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

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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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Ultrasonics 136 (2024) 107157 Available online 3 September 2023 0041-624X/© 2023 Elsevier B.V. All rights reserved.

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 Keywords:

Ultrasonic modeling and simulation Cast austenitic stainless steel Nondestructive examination A B S T R A C T Ultrasonic inspection of cast austenitic stainless steel (CASS) in the nuclear industry is particularly challenging because of sound field scatter and attenuation caused by the coarse-grained microstructure. Modeling and simulation are important tools in ultrasonic testing, as they can be used to help address key aspects of in 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 Inservice inspections with ultrasonic testing are required in all operating nuclear power plants in the U.S. to assure component integrity and continued safe operation. Computational models of ultrasonic sound fields have been of growing interest to the nuclear power industry because of the potential to predict the quality and effectiveness of an inspection. For example, modeling in nuclear nondestructive examina tion (NDE) has been used to help predict inspection reliability [1,2],

predict beam coverage [3], develop and test procedures [4-6], test focal laws [7-9], and inform wedge, probe, and mockup design [10-12].

Ultimately, the goal of modeling is to save time, money, and resources while maintaining or improving safety of the nuclear fleet. Of particular interest is the simulation of sound fields through challenging materials, such as austenitic welds and cast austenitic stainless steel (CASS)

[13-17]. These materials pose challenges for ultrasonic inspections because the coarse grain morphology partitions, redirects, and attenu ates the sound field, resulting in significant scatter, high noise levels, and poor sound field penetration [18]. Indeed, these challenges have prevented performance demonstration criteria for procedures and in spectors from being established in the U.S., so inspectors have not been able to perform effective inspections of CASS components [19]. Suc cessful ultrasonic models of CASS material may help guide the devel opment of inspection approaches.

Specimen material properties typically have a large effect on simu lation accuracy, so it is important to use a specimen model that most closely emulates the materials impact on the sound field. Precise specimen properties of grain size, shape, and orientation can be gener ated from electron backscatter diffraction (EBSD) measurements. For example, CASS specimen models created from EBSD scans by Chen et al.

[20] showed that sound field simulations using CASS models produced noise and signal distortion that were consistent with experimental re sults. They suggested that the accurate description of specimens is key for modeling, and that the EBSD approach to defining specimen models is effective. Nakahata et al. [21] used EBSD data to create elongated grain structures for simulating sound propagation through coarse-and

• Corresponding author.

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

Contents lists available at ScienceDirect Ultrasonics journal homepage: www.elsevier.com/locate/ultras https://doi.org/10.1016/j.ultras.2023.107157 Received 5 May 2023; Received in revised form 25 July 2023; Accepted 1 September 2023

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fine-grained CASS parallel to the grain elongation direction. They showed that at 2 MHz (the wavelength in steel at 2 MHz is approxi mately 3 mm), average grain diameters of 0.3 mm behave similarly to homogeneous material, whereas average grains of 1.1 mm cause sig nificant scatter and attenuation. The EBSD approach can allow for an accurate specimen model, but it requires destructive analysis, generates very large data files and, in the end, results in a model that is inherently only two-dimensional (2D). Three-dimensional (3D) models can be generated by using a serial sectioning approach, but this would be impractical. Every slice would need to be polished, and the minimum 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 not feasible for generating 3D models, models of large sections, or models of intact specimens.

It is impossible to nondestructively replicate the grain morphology (e.g., sizes, shapes, and crystalline orientations), so alternative ap proaches with simplified models must be used. Wan et al. [17] used specimen models with a regular square lattice and models based on a physical specimen to investigate the effects of grain size on sound attenuation in coarse-grained materials. They showed that different grain sizes resulted in different types of scattering (i.e., Rayleigh, sto chastic, or geometric), but that a few large grains in a fine-grain model can have a disproportionately large effect on the scatter at a given fre quency. They also showed that higher inhomogeneity of grain size dis tributions may introduce a stronger frequency dependence to attenuation. More realistic models have been created using Voronoi regions as grains. Voronoi regions can be generated rapidly in 2D or 3D with a variety of grain sizes. Van Pamel et al. [22] used 2D Voronoi models and a full matrix capture phased array ultrasonic approach with finite element modeling to study the effects of probe aperture size and array type on predicted signal-to-noise ratio. They concluded that a 2D array would be beneficial over a 1D array, and that pitch-catch probe configurations can be advantageous when trying to minimize noise.

Shivaprasad et al. [23] also used Voronoi models in multiple simulations to study the effects of grain size, orientation, and randomization on sound propagation. They showed that model-to-model variations in Voronoi region orientation and distribution can be overcome through multiple simulation trials. They performed convergence studies to determine the optimal number of trials needed.

CIVA (EXTENDE, Inc.) is a commercial software package that has been used by several different research groups to model ultrasonic propagation in coarse-grained materials. For example, noise and atten uation were simulated in coarse-grained models with CIVAs built-in 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 specimen configurations. Jenson et al. [25] showed that CIVA Voronoi regions result in significant beam scatter, but additional attenuation may be needed for simulation results to agree with experimental results.

In other work, sound beam propagation and flaw responses were modeled in CIVA using Voronoi models, and results were compared to experimental scans [26]. Results showed that through trial and error, simulation parameters can be adjusted so that simulated and experi mental results agree well. Additionally, Ribay et al. [27] simulated probability of detection calculations under various scenarios in CIVA.

Simulation results showed that the Voronoi regions reduced the proba bility of detection, as expected. Some work has been done to methodi cally assess commercially available modeling tools. For example, limited evaluations of strengths and weaknesses of CIVA have been conducted

[28-31].

Previous sound field modeling of coarse-grained structures was 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 models with two key differences. First, our models are based on realistic coarse-grained equiaxed and columnar CASS structures taken directly from laboratory specimens. Second, our models were executed in 3D to better replicate volumetric scattering. Our realistic structures were developed in 2D and extrapolated to 3D for sound field simulations in CIVA. Results of the sound field simulations were then compared to simulations using models generated from 3D Voronoi regions to deter mine which approach is the more accurate and more practical repre sentation of CASS. Simulation results were compared to experimental maps of sound fields transmitted through test blocks. CIVA software was used to perform the simulations.

2. Materials and methods The grain structures that would form the basis of our specimen models were obtained from cut, polished, and chemically etched CASS sections. One section was coarse-grained equiaxed (labeled AAD-3) and the other was coarse-grained columnar (labeled B-519C). Photographs of the sections are shown in Fig. 1, and the specimens are described by Crawford et al. [32]. AAD-3 came from a cast stainless steel pipe section (exact material is unknown) with an outer diameter of 965 mm and a wall thickness of 83 mm. B-519C came from a CF-8A (a nuclear-grade CASS alloy) pipe section with an outer diameter of 846 mm and a wall thickness of 60 mm. Both sections are centrifugally cast stainless steel.

Equiaxed grains have no preferred axis of elongation, and columnar grains are elongated radially. Coarse-grained is a qualitative desig nation. The designation between fine and coarse grains is typically made in terms of the ultrasonic wavelength, with coarse grains being approximately equal to or larger than the wavelength and fine grains being smaller. For reference, the ultrasonic wavelength in steel is approximately 6 mm at 1 MHz. Whatever the definition used, every specimen has a continuum of grain sizes between the largest and smallest grain, and the designation of whether a specimen is primarily fine-or coarse-grained is largely subjective.

EBSD can be used to precisely characterize grain boundaries and crystalline orientations, or Euler angles [16,20,21,33]. However, we chose to use an alternative approach for three reasons. First, the EBSD system at PNNL could not accommodate the size of the specimens.

Second, in our previous work with austenitic welds [16], the EBSD data files that we acquired from relatively small specimens challenged stan dard desktop computing capacity for processing the data and generating a CIVA model. Third, we wanted to develop a method that could be easily implemented for those without access to EBSD capabilities..

Therefore, the microstructure was captured with light photography, and Euler angles in CASS material were taken from Chen et al. [20]. The process of extracting the grain boundaries is described below.

2.1. CASS equiaxed model The grain boundaries were extracted from photographs taken with two different lighting angles. Due to directional reflectance of chemically-etched crystalline materials, reflected light intensity is dependent on the incident angle [34]. Thus, illuminating the specimen from different angles helped improve grain-to-grain contrast. A portable halogen lamp was used as the light source in an otherwise dark room, and an SLR camera was mounted on a tripod and operated with a wireless remote shutter control to prevent camera motion between shots. Two images were acquired on each specimen, with the light from the right and from the left. Image resolution was 20 MB, the highest setting of the camera. We processed the photos using ImageJ [35] to extract the grain boundaries; Fig. 2 illustrates the steps used. A similar but less-involved approach was described briefly by Ribay et al. [27] to measure grain size. Our process was as follows:

1. Color photographs (Panel A of Fig. 2) were split into separate RGB (red/green/blue) channels, resulting in three grey-scale images. The image histograms were evaluated to determine the image with the largest spread of grey-scale values (i.e., that with the greatest R.E. Jacob et al.

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contrast), and that image was retained (here it was the red channel, shown in Panel B).

2. The specimen outline was used to create a mask. The mask was applied to the grey-scale image (Panel C) to remove the background.

3. The masked image was filtered to enhance contrast, remove speckles and noise, and sharpen grain boundaries (Panel D). This was done in three steps with the Enhance Contrast filter, Median filter, and Un sharp Mask filter functions of ImageJ. Optimal filter parameters were determined by trial-and-error.

4. The window/level of the image was set to two different rangesone to emphasize bright grains and the other to emphasize dark grains. A binary (black and white) image was then made from each window/

level setting. Panel E shows the binary image with the dark grains emphasized. Additional window/level settings can be helpful if image contrast is poor.

5. A particle removal algorithm in ImageJ eliminated grains that were below a size threshold, typically about 1/10 of the wavelength that will be used for simulations. Panel E shows the binary image with particles already removed.

6. The edge-finding algorithm in ImageJ was used to outline the grain boundaries and create a partial grain skeleton (Panel F).

7. The process was repeated with both photographs until all the grains were outlined.

8. The partial skeleton images from the different window/level settings were combined to create a single image with all the grain outlines.

Some additional processing was done to clean up regions where edge outlines did not line up exactly and where grain boundary segments did not form an enclosed region. This included a final particle removal step and successive region dilate/erode steps.

Fig. 3 shows the final grain skeleton that was the basis of the specimen model.

CIVA requires that the specimen model comprise line segments and be in a CAD file format. However, because the grain outlines are generally not straight lines, converting the model directly into a CAD file would result in tens of thousands of individual line segments, most of which would only be one or two pixels long. This would be too many segments for CIVA to handle in a reasonable time. To simplify the model, we applied a line reduction algorithm to straighten curves in order to reduce the total number of line segments while substantially maintain ing the grain boundaries.

To test the algorithm, it was applied to a subsection of the grain skeleton with four different threshold values: 3, 6, 10, and 20 resulting in 2575, 1887, 1585, and 1342 line segments, respectively; see Fig. 4. As the threshold was increased, the number of segments needed to define the geometry decreased, but at the same time the representation of the grain boundaries lost fidelity. This was observed qualitatively through visual comparison.

The final specimen model (Fig. 5) was taken from the central section of Fig. 3. The model used the threshold value 6 and was 80 mm x 80 mm with 810 regions. Note that a key consideration in determining which threshold level to use was the number of line segments, because CIVAs capacity to handle complex geometries is limited. With the threshold levels tested, the number of line segments decreased with increasing threshold, but not rapidly. The average region size was about 7 mm2 with a standard deviation of 25 mm2 and the maximum grain size was about 430 mm2. This represents a large range of grain sizes, with a non-normal distribution heavily weighted by small grains. Each region in the specimen model was defined with one of ten different sets of Euler an 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 definitions were implemented with a CIVA XML file in a manner similar 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.

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to that described in [16]. The Euler angles were assigned quasi-randomly such that regions that shared a boundary would not have the same set of angles. If two neighboring regions did have the same Euler angles, the two regions would behave as one region in the simu lation and the grain boundary would be effectively ignored. To explore model variability, ten different versions of the specimen model were generated, each with a different random distribution of Euler angles (but the same grain boundaries and elastic constants). Fig. 5 shows an example of the Euler angle assignments for one of the models where each color represents a different set of angles.

The model was 2D, so the geometry was extruded by 200 mm in the orthogonal dimension (i.e., in and out of the page) to make a 3D model.

CIVA performs this operation automatically; the user enters the extru sion parameter. The probe was oriented parallel to the extruded 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.

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direction, and the sound field was simulated in a plane perpendicular to the extruded dimension.

2.2. Voronoi equiaxed model An alternative and much simpler model approach to creating a coarse-grained specimen model was also tried using Voronoi regions.

Models with grains derived from Voronoi regions were developed for comparison to the realistic-grain models. CIVA has a built-in capability of generating 3D Voronoi regions in certain model geometries. An aspect ratio can be defined in order to elongate the regions in one dimension.

The grains in AAD-3 were defined in a 2D plane and extruded in the orthogonal dimension to create a 3D model, so the same was done with the Voronoi specimen by giving the regions a high aspect ratio of 100.

For consistency, the same specimen dimensions and numbers of regions 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 grain skeleton (top) and the final specimen model (bottom). As with the equiaxed model in Fig. 5, different Euler angles are indicated by the 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 by 200 mm to form a 3D model. As with the equiaxed model, 10 versions 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.

2.4. Voronoi columnar model Columnar CASS models were also made with 3D Voronoi regions. In the Voronoi equiaxed model described above, grains were elongated to imitate the extrusion of the 2D realistic model. However, the CIVA-generated Voronoi regions can be elongated in only one dimension.

For the Voronoi columnar model, the elongation was used to make the grains columnar, which means they could not be elongated in the orthogonal dimension to imitate the extrusion of the 2D realistic model.

Thus, the columnar Voronoi grains were 3D while the specimen-based grains were extruded 2D. The Voronoi specimen was 100 mm x 80 Fig. 4. Subsection of AAD-3 grain skeleton with line reduction algorithms applied using different threshold levels.

Fig. 5. Example of how Euler angles were applied to AAD-3. Each color rep resents a different set of Euler angles. Assignments were made randomly with the condition that neighboring grains could not have the same Euler angles.

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mm x 60 mm and had 10,000 regions, so the average grain volume was 48 mm3. The Voronoi aspect ratio was 7. Unfortunately, since the columnar Voronoi regions are inherently 3D, the region sizes cannot be directly compared to those of the 2D realistic model. Fig. 8 shows a side-by-side comparison of a cross-sections of B519-C (left) and a columnar Voronoi model (right).

2.5. Simulation parameters Prior to running simulations in CIVA, it is important to determine the accuracy factor (AF) that will provide the best results in the minimum simulation time. AF is a CIVA setting analogous to the mesh density in 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 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.

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that will give results with minimum acceptable error. To determine the ideal AF, we ran initial AAD-3 and Voronoi simulations with AF = 1, 2, 4, 8, 16, 32, and 64 (note that AF = 64 did not complete for AAD-3 due to a user error). With low AF, some pixels were apparently not computed and were blank in the simulation result; this was especially noticeable in the AAD-3 simulations. The mean-square-error (MSE) was calculated pixel-by-pixel using the highest AF image as the baseline. An appro priate AF was determined when the MSE stopped decreasing (or, from a practical level, the MSE became < 1%). For the Voronoi simulations, MSE was 2.3% for AF = 1 and < 1% for AF 4. For the AAD-3 simu lations, MSE was 27% for AF = 1, 18% for AF = 8, and < 1% for AF = 16.

We selected an accuracy factor of 16 for all the remaining sound field simulations.

Ten beam simulations were performed on each model geometry using a CIVA accuracy factor of 16. V was set to 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). A 1 MHz, 5 x 10 element 2D-matrixed PA probe (1.1 MHz, 58% bandwidth at 6 dB) was used in transmit-receive-longitudinal configuration with a 45refraction anglethese parame ters were taken from those used by Crawford et al. (2014) so that simulation results could be compared to the experimental sound field maps. The element size was 3.5 mm x 3.5 mm with a 0.5 mm gap be tween elements in each direction; thus, the aperture was 39.5 mm in the primary direction and 19.5 in the secondary direction. The wedge di mensions, as entered into CIVA, were 22 mm front length, 22 mm back length, 44 mm width, and 8.76 mm height. The wedge material was Rexolite with a longitudinal sound speed of 2450 m/s and an angle of 17.856. To reduce computation time, a 2D sound field was computed through the specimen cross section at the focal point of the beam, and no mode conversions or internal reflections were simulated.

Fig. 9 shows CIVA screen captures of the top, side, and front views of the simulation setup. The extrusion direction is shown by the black arrow, and the computation plane is shown by the red arrow.

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.

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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2.6. Voronoi model variability To test how changes to Voronoi model grain structures affect echo amplitude, a simple specimen model with a side drilled hole was created in CIVA. The modeled specimen was 100 mm x 50 mm x 60 mm with V

= 5,900 m/s and V = 4% (V = 5,900 +/- 236 m/s). The hole was 3 mm diameter and 50 mm deep. The Voronoi geometry was randomized prior to each simulation by clicking the Voronoi diagram reset button in CIVA. An identical side drilled hole was used for calibration in a ho mogeneous, isotropic material. A 10 x 5 element, 1 MHz phased-array probe was modeled with a 45refraction angle focused at the side-drilled hole. Direct Mode (no specimen echoes) was used to reduce simulation time and because it is ideal for side drilled hole simulations.

Four scenarios were tested, with ten runs of each. The first scenario used 2,800 equiaxed Voronoi regions to model coarse-grained equiaxed CASS, the average region size equating to a 5.9 mm diameter sphere of equivalent volume, or about one wavelength. The second scenario was with 22,000 equiaxed regions, equating to about one half wavelength.

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

2.7. Beam partitioning metric Sound field partitioning is the sectioning of the beam by the pre dominant orientation of the CASS grain structure. Crawford et al. [32]

observed that beam partitioning is a signature of columnar grains and developed a metric to compare empirical sound fields through different materials. The metric was calculated by acquiring horizontal and ver tical beam profiles and counting every instance that the signal intensity exceeded a threshold as a crossing. Fig. 9 shows an example of the crossings from a horizontal and vertical line profile through a columnar Voronoi beam simulation. Panel A shows the image with a median filter applied; the filter reduces pixel-to-pixel fluctuations while preserving edges and boundaries. Panels B and C are the image profiles through the horizontal and vertical lines in A, respectively. The black lines in B and C represent the threshold level (in this case, 70% of the maximum signal),

and the red circles show the rising-edge crossings. The process was repeated for every horizontal line through the image, and the sum of all crossings was taken. Similarly, the sum of all vertical crossings was counted. The ratio of horizontal to vertical crossings is the crossing ratio, or partitioning metric. Beam partitioning from columnar grains should result in more horizontal crossings than vertical crossings, resulting in a ratio > 1. For equiaxed grains, there should be no preferred direction of beam segmentation, and the ratio should be 1. We applied the metric to compare the Voronoi simulations, the B519-C simulations, and the empirical beam maps.

3. Results 3.1. Voronoi model variability 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 the calibration signal. The box indicates the upper and lower data quartiles, and the bars show the lowest and highest extents. The hori zontal line within the box is the median, and the x is the mean. The 2,800 grain equiaxed and 2,800 grain columnar (Eqx-2,800 and Col-2,800 in the figure) scenarios had the lowest average signal reduction 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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(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.

3.3. Columnar model 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).

Simulation results were qualitatively compared to previously-acquired experimental sound field maps [32], as shown in Fig. 16. The experimental sound fields show partitioning along the horizontal axis, consistent with the orientation of the grains. The Voronoi simulation 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.

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

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4. Discussion We showed a method of creating a CASS specimen model from a polished and chemically etched specimen that has visible grains. Spec imen photographs captured the grain structure, and multiple photos with a light source from different directions helped differentiate the grains for image processing. Unfortunately, the photography method of creating a model did not capture small grains well. Previous efforts to capture grain boundaries in a specimen with finer grains and an austenitic weld failed due to the image filtering and edge-finding algo rithms having slight but significant effects on the grain boundaries [15].

Thus, the photography method was not precise enough to define small grains without higher resolution images. We note that in a coarse-grained model, the smallest grains can be removed with little conse quence, as they contribute least to the sound field scatter [17]. The problem of rendering small grains might be rectified by using higher resolution photographs or acquiring magnified images and stitching them together as a mosaic. We did not explore these alternatives. In previous work, we used high-resolution EBSD to characterize the grains in an austenitic weld [16]. However, because of sample size limitations and data file sizes, this approach was not practical for the considerably larger CASS specimens in this study.

Two 2D models of coarse-grained equiaxed CASS (Fig. 5) and columnar CASS (Fig. 7) were created. To differentiate the grains and provide a mechanism for sound field scatter, Euler angles were assigned to each region. The models were imported into the modeling and simulation platform CIVA for sound field simulations, examples of which are shown in Fig. 13 and Fig. 15. The models show beam scatter and attenuation, attributes that are observed experimentally in CASS.

For the equiaxed scenario, the Voronoi and realistic models both showed similar scatter patterns; however, the realistic model appeared to attenuate the beam too much whereas the Voronoi model with V = 6%

agreed well with experiment. For the columnar scenario, the Voronoi model showed beam partitioning scatter patterns that agreed better with experiment than those of the realistic model. Beam partitioning from the V = 4% (V = 5,900 +/- 236 m/s) and V = 6% (V = 5,900 +/- 354 m/s)

Voronoi models, as measured by the beam partitioning metric, agreed well with experimental results. There was less beam partitioning from the realistic model. The beam partitioning may have been affected by 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.

Table 1 Signal intensities of simulated and experimental sound fields as a fraction of the respective control scenarios.

Scenario Fractional Signal Average of 4% Voronoi simulations (V = 5,900 +/- 236 m/s) 0.43 Average of 6% Voronoi simulations (V = 5,900 +/- 354 m/s) 0.25 Average of 8% Voronoi simulations (V = 5,900 +/- 472 m/s) 0.13 Average of AAD-3 simulations 0.15 Experimental data from AAD-3 0.24 R.E. Jacob et al.

Ultrasonics 136 (2024) 107157 11 the model dimensionality; in the columnar scenario the Voronoi model was 3D while the realistic model was 2D.

The partitioning metrics of AAD-3 and B519-C simulations did not differ from each other (see Table 2). The models were not ideal repre sentations of the different grain structures because they were inherently 2D and were extruded in the third dimension. For AAD-3 (simulated),

the metric is higher than empirical, and for B519-C (simulated) it is lower than empirical. Notably, the Voronoi columnar simulations and the B519-C empirical results agree. The partitioning metric of the Vor onoi models was largely independent of V, so the optimal value of V should be determined based on other factors, such as signal intensity or scatter. The V was not optimized in this study, but an optimization process was outlined in [15].

Signal response variations of about a factor of 2 were observed by randomizing a Voronoi model (see Fig. 11). Grain sizes and shapes in Voronoi models are comparatively uniform, as shown in Fig. 6 (although the uniformity can vary depending on the Voronoi regularity set by a distance constraint between Voronoi region nuclei [23]). Thus, random changes in grain size and shape from one Voronoi model to the next are expected to be relatively small compared to microstructural variations within a laboratory specimen. For example, Fig. 12 shows three serial sections of AAD-3, each 6 mm thick. There is some consistency in the overall grain patterns, but the size, shape, and orientation of grains can change substantially from one slice to the next. Additional examples are shown in Chapter 8 of [18], where we show seven polished and etched CASS specimens, each with different grain morphology. This is relevant to CASS modeling because if randomizing a relatively uniform Voronoi model changes the signal response by a factor of 2, then randomizing a realistic modelor simply selecting a different specimen to create a model fromshould have a much stronger effect. Fig. 14 illustrates the point: the two sound field maps were acquired after removal of one of the 6 mm slices in Fig. 12, and each sound field is unique in appearance in spite of being from nearly the same location of the same specimen.

Therefore, it is unfeasible to use a single specimen model to accurately simulate an empirical sound field map or flaw response in CASS mate rial. Indeed, the authors of [27] concluded that microstructural 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.

Table 2 Comparison of partitioning metric.

Case Mean Partitioning Metric +/- SD Voronoi columnar V = 4%

(V = 5,900 +/- 236 m/s) 2.3 +/- 0.05 Voronoi columnar V = 6%

(V = 5,900 +/- 354 m/s) 2.4 +/- 0.06 Voronoi columnar V = 8%

(V = 5,900 +/- 472 m/s) 2.2 +/- 0.05 B519-C (simulated) 2.0 +/- 0.02 B519-C (from [32])(a) 2.4 +/- 0.04 AAD-3 (simulated) 2.0 +/- 0.04 AAD-3 (from [32])(a) 1.4 +/- 0.03 R.E. Jacob et al.

Ultrasonics 136 (2024) 107157 12 variations in CASS are the most influential factors affecting the simu lation outcomes. CASS models may be considered representative of general effects of grain structures on simulated sound fields and signal responses, but simulation results that exactly represent reality should not be expected. In practice, the microstructural randomness and unpredictability can have important impacts on an ultrasonic inspec tion. For example, in Chapter 8 of [18] we showed that microstructural 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 probe position.

Sectioning a specimen is the only method of acquiring the true grain structure. Accurate 3D models would require many thin slices in order to capture the microstructural variations that would otherwise be lost to interpolation. To wit, the 6 mm slice thickness in Fig. 12 is about the same as the wavelength at 1 MHz; slices approximately ten times thinner would be needed to obtain the required fidelity for a 3D model.

Furthermore, creating models using the demonstrated method (cutting, polishing, etching, etc.) is impractical, time consuming, and expensive.

On the other hand, sound field simulations show that Voronoi regions provide as good or better simulation results than 2D realistic models.

Voronoi regions can be implemented rapidly in CIVA with little addi tional effort. Note that there are some limitations in CIVA for using Voronoi regions. Users can apply Voronoi regions only to simple spec imen models. For example, it is not possible to add Voronoi regions to a weld model to simulate dissimilar metal welds or CASS-to-CASS welds.

Such a weld model would have to be created manually, such as shown in

[15].

For complex grain structures in custom-built models, finite element modeling may have benefits over the ray tracing approach of CIVA.

Complex grain structures increase CIVA simulation time significantly, and the high frequency approximation that CIVA uses may cause inac curate results if the typical grain size is much smaller than the wave length. These problems can be avoided in finite element modeling. For example, in [36], using an identical 2D austenitic weld model in CIVA and a finite element platform, we showed that the latter generated a more realistic sound field. Although we have not tested it, the realistic 2D coarse-grained specimen model developed herein may have advan tages over a 2D Voronoi specimen model when simulating in a finite element modeling platform.

5. Conclusions We demonstrated an approach to creating realistic models of coarse-grained microstructures from polished and chemically etched CASS sections. We compared the models performance in simulations of ul trasonic sound fields to that of models generated using Voronoi regions.

Results showed that both approaches resulted in sound field scatter that was comparable to that observed experimentally. However, attenuation and beam partitioning observed in the Voronoi models better agreed with experimental results. Voronoi models were also easier to generate, as CIVA has a built-in function for creating 3D coarse-grained structures.

We also showed that random variations in Voronoi grain morphology resulted in about a factor of two variation in echo amplitude. Therefore, because of grain morphology randomness from specimen-to-specimen or even within a single specimen, CASS models should be considered representative of coarse-grained morphologies in general and not of a specific scenario. To obtain meaningful results from CASS models, it may be necessary to determine probabilistic outcomes from ensembles of simulations using specimen model variations.

Funding This work was supported by the US Nuclear Regulatory Commission (NRC) Office of Research (RES) under Contract NRC-HQ-60-17-D-0010 (Carol Nove, NRC Contracting Officer Representative).

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability Data will be made available on request.

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