This article is a quick summary of a publication in Acta Materialia by Mondal et al. There is more detail than the abstract, and less detail that the full paper. 

Introduction (skip if familiar with L-PBF)

This paper attempts to demonstrate the effectiveness of physics informed machine learning in predicting crack formation (or the lack there of) in Laser Powder Bed Fusion, which is a laser-based metal 3D printing process. In this process, a laser beam selectively melts regions of a bed of metal powder, and if the melting and subsequent cooling happens as desired, then it results in a fused metal component.

For those unfamiliar with L-PBF, here’s is a 1 minute introduction:

What Is Laser Powder Bed Fusion?

As you can imagine, the point where the laser beam meets the powder bed is the critical region. That’s where the melt-pool is created, which is highly transient and it’s effective formation, movement and subsequent cooling defines the success of the final part.

Here is a nice visual simulation of the powder bed and melt-pool formation.

Simulation of melt-pool in L-PBF

Idea and approach.

L-PBF components often have cracking issues. And there is some data in exisiting literature that reports whether or not a certain part, made from a certain material at certain machine settings has cracks. This paper turns this into a classification problem that can be solved by machine learning. Except one issue. There are a lot of features. Each material reported is a cluster of features and each machine setting is also a feature. For this paper training dataset spans 3 different materials (2024 Al, 6061 Al and AlSi10Mg). According to the authors, each material has 12 thermo-physical properties that could affect cracking. The machine settings (i.e. process parameters) are laser power, speed, Hatch spacing, Layer thickness, Beam radius, Preheat Temperature. This brings the total feature count to 17. That’s a lot of features, specially considering the number of data-points is only 102. A training dataset to classify crack vs. no crack using a 102 x 17 dataset is not the best bet. It’s the infamous curse of dimensionality. What if we could reduce the feature space from 17 to 4 and preserve most of the information? Now the training dataset would be 102 x 4 to predict between two classes. Much, much better. And that’s exactly what the authors do by using a heat-transfer fluid flow model to get 4 mechanistic variables which affect cracking.

The 4 physics based features are:

1. Cooling rate during solidification
2. Ratio : temperature gradient/solidification growth rate
3. Solidification stress
4. Ratio : Vulnerable/relaxation times

Armed with a ‘leaner’ dataset, lightweight machine learning (ML) models like Decision Tree, Logistic Regression, Support Vector Machine (SVM) and Linear Regression were tested to predict whether a crack can be expected or not.

Results and Discussion

Out of the 4 ML models tried, SVM gave the best accuracy (~90%), but the 4 features do not allow the visualization of the hyperplane that divides the search space. The authors therefore favor the linear regression solution, which not only has a good accuracy in predicting which cases will lead to cracks (~84%), but also leads to a user friendly equation for cracking susceptibility of a part. Cracking Susceptibility Index or CSI is defined as:

CSI = 0.182(solidification stress) + 0.135(ratio of vulnerable to relaxation time) + 0.014 (ratio of temperature gradient to solidification growth rate) - ((1.1e-8)*(cooling rate))-0.85

Concluding remarks

• Physics based approaches not only ease computation burden for ML models by helping reduce feature space, but also help improve our understanding of the complex process physics of L-PBF process.
• The reduction of feature space reduces our reliance on black box machine learning approaches that are heavily reliant of large datasets and computation power.
• Solidification stress was found as the most influential factor in determining whether a part will be cracked or not.

References

B. Mondal, T. Mukherjee, T. DebRoy, Crack free metal printing using physics informed machine learning, Acta Materialia, Volume 226, 2022, 117612, ISSN 1359-6454, https://doi.org/10.1016/j.actamat.2021.117612.

If this triggers the need to read the paper in full detail:

• Link to the paper
• Link to the video explanation by the authors