Experimental Testing for Material Model Calibration of a Rubber

Introduction

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.

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.