Residual Strain Prediction

Introduction

It is a good idea to also measure the residual strain after a tension or compression test has been completed. This can be done using either DIC or direct measurements.
One problem when analyzing the residual strain data is that most experimental tests are performed in displacement control, but residual strain is measured in load control.
In this article I will show how you can use experimental test data that contain BOTH displacement and load control steps in your material model calibration (using MCalibration).

Note! If you want your material model to be able to predict the residual strain in a product, then you need to experimentally measure the residual strain after different applied load histories. There is no material model that can accurately predict the residual strain without having experimental data to guide the parameter calibration. In other words, residual strain predictions do not come for free.

Experimental Data

Figure 1 shows typical experimental data for a soft rubber that is loaded in tension to an engineering strain of 0.3, and then unloaded to zero stress. After that, the lower grip was released, and the strain was slowly recovering over time (under zero stress).

Figure 1. Experimental tension data with unloading and final recovery.

Compression Set

If your goal is to predict the compression (or permanent) set of a a rubber, then I recommend that you perform experiments following ASTM D395. This is discussed in more detail in my article “How to Predict Permanent Set in Rubber“. The results from this type of test is easy to analyze using MCalibration. All you need to do is to use the Permanent Set load case, see Figure 2.

Figure 2. MCalibration has a built-in load case for Permanent Set predictions.

Stress vs Strain Control in MCalibration

One way MCalibration can analyze a data set is to use Strain Control. In strain control, the experimental strain history is exactly followed (see the image to the right). This is OK for the first part of the test, but not during the stress relaxation segment.

Another option in MCalibration is to use Stress Control. In stress control, the experimental stress history is exactly followed (see the image to the right). This is not correct for the first part of the test.

Calibration to Mixed Stress and Strain Control

A third option in MCalibration is to set up a Virtual Experiment using exactly the same load steps as in the real experiment (see Figure 5). In this case you should also activate the Experimental Data option, which allows you to use the load case for the material model calibration.

Figure 5. Definition of a Virtual Experiment with experimental data.

This type of load case can be useful for the material parameter calibration since it follows the exact steps that were used in the experiment. Figure 6 shows the predictions of the initial parameter guess, before the parameter calibration was performed.

Figure 6. Predictions from a virtual load case with experimental data.

Summary

In MCalibration you can use Strain Control, Stress Control, or a Virtual Experiment to calibrate a material model.
A Virtual Experiment with experimental data can be particularly useful when the experiment used mixed conditions.
I recommend that you always measure the final residual strain after a test.