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Smart Mechanical Testing of Polymers


What does it mean to perform “smart” mechanical test? The idea is to extract as much information as possible using a small number of experiments. Clearly, testing a rubber material in uniaxial tension to a strain of 1% can be useful, but if the same test was run to 10% strain that would be a better test since it would be more information rich. After all, it contains both the behavior up to 1% AND the behavior from 1% to 10% strain, using the same number of specimens (one) and essentially the same amount of work. In other words, for the same experimental cost we get more information. But why stop at 10% strain? There is no reason why we would not continue the tension test to failure, or at least to the max strain the test machine can reach.  The reason, again, is that we get more data for the same experimental cost. This leads to the concept of “Smart Mechanical Testing”. Is there an optimal set of tests that one can use to get as much info about a polymer using as little effort as possible? What should such a test program look like? Read on to find out my thoughts on this…

Why to Perform Mechanical Tests?

There are many reasons to perform mechanical tests on a rubber, elastomer, thermoplastic elastomer, thermoplastic, biomaterial, or thermoset (i.e. polymer). For example, it could be for quality control purposes, or simply someone asked for the data. Here, I am only concerned with one specific reason: to get enough information to select and calibrate a suitable material model for finite element simulations.

Testing According to ASTM, ISO, and Other Standards

There are many different standards focusing on mechanical testing of polymers, for example, ASTM D638 (Standard Test Method for Tensile Properties of Plastics), ASTM D412 (Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers – Tension), and ASTM D575 (Standard Test Method for Rubber Properties in Compression). All standards that I recall reading prescribe a constant cross head speed, which clearly does not fulfill my definition of a smart test.

I like the tensile specimen geometries (dog-bone shapes) that are prescribed in the standards, but the details of the load history are not optimized for material model calibration purposes. We can do better!

A Better Idea: Cyclic Tests

One of the main challenges predicting the mechanical deformation response of a polymer is that the mechanical response is typically very non-linear. Almost all polymers exhibit the following behaviors:

  • Distributed yielding that starts locally and then gradually percolates to large-scale yielding.
  • Viscoplastic flow that is rate-dependent.
  • Viscoplastic flow that is strain-dependent.

In addition, some polymers exhibit damage accumulation during cyclic loading. For rubbers, this effect is called the Mullins effect.

The viscoplastic behavior can be experimentally measured by running tests over a wide range of strain rates, together with stress relaxation (or creep) experiments at different strains (or stresses for creep tests). Unfortunately, that becomes a large number of tests. If we select 5 strain rates and 5 strains for the stress relaxation, that  becomes 25 different tests. That does not sound very smart, does it?

To overcome this issue I am big fan of cyclic tests with stress relaxation segments. The following image shows the general idea.

In this example, the material is pulled to 2% strain, that strain is then held for a short time, after which the strain is unloaded back to zero (0). The load cycle is then repeated with larger and larger strain amplitudes. This type of test allows for direct measurement of the non-linear elastic response, the viscoplastic response, the stress relaxation response at different strain levels, and the unloading and recovery response at different strain levels.  That is a very comprehensive and rich data set.


Cyclic Tests - Option 2

The figure below shows a similar, but slightly different test program. In this case each load-hold-unload cycle is repeated 3 times, before continuing with the next larger strain level. The idea with this modifaction is to determine if the material gets damaged during repeated cycles. Some elastomers certainly exhibits this type of damage accumulation, and experimentally quantifying it can be quite useful for the material model selection and calibration.

Cyclic Tests - Option 3 and 4

There are many other options for how to perform cyclic tests for material model calibration. The figure below shows a test with 10 load control cycles at a fixed stress amplitude, followed by additional cycles with increasing stress amplitude. The figure also shows experimental stress-strain data for a thermoplastic material illustrating how the material gradually  creeps during the load cycles. This type of test is useful for extracting the viscoplastic response, but could be modified to extract even more info if each load cycle contains a segment with constant stress.

The following example shows data from a strain controlled experiment with increasing strain amplitude. In each cycle, the strain is held constant for a short amount of time allowing for some stress relaxation. Another interesting feature of this test is that the stress goes to both tension and compression, which can be quite useful for material models calibration since the yield stress is often higher in compression than in tension.

Conclusions - Smart Mechanical Testing

If you run Smart Experiments of the type promoted here then you will get experimental that that has a rather complicated strain history with non-constant strain rate. At first sight you might wonder what to do with that type of experimental data. Do not worry, MCalibration is the perfect tool for analyzing the generated experimental data.

The approach that MCalibration is using is to follow the exact strain history that what used in the experiments, there is no need for the experiment to have constant strain rate. You can go as crazy as you like when you design your experimental test programs!

The exact details of what strain history will be most useful depends on the material. I often  perform load cycle options 1 and 2, and I often repeat each test program at two different strain rates. Let me know in the comments below what load history that you think is most useful.

Video tutorial on smart mechanical testing.


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11 thoughts on “Smart Mechanical Testing of Polymers”

  1. How about temperature dependence? Would one simply run 2 strain rates of cycle options 1 and 2 at both ends of the temperature range, say at -40C and 40C? Or would more temperatures be required for interpolation?

    1. Great questions! I typically repeat the tests (in, for example, cycle 1 or 2) at multiple temperatures. At a minimum at both end temperatures. I then often perform a DMA (dynamic mechanical analysis) temperature sweep over the complete range of temperatures in order to see how the storage and loss moduli depend on the temperature. If the DMA-determined temperature dependence is almost linear then it should be sufficient to perform the cyclic tests at the two end temperatures. If the temperature dependence is more non-linear then I would let the DMA results guide the selection of one or more additional temperatures for the cyclic tests.

  2. What if you are most interested in the long-term permanent strain? For a highly nonlinear viscoplastic material it seems quite difficult to separate the nonlinear viscoelastic response from the nonlinear viscoplastic deformation that remains when the specimen is unloaded and fully relaxed. I was considering uniaxial tests at multiple strain rates up to different peak strains, followed by force-control with a very low constant force in order to see the strain path of the material to the final permanent strain. The reason to choose a low constant force is if the force or specified strain is 0 like in the experiments above, the specimen might simply buckle if it is thin (and has a long relaxation time) and then there would be no useful data in this part of the load history. Perhaps there is a better way to obtain the plastic strain experimentally for calibration of a viscoplastic model. If you have any suggestions, they would be greatly appreciated. Thank you very much.

    1. I like your proposed test plan. I often perform 2 additional types of tests; (1) At the end of the tension cycle I release the bottom grips while I continue to measure the strain using DIC. This way I can quantify how much the strain recovers as a function of time in an unloaded state. (2) If the material is not too stiff then I also perform compression set experiments similar to ASTM D395. Best of luck.

  3. Hi Jorgen,
    if we want to use the direct test data in Abaqus for the quasi-static analysis of compressive stress-strain behaviour of polyurethane foam, do we have to input all the cyclic test data (at all strains) or just the loading bit at a certain strain?

    Also, if we want to use LSQ to obtain the Proney data, is that better to use DMA data or shear relaxation data or compression relaxation data?

    Many thanks

    Many thanks

    1. If you FE simulations will only be monotonic loading (and that is all you care about), then you do not need to perform cyclic experiments. I would only do DMA tests if the strains are really small, otherwise I would use stress relaxation tests to get the Prony parameters.

  4. Hi Jorgen,
    if the experiment is inflation-extension for a soft biological tissue, where the internal pressure vs outer diameter is plotted. How can I use this data to calibrate the BB model

    1. Can you calculate the biaxial stress as a function of the applied biaxial strain from the pressure – diameter data that you have?
      If so, then you could just use a Load Case with biaxial loading. If you cannot convert the pressure – diameter data then you will need to use an inverse calibration approach where MCalibration runs a FE model of your experiment as part of the calibration.

  5. Hey Jorgen,

    is it possible/useful to do a cyclic test to furtherly increasing strains (load, hold, unload x5) with also an increasing strain rate after every cycle?
    Im thinkinking of even omitting to do additional tests at different strain rates but integrate that into a single cyclic test procedure.
    Thats because I couldnt find a way to let the ANSYS APDL curve fitting tool to work with multiple uniaxial data files and i wanted to do as few tests as possible.

    Thanks a lot for Your Help

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