Metals are made of randomly oriented crystals at the microscopic-length scale. The alignment of the crystal faces creates an infinite number of configurations and complex patterns, making simulations of specific patterns difficult and expensive. Aerospace engineers in The Grainger College of Engineering, University of Illinois Urbana-Champaign created a model to capture the metal material’s response to stress and predict failure hotspots at a scale equivalent in pixels to over 600 million dots per inch.

“We developed a computer vision-based machine learning algorithm to output strain fields from computational simulations, predicting the mechanical response of polycrystalline metals using pictures of how the crystals are oriented at the microscopic scale,” said Huck Beng Chew’s Ph.D. student, William Noh, who earned his B.S. in aerospace engineering in 2020 from Illinois.

Although mathematical equations run the model that identifies spatial trends within the crystal images, it began with real physics-based insights in grain boundaries and material failure from experimental measurements performed by Renato Vieira, a 2021 Ph.D. graduate from John Lambros’ group and currently a professor of mechanical engineering at Pontifícia Universidade Católica do Rio de Janeiro in Brazil.

“The experimental data were a very important point of reference for understanding what image data we could use to teach the machine-learning algorithm to predict strain fields. Machine learning is not like human eyes and does not need to see in traditional RGB-colored images. What we wanted it to see is how the crystals are oriented and which crystals may fail first.”

As a computational cost-saver, Noh said they wanted to use the least amount of data possible but still properly predict strain fields.

“We were able to use just the crystal orientation plus how much the material was loaded. We show that the machine-learning algorithm is very capable of learning all this heterogeneous material response at the microstructure with only a small amount of input information.”

Chew said failure is concentrated at locations where there are very high strains from the load exerted on the structure.

“The algorithm predicted the shape and location of these hotspots and can eventually be used in designing the microstructure of a material so as to avoid the generation of hotspots.”

Noh said understanding the materials science aspects of crystal orientations posed a significant challenge for him at the beginning of the project.

“There are different conventions used to describe crystal orientations,” he said. “That’s not something we learn in our undergrad courses as it is a materials-related field.”

He said the convention of Euler angles—like what pilots use with pitch, roll and yaw—didn’t work for this problem.

“We wound up using rotation matrix components that describe crystal orientation by how the crystal axes are oriented to a reference axis. Changing that made the problem work.”

At the start of the project, Noh was also very new to machine learning and the best practices for training the models.

“Due to the black box nature of machine learning in general, if something doesn't work you can’t always explain where it went wrong. I realized I had to start with what works and what doesn’t and then only change one thing at a time before running it again. That’s something Professor Chew hammered into me. I just had to keep making mistakes and building up a repertoire of experience.”

He said understanding the limitations of the machine learning model came into play when determining when it was appropriate to use the model, that is, the applicable range of crystal sizes and shapes. If they trained it on a single distribution, would it be able to generalize to different distributions? At what size distribution would the predictions deviate from trained performance so that we know when to use the model confidently?

“We tried a variety of grain size distributions and show that for smaller grain sizes, we can attain very good predictions. For large grain sizes, we got large deviations. We show that our model can capture 80 percent of the hotspots.

“We also show that you can take our model that's been trained on one material and train it again to predict the strain fields of another material by changing the material parameters in the physics—all while using an order of magnitude smaller data set,” Noh said.

According to Chew, the ultimate goal for this work is to design stronger crystal microstructures.

“With this tool, we can know what combination of orientations to avoid and, given a certain microstructure, predict where a crack will initiate, which is very important in aircraft design and structural health monitoring. You need to know where to look, otherwise, it's a needle in a haystack. When you know where the hotspots are, you can then make corrections to a design.”

This work was supported by a grant from the National Science Foundation.

The study, “Microscale strain field predictions from grain microstructure of polycrystalline metals using fully convolutional networks,” by William Noh, Renato Bichara Vieira, John Lambros and Huck Beng Chew, is published in the International Journal of Solids and Structures. DOI:10.1016/j.ijsolstr.2025.113801