ML23318A217

Technical Paper Entitled Development and Testing of Coarse-Grained Models for Ultrasonic Simulations of Cast Austenitic Stainless Steel

ML23318A217
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Issue date:	11/22/2023
From:	Hutchinson C, Jacob R, Carol Nove, Prowant M NRC/RES/DE, Pacific Northwest National Laboratory
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Carol Nove 301-415-2217
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Ultrasonics 136 (2024) 107157 Contents lists available at ScienceDirect Ultrasonics journal homepage: www.elsevier.com/locate/ultras Development and testing of coarse-grained models for ultrasonic simulations of cast austenitic stainless steel Richard E. Jacob *, Matthew S. Prowant, Chris A. Hutchinson Pacific Northwest National Laboratory, Richland, WA, USA A R T I C L E I N F O A B S T R A C T Keywords: Ultrasonic inspection of cast austenitic stainless steel (CASS) in the nuclear industry is particularly challenging Ultrasonic modeling and simulation because of sound field scatter and attenuation caused by the coarse-grained microstructure. Modeling and Cast austenitic stainless steel simulation are important tools in ultrasonic testing, as they can be used to help address key aspects of in Nondestructive examination spections, such as developing new probe designs, predicting inspection reliability, and testing phased-array focal laws. However, developing a useful and reliable CASS model is challenging due to the many grain interfaces and crystalline orientations that must be captured. We demonstrate a method of creating a realistic CASS model that is usable in CIVA, a commercially available modeling and simulation software platform. Using polished and chemically etched sections to highlight the grain structure and orientation, we generate models of a coarse-grained equiaxed specimen and a columnar specimen. We also test an alternative method of generating a coarse-grained model using Voronoi regions. We qualitatively compare sound field scatter and quantitatively compare sound field attenuation and beam partitioning in simulated sound fields to those of laboratory-measured sound fields. Results show that the Voronoi models perform as well as or better than the models based on actual grain morphology. We also show that model-to-model randomness in Voronoi grain structure can impact the magnitude of a simulated echo response by a factor of two or more. Although CASS models are potentially a good depiction of reality for a given scenario, they should not be considered representative since CASS morphology can change significantly from specimen to specimen or within the same specimen.

1. Introduction and poor sound field penetration [18]. Indeed, these challenges have prevented performance demonstration criteria for procedures and in Inservice inspections with ultrasonic testing are required in all spectors from being established in the U.S., so inspectors have not been operating nuclear power plants in the U.S. to assure component integrity able to perform effective inspections of CASS components [19]. Suc and continued safe operation. Computational models of ultrasonic sound cessful ultrasonic models of CASS material may help guide the devel fields have been of growing interest to the nuclear power industry opment of inspection approaches.

because of the potential to predict the quality and effectiveness of an Specimen material properties typically have a large effect on simu inspection. For example, modeling in nuclear nondestructive examina lation accuracy, so it is important to use a specimen model that most tion (NDE) has been used to help predict inspection reliability [1,2], closely emulates the materials impact on the sound field. Precise predict beam coverage [3], develop and test procedures [4-6], test focal specimen properties of grain size, shape, and orientation can be gener laws [7-9], and inform wedge, probe, and mockup design [10-12]. ated from electron backscatter diffraction (EBSD) measurements. For Ultimately, the goal of modeling is to save time, money, and resources example, CASS specimen models created from EBSD scans by Chen et al.

while maintaining or improving safety of the nuclear fleet. Of particular [20] showed that sound field simulations using CASS models produced interest is the simulation of sound fields through challenging materials, noise and signal distortion that were consistent with experimental re such as austenitic welds and cast austenitic stainless steel (CASS) sults. They suggested that the accurate description of specimens is key

[13-17]. These materials pose challenges for ultrasonic inspections for modeling, and that the EBSD approach to defining specimen models because the coarse grain morphology partitions, redirects, and attenu is effective. Nakahata et al. [21] used EBSD data to create elongated ates the sound field, resulting in significant scatter, high noise levels, grain structures for simulating sound propagation through coarse- and

• Corresponding author.

E-mail address: richard.jacob@pnnl.gov (R.E. Jacob).

https://doi.org/10.1016/j.ultras.2023.107157 Received 5 May 2023; Received in revised form 25 July 2023; Accepted 1 September 2023 Available online 3 September 2023 0041-624X/© 2023 Elsevier B.V. All rights reserved.

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 fine-grained CASS parallel to the grain elongation direction. They better replicate volumetric scattering. Our realistic structures were showed that at 2 MHz (the wavelength in steel at 2 MHz is approxi developed in 2D and extrapolated to 3D for sound field simulations in mately 3 mm), average grain diameters of 0.3 mm behave similarly to CIVA. Results of the sound field simulations were then compared to homogeneous material, whereas average grains of 1.1 mm cause sig simulations using models generated from 3D Voronoi regions to deter nificant scatter and attenuation. The EBSD approach can allow for an mine which approach is the more accurate and more practical repre accurate specimen model, but it requires destructive analysis, generates sentation of CASS. Simulation results were compared to experimental very large data files and, in the end, results in a model that is inherently maps of sound fields transmitted through test blocks. CIVA software was only two-dimensional (2D). Three-dimensional (3D) models can be used to perform the simulations.

generated by using a serial sectioning approach, but this would be impractical. Every slice would need to be polished, and the minimum 2. Materials and methods grain size that could be visualized would be limited by the slice thick ness. Overall, the EBSD approach is an important validation tool, but it is The grain structures that would form the basis of our specimen not feasible for generating 3D models, models of large sections, or models were obtained from cut, polished, and chemically etched CASS models of intact specimens. sections. One section was coarse-grained equiaxed (labeled AAD-3) and It is impossible to nondestructively replicate the grain morphology the other was coarse-grained columnar (labeled B-519C). Photographs (e.g., sizes, shapes, and crystalline orientations), so alternative ap of the sections are shown in Fig. 1, and the specimens are described by proaches with simplified models must be used. Wan et al. [17] used Crawford et al. [32]. AAD-3 came from a cast stainless steel pipe section specimen models with a regular square lattice and models based on a (exact material is unknown) with an outer diameter of 965 mm and a physical specimen to investigate the effects of grain size on sound wall thickness of 83 mm. B-519C came from a CF-8A (a nuclear-grade attenuation in coarse-grained materials. They showed that different CASS alloy) pipe section with an outer diameter of 846 mm and a wall grain sizes resulted in different types of scattering (i.e., Rayleigh, sto thickness of 60 mm. Both sections are centrifugally cast stainless steel.

chastic, or geometric), but that a few large grains in a fine-grain model Equiaxed grains have no preferred axis of elongation, and columnar can have a disproportionately large effect on the scatter at a given fre grains are elongated radially. Coarse-grained is a qualitative desig quency. They also showed that higher inhomogeneity of grain size dis nation. The designation between fine and coarse grains is typically made tributions may introduce a stronger frequency dependence to in terms of the ultrasonic wavelength, with coarse grains being attenuation. More realistic models have been created using Voronoi approximately equal to or larger than the wavelength and fine grains regions as grains. Voronoi regions can be generated rapidly in 2D or 3D being smaller. For reference, the ultrasonic wavelength in steel is with a variety of grain sizes. Van Pamel et al. [22] used 2D Voronoi approximately 6 mm at 1 MHz. Whatever the definition used, every models and a full matrix capture phased array ultrasonic approach with specimen has a continuum of grain sizes between the largest and finite element modeling to study the effects of probe aperture size and smallest grain, and the designation of whether a specimen is primarily array type on predicted signal-to-noise ratio. They concluded that a 2D fine- or coarse-grained is largely subjective.

array would be beneficial over a 1D array, and that pitch-catch probe EBSD can be used to precisely characterize grain boundaries and configurations can be advantageous when trying to minimize noise. crystalline orientations, or Euler angles [16,20,21,33]. However, we Shivaprasad et al. [23] also used Voronoi models in multiple simulations chose to use an alternative approach for three reasons. First, the EBSD to study the effects of grain size, orientation, and randomization on system at PNNL could not accommodate the size of the specimens.

sound propagation. They showed that model-to-model variations in Second, in our previous work with austenitic welds [16], the EBSD data Voronoi region orientation and distribution can be overcome through files that we acquired from relatively small specimens challenged stan multiple simulation trials. They performed convergence studies to dard desktop computing capacity for processing the data and generating determine the optimal number of trials needed. a CIVA model. Third, we wanted to develop a method that could be CIVA (EXTENDE, Inc.) is a commercial software package that has easily implemented for those without access to EBSD capabilities..

been used by several different research groups to model ultrasonic Therefore, the microstructure was captured with light photography, and propagation in coarse-grained materials. For example, noise and atten Euler angles in CASS material were taken from Chen et al. [20]. The uation were simulated in coarse-grained models with CIVAs built-in process of extracting the grain boundaries is described below.

noise-simulating capability that uses a point-scatterer model [15,24].

To create coarse-grained specimen models, Voronoi regions are conve nient surrogates because they are a built-in option in CIVA for certain 2.1. CASS equiaxed model specimen configurations. Jenson et al. [25] showed that CIVA Voronoi regions result in significant beam scatter, but additional attenuation The grain boundaries were extracted from photographs taken with may be needed for simulation results to agree with experimental results. two different lighting angles. Due to directional reflectance of In other work, sound beam propagation and flaw responses were chemically-etched crystalline materials, reflected light intensity is modeled in CIVA using Voronoi models, and results were compared to dependent on the incident angle [34]. Thus, illuminating the specimen experimental scans [26]. Results showed that through trial and error, from different angles helped improve grain-to-grain contrast. A portable simulation parameters can be adjusted so that simulated and experi halogen lamp was used as the light source in an otherwise dark room, mental results agree well. Additionally, Ribay et al. [27] simulated and an SLR camera was mounted on a tripod and operated with a probability of detection calculations under various scenarios in CIVA. wireless remote shutter control to prevent camera motion between Simulation results showed that the Voronoi regions reduced the proba shots. Two images were acquired on each specimen, with the light from bility of detection, as expected. Some work has been done to methodi the right and from the left. Image resolution was 20 MB, the highest cally assess commercially available modeling tools. For example, limited setting of the camera. We processed the photos using ImageJ [35] to evaluations of strengths and weaknesses of CIVA have been conducted extract the grain boundaries; Fig. 2 illustrates the steps used. A similar

[28-31]. but less-involved approach was described briefly by Ribay et al. [27] to Previous sound field modeling of coarse-grained structures was measure grain size. Our process was as follows:

limited to 2D Voronoi regions [22,23] or geometric shapes [17]. In this paper, we build on the work described above to develop coarse-grained 1. Color photographs (Panel A of Fig. 2) were split into separate RGB models with two key differences. First, our models are based on realistic (red/green/blue) channels, resulting in three grey-scale images. The coarse-grained equiaxed and columnar CASS structures taken directly image histograms were evaluated to determine the image with the from laboratory specimens. Second, our models were executed in 3D to largest spread of grey-scale values (i.e., that with the greatest 2

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 1. Photographs of AAD-3 (top) and B-519C (bottom). AAD-3 is 83 mm thick with equiaxed grains, and B519-C is 60 mm thick with columnar grains. These sections were polished and chemically etched to reveal the grain microstructure.

contrast), and that image was retained (here it was the red channel, specimen model.

shown in Panel B). CIVA requires that the specimen model comprise line segments and

2. The specimen outline was used to create a mask. The mask was be in a CAD file format. However, because the grain outlines are applied to the grey-scale image (Panel C) to remove the background. generally not straight lines, converting the model directly into a CAD file

3. The masked image was filtered to enhance contrast, remove speckles would result in tens of thousands of individual line segments, most of and noise, and sharpen grain boundaries (Panel D). This was done in which would only be one or two pixels long. This would be too many three steps with the Enhance Contrast filter, Median filter, and Un segments for CIVA to handle in a reasonable time. To simplify the model, sharp Mask filter functions of ImageJ. Optimal filter parameters were we applied a line reduction algorithm to straighten curves in order to determined by trial-and-error. reduce the total number of line segments while substantially maintain

4. The window/level of the image was set to two different rangesone ing the grain boundaries.

to emphasize bright grains and the other to emphasize dark grains. A To test the algorithm, it was applied to a subsection of the grain binary (black and white) image was then made from each window/ skeleton with four different threshold values: 3, 6, 10, and 20 resulting level setting. Panel E shows the binary image with the dark grains in 2575, 1887, 1585, and 1342 line segments, respectively; see Fig. 4. As emphasized. Additional window/level settings can be helpful if the threshold was increased, the number of segments needed to define image contrast is poor. the geometry decreased, but at the same time the representation of the

5. A particle removal algorithm in ImageJ eliminated grains that were grain boundaries lost fidelity. This was observed qualitatively through below a size threshold, typically about 1/10 of the wavelength that visual comparison.

will be used for simulations. Panel E shows the binary image with The final specimen model (Fig. 5) was taken from the central section particles already removed. of Fig. 3. The model used the threshold value 6 and was 80 mm x 80 mm

6. The edge-finding algorithm in ImageJ was used to outline the grain with 810 regions. Note that a key consideration in determining which boundaries and create a partial grain skeleton (Panel F). threshold level to use was the number of line segments, because CIVAs

7. The process was repeated with both photographs until all the grains capacity to handle complex geometries is limited. With the threshold were outlined. levels tested, the number of line segments decreased with increasing

8. The partial skeleton images from the different window/level settings threshold, but not rapidly. The average region size was about 7 mm2 were combined to create a single image with all the grain outlines. with a standard deviation of 25 mm2 and the maximum grain size was Some additional processing was done to clean up regions where edge about 430 mm2. This represents a large range of grain sizes, with a non-outlines did not line up exactly and where grain boundary segments normal distribution heavily weighted by small grains. Each region in the did not form an enclosed region. This included a final particle specimen model was defined with one of ten different sets of Euler an removal step and successive region dilate/erode steps. gles taken from [20]; elastic constants were defined by a single stiffness matrix that was based on the default CIVA values for steel. The grain Fig. 3 shows the final grain skeleton that was the basis of the definitions were implemented with a CIVA XML file in a manner similar 3

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 2. Process of extracting grain boundaries. A) Photograph with the light source to the left. B) The red channel of the photograph. C) Panel B with a mask applied.

D) Panel C with contrast enhancement and unsharp mask filter applied. E) Binary (black/white) image showing the dark grains from Panel D. F) Partial grain skeleton comprising extracted grain boundaries.

Fig. 3. Final grain skeleton of AAD-3.

to that described in [16]. The Euler angles were assigned quasi- the same grain boundaries and elastic constants). Fig. 5 shows an randomly such that regions that shared a boundary would not have example of the Euler angle assignments for one of the models where each the same set of angles. If two neighboring regions did have the same color represents a different set of angles.

Euler angles, the two regions would behave as one region in the simu The model was 2D, so the geometry was extruded by 200 mm in the lation and the grain boundary would be effectively ignored. To explore orthogonal dimension (i.e., in and out of the page) to make a 3D model.

model variability, ten different versions of the specimen model were CIVA performs this operation automatically; the user enters the extru generated, each with a different random distribution of Euler angles (but sion parameter. The probe was oriented parallel to the extruded 4

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 4. Subsection of AAD-3 grain skeleton with line reduction algorithms applied using different threshold levels.

were used. The Voronoi model had an average grain cross-section of about 7 mm2 and a maximum grain size of about 26 mm2. The maximum grain size of the AAD-3 model was 430 mm2, so there was a much larger size range in the realistic model. Fig. 6 shows the Voronoi model side-by-side with the AAD-3 model.

To simulate sound field scatter in Voronoi regions, CIVA varies the speed of sound from grain to grain instead of using Euler angles. The user enters the average speed of sound V of the specimen and a range of velocities, defined by the parameter V. Then velocities within V +/- V are randomly assigned to the regions. For example, if V is set to 6,000 m/

s and V is set to 10% (or 600 m/s), then each Voronoi region will be randomly assigned a velocity between 5,400 m/s and 6,600 m/s. Be tween simulations, CIVA allows the user to randomize the Voronoi re gions, essentially creating a new specimen, or to randomly reassign velocities to the existing regions without changing the region bound aries. For this work, multiple simulations were run with the same Vor onoi geometry but with the sound velocities reassigned. V was 5,900 m/

s, and the values of V tested were: 4%, 6%, and 8% (i.e., 5,900 +/- 236 m/s, 5,900 +/- 354 m/s, and 5,900 +/- 472 m/s).

2.3. CASS columnar model The process used to make the realistic equiaxed model was repeated on B-519C to make a columnar-grained model. Fig. 1 shows a photo graph of B-519C under ambient light, and Fig. 7 shows the resulting Fig. 5. Example of how Euler angles were applied to AAD-3. Each color rep grain skeleton (top) and the final specimen model (bottom). As with the resents a different set of Euler angles. Assignments were made randomly with equiaxed model in Fig. 5, different Euler angles are indicated by the the condition that neighboring grains could not have the same Euler angles. different colors. The model was 60 mm x 80 mm with 1041 regions resulting in an average region size of 4.6 mm2. The model was extruded direction, and the sound field was simulated in a plane perpendicular to by 200 mm to form a 3D model. As with the equiaxed model, 10 versions the extruded dimension. were created, each with random assignments of Euler angles taken from

[20]. The other material properties were the same as those of the equiaxed model.

2.2. Voronoi equiaxed model 2.4. Voronoi columnar model An alternative and much simpler model approach to creating a coarse-grained specimen model was also tried using Voronoi regions. Columnar CASS models were also made with 3D Voronoi regions. In Models with grains derived from Voronoi regions were developed for the Voronoi equiaxed model described above, grains were elongated to comparison to the realistic-grain models. CIVA has a built-in capability imitate the extrusion of the 2D realistic model. However, the CIVA-of generating 3D Voronoi regions in certain model geometries. An aspect generated Voronoi regions can be elongated in only one dimension.

ratio can be defined in order to elongate the regions in one dimension. For the Voronoi columnar model, the elongation was used to make the The grains in AAD-3 were defined in a 2D plane and extruded in the grains columnar, which means they could not be elongated in the orthogonal dimension to create a 3D model, so the same was done with orthogonal dimension to imitate the extrusion of the 2D realistic model.

the Voronoi specimen by giving the regions a high aspect ratio of 100. Thus, the columnar Voronoi grains were 3D while the specimen-based For consistency, the same specimen dimensions and numbers of regions grains were extruded 2D. The Voronoi specimen was 100 mm x 80 5

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 6. Voronoi equiaxed model (left) and AAD-3 model (right). Both models have the same number of grains, and both models were extruded in the third dimension (into the page).

Fig. 7. Model of B519-C. Top: Resulting grain skeleton. Bottom: final model. Each color represents a different set of Euler angles. Assignments were made randomly with the condition that neighboring grains could not have the same Euler angles.

mm x 60 mm and had 10,000 regions, so the average grain volume was 2.5. Simulation parameters 48 mm3. The Voronoi aspect ratio was 7. Unfortunately, since the columnar Voronoi regions are inherently 3D, the region sizes cannot be Prior to running simulations in CIVA, it is important to determine the directly compared to those of the 2D realistic model. Fig. 8 shows a side- accuracy factor (AF) that will provide the best results in the minimum by-side comparison of a cross-sections of B519-C (left) and a columnar simulation time. AF is a CIVA setting analogous to the mesh density in Voronoi model (right). finite element modelsa higher AF produces more accurate results but at the cost of longer simulation times. The idea is to use the lowest AF 6

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 8. Voronoi columnar model (left) and B519-C model (right). The Voronoi model was 3D and the B519-C model 2D, so direct comparison of region sizes is not possible.

that will give results with minimum acceptable error. To determine the probe (1.1 MHz, 58% bandwidth at 6 dB) was used in transmit-receive-ideal AF, we ran initial AAD-3 and Voronoi simulations with AF = 1, 2, longitudinal configuration with a 45 refraction anglethese parame 4, 8, 16, 32, and 64 (note that AF = 64 did not complete for AAD-3 due to ters were taken from those used by Crawford et al. (2014) so that a user error). With low AF, some pixels were apparently not computed simulation results could be compared to the experimental sound field and were blank in the simulation result; this was especially noticeable in maps. The element size was 3.5 mm x 3.5 mm with a 0.5 mm gap be the AAD-3 simulations. The mean-square-error (MSE) was calculated tween elements in each direction; thus, the aperture was 39.5 mm in the pixel-by-pixel using the highest AF image as the baseline. An appro primary direction and 19.5 in the secondary direction. The wedge di priate AF was determined when the MSE stopped decreasing (or, from a mensions, as entered into CIVA, were 22 mm front length, 22 mm back practical level, the MSE became < 1%). For the Voronoi simulations, length, 44 mm width, and 8.76 mm height. The wedge material was MSE was 2.3% for AF = 1 and < 1% for AF 4. For the AAD-3 simu Rexolite with a longitudinal sound speed of 2450 m/s and an angle of lations, MSE was 27% for AF = 1, 18% for AF = 8, and < 1% for AF = 16. 17.856 . To reduce computation time, a 2D sound field was computed We selected an accuracy factor of 16 for all the remaining sound field through the specimen cross section at the focal point of the beam, and no simulations. mode conversions or internal reflections were simulated.

Ten beam simulations were performed on each model geometry Fig. 9 shows CIVA screen captures of the top, side, and front views of using a CIVA accuracy factor of 16. V was set to 5,900 m/s and the values the simulation setup. The extrusion direction is shown by the black of V tested were: 4%, 6%, and 8% (i.e., 5,900 +/- 236 m/s, 5,900 +/- 354 arrow, and the computation plane is shown by the red arrow.

m/s, and 5,900 +/- 472 m/s). A 1 MHz, 5 x 10 element 2D-matrixed PA Fig. 9. Top, front, and side views of the simulation setup. The black arrow indicates the extrusion direction, and the red arrow indicates the computation plane.

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R.E. Jacob et al. Ultrasonics 136 (2024) 107157 2.6. Voronoi model variability exceeded a threshold as a crossing. Fig. 9 shows an example of the crossings from a horizontal and vertical line profile through a columnar To test how changes to Voronoi model grain structures affect echo Voronoi beam simulation. Panel A shows the image with a median filter amplitude, a simple specimen model with a side drilled hole was created applied; the filter reduces pixel-to-pixel fluctuations while preserving in CIVA. The modeled specimen was 100 mm x 50 mm x 60 mm with V edges and boundaries. Panels B and C are the image profiles through the

= 5,900 m/s and V = 4% (V = 5,900 +/- 236 m/s). The hole was 3 mm horizontal and vertical lines in A, respectively. The black lines in B and C diameter and 50 mm deep. The Voronoi geometry was randomized prior represent the threshold level (in this case, 70% of the maximum signal),

to each simulation by clicking the Voronoi diagram reset button in and the red circles show the rising-edge crossings. The process was CIVA. An identical side drilled hole was used for calibration in a ho repeated for every horizontal line through the image, and the sum of all mogeneous, isotropic material. A 10 x 5 element, 1 MHz phased-array crossings was taken. Similarly, the sum of all vertical crossings was probe was modeled with a 45 refraction angle focused at the side- counted. The ratio of horizontal to vertical crossings is the crossing ratio, drilled hole. Direct Mode (no specimen echoes) was used to reduce or partitioning metric. Beam partitioning from columnar grains should simulation time and because it is ideal for side drilled hole simulations. result in more horizontal crossings than vertical crossings, resulting in a Four scenarios were tested, with ten runs of each. The first scenario ratio > 1. For equiaxed grains, there should be no preferred direction of used 2,800 equiaxed Voronoi regions to model coarse-grained equiaxed beam segmentation, and the ratio should be 1. We applied the metric CASS, the average region size equating to a 5.9 mm diameter sphere of to compare the Voronoi simulations, the B519-C simulations, and the equivalent volume, or about one wavelength. The second scenario was empirical beam maps.

with 22,000 equiaxed regions, equating to about one half wavelength.

Two additional scenarios used the same numbers of regions but with an 3. Results aspect ratio of 7 to model columnar-grained CASS.

3.1. Voronoi model variability 2.7. Beam partitioning metric Fig. 10 is a box plot of the results of the side drilled hole echo tests through the various Voronoi models. The echo strength is in dB below Sound field partitioning is the sectioning of the beam by the pre the calibration signal. The box indicates the upper and lower data dominant orientation of the CASS grain structure. Crawford et al. [32] quartiles, and the bars show the lowest and highest extents. The hori observed that beam partitioning is a signature of columnar grains and zontal line within the box is the median, and the x is the mean. The developed a metric to compare empirical sound fields through different 2,800 grain equiaxed and 2,800 grain columnar (Eqx-2,800 and Col-materials. The metric was calculated by acquiring horizontal and ver 2,800 in the figure) scenarios had the lowest average signal reduction tical beam profiles and counting every instance that the signal intensity Fig. 10. An example of the how the beam partitioning metric is calculated. A) The sound field with a median filter applied. B) Sound field profile from the horizontal line in A. C) Sound field profile from the vertical line in A. The rising-edge of each profile at the 70% peak level are circled. In this example, there were two horizontal crossings and one vertical crossing.

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R.E. Jacob et al. Ultrasonics 136 (2024) 107157 (about 14 dB and 19 dB, respectively). The 22,000 grain models had larger reductions in signal intensity ( 26 dB and 39 dB), which in dicates more beam scatter. More important for model variability is the range of signal responses obtained within each scenario. The signal re sponses of the coarse-grained equiaxed results (the 2,800 grain equiaxed model) varied from 12.0 dB to 19.4 dB, a range of 7.4 dB (a factor of 2.3). In the 22,000 equiaxed case, the range was 6.4 dB, or a factor of 2.1. In the 22,000 grain columnar case, the range was 9.7 dB, or a factor of 3. Results show that random variations in specimen granular structure can affect the simulation results by more than a factor of 2 and will likely dominate uncertainty of simulation results.

Microstructural variability can be seen in serial sections from the same specimen. Crawford et al. [32] cut serial slices from the end of AAD-3. Each slice was polished and etched to reveal the grain structure.

Fig. 12 shows three adjacent slices, each about 6 mm thick. The overall grain pattern is similar from slice to slice, but individual grain bound aries and sizes vary randomly.

3.2. Equiaxed model Fig. 13 shows a representative AAD-3 simulated sound field and an equiaxed Voronoi sound field with V = 6% (V = 5,900 +/- 354 m/s).

Simulation results were qualitatively compared to previously-acquired experimental sound field maps [32], as shown in Fig. 14. Both simula tion and experimental results show sound field scatter and poor beam formation.

Direct comparisons to experimental results cannot be made because the signal intensities are totally different in simulations compared to experiment. The images were therefore normalized to a control image of the same gain. The control scenarios were sound fields measured (or simulated) through fine grained wrought stainless steel (or isotropic) material. The AAD-3 simulation set and Voronoi set were each averaged, then the ratio was taken of the total signal in the coarse-beam image to that of the control image. Table 1 shows the results of the calculated ratios. The fractional signal intensities for the average V = 6% (V =

5,900 +/- 354 m/s) Voronoi case was closest to the experimental value while the ratio of the AAD-3 simulations suggest more scatter than observed experimentally.

Fig. 12. Three polished and etched slices cut serially from AAD-3 illustrating 3.3. Columnar model the variability in grain structure within a specimen. The slices are about 6 mm thick.

Fig. 15 shows a representative AAD-3 simulated sound field and an equiaxed Voronoi sound field with V = 6% (V = 5,900 +/- 354 m/s).

experimental sound fields show partitioning along the horizontal axis, Simulation results were qualitatively compared to previously-acquired consistent with the orientation of the grains. The Voronoi simulation experimental sound field maps [32], as shown in Fig. 16. The also shows some partitioning, whereas the B-519C simulation does not show clear partitioning.

The crossing ratios method of measuring beam partitioning was used to compare the simulation results of the columnar models to those of the equiaxed models and experimental data. Table 2 shows the mean crossing ratios of the Voronoi columnar, B519-C (columnar), and AAD-3 (coarse-grained equiaxed) simulations. Also included are approximate values taken from the 1 MHz data shown in figure 12 of [32]. Note that the high number of samples taken (every row and column of each image) resulted in low standard deviation. In the table, the standard deviation (SD) is presented with an extra level of precision, (i.e., to the second decimal point) to avoid misrepresentations from rounding. The Voronoi cases with V = 4% and V = 6% (V = 5,900 +/- 236 m/s and V = 5,900

+/- 354 m/s) had the closest agreement with the experimental sound field map results. The B-519C simulations showed some partitioning, but the partitioning was not significantly different from that of the AAD-3 simulations.

Fig. 11. Box plot showing the range of simulated echo amplitudes with different Voronoi region configurations.

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R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 13. Representative sound field simulations. A)The isotropic control, B) the AAD-3 model, and C) the Voronoi equiaxed model. Each image is self-normalized to its peak sound field intensity.

Fig. 14. Laboratory-acquired sound field maps. A) Control map through wrought stainless steel. B) and C) Maps through AAD-3. The AAD-3 maps were made on the same end of the specimen but after sections of material had been removed. The sound field maps in B and C were made through an equivalent metal path. Each image is self-normalized.

grained model, the smallest grains can be removed with little conse Table 1 quence, as they contribute least to the sound field scatter [17]. The Signal intensities of simulated and experimental sound fields as a fraction of problem of rendering small grains might be rectified by using higher the respective control scenarios.

resolution photographs or acquiring magnified images and stitching Scenario Fractional Signal them together as a mosaic. We did not explore these alternatives. In Average of 4% Voronoi simulations 0.43 previous work, we used high-resolution EBSD to characterize the grains (V = 5,900 +/- 236 m/s) in an austenitic weld [16]. However, because of sample size limitations Average of 6% Voronoi simulations 0.25 and data file sizes, this approach was not practical for the considerably (V = 5,900 +/- 354 m/s)

Average of 8% Voronoi simulations 0.13 larger CASS specimens in this study.

(V = 5,900 +/- 472 m/s) Two 2D models of coarse-grained equiaxed CASS (Fig. 5) and Average of AAD-3 simulations 0.15 columnar CASS (Fig. 7) were created. To differentiate the grains and Experimental data from AAD-3 0.24 provide a mechanism for sound field scatter, Euler angles were assigned to each region. The models were imported into the modeling and

4. Discussion simulation platform CIVA for sound field simulations, examples of which are shown in Fig. 13 and Fig. 15. The models show beam scatter We showed a method of creating a CASS specimen model from a and attenuation, attributes that are observed experimentally in CASS.

polished and chemically etched specimen that has visible grains. Spec For the equiaxed scenario, the Voronoi and realistic models both showed imen photographs captured the grain structure, and multiple photos similar scatter patterns; however, the realistic model appeared to with a light source from different directions helped differentiate the attenuate the beam too much whereas the Voronoi model with V = 6%

grains for image processing. Unfortunately, the photography method of agreed well with experiment. For the columnar scenario, the Voronoi creating a model did not capture small grains well. Previous efforts to model showed beam partitioning scatter patterns that agreed better with capture grain boundaries in a specimen with finer grains and an experiment than those of the realistic model. Beam partitioning from the austenitic weld failed due to the image filtering and edge-finding algo V = 4% (V = 5,900 +/- 236 m/s) and V = 6% (V = 5,900 +/- 354 m/s) rithms having slight but significant effects on the grain boundaries [15]. Voronoi models, as measured by the beam partitioning metric, agreed Thus, the photography method was not precise enough to define small well with experimental results. There was less beam partitioning from grains without higher resolution images. We note that in a coarse- the realistic model. The beam partitioning may have been affected by 10

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 Fig. 15. Representative sound field simulations. A) Isotropic control, B) the B-519C model, and C) the Voronoi columnar model. Each image is self-normalized to its peak sound field intensity.

Fig. 16. Laboratory-acquired sound field maps. A) Control map through wrought stainless steel. B) and C) Maps through B-519C. The B-519C maps were made on the same end of the specimen but after sections of material had been removed. The sound field maps in B and C were made through an equivalent metal path. Each image is self-normalized.

scatter. The V was not optimized in this study, but an optimization Table 2 process was outlined in [15].

Comparison of partitioning metric.

Signal response variations of about a factor of 2 were observed by Case Mean Partitioning Metric +/- SD randomizing a Voronoi model (see Fig. 11). Grain sizes and shapes in Voronoi columnar V = 4% 2.3 +/- 0.05 Voronoi models are comparatively uniform, as shown in Fig. 6 (although (V = 5,900 +/- 236 m/s) the uniformity can vary depending on the Voronoi regularity set by a Voronoi columnar V = 6% 2.4 +/- 0.06 distance constraint between Voronoi region nuclei [23]). Thus, random (V = 5,900 +/- 354 m/s)

Voronoi columnar V = 8% 2.2 +/- 0.05 changes in grain size and shape from one Voronoi model to the next are (V = 5,900 +/- 472 m/s) expected to be relatively small compared to microstructural variations B519-C (simulated) 2.0 +/- 0.02 within a laboratory specimen. For example, Fig. 12 shows three serial B519-C (from [32])(a) 2.4 +/- 0.04 sections of AAD-3, each 6 mm thick. There is some consistency in the AAD-3 (simulated) 2.0 +/- 0.04 overall grain patterns, but the size, shape, and orientation of grains can AAD-3 (from [32])(a) 1.4 +/- 0.03 change substantially from one slice to the next. Additional examples are shown in Chapter 8 of [18], where we show seven polished and etched the model dimensionality; in the columnar scenario the Voronoi model CASS specimens, each with different grain morphology. This is relevant was 3D while the realistic model was 2D. to CASS modeling because if randomizing a relatively uniform Voronoi The partitioning metrics of AAD-3 and B519-C simulations did not model changes the signal response by a factor of 2, then randomizing a differ from each other (see Table 2). The models were not ideal repre realistic modelor simply selecting a different specimen to create a sentations of the different grain structures because they were inherently model fromshould have a much stronger effect. Fig. 14 illustrates the 2D and were extruded in the third dimension. For AAD-3 (simulated), point: the two sound field maps were acquired after removal of one of the metric is higher than empirical, and for B519-C (simulated) it is the 6 mm slices in Fig. 12, and each sound field is unique in appearance lower than empirical. Notably, the Voronoi columnar simulations and in spite of being from nearly the same location of the same specimen.

the B519-C empirical results agree. The partitioning metric of the Vor Therefore, it is unfeasible to use a single specimen model to accurately onoi models was largely independent of V, so the optimal value of V simulate an empirical sound field map or flaw response in CASS mate should be determined based on other factors, such as signal intensity or rial. Indeed, the authors of [27] concluded that microstructural 11

R.E. Jacob et al. Ultrasonics 136 (2024) 107157 variations in CASS are the most influential factors affecting the simu Declaration of Competing Interest lation outcomes. CASS models may be considered representative of general effects of grain structures on simulated sound fields and signal The authors declare that they have no known competing financial responses, but simulation results that exactly represent reality should interests or personal relationships that could have appeared to influence not be expected. In practice, the microstructural randomness and the work reported in this paper.

unpredictability can have important impacts on an ultrasonic inspec tion. For example, in Chapter 8 of [18] we showed that microstructural Data availability variations can cause the signal levels in a CASS material to vary by a factor of two or more, or even disappear entirely, depending only on the Data will be made available on request.

probe position.

Sectioning a specimen is the only method of acquiring the true grain References structure. Accurate 3D models would require many thin slices in order to capture the microstructural variations that would otherwise be lost to [1] Q. Liu, H. Wirdelius, A 2D model of ultrasonic wave propagation in an anisotropic weld, J NDT&E Int. 40 (3) (2007) 229-238.

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