separated modes so as to facilitate identification of the second harmonic and to quantify its amplitude. A practical mode pair is “s1 and s2” at normalized frequency 3.57 and 7.14 MHz-mm, respectively, for the present aluminum alloys. The synchronous phase velocity is 6166 m/s and group velocity at 4355 m/s are indicated in Figs. 1 and 2. Since the second harmonic propagates faster, it can be measured and analyzed without any contribution by other nonsynchronous second-harmonic modes. Other mode pairs were also studied [24,33] for measuring material nonlinearity. This study considers aluminum specimens with thickness 7.2 mm for the second-harmonic generation investigation by using the s1–s2 mode pair; excitation frequency of 500 kHz and monitoring frequency of 1 MHz.

### Tensile Properties.

Additively manufactured aluminum rectangular plate specimens (AlSi7Mg) of dimensions 350 mm × 40 mm with 7.2 mm thickness are considered in this study. Another set of test specimens with identical geometry was also prepared from the aluminum alloy 6060-T5 (Al6060-T5). The AlSi7Mg sample is constructed using SLM by Monash Centre for Additive Manufacturing (MCAM) (see Table 1 for material composition). After printing, the AlSi7Mg specimens were subjected to a standard stress relief at 300 °C for 2 h, with no heat treatment/hardening.

A monotonic tensile test was first conducted to determine the engineering properties of the two aluminum specimens. The tensile tests were performed using an INSTRON 1342 servo-hydraulic fluid controlled universal testing machine, which is controlled by MTS FlexTest controller. Digital output for force is recorded from the MTS FlexTest controller at a rate of five samples per second. The test specimen was uniaxially loaded at a displacement rate of 10 mm/min. An MTS Extensometer 634.12F-24 is used to determine the strain of the test specimens. The experimental stress–strain curve and engineering properties are shown in Fig. 3 and Table 2, respectively.

### Preliminary Investigations.

Preliminary experiments were undertaken to determine the dispersion curves for AlSi7Mg, as illustrated schematically in Fig. 4. A strip of POLYTEC retro-reflective film is bonded to the specimen to improve the signal to noise ratio. Due to the dispersive nature of Lamb waves, it is conventional to use a tone burst excitation. The National Instrument NI PCI-FGEN Soft Front Panel is used to excite the 5.5 cycle Hann-windowed tone burst signals with center frequencies ranging from 50 kHz to 1.2 MHz. The excitation signals are filtered and amplified by a Krohn-Hite model 3944 programmable four-channel 2 MHz filter and 7602 wideband power amplifier. The specimen is mounted onto a Parker Automation 404XE XY positioning system, and the experimental rig is mounted on a DAEIL system vibration isolation optical table to minimize vibration. The output wave signal is recorded by 3D laser vibrometer (POLYTEC CLV-3D), which is capable of recording in-plane as well as out-of-plane surface velocities. Data acquisition is processed through a National Instrument PCI-6115 board and BNC-2110, to convert the measured analog signal to digital signal.

#### Dispersion Curve.

The dispersion curves of the AlSi7Mg derived from in-plane and out-of-plane measurements are shown in Fig. 5. Different transducers and PZT were used to excite waves ranging from 50 kHz to 1.2 MHz and frequency sweeps were conducted. In Fig. 3, it is evident that the dispersion curves of the additively manufactured AlSi7Mg are identical to that of the wrought aluminum, which is consistent with their Young's modulus being the same.

#### s1 Lamb Wave Excitation.

The nonlinear second-harmonic Lamb wave generation is known to be small compared with the primary Lamb wave mode. To assist with the interpretation of the results, the input function has to be carefully characterized. The test setup adopted is similar to that reported by Pruell et al. [1,32]. The transducer OLYMPUS A414S 500 kHz is used for exciting the s1 Lamb wave mode at 500 kHz. The OLYMPUS A414S is coupled to a customized Perspex wedge to excite and detect the desired Lamb waves by adjusting the oblique angle of the wedge in accordance with Snell's Law; $θ=sin−1(cL/cp)$, where $cL$ is the longitudinal wave velocity of the wedge material and $cP$ is the desired phase velocity of the Lamb wave to be generated. The transducer and wedge combination is coupled to the specimen using a high viscosity SONOTECH Shear Gel Ultrasonic Couplant. Excitation at this frequency-thickness will result in several Lamb modes being excited. The in-plane direction (parallel to the propagating direction) is measured by a POLYTEC CLV-3D laser vibrometer to determine the excited Lamb wave modes on a dispersion curve, as shown in Fig. 6(a). Employing this transducer and wedge setup with a 30-cycle Hann-windowed tone burst at a center frequency of 500 kHz excites a dominant mode s1, followed by a1, and also the two fundamental symmetric and antisymmetric modes, as illustrated in Fig. 6(b); the relative amplitudes are given in Table 3. These results show the ability to generate an s1 mode using this method of excitation. According to the dispersion curves, the a2 mode has a lower group velocity than the s2 mode. This will help with the identification of the presence of any nonlinear response pertaining to both the s1 and the a1 input.

## Acoustic Nonlinearity Experiment

### Experimental Setup.

The wave input signal is generated by National Instrument NI PCI-5412 FGEN Soft Front Panel which is signal filtered by Krohn-Hite multichannel filter model 3944 and then amplified by Krohn-Hite wideband amplifier model 7602, refer to schematic diagram in Fig. 7. A peak-to-peak voltage tone burst of 30Vpp was applied with a delay of 5 ms between each successive tone burst. The input and output signal are recorded by Picoscope 5204 VDR64. The signals were recorded for 150 μs at a sample rate of 500 MHz. The average function in the software is used to obtain an average of 256 waveforms in the time domain.

Due to the dispersive and multimodal characteristic of Lamb wave mode, it is difficult to measure the Lamb wave amplitude at a higher frequency-thickness product. The s1–s2 mode pair propagates the fastest and is the first two Lamb wave modes to arrive in the time domain. The results are best analyzed using the spectrogram of the responses obtained. The spectrogram is an energy density of the short-time Fourier transform and allows a more convenient mode identification (based on the mode's arrival time) in a transient time-frequency domain. Since the s2 generation is orders of magnitude smaller than the s1 wave [33], the spectrogram is logarithmically scaled relative to the maximum value. This study uses 8000 points Hann-windowed with 7950 points overlaps for measurement. The spectrogram results with the dispersion curve are adjusted to the time when the first cycle of the excitation s1 Lamb wave arrives.

### Second-Harmonic Lamb Wave Detection.

The amplitude of the second-harmonic Lamb wave was measured for input tone bursts of varying number of cycles, i.e., 5, 10, 20, and 30 cycles, with Hann-windowed excitation at a center frequency 500 kHz, and the respective spectrograms are shown in Fig. 8. For this study's configuration, it is required to have at least 20 cycles to produce sufficient acoustic energy for second harmonic to be generated and detected accurately, as shown in Fig. 8. It is common for authors [1,2,1012,24,32,33,38] to excite more than 20 cycles. However, other studies [8,9,26] have used fewer cycles with a high-power gated amplifier at a significantly higher voltage for higher-order harmonic generation.

The experimental setup for the second-harmonic investigation consists of dual transducers: transmitter OLYMPUS A414S 500 kHz and receiver V539-SM 1 MHz. The second-harmonic signal can be obtained from an angled wedge receiver, as in previous studies [1,24,32]. This setup is highly advantageous as the wedge transducer is sensitive to both s1 and s2 modes, because their phase velocities are the same. It is noted that the second-harmonic could also be detected by a 3D laser vibrometer. However, the resulting signal is weaker and has a lower signal-to-noise ratio compared with the dual wedge transducer setup.

The time delay in the wedge and others electronics are taken into account to obtain the correct arrival times of Lamb wave modes. The couplant applied must be consistent otherwise small variation in coupling can have a significant influence on the recorded measurements. Couplant consistency is known to be difficult in practice. Furthermore, the variation in nonlinear measurements is known to be quite significant. Therefore, averages of multiple data sets are considered to obtain accurate readings. Measurements are recorded in the aluminum specimens at locations from 10 mm to 140 mm with 10 mm increments, refer to Fig. 7. For each location, the transducers are removed completely and reattached back to be repeated for ten times and then averaged to achieve a more accurate set of results. Data extracted from the PICOSCOPE are then post-process in matlab R2014b. matlab functions and scripts are coded to analyze the wave signals.

The nonlinearity parameter, β, is related to the measured amplitudes of the first- and second-harmonic waves, $A1$ and $A2$, as follows:
$β∝A2A12$
(1)

This relation is derived for Lamb waves in Ref. [30] based on a two-dimensional plane strain analysis; 3D modeling of the nonlinear response is discussed in Ref. [54]. In previous bulk and Rayleigh wave nonlinear studies, the normalized acoustic nonlinearity parameter (relative to acoustic nonlinearity parameter measured at undamaged state) is measured against fatigue life, plastic strain, and propagating distance [1,2,33,55]. The corresponding correlations for Lamb waves are investigated in the present work.

### Fatigue Cycle Investigation.

In order to investigate the material nonlinearity, cyclic loading is considered to form dislocations in the aluminum specimens [11,29]. The stress load applied for fatigue testing is conducted by INSTRON 1342. A sinusoidal axial force load with stress ratio R = 0.1 to ensure the specimen is under tensile loading. The stress amplitude, maximum stress, frequency, and fatigue cycle to failure are shown in Tables 4 and 5 for each set of investigations. Set of readings start from the undamaged state of the specimen (no cycle) until the fatigue failure of the specimen. The results are first presented for specimens that have experienced a stated number of load cycles. Later, results are presented in terms of the percentage of the fatigue life, i.e., a percentage of the number of cycles to failure at a given maximum stress.

The specimens are tested to failure under three different fatigue regimes, as indicated in Tables 4 and 5. The high-cycle fatigue (HCF) tests refer to specimens that are fatigued below the yield strength, whereas, for mid-cycle fatigue (MCF) and low-cycle fatigue (LCF) tests, the maximum stress in the load cycle exceeds the yield strength of the material. The positioning, removal, and reattachment of the specimens to the MTS fatigue machine was conducted with great care, but it is recognized that this procedure may have introduced unintended variations which affect the fatigue life and hence the nonlinearity results. Nevertheless, it is believed that the results are sufficiently reliable to show a potential relationship between acoustic nonlinearity parameter, normalized propagating distance and fatigue life for Al6060-T5 and AlSi7Mg specimens.

## Experimental Results

### Second-Order Harmonic Generation Verification.

Al6060-T5 and AlSi7Mg spectrograms at different fatigue life in HCF investigation are shown Figs. 9 and 10, respectively. It can be seen that as the number of applied load cycles increases, the second-harmonic Lamb wave becomes more apparent.

The first peak in the 1 MHz is the second-harmonic wave mode as shown in the spectrogram; refer to Figs. 9 and 10. A peak-to-peak tracing from different propagating distances is recorded to determine group velocity. The results indicate that the measured group velocity is 4298.7 m/s as shown in Fig. 11. Since no other wave mode has a similar velocity at 1 MHz, the first peak is indeed the s2 Lamb wave, and the amplitude of this peak will be denoted by $A2$.

The value of the acoustic nonlinearity parameter is greatly affected by the s1 Lamb wave amplitude $A1$, as indicated by Eq. (1), and hence it is important to record this amplitude correctly. Previous second-harmonic generation studies [1,2,24,32] used a higher center-frequency excitation of 2.25 MHz, and $A1$ was determined as the s1 Lamb wave peak from the spectrogram. However, in the present work, the spectrogram contains other contributions at 500 kHz in addition to s1. Due to excitation of a lower frequency, which implies a larger wavelength, and in turn a later arrival time for the peak of the incident wave, thereby results in contamination from other modes, as indicated in Fig. 6(b). To circumvent this contamination, the amplitude of the first harmonic is taken at an earlier time, corresponding to the time when the generated s2 maximum peak occurs, when there is no overlapping of other modes, as indicated in Fig. 12. This s1 wave amplitude is denoted as $A1*$, and a modified nonlinearity parameter $β*$ is defined as $β*=A2/A1*2$.

### Acoustic Nonlinearity Parameter Versus Normalized Propagating Distance.

In Fig. 13, AlSi7Mg spectrograms are shown in logarithmic scale relative to the maximum value and for all investigations, a distinguishable s2 mode at 1 MHz is generated as incident s1 Lamb waves propagate.

The measured acoustic nonlinearity parameter, β*, is shown as a function d/λ (propagating distance, d, over incident s1 Lamb wave wavelength, λ) in Figs. 1416 for Al6060-T5, and for AlSi7Mg in Figs. 1720. For both alloys, the normalized acoustic nonlinearity can be seen to increase linearly with d/λ, which is consistent with the expected cumulative behavior due to material nonlinearity [16,17]. Previous second-harmonic generation Lamb wave studies also observed similar linear trend [1,2,16,32]. It is observed in both aluminum specimens, as fatigue cycle increases the rate of change β* with respect to d/λ (gradient) also increases. However, for the last few cycles for almost all fatigue tests, there is a slight decrease in β*. The rate of increase of β* with respect to propagating distance also depends on the material, as observed in previous studies [2,9,32].

Furthermore, the maximum value of β* recorded during fatigue testing is relatively larger in the AlSi7Mg specimens. Al6060-T5 and AlSi7Mg LCF tests have indicated maximum β* of 0.401 and 0.405, respectively, whereas MCF tests have indicated maximum β* of 0.358 and 0.480, respectively. Finally, Al6060-T5 HCF and AlSi7Mg HCF#1 and HCF#2 tests have indicated maximum β* of 0.224, 0.263 and 0.410, respectively.

The nonlinearity parameter for the undamaged state is denoted by β0. The value of β0 for AlSi7Mg is found to be approximately 2–2.6 times larger than for Al6060-T5. This difference suggests that AlSi7Mg specimens at the undamaged state have microstructural features or imperfections that can plausibly be identified as pores and nonmelted spots [4346,56,57] during manufacturing, which promote a nonlinear material response resulting in the generation of s2 Lamb waves.

### Acoustic Nonlinearity Parameter Versus Fatigue Life.

For the purpose of analyzing the variation of material nonlinearity over the fatigue life, the experimental nonlinearity parameter is normalized relative to β0, $β¯$ = β*/β0. The advantage of using this normalized parameter is that the results presented below can be more easily compared with previous work. The variation of $β¯$ with the percentage of fatigue life at various load levels is shown in Figs. 21 and 22 for Al6060-T5 and AlSi7Mg specimens, respectively. The error bars in Figs. 21 and 22 indicate the minimum and maximum of the set of values recorded. A best-fit curve is included in the normalized acoustic nonlinearity parameter versus fatigue life to facilitate visualization of the overall trend.

## Discussion

It is conventional to divide the fatigue life of structural alloys into a crack initiation and a crack propagation stage, where initiation is defined pragmatically as the emergence of a readily detectable crack, typically a few millimeters long [58,59]. For high maximum stress, leading to relatively few cycles to failure, i.e., LCF, crack initiation occurs relatively easily, and the crack initiation stage constitutes a relatively low fraction of the total fatigue life. By contrast, at the other extreme of HCF, initiation is relatively difficult, and crack initiation occupies a substantial fraction of the fatigue life, typically 80% or more, with crack propagation to failure occurring over a relatively short portion of the total life [60,61]. The present work indicates a qualitatively and quantitatively different evolution of the nonlinearity parameter $β¯$ in those two regimes, for both the conventional wrought alloy Al6060-T5 (Fig. 21), and the additively manufactured AlSi7Mg (Fig. 22). In both cases, $β¯$ increases very rapidly at first for LCF, reaching a plateau at around 10–20% of the fatigue life, whereas it increases more gradually for HCF, particularly for the HCF#2 AlSi7Mg specimen. Furthermore, the maximum value attained by $β¯$ increases with increasing cyclic stress level, as shown in Fig. 23. The observed behavior for MCF lies between these two extremes of LCF and HCF, but closer to the former, particularly for the AM specimens.

This behavior is consistent with the view that the micromechanism underpinning the nonlinear material response is the presence of uniformly distributed dislocation substructures, in effect dislocation dipoles, generated by cyclic stressing [2729]. The dipole density can be expected to increase during the crack initiation stage, when damage accumulation is still uniformly distributed throughout the bulk of the material. On the other hand, once detectable cracks have appeared (corresponding to the end of the initiation stage), further plastic deformation tends to be localized around the crack tips, so that the nonlinear response of the bulk of the material remains largely unchanged, giving rise to a plateau in the value of $β¯$. Thus, an in situ measurement of $β¯$ provides a promising approach for tracking the evolution of damage accumulation, and hence the residual fatigue life, particularly in the HCF regime. This approach seems particularly promising for additive manufacturing, due to the more gradual increase of $β¯$ throughout the fatigue life under HCF, as indicated in Fig. 22, although the quantitative increase in $β¯$ is relatively low compared with the wrought product.

The present results in Figs. 2123 are consistent with, and significantly extend, previous work. For the LCF regime, other researchers have also reported an initial rapid increase in $β¯$, followed by a plateau [9,10,32], although in that previous work the plateau appears at around 50% of the fatigue life, i.e., significantly later than observed here for LCF and MCF. Analytical modeling by Cantrell [29] suggests an increase in $β¯$ by a factor of 3.6 over the course of the fatigue life in LCF, which is close to the value of 3.5 shown in Fig. 22 for the AM specimens, but much lower than the factor of 6.8 shown in Fig. 21 for the wrought alloy. Other researchers have reported increases by a factor of only 1.6 for a nickel-based super alloy and Al1100-H14 [32]. Thus, the quantitative increase in $β¯$ can vary significantly for different structural alloys.

In the HCF regime, Cantrell and Yost [11] reported an increase in $β¯$ by a factor of 3.9 for Al2024-T3 at 100,000 cycles, which is comparable with the factor 3.8 shown in Fig. 21 for Al6060-T5, and 2.5 for the HCF#2 AlSi7Mg specimen in Fig. 22. These authors also attempted to account for the effect of nonuniformity in the dislocation substructure, concluding with an experimental increase by a factor of 3, which was in very close agreement with their theoretical model prediction of 3.1. This close agreement provides a measure of confidence in the potential use of $β¯$ for monitoring the residual fatigue life.

It can be seen from Figs. 14 to 20 that the second-harmonic amplitude exhibits a consistent linear increase with propagation distance, in accordance with the expectation for internal resonance, although individual measurements can display significant variations from that linear trend. Thus, the values of $β¯$ obtained from the linear trend can be considered to be much more reliable than the individual measurements. Figures 1420 also show that $β¯$ is generally higher for additive manufacturing. In particular, the initial value β0 prior to cyclic loading is 2–2.6 times higher than for the wrought alloy, suggesting that this initial value could be useful for assessing the as-fabricated quality, and hence for quality control of AM components.

Finally, it is worth noting that the use of $β¯$ to characterize the nonlinear response is only appropriate if the micromechanisms responsible for the nonlinearity can be considered to be uniformly distributed on a length scale comparable with the second-harmonic wavelength, and furthermore that any damage accumulated, e.g., microcracks, is small compared with that wavelength [5,911,13]. As stated earlier, in HCF, readily detectable cracks occur relatively late in the fatigue life. This can lead to an apparent decrease in the value of $β¯$, as reported in [9,10,13], but the underlying assumption of homogeneity may no longer apply in the presence of isolated macrocracks, so that the use of $β¯$ to characterize the material response may no longer be appropriate.

## Conclusion

An acousto-ultrasonic measurement technique based on second-harmonic Lamb wave generation has been developed and demonstrated for assessing fatigue damage in additively manufactured aluminum AlSi7Mg, and a conventional wrought alloy Al6060-T5. The results indicate that the measured acoustic nonlinearity parameter increases monotonically with increasing number of fatigue cycles and reaches a plateau at various fractions of the fatigue life depending on the cyclic stress regime, for the case of constant amplitude loading with R = 0.1. This behavior provides a plausible approach for monitoring the evolution of fatigue damage prior to the emergence of readily detectable cracks, and hence for estimating the residual fatigue life at an early stage that is not accessible to conventional linear NDE techniques. This is also a promising approach for assessing the as-fabricated quality of additively manufactured components, which could facilitate structural integrity management, and hence promote the implementation of this new manufacturing route for high-value applications such as aerospace.

## Acknowledgment

The authors acknowledge Monash Centre for Additive Manufacturing (MCAM) for the customized printed aluminum specimens.

## Funding Data

• This research was funded by the Australia Government through the Australia Research Council DP150101894.

## Nomenclature

• a1 =

first-order harmonic antisymmetric Lamb wave

•
• a2 =

second-order harmonic antisymmetric Lamb wave

•
• $A1$ =

first-harmonic wave amplitude

•
• $A1*$ =

measured first-harmonic wave amplitude where second-harmonic wave peaks

•
• $A2$ =

second-harmonic wave amplitude

•
• AlSi7Mg =

•
• Al6060-T5 =

aluminum alloy 6060 T5

•
• $cL$ =

longitudinal wave velocity

•
• $cP$ =

phase velocity

•
• d =

propagating distance

•
• R =

stress ratio

•
• s1 =

first-order harmonic symmetric Lamb wave

•
• s2 =

second-order harmonic symmetric Lamb wave

•
• β =

acoustic nonlinearity parameter

•
• β* =

experimental measured acoustic nonlinearity parameter

•
• β0 =

experimental measured acoustic nonlinearity at the undamaged state

•
• $β¯$ =

normalized acoustic nonlinearity parameter

•
• $θ$ =

oblique angle

•
• λ =

incident first-harmonic Lamb wave wavelength

•
• σa =

stress amplitude

•
• σmax =

maximum stress

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