Towards standardisation of average grain size measurement of additively manufactured microstructures using EBSD

This paper proposes a new standard for measuring average grain size in additively manufactured materials based on an interlaboratory comparison study, demonstrating its suitability and limitations across various Ni and Al components using EBSD.

The Gist

Imagine you are trying to describe the size of a crowd of people at a concert. In a normal crowd, everyone is roughly the same height, so you could just say, "The average person is 5 feet 9 inches." But in Additive Manufacturing (3D printing), the "crowd" (the metal grains) is chaotic. Some grains are tiny specks, others are massive skyscrapers, and they are stretched out like long, thin noodles rather than round balls.

This paper is about creating a standard rulebook for measuring the "average size" of these chaotic metal crowds using a special camera called EBSD (Electron Backscatter Diffraction). Without a standard rulebook, different scientists were using different rulers and different math, leading to confusing and conflicting results.

Here is the breakdown of their findings using simple analogies:

1. The Problem: Everyone Measuring Differently

Previously, if two scientists looked at the same 3D-printed metal part, they might report completely different "average grain sizes."

• The Issue: Some scientists threw away the tiny grains (like ignoring the toddlers in a crowd), while others counted them. Some used a "number average" (counting heads), while others used an "area average" (counting how much floor space they take up).
• The Result: It was like one person saying the crowd is small because they only counted the kids, and another saying it's huge because they counted the space the adults occupy. This made it impossible to compare materials or write patent claims (legal descriptions of the metal).

2. The Solution: A New "Gold Standard"

The authors tested various methods across different software and materials (Nickel and Aluminum alloys) to find the most reliable way to measure. They propose a new standard with three main pillars:

A. The Best Ruler: "Maximum Feret Diameter" (MFD)

Instead of trying to fit a perfect circle around a weirdly shaped grain (which is like trying to fit a round peg in a square hole), they suggest measuring the longest straight line you can draw across the grain.

• Analogy: Imagine a stretched-out piece of dough. Instead of asking "What is the diameter of a circle this big?", just measure the length of the dough from end to end. This captures the true "stretch" of the grain without making bad guesses about its shape.

B. The Best Math: The "Median" (The Middle Child)

Most people use the "Average" (Mean), but in 3D printing, the grain sizes are so uneven that the average gets skewed by a few giant grains.

• The Fix: They recommend using the Median.
• Analogy: If you line up 100 grains from smallest to largest, the Median is the one right in the middle (the 50th grain). This is much more stable. If you accidentally miss a few tiny grains or include a few huge ones, the "middle" grain doesn't move much. It's a "conservative" number that tells you what a typical grain looks like without being tricked by outliers.

C. The Best Picture: The "Cumulative Histogram"

Instead of a standard bar chart, they suggest a "cumulative" graph.

• Analogy: Imagine a staircase. Each step up represents a percentage of the total area covered by grains of that size or smaller.
  • If the staircase is smooth, you have a good measurement.
  • If the staircase has giant, jagged jumps (like a cliff), it means your camera view was too small, and you missed the big grains. This graph instantly tells you if your data is trustworthy.

3. The Rules of the Game (The "Do's and Don'ts")

To get a reliable result, the paper sets strict rules for the "photographer" (the scientist):

• Don't Clean Too Much: Sometimes, the camera misses a few spots (unindexed points). You can fix a few, but if you clean up too much, you might accidentally glue two separate grains together or break a big one apart. The rule is: Clean up less than 5% of the map.
• Don't Cut the Edges: If a grain is cut off by the edge of your photo, don't measure it. It's like trying to guess the size of a person when you can only see their arm. However, because big grains are more likely to get cut off, the math needs to account for this bias.
• Zoom Out Enough: Your camera view (Field of View) needs to be big enough to catch at least 20 grains across. If you zoom in too tight, you might only see one giant grain and think the whole metal is made of giants.
• Report the Settings: Because 3D-printed metals have "sub-grains" (tiny internal structures), you must always report exactly how you took the picture (the step size and the angle threshold). Changing these settings changes the result, so you can't compare apples to oranges.

4. The Result: A Reliable Measurement

By following these rules, the authors found they can measure the grain size of 3D-printed metals with an uncertainty of about 20%.

• Why this matters: In the world of patents and engineering, you need to know if two metals are truly different. If the measurement tool is shaky, you can't prove your invention is unique. This new standard provides a sturdy, reliable ruler that everyone can use to compare 3D-printed parts, regardless of which software or machine they use.

Summary

The paper says: "Stop guessing and stop using different rules. To measure the size of 3D-printed metal grains, measure the longest length (MFD), find the middle value (Median), use a cumulative graph to check for errors, and make sure your camera view is wide enough. If you do this, you get a result that is fair, repeatable, and legally defensible."

Technical Summary

Technical Summary: Standardisation of Average Grain Size Measurement in Additively Manufactured Microstructures using EBSD

Problem Statement
Additively manufactured (AM) alloys exhibit heterogeneous microstructures characterized by broad grain size distributions, highly anisotropic shapes, and non-convex geometries. Unlike traditional metallic materials, AM components often possess complex geometries and porosity that influence local microstructures. Currently, there is no Electron Backscatter Diffraction (EBSD)-based standard suitable for measuring average grain size in typical AM materials. Existing standards, such as ASTM E112 (optical methods), ASTM E2627, and ISO 13067 (EBSD methods), were not designed for the specific complexities of AM microstructures. Consequently, grain size measurements are highly sensitive to operator choices regarding data cleaning, grain reconstruction, and statistical analysis, leading to significant variability that limits the utility of these measurements in patent claims and alloy grade specifications.

Methodology
The study employs an interlaboratory comparison approach to evaluate current practices and propose a standardized workflow. The methodology involves:

1. Software-Agnostic Testing: Grain reconstruction and size metrics were tested across major commercial and open-source software packages (AZtecCrystal, OIM Analysis, and MTEX) to ensure consistency.
2. Parameter Sensitivity Analysis: The authors systematically varied EBSD map step sizes, grain boundary threshold angles, and data cleaning routines (e.g., removing wild spikes, neighbor orientation correlation) to quantify their impact on measured grain sizes.
3. Statistical Evaluation: Different grain size metrics (equivalent circle diameter, Feret diameters) and summary statistics (arithmetic mean, geometric mean, percentiles) were compared. Special attention was paid to the weighting methods (number-weighted vs. area-weighted) and the treatment of excluded grains (small grains and map-edge grains).
4. Uncertainty Quantification: Uncertainty components were modeled for three primary sources:
   • Data Cleaning: Modeled as Type B uncertainty (rectangular distribution) based on the difference between no cleaning and maximum allowable cleaning.
   • Histogram Binning: Modeled as Type B uncertainty based on bin half-widths.
   • Microstructure Sampling: Modeled as Type A uncertainty using bootstrap analysis of 30 subsamples to determine the effect of Field of View (FoV) size.
5. Case Studies: The proposed methods were applied to various AM components, including Hastelloy-X (Ni-base superalloy) and AlSi10Mg (Aluminum alloy), covering large solid parts, lattice structures, and components with varying indexing rates and porosities.

Key Contributions and Results
The paper identifies several critical issues with current practices and proposes specific updates:

• Reconstruction and Cleaning: Grain reconstruction results are consistent across software when no cleaning is performed. However, data cleaning introduces significant variability. Number-weighted metrics are highly sensitive to cleaning (varying by ±26–100%), whereas area-weighted metrics are far more robust (±0.2–10%). The study recommends limiting map orientation changes to ≤5% (per ISO 13067) and treating the cleaning uncertainty explicitly.
• Metric Selection: The Maximum Feret Diameter (MFD) is identified as the most suitable metric for AM microstructures, as it effectively captures the elongated nature of grains along the build direction without the shape assumptions required by equivalent circle diameters.
• Statistical Representation: The arithmetic mean is deemed inappropriate due to the non-Gaussian nature of grain size distributions. The indexed-area-weighted median is proposed as the primary statistic. This metric is read from a cumulative histogram and is less sensitive to the exclusion of small grains or map-edge grains compared to conventional means.
• Handling Excluded Grains: The study demonstrates that excluding small grains or edge grains without correction leads to underestimation of grain size. A method is proposed where the area fraction of excluded small grains is appended to the low-end of the cumulative histogram, and edge grains are excluded but accounted for in the total indexed area.
• Sampling Requirements: Bootstrap analysis reveals that a Field of View (FoV) of at least 20 times the median grain length is required to achieve a sampling uncertainty of approximately 10%. Smaller FoVs lead to high stochasticity and overestimation of grain size due to the dominance of single large grains.
• Step Size and Thresholds: In AM microstructures with sub-grain structures, step size and boundary threshold angles are interdependent. The paper emphasizes that grain size must always be reported alongside the specific step size and threshold angle used, as these parameters significantly alter the measured values.

Significance and Claims
The paper claims to provide a robust, standardized procedure for measuring average grain size in AM materials, addressing the lack of suitable standards for these complex microstructures. The proposed workflow, centered on the indexed-area-fraction-weighted median MFD and a cumulative histogram visualization, offers several advantages:

• Robustness: It is less sensitive to operator choices regarding data cleaning and small grain exclusion.
• Transparency: The cumulative histogram allows for immediate visual identification of sampling issues (e.g., small FoVs resulting in discrete jumps or undefined medians).
• Uncertainty Management: By explicitly quantifying uncertainties from sampling, cleaning, and binning, the method achieves a relative combined expanded uncertainty (k=2) of approximately 20%.

The authors conclude that while the procedure significantly improves consistency, the total uncertainty is dominated by random sampling uncertainty. Therefore, for components with complex geometries (such as lattice struts where local thermal history varies), multiple similar samples may be required to obtain a statistically significant average. The work aims to facilitate more reliable grain size reporting for patent claims and material specifications in the additive manufacturing sector.