How to Calibrate an Abaqus Material Model to Tension Data with Necking

Introduction

In this article I discuss how to calibrate an Abaqus material model in a case where you have uniaxial tension data of a thermoplastic that undergoes necking, and the specimen geometry was: ASTM D638 or ASTM D1708. I will show how to perform the calibration quickly using the “Tension Test” load case in MCalibration.

Note: This article is part 4 in my series on how to use experimental uniaxial tension (cold drawing) data from specimens that undergo necking during the deformation. Here are the other articles:

Step 1: Load the Force-Displacement Data

Add a Tension Test load case and load the experimental force-displacement data. The following video shows the steps.

Step 2: Create Approximate Stress-Strain Data

In this example I will examine experimental data of a polypropylene (PP) thermoplastic that undergoes necking during monotonic uniaxial tension. The test specimen used in the testing was ASTM D638 Type IV, which has a width of 6 mm, and a length of the narrow section of 33 mm. With this information we can convert the measured force data to an engineering stress by dividing the force by 18 mm2 (which was the initial cross sectional area). The engineering strain be approximated by dividing the applied crosshead displacement by 33 mm. In this case the engineering strain in the gauge section will be inhomogeneous, so this is only an approximation. MCalibration can quickly perform these calculations as shown in the following video.

Step 3: Calibrate Material Models to the Approximate Stress-Strain Data

I then calibrated an Abaqus Elastic-Plastic with Isotropic Hardening model to the approximate stress-strain data. This material model matches the data very well, as shown in the following figure.

I also calibrated the PolyUMod TNV material model to the experimental data. This is a viscoplastic material model that needs experimental data at different strain rates (or stress relaxation, or creep) for proper calibration. But that is not a problem here since this is only a demonstration example. Here are the predictions from the calibrated TNV model.

The purpose of these preliminary calibrations is to quickly find material model parameters that are close to the optimal set. This will significantly speed up the material model calibration.

Step 4: Calibrate the Material Model to the Force-Displacement Data

Before starting the calibration of the elastic-plastic material model to the force-displacement data, I ran the Tension Test load case once using the preliminary material model that was calibrated using the approximate stress-strain data. The results are shown in the following figure. It is really interesting to see how terrible the predicted force response is. The reason for the bad prediction is that the FE simulated specimen undergoes unrealistic strain localization. It might be possible to fix this, but it would not be an easy task since the material model used in that simulation matched the approximate stress-strain response from a single finite element simulation.

Instead I calibrated the PolyUMod TNV model to the force-displacement  data using the Tension-Test load case. The predicted results after about 150 function evaluations are shown in the following figure. The predicted results look very good. The predicted specimen deformation is similar to what was observed in the physical experiment.

Summary

  • The MCalibration software can calibrate a material model using any combination of the supported experimental data types, including tension data from dog bone shaped specimens.
  • The tension tests are simulated using Abaqus FE simulations that reproduce the specimen geometry and experimental conditions.
  • These inverse calibration typically take longer time to run since multi-element FE simulation are required.
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