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Metal Plasticity       ;      Power-Law Plasticity

One of the drawbacks in some of my earlier examples is that they used synthetic data; realistic, but synthetic (made from Abaqus runs).  I dug around and was able to find some real test data for a 304 stainless steel, shown in the images above.  I had been toying with the idea of creating a special UHARD user-subroutine to see if a "strain partitioned" approach to the hardening curve would be superior to any of the prepackaged hardening laws.  By "strain partitioned", I mean something like using a Johnson-Cook equational form up to ultimate, then a Voce (aka Exponential) equational form beyond ultimate. This idea has been raised in some of the papers on Continuum Damage Mechanics for Metals (CDM). 

This post is a worked example of an FE mode calibration of this test on 304 stainless steel.  The test was performed on a smooth round bar, diameter in the measurement region of 7.12 mm, gauge length of the strain extensometer of 25.4mm.  The FE mesh used for calibration was an axisymmetric mesh/model of just the measurement region, with a symmetry plane used in the length dimension. The FE model used 1200 CAX4 elements  and the runtime on my laptop using 1 cpu was 66 secs (no odb field output).

Step #1:  Calibrate in numerical mode to the test data truncated at ultimate.

Step #2 : Switch to FE mode to finish the calibration all the way out to failure.

The units used in this example are N, mm, MPa.

After a bit of experimenting with various hardening laws, I liked the Exponential law for this data.

The video below was created on July 7, 2023 using the public cloud R2023 HF 2.23. This video performs Step #1

The Elastic-Plastic material model with Isotropic Exponential hardening law determined from this numerical mode calibration is this:
 

When you export that Abaqus material model snippet to a file, it looks like this:
 

The video below was created on July 7, 2023 using the public cloud R2023 HF 2.23. This video performs Step #2
 

At the end of the above video, I performed an FE mode calibration.  Since the solution was already so close, the three Isotropic Exponential hardening parameters did not change much, but they did change a bit. The image below shows the state at the end of that calibration:
 

Of course running a calibration for a long time looking for a "line on line" match is pretty silly in cases where the test variability is high.  It is always a good idea to keep in mind the variability in the real material response(s).  For 304 stainless steel, here is a glimpse of the variability across seven separate tests...
 

The zip file below contains all the files needed to reproduce this example.

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