Phase transformation modeling in Heat Treatment using UKF

Welcome to the 9th edition of my newsletter. 2 editions back we delved on how we can use Kalman filters in Steel. However there are limitation of it and therefore we are blessed with many other filters, each with its own pros and cons. One of the many filters available is the Unscented Kalman Filter (UKF).

This UKF is an extremely powerful tool for state examinations in systems where the dynamics are highly on linear. In steel processes, the UKF can play a crucial role in optimizing operations, improving quality, and reducing waste .

In Feb 2024, when I was in Barca for an Alumni meet, I had met my friend who is now a co-founder of a material science lab dealing with the nuances of phase transformation. At lunch we had an exciting discussion on the challenges of phase transformation modeling in Heat treatment. I listened to his problem statement and that was when I decided to use ML models to try and figure it out. This newsletter is on the same. It took some time for the model build, analysis and training, the result was definitely worth this wait.

Explaining the set up in brief,

1)??? Process model definition

a.???? Governing equations- Heat conduction equation, Coupled equation just to check if stress and strain affect the transformation behavior, JMAK equation to describe the phase transformation Kinetics (remember Callisto ??)

b.???? Input- Heating and cooling rates, chemical composition

c.???? Output- Temperature, phase fractions, Hardness, residual stresses,

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2)??? Initial data for Model Calibration

a.???? Running experiments- conduction of controlled heat treatment cycles

b.???? Measurement of temperature, dimensional changes and phase fractions.

c.???? Build Baseline Models- Fitting the phase transformation kinetics (JMAK)

d.???? Determining material specific constants- rate constants

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3)??? Designing the UKF process (brief)

a.???? State Vector

b.???? Process Model

c.???? Measurement Model

(Note- Not drilling down deeper on this – feedback from previous editions :) , however happy to discuss technically in case needed)

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4)??? Implementation of UKF

a.???? Initialization

b.???? Prediction

c.???? Updation

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Actual Scenario

Objective:

·?????? Ensure proper martensitic transformation during quenching.

·?????? Accurately track phase fractions in real-time using UKF.

·?????? Improve hardness consistency after treatment.

·?????? Steel Grade taken- AISI 1045 (Medium Carbon steel)

·?????? Heat treatment- ‘Austenization’ at 850 deg C followed by quenching to room temperature.

Experimental Set up:

1)??? Temperature Profile

a.???? Heating to 850 deg C in 5 mins

b.???? Holding at 850 deg C for 10 mins

c.???? Cooling to room temperature in 2 mins

2)??? Initial conditions

a.???? Steel is at room temperature 25 deg C

b.???? 100% pearlite microstructure

3)??? Outputs

a.???? Temperature

b.???? Phase fractions

Before getting the actual results, the following is the results that were noted before implementing the UKF

What were the issues with this?

1)??? Inaccurate Phase tracking

2)??? Temperature Overshoots

3)??? Hardness variability

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After implementing the UKF, the results were

Improvements after implementing UKF,

1)??? Accurate Phase tracking

2)??? Noise Reduction

3)??? Consistent Hardness

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Takeaways

Before Implementing UKF

1)??? Relied on fixed cooling curves- which led to variability in phase fractions and hardness

2)??? Sensor noises that affected the process control

After Implementing UKF

1)??? Real time phase fraction estimation thereby improving the process control

2)??? Reduction of Hardness variability, implying higher quality

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The temperature profile from 'MATRIC'

Key Observations:

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·?????? The UKF significantly reduces noise in the temperature feedback, which leads to more accurate phase transformation tracking.

·?????? Austenite-to-martensite conversion aligns better with the expected material behavior, resulting in consistent mechanical properties like hardness.

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The simplified Iron-Iron Carbide diagram:

·?????? A3 Line (Blue): The upper boundary of the ferrite + austenite region.

·?????? Acm Line (Green): The upper boundary of the cementite + austenite region.

·?????? A1 Line (Red Dashed): The eutectoid temperature at 727°C, where austenite transforms into pearlite for steel with 0.8% carbon.

Highlights:

• The orange dashed line marks the 0.45% carbon content (AISI 1045 medium carbon steel).
• The purple point indicates the austenitization temperature (850°C) used in my example. At this point, the microstructure is fully austenitic.

Happy to discuss and learn!

My special thanks to Ajit Narayan, Duffy Wilbert, Marcelo Rhodes and Vivek Kumar Raina.