A look at Deep Learning for predicting strain and displacement fields in material grains with cracking voids, using computer vision and Digital Image Correlation

Materials manufacturing processes have complex material flow and boundary conditions. Furthermore, quality of the process is critical to component design and the resulting functional performance of the components. Accounting for displacement and strain fields experienced by material grains is of utmost importance to ensuring high quality materials processing.

Digital Image Correlation (DIC) is an established computer vision technique with industrial applications in metrology, semiconductor inspection, materials tensile testing, and more. It has been widely applied in experimental solid mechanics to accurately measure two-dimensional (2D) and three-dimensional (3D) displacement and strain fields in various material systems, including engineering metals, and polymers.

The work discussed in this project is a continuation of the efforts of Professor Ping Guo and Ru Yang at Northwestern University and can be read about here [1]: https://doi.org/10.1016/j.jmatprotec.2021.117474 .

Technical Overview

Current Industry Standard DIC method

Limitations of industry standard is that it requires data from real material tensile testing and this becomes difficult to scale for generality of the solution. However, the science of mechanical and materials engineering and finite element analysis is an established science and can be used as a robust groundtruth to inform a deep learning approach to the same problem.

Proposed Deep Learning with DIC

Extension of Synthetic Dataset Generation Capabilities

Existing training and testing datasets of tensile testing experiments quickly become the bottleneck to scale the development of a displacement & strain field prediction method using deep learning. This project extends the capability of the synthetic image dateset generation algorithm outlined in the deepDIC paper with the addition of randomly rotated speckles, user input of speckle density, randomized generation and propagation of cracks simulating fatigue and failure in the material, and severe deformation of the speckle pattern. All of these added features seek to improve the robustness of the deepDIC models to identify a material’s dynamic condition undergoing a tensile test from start to finish.

Generation of baseline speckle patterned image:

The speckle generation is replicated using methods as described in the paper [1] and reproduced below. The image samples start as a 512×512 empty image array and is filled in with randomly generated elliptical geometry based on pre-selected parameters to satisfy the variables in the standard equation for an ellipse:

While x and y are indices in the image array, h, k, a, and b are randomly generated using a uniform distribution. Further, the angle of ellipse orientation θ, between major axis and the global coordinate system is also generated from a uniform random distribution.

Forming and propagating a crack into the simulated material grain:

As similarly done to generate ellipses geometry with parameter randomly generated, we have modeled the “cracking” of a material as a triangular void forming from the edge of the image and propagating toward the center of the image. To do this, we generate the triangular geometry as two lines with slope m1, m2 originating at the edge of the image array and interesting at some point L distance into the image. Any image pixels contained within the intersecting boundaries are turned to a black pixel, representing a void. The triangular crack voids are generated before image deformation is applied.

Warping of speckle image to simulate stress and strain in the material grain

A 2D displacement field is generated using equations (1) and (2) below to simulate material deformation in translation, rotation, stretch/compression, shear, and localized deformation formulated with 2D Gaussian functions [1]. The coefficients in the equations below are generated using a uniform random distribution.

The resulting warpage in the speckle image looks as above and final image outputs are saved as 256×256 PNG files. Deformation can be seen in both X & Y directions. Gif is animated from image before and after displacement field is applied

Results and discussion

I: With no crack propagated into material grain

As shown in the figure below, the predicted displacement field (u,v) corresponding to (x,y) directions are as expected (seen in the groundtruth fields (u,v)). We also see mean-squared error training loss fall dramatically and converge toward zero within 20 epochs. The autoencoder model performs very well on images without cracks; however, it has some problems with images that have cracks as we will see below.

II: With crack propagated into material grain

The model’s inference definitely picks up where the crack void is but has a hard time correctly identifying the shape of the void. However, we still see an acceptable training loss convergence toward 0.

III: Real data from tensile testing EXPERIMENT

The inference of the model done on a series of real data from a tensile testing experiment shows some expected and unexpected behaviors. We expected the deformation to be negligible in the X direction and we can see in this correctly predicted in the u field; note the scale of the plot as indicated by the colorbar is in the scale of 10e-4 pixels. This is negligible for us in the material deformation context.

Furthermore, we do see voids forming along the edges of the material sample but we note that they are elliptical in shape with a long gradual curve. As discussed earlier, when designing the synthetic dataset with crack formation, we chose to implement triangular cracking and this may be unsuitable for testing against real-world tensile data. Triangular cracking may be more indicative of material samples that are already experiencing fracture rather than ones that are still in the yielding zone.

Lastly, we observe that the v field prediction does not accord to intuition. We note that there is high deformation in the y band region 50+/- 20pixels and then again after 150 pixels while minimal deformation for most of the length of the edges. These two bands of high deformation are inconsistent with what we expect, given the warped image shown below. At the very least, we should see some high deformation areas along the left and right edges of the prediction field as shown in the groundtruth image.

Conclusion and Future Work

The Deep DIC work on synthetic speckle image dataset that simulates stress and strain of material grain has shown that training an autoencoder ML model on a synthetic dataset can result in robust predictions on a tensile dataset. Furthermore, we see that the model can begin to recognize the formation of triangular cracking voids in the speckle pattern despite the geometry of the void being randomly generated and sparsely present throughout the dataset. However, there is work to be done when tested on real tensile data with voids.

Intuition at first glance suggests the triangular geometry may not be the best approach to modeling the crack voids as we see in one of the tensile samples above, rather, a ellipse geometry should be used before the cracking propagates. It is seen later in the tensile images that the crack does form at the center of the material sample in the form of a thin sharp line until complete failure. Further, the ellipse void should be present on both left/right edges of the synthetic image. Lastly, the prediction of the void geometry being slightly incorrect shape, mentioned above, will likely be rectified with training the model on a larger dataset.

Future work on this project will align the currently separated model inferences of small deformations, to severe deformations, to void generation, and finally complete material failure as an end-to-end predictive algorithm packaged into one ML model. Currently, they are separate and sequential in use.