Don’t Forget the Young’s Modulus

Introduction

Thomas YoungThis article demonstrates one problem that can occur if you calibrate a material model to all experimental data, but forget to consider the initial Young’s modulus. As I will show below, it is possible to calibrate a material model that accurately matches the experimental data in an average sense, but still gives really bad predictions in a FE model. In this case the problem can be caused by a bad prediction of the Young’s modulus.

Experimental Data

In my example I will use the experimental data shown below. The CPVC material was tested in uniaxial tension at two different strain rates. Two of the tests also measured the unloading response of the material. The monotonic tension test was to failure, but I will not calibrate a failure model in this case.

CPVC Exp Data

In addition to the uniaxial stress-strain data, I also experimentally measured the force it takes to stretched a 100 mm long strip (with a single center hole with a diameter of 2 mm) a total distance of 1 mm. The experimentally measured force was 212.1 N. The plan here is to calibrate a material model to the uniaxial tension data, and then see how accurately that model can predict the tension test of a strip with a hole!

Tensile strip with a hole.

Material Model Calibration 1: Bergstrom-Boyce Model

I calibrated the Ansys implementation of the Bergstrom-Boyce (BB) model to the experimental data using MCalibration. I would typically not recommend or use the BB-model for thermoplastics (it is better for elastomers), but the model is a good example model in this case. The best calibration that I could create is shown in the figure below. The average error of the model is about 17%, not too great but not terrible either…

Bergstrom-Boyce Prediction of CPVC

I then inserted the calibrated BB-model into an Ansys FE model of the tension strip with a hole. The predicted force required to reach the target displacement was 109.4 N. This is about 50% of the real value. Terrible. It is interesting that the prediction is to bad since the uniaxial calibration had an error of “only” 17%.

The reason the FE simulation is so inaccurate is that although the average material model model prediction error is low, the predicted error at small strains is very large! That is, we forgot about the Young’s modulus.

Material Model Calibration 2: Bergstrom-Boyce Mode

To investigate this further I created another calibration again using the Ansys Bergstrom-Boyce (BB) material model. In this case I added one more load case for “E-modulus” with a target E-modulus value of 2,380 MPa, and a load case fitness weight factor of 10. This additional constraint forces MCalibration to select material parameters that give that target modulus value. The figure below shows the final stress-strain predictions. Note that the average error for this material model is 22%, which is worse than in example 1 above. 

Seconds BB model prediction of CPVC.

I then reran the Ansys FE simulation of a strip with a hole with the new material model (see figure below). In this case the force required to pull the strip to the target length was 234 N. Which is significantly more accurate than in the first case!

2nd BB model prediction of strip with hole.

Summary

The key lesson here is: Don’t forget the Young’s modulus. A material model material model with a low average error may still be VERY inaccurate if the initial modulus is not accurately captured. Fortunately, it is easy to fix this in MCalibration: just add a E-modulus load case!

E-modulus load case
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