Experimental Testing for Material Model Calibration of a Rubber


In this article I will give my recommendations for what experiments to run if you want to calibrate a material model for a rubber. I have found a lot of misinformation about this, and here I will try to give a modern answer to this. To make my recommendations are useful as possible, I divided them into 3 different applications:

Dynamic (Frequency) Loading

  • Frequency domain FE simulations
  • Super small strains (<1%)

Slow Monotonic Loading

  • Time domain simulations
  • Monotonic loading at one strain rate
  • Finite strains

General Loading

  • Time domain simulations
  • Any strain history
  • Finite strains

In the following sections I will propose test plans for each of these applications.

Dynamic (Frequency) Loading

Run the following Dynamic Mechanical Analysis (DMA) tests:

  • First perform a strain amplitude sweep at constant frequency (about 1 Hz). This is used to establish the strain range in which the material response is strain amplitude independent. The material will be linear viscoelastic only in this strain range.
  • Run a frequency sweep in order to measure the storage modulus (E’) and loss modulus (E’’) data.
  • Repeat the frequency sweeps if you are interested in calibrating a WLF or Arrhenius type time-temperature superposition (TTS) model.

The results from these tests can be used to calibrate a linear viscoelastic material model.

DMA Test Machine

Slow Monotonic Loading

Run the following monotonic uniaxial tension tests:

  • Uniaxial tension using a dog-bone shaped specimen (e.g. ASTM D638 Type IV).
  • Deform the specimen to large strain.
  • Repeat the test 2 to 3 times using different specimens (in order to determine the experimental variability).
This data can be used to calibrate an I1.-based hyperelastic material model like the Arruda-Boyce or Yeoh model. Some people claim that you should also perform tests in 2 other loading modes (biaxial, shear, etc). This is NOT necessary as long as you use a I1-based hyperelastic material model.

General Loading

Run the following cyclic uniaxial tension tests:

  • Load to 5% strain, hold the strain for 1 min, unload to a force that is close to 0;
  • then continue to load to 10% strain, hold the strain for 1 to 10 min, unload to a force that is close to 0;
  • then continue to load to 50% strain, hold the strain for 1 to 10 min, unload to a force that is close to 0;
  • finally either load to failure in tension, or unload to zero.
  • Repeat this experiment 2-3 times (using different specimens) in order to determine the experimental repeatability.
  • The testing should be performed using ASTM D638 type IV (or similar) dogbone-shaped specimens.
  • All loading and unloading should be performed at a constant engineering strain rate of about 0.01/s to 0.1/s.
  • Repeat each load cycle 2 or 3 times if you are interested in also calibrating a Mullins damage material model.
This data can be used to calibrate an I1-based non-linear viscoelastic material model.
  • Repeat the testing at multiple temperatures if needed.
  • Use MCalibration to calibrate a suitable material model to experimental data.

More to explore

LLDPE Material Modeling

Demonstration of how you can use the PolyUMod Material Database model for LLDPE. This is an excellent model for generic LLDPE.

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