Nonlinear ultrasonic technique for the characterization of microstructure in additive materials^a)

Additive manufacturing (AM) allows for the rapid creation of complex parts that would be difficult to achieve through traditional subtractive manufacturing methods. Internal geometries can be tailored to have material properties individualized per use case (Yang et al., 2017). A variety of materials can be used in AM, including stainless steels that are commonly employed in mission critical components for the energy, defense, and aerospace industries. Concerns about the qualification procedure of AM parts has delayed the adoption of AM in these consequential industries (Waller et al., 2015). Qualification challenges include novel material modeling problems (Gouge and Michaleris, 2018; Seifi et al., 2016) and variances in the manufacturing process (Beese, 2018).

Manufacturing variables (e.g., laser scanning velocity, powder deposition rate, timing between layers, laser power) can change the thermal history of a part (Beese, 2018). Large thermal gradients are generated between the pool of molten metal and the remaining structure (Gouge and Michaleris, 2018). Heterogeneous thermal expansion resulting from these thermal gradients can create high local stresses leading to the formation of plastic strains and distortions (Gouge and Michaleris, 2018). Distortions of the crystal lattice are resolved by the creation of dislocations (Gorsse et al., 2017; Wright et al., 2011). The mechanical performance of a part is strongly dependent on its microstructure including grain structures, dislocations, porosity, and residual stresses (Matlack et al., 2014).

Mechanical testing can give information on material parameters, but sometimes at the cost of physically altering the part. Inconsistencies in printing variables can cause microstructural changes that change the mechanical properties between print iterations (Beese, 2018). Nondestructive evaluation (NDE) could be used as a comparative tool to analyze the microstructures from different print iterations, helping to validate an AM part before its use in critical scenarios. In addition, any new microstructural data obtained from NDE can be integrated into a qualification procedure for AM. Previous efforts to integrate NDE into the qualification and validation of AM have been made (Waller et al., 2015). These efforts span a wide variety of NDE techniques including linear ultrasound and eddy current testing.

This work proposes the use of nonlinear ultrasound as a quantitative measure to track changes in the microstructure of AM metals. Second harmonic generation (SHG) is the measurement technique used in this work and has been previously demonstrated to detect microstructural changes including dislocation formation during fatigue (Kim et al., 2006), precipitate formation (Cantrell and Zhang, 1998), thermal aging (Ruiz et al., 2012), and radiation damage (Matlack et al., 2012). The acoustic nonlinearity parameter, β, is used to quantify the dislocation-induced material nonlinearity (Akira Hikata et al., 1965). SHG techniques have previously shown to be sensitive to changes in dislocation density, but their use in the qualification of AM materials has not been fully explored. This study explores the sensitivity of the acoustic nonlinearity parameter, β to the microstructural features in AM parts. It relates changes in the measured β to decreases in the dislocation density that are approximated by geometrically necessary dislocations (GNDs) that are independently measured with electron backscatter diffraction (EBSD). GNDs are dislocations required to accommodate curves in the crystal lattice caused by plastic deformation (Gao and Huang, 2003). As discussed by many others, e.g., see Arsenlis and Parks (1999) and Brewer et al. (2009), these dislocations can be estimated from the curvature seen in EBSD data. GNDs have been shown to account for the majority of the total dislocation population in face-centered cubic metals (Smith et al., 2018). Therefore, tracking the changes in GND density can give indication to the relative changes in dislocation populations for comparison with β.

A post-AM heat treatment plan is used to force a change in the material microstructure, i.e., the reduction of the dislocation density. A final heat treatment at a higher temperature and longer holding time is used to cause significant recrystallization. The β parameter is measured through successive steps of this annealing heat treatment, while complementary linear ultrasound (attenuation), hardness, and EBSD measurements are used to provide independent evidence of microstructural changes. Specimens for hardness and EBSD are cut from the “parent” samples with each successive stage of heat treatment.

Four specimens varying in material composition and manufacturing technique are used in this study: two are made of 316 L grade stainless steel, and two of 304 L grade stainless steel. For each stainless steel variant, one specimen is made with an AM technique and the other is a traditional wrought manufactured specimen for comparison purposes; see Tables I and II for details. All four specimens are L variants which indicates a carbon content no more than 0.04 wt. %. While AM can allow for complex part geometry, these test specimens are rectangular bars with the smallest dimension being 5 cm width by 13 cm length to avoid the effects of reflections. The thinnest specimen is the 316 L laser powder bed fusion specimen with a thickness of 1 cm, noting the largest Rayleigh wavelength is below 0.396 cm, so the specimen can be treated as a half-space, without interference from the bottom surface (Zeitvogel et al., 2014).

Two different additive manufacturing techniques are investigated in this study. A 3D Systems ProX DMP 200® printing system was used to make the 316 L AM specimen through laser powder bed fusion (L-PBF). In L-PBF, a thin layer of metal powder is spread across the print surface and then transformed into the desired solid material shape with a laser energy source through rapid melting and solidification. The next layer is then deposited, and the process is repeated layer by layer until the part is manufactured. The specimens in this study are produced using a 3D Systems “hexagon” scan pattern with further details found in Garlea et al. (Garlea et al., 2019). Each layer is scanned in a direction 90° from the previous layer with the scan directions alternating back and forth for each layer. The printing parameters are found in Table III.

The 304 L AM specimen is manufactured by laser Directed Energy Deposition (DED) in a Laser Engineered Net Shaping (LENS) 750 (Optomec Inc., USA) workstation. Multiple nozzles are used to blow metal powder into the path of a co-axial vertical laser. The thermal source and nozzles are co-located which allows for complex shapes to be built in a short time (Yang et al., 2017).

An annealing heat treatment is used to cause microstructural changes and reduce dislocation density in the specimens. A comparative study of 304 L LENS and 304 L Wrought by Smith et al. (2018) observed a significant decrease in dislocation density. These microstructural changes were first observed from hardness measurements, that were later confirmed with EBSD imaging.

Based on the annealing success of Smith et al. (2018) and Susan et al. (2018), a similar heat treatment plan is developed and listed in Table IV, with an x-mark indicating where accompanying β measurements are made. The 316 L L-PBF and 316 L Wrought specimens have finer temperature increments to allow for a more detailed comparison between the two manufacturing methods.

The heat treatments are performed in near-vacuum stainless steel bags or in a vacuum furnace with an argon atmosphere to prevent oxidization on the specimen surface. Following the heat treatment, each specimen is gradually cooled to room temperature and then hand sanded to prepare the surface for the Rayleigh wave measurement.

After each stage of heat treatment and accompanying nonlinear ultrasound measurement, specimens were cut from the AM material and mounted in cold-setting epoxy and prepared metallographically using standard techniques to enable microstructure observation and EBSD. The specimens were sectioned normal to the AM build direction. Vickers microhardness measurements were performed on the polished as-built and annealed specimens. The Vickers measurements were performed with a 300 g load and 15 s dwell time using a Struers Durascan-80 microhardness mapper. The average and standard deviation of 15 to 40 hardness measurements are reported from each specimen.

Second harmonic generation (SHG) is the phenomenon where higher harmonics are generated when an initially monochromatic wave interacts with a nonlinear material. There are a number of sources of nonlinearity in these materials, including dislocations. This SHG effect is quantified with the acoustic nonlinearity parameter, β, and for a Rayleigh wave is given by (Jan Herrmann et al., 2006)

where $u¯z(ωo)$ and $u¯z(2ωo)$ are the respective vertical displacement components of the fundamental and second harmonic Rayleigh waves on the material surface; $x$ is the propagation distance; $p2=kR2−kL2$ and $s2=kR2−kS2$⁠; and $kR$⁠, $kL$⁠, and $kS$ are the wavenumbers for Rayleigh, longitudinal, and shear waves, respectively. The following proportionality can be deduced from Eq. (1):

The relative form of the acoustic nonlinearity parameter of Eq. (2) is used in this study. The effect of diffraction is constant for all measurements since the same measurement configuration is used. The effect of attenuation at the SHG measurement frequencies is negligible as shown later.

Following Bellotti et al. (2019), a schematic of the Rayleigh wave experimental setup is shown in Fig. 1. A function generator outputs a sinusoidal tone burst signal at 2.1 MHz with a peak-to-peak voltage of 800 mV. This signal consists of 20 cycles with a spacing of 20 ms and is amplified through a high-power gated amplifier (RITEC GA-2500A). From this signal, a Parametrics V106 (2.25 MHz nominally centered) contact transducer generates a longitudinal wave into an acrylic wedge that is coupled to the surface of the test specimen. All contact surfaces are coupled with an oil based couplant. The acrylic wedge is cut to a specific geometry to maximize the mode conversion from the P-wave transducer into a Rayleigh surface wave in the stainless steel specimens.

The Rayleigh surface wave travels along the surface of the specimen and interacts with the material microstructure, creating a second harmonic wave. Leaked Rayleigh waves are then detected with an Ultran NCT4-D13 (4 MHZ nominally centered) air-coupled transducer connected to a 6° of freedom stage. This movement allows for a calibration to find a measurement path that maximizes the fundamental frequency signal, therefore increasing the signal to noise ratio. The material nonlinearity will cause an increase in second harmonic amplitude with increasing propagation distance, while any initial system nonlinearity remains constant (Torello et al., 2015).

The output from the air-coupled transducer can be seen in Fig. 2(a); this recorded signal is taken from an average of 512 samples. A Hann window is applied to reduce the transient effects of voltage overshoot and ringing that can be seen in the air-coupled transducer output (Thiele et al., 2014). The time domain signal is analyzed in the frequency domain after a fast Fourier transform (FFT) as seen in Fig. 2(b). The two distinct peaks are centered at the fundamental frequency of 2.1 MHz and the second harmonic of 4.2 MHz. As expected, the amplitude of the fundamental frequency is much higher than that of the second harmonic.

Figure 3(a) shows that the amplitude of the fundamental frequency decreases with increasing propagation distance due to cylindrical geometric spreading and attenuation effects. Conversely, the second harmonic increases with propagation distance, as the wave continues to interact with the material microstructure. In Fig. 3(a), A₂ is electrical signal corresponding to the physical displacement of the second harmonic, $u¯z(2ωo)$⁠, and A₁ corresponds to the fundamental $u¯z(ωo)$⁠. The electronic devices involved in the measurement are a linear system as a whole, so the relationship between the electrical signal and physical response is linearly proportional. The ratio of A₁ and A₂ are used in Eq. (2) to calculate the relative acoustic nonlinearity parameter, β. A graphical representation of the ratio of these two peaks as a function of propagation distance is seen in Fig. 3(b). A linear polynomial is fit to this data and the slope is taken as the relative acoustic nonlinearity parameter, β.

Following the heat treatment plan described in Table IV, β is measured for each specimen at each heat treatment stage, and the results are shown in Fig. 4. Each box plot represents the results of five independent measurements of β at each stage in the heat treatment cycle. Maximum and minimum measurements are shown by the vertical dotted lines; the median for each data set is marked by the middle horizontal line in each box. The vertical axis is normalized to the lowest measured value of β. This normalization is performed as only the relative changes in β are considered with this research procedure. The results of β after the 1200 °C heat treatment may be associated with entirely different microstructural changes caused by recrystallization and are analyzed separately. Figure 4 shows that excluding the recrystallization results, β decreases with each consecutive heat treatment in each specimen, regardless of manufacturing technique. This trend is expected, as the annealing profile was selected to reduce dislocation density and other sources of material nonlinearity with increasing temperature and holding time.

The finer increments in the heat treatment profile for both the 316 L L-PBF and 316 L Wrought specimens allows for a comparison to be made between AM and traditional manufacturing techniques. Prior to complete recrystallization, the measured β linearly decreases in the 316 L L-PBF specimen. Conversely, β in the 316 L Wrought specimen begins to plateau after the heat treatment at 650 °C for 0.5 h. As β is a surrogate for microstructural characteristics in a specimen, the different trends indicate a difference in microstructural evolution between the manufacturing techniques. These differences were previously observed by Smith et al. (Smith et al., 2018) in their comparison of 304 L AM and wrought, as they saw a difference in hardness measurement trends between wrought and AM specimens through the heat treatment profile. The results of (Smith et al., 2018) shows that the 304 L Forged specimen drops in hardness faster than the 304 L LENS, and then begins to plateau while the LENS specimen continues to decrease. In (Smith et al., 2018), the divergence in AM and wrought behavior is attributed to compositional microsegregation, found in AM material, that inhibits dislocation mobility and requires an increase in energy to begin recrystallization. The plateau seen in their hardness measurements is similar to the plateau seen in the β measurements when comparing the 316 L Wrought and 316 L L-PBF specimens.

Complementary hardness measurements for the 316 L L-PBF specimen are made in this study. These measurements are made after 15–30 Vickers microindentation hardness tests. Comparison of hardness and β over the different heat treatment stages shows a potential that both metrics are sensitive to similar microstructural features. The two metrics are plotted concurrently in Fig. 5(a), with a correlation coefficient of 0.997.

EBSD is also used to assess the microstructural changes occurring in the 316 L L-PBF specimen. A Zeiss Supra 55VP field emission scanning electron microscope (SEM) is used to perform EBSD using Oxford HKL Aztec^TM software. For all samples, EBSD data are collected using a stepsize of 0.1 μm. EBSD data are subsequently analyzed using MTEX (Bachmann et al., 2010), an extension for matlab^TM. Microstructural evolution can be seen qualitatively in the inverse pole figure orientation mapping (IPF-z) results from EBSD in Fig. 6. In these figures, the samples are oriented in a transverse direction with the build direction coming out of the page. This orientation results in showing a crosshatch scan pattern. The color key of Fig. 6 shows each color's corresponding orientation defined by the three Miller indices on each point of the inverse pole figure color key. Since the EBSD results are performed on different sample cuts, the orientation change of each grain cannot be tracked through the heat treatment. Instead, observable differences in grain size confirm the suspicion that the microstructure of these stainless steel specimens have undergone a radical change during the final heat treatment that corresponds to a large amount of recrystallization and grain growth. This final heat treatment step was intended to cause a complete recrystallization of all material specimens, followed by an investigation into how this changes the measured value of β.

EBSD data can be used to estimate the lattice curvature created by GNDs (Arsenlis and Parks, 1999; Brewer et al., 2009). Because this measurement is sensitive to the stepsize used for data collection, direct comparison of GND density between different materials requires that all data be collected using the same stepsize, as was done in this study. Moreover, it is important to note that EBSD only provides an estimate for the lower bound of the GND density in a sample. The method presented by Pantleon (2008) as implemented in MTEX (Bachmann et al., 2010) is used in this study to measure the lower bound of the GND density in as-built and annealed stainless steel specimens. It is important to note that, while this approach is slightly different from that used by Smith et al. (2018), both approaches provide similar results (Fressengeas et al., 2018). A visual map the GND density at every pixel of the EBSD data can be seen in Fig. 7. The color bar shows the logarithmic scale used to define the GND density for each pixel of the EBSD data with grain boundaries colored in gray. Note that the straight lines of GND density in the sample annealed at 1200 °C are scratches from metallographic preparation. This map suggests that the primary source of measured GND density in this sample was from specimen preparation and measurement noise. The general shift to black shows GNDs generally decrease through the progression of heat treatments.

By comparing the probability distribution functions of the GND density between material states, GND density can be quantitatively compared. The average GND densities are plotted in Fig. 5(b) for each material state in comparison with the measured β before recrystallization. The correlation coefficient between these two variables before the final recrystallization is 0.85. While β is sensitive to dislocations as predicted by the Hikata model (Akira Hikata et al., 1965) and others, it is also sensitive to other microstructural features (Matlack et al., 2014). GNDs do not account for all dislocations within the microstructure, further accounting for any deviations between β and the comparative measure.

The largest deviation in the relationship between β and GND density for the 316 L L-PBF specimen comes after the final heat treatment at 1200 °C for 2.5 h. This final heat treatment was intended to fully recrystallize the material and explore if any residual microstructural features are detectible with the nonlinear ultrasonic techniques. Diverging from the previous trend, β increases by 11% after the final heat treatment despite a continued decrease in GND density by 21%. The correlation coefficient between β and the mean GND density is reduced to 0.82, when results from the recrystallized state are included. After recrystallization, there is also a divergence in trends between hardness and β. The hardness significantly decreases after recrystallization by 27% causing the correlation coefficient between β and hardness to reduce to 0.54.

From the EBSD plots shown in Fig. 6, the large microstructural changes due to recrystallization can be seen at this heat treatment state. These changes may have introduced new sources of acoustic nonlinearity causing an increase in β, despite the continued decrease in GND density. The large microstructural change caused by this recrystallization can be seen in Fig. 8, which shows the change in crystalline texture, as defined by the distribution of crystallographic orientation, between the first and last heat treatment states. The top row of images shows the distribution of grains aligned with each of the defined Miller indices ([001], [111], [011]) in three stereographic projections for the 316 L L-PBF sample after the 650 °C heat treatment. The texture is defined to have a weak 100 fiber indicating more grains than average have their 100 axis parallel to the cartesian coordinate system with a stronger 100 fiber parallel to the build direction (Z-axis). The scale, with units of multiples of uniform density, gives the ratio of a given orientation relative to the same orientation in a random texture. The bottom row of images shows the same information following recrystallization, where the previous texture is replaced by a relatively random texture. Since the β calculated here is a relative measure of second harmonic generation, it is difficult to make absolute statements about the impact of the large microstructural changes caused by recrystallization on β. EBSD was only performed on the 316 L L-PBF sample, so the results from these techniques were not studied with the other manufacturing methods.

While, linear ultrasonic attenuation has previously been used to characterize damage and track microstructural changes in a material (Evans et al., 1978; Ogi et al., 1997), attenuation measurements comparing different heat treatment steps within a single specimen do not provide significant differentiation between heat treatment steps (Bellotti, 2020). Figure 9 shows the results of bulk longitudinal wave attenuation measurements performed at the different heat treatment stages for the 316 L L-PBF specimen. Below the 20 MHz range, these attenuation measurements are not sensitive to the material changes caused by annealing where the characteristic length (the grain size) is an order of magnitude smaller than the wavelength of the ultrasonic wave (∼300 μm) (Van Pamel et al., 2016). These results also show that the differences in attenuation at lower frequencies are small; therefore, the attenuation effects on β at the highest operating frequency (4.2 MHz) are also small.

This research demonstrates the sensitivity of the acoustic nonlinearity parameter, β, to changes in the microstructure of additively manufactured metals. The different trends in measured β between the 316 L L-PBF and 316 L Wrought specimens follow the expected microstructural changes from previous literature comparisons between AM and traditional manufactured specimens. Quantitative measures of GNDs show that the heat treatment profile is effective in reducing the number of dislocations. The statistical correlation between β and GND density is strong, but β is not uniquely sensitive to dislocations. Other microstructural features influence acoustic nonlinearity and the trend between β and GND density diverges following large-scale recrystallization. The effects on β at the final recrystallization heat treatment state are to be explored in future works. On the other hand, β appears to have an excellent correlation with hardness of the material. Note that hardness is a macroscopic consequence of the dislocations as well as other features (grain boundaries) in the microstructure.

A multi-physics approach to the qualification of AM parts would provide multiple facets of understanding and insurance of a printed part before it is used in critical scenarios. Nonlinear ultrasound can provide useful information of the microstructure and can act as a comparative measure between specimens.

Financial support and materials for this research are provided by Sandia National Laboratories and the Nuclear Energy University Program from the U.S. Department of Energy. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA-0003525.SAND 2018-10721 C. Special thanks to David Saiz who operated the ProX 200 to print the L-PBF sample, and Dennis De Smet who performed Sandia heat treatments.