A serious look at plastic creep, and in particular how the triple cocktail of temperature, time, and stress affect it, provides invaluable help to metal-focused design engineers looking for a plastic substitute.
As has been suggested in the past two articles, the mechanical behavior of plastic materials is influenced by the combined factors of temperature, time, and stress. When evaluating long-term responses such as creep, stress relaxation, and fatigue, it is essential that all three be considered as an organic whole. They cannot be considered in a vacuum and if any one of them changes, the calculations of fitness for use for a given material must be re-evaluated.
In this article we will consider in depth the phenomenon of creep and techniques for arriving at assessments of long-term behavior using accelerated testing methods that shorten the timeline from years to weeks or even days.
Any material, when placed under stress, will exhibit a particular deformation or strain. The ratio of this stress to strain is known as the modulus of the material and is understood to be a measurement of a material’s stiffness. The relationship is expressed mathematically as
E = s/e
where E is the modulus, s is the stress, and e is the strain. (Scientists employ a lot of Greek characters in their equations to make themselves seem more knowledgeable and to scare laypeople.) A rigid material will resist deformation to a greater degree, resulting in a higher calculated modulus.
In a plastic material, if the applied stress is maintained for a period of time, the strain will increase above the initial value obtained when the stress was applied. This additional deformation is known as creep strain and the behavior is expressed by a modified version of the same equation
Ea = st/(eo+ec)
where ec is the creep strain and eo denotes the initial strain that the part exhibits when the stress is first applied. The stress term (st) is constant and now has duration (t = time).
The additional strain due to creep causes the denominator of this equation to increase while the numerator remains constant. This results in a decline in the calculated modulus, which is denoted with the subscript “a” and is known as the apparent modulus because the calculation appears to suggest that the stiffness of the material is dropping. However, the material is not really losing rigidity; the Ea is a mathematical construct for illustrating the effects of creep. If we know the behavior of the Ea over time, we can calculate the creep strain at any given time by plugging in different stress levels.
Temperature
There was a time when polymer scientists devoted considerable effort to measuring the long-term behavior of plastic materials. The results of some of these studies can still be found in the literature if you look hard enough. But for the most part, we seem content to look at data sheets that have nothing to say about long-term behavior and do not capture the effect of temperature on the behavior of a plastic material.
This is (or should be) a source of great frustration for design engineers attempting to select the correct material for an application, and it is a serious obstacle to the metal-to-plastic conversion process. Imagine telling an engineer that the properties of a material change as the temperature increases, but being unable to provide any quantitative answer as to the degree of that change.
It is not a matter of not knowing how to provide these answers. Any tensile testing machine can be fitted with an environmental chamber and specimens can be tested at multiple temperatures to provide the necessary stress-strain curves. Dynamic mechanical analysis (DMA) can be performed on a material to provide a wealth of information about the behavior of a material as a function of temperature.
For instance, Figure 1 gives a plot of elastic modulus vs. temperature for a 33% glass-fiber-reinforced PA 66. Using this curve, an engineer can determine the stiffness of the material at any point between room temperature and the melting point. Instead, all we usually provide to the engineering community is the deflection temperature under load, a value that is so useless and irrelevant that it defies reason.
Time
But knowing the effects of temperature alone are not enough. We must have a way of capturing the effect of time and stress as well. The big excuse for not conducting long-term evaluations such as creep tests is that in our time-compressed world, there just is no time for such endeavors. The good news is that when it comes to relaxation phenomena such as creep, we can leverage the relationship between temperature and time to rapidly develop very good assessments of the long-term effects of sustained loading at virtually any condition we care to define.
To do this, we rely on the principle that the same relaxation processes that happen rapidly at elevated temperatures will also happen at lower temperatures, but more slowly. If we can experimentally establish a quantitative correlation between time and temperature, we can use the results of short-term tests to make predictions about long-term behavior.
Figure 2 shows the results of a series of short-term creep tests performed on a vinyl ester glass-fiber composite at temperatures between 100°C and 135°C at increments of 5 deg C. The data for each temperature step are presented as a logarithmic plot of Ea as a function of time. We can use a technique known as time-temperature superpositioning to develop what is known as a master curve of Ea vs. time for any given temperature.
Here’s how: A temperature of interest, known as the reference temperature, is selected. The other data sets are shifted until they lie on the same line as the set of points described by the reference temperature. Data sets generated at temperatures higher than the reference temperature are moved to the right while data sets developed at lower temperatures are moved to the left. Since we are primarily interested in predicting the future, we are more likely to select the lowest temperature in the data set and move all the other data to the right, to longer time frames.
Figure 3 shows the master curve in the process of being constructed. Some of the data sets have already been shifted and the curve is beginning to take shape, but it has not produced anything particularly exciting because we have not taken advantage of all the available data. The curve at this point only extends to about 30 hours—not a very good return on data that may have taken up to 16 hours to generate.
However, by using the additional data obtained at the higher temperatures, we can produce the finished master curve shown in Figure 4. Now we have something of interest. A test that took about 16 hours to run has generated a prediction of behavior that extends past 100,000 hours, or about 11.5 years. Annotated values on the curve help us read the logarithmic plot and give us valuable quantitative information about the material.
The product is obviously quite rigid at 100°C with an initial modulus of 12.11 GPa (more than 1.75 million psi). But after just 10 hours under load, the apparent modulus has declined by approximately 50%. Going back to our equation relating apparent modulus to strain, we can see that a 50% reduction in apparent modulus equates to a doubling of the total strain. In other words, the creep strain at this point approximately equals the initial strain.
After 1000 hours (six weeks), the Ea has declined by a little more than 75%. This means that the total strain is now four times greater than the initial strain. At 10,000 hours (14 months), it is five times greater. We can model this behavior for any set of conditions.
Stress
We have now accounted for two of the three factors in our model. The only thing left to do is define the stress. Once we have a defined stress, we can convert the apparent modulus calculation into a strain calculation. For example, if we apply a stress of 12.1 MPa (1755 psi) we will obtain an initial strain of 0.1%. In 10 hours this will have increased to 0.2%. In 1000 hours it will be 0.4% and in 10,000 hours it will be 0.5%.
We know that all materials have a limiting strain beyond which they will either yield or rupture. In the case of a very stiff material like a glass-fiber composite, the failure mode will tend to be brittle and excessive strain will result in cracking. If plastic materials were perfectly elastic, all we would need to do is measure the ultimate strain and we could readily calculate the expected time to failure for any given stress. Stresses that produced predicted failure before the desired end of product life would need to be avoided.
Unfortunately, plastic materials do not exhibit perfectly elastic behavior across the entire stress-strain curve. As we saw in last month’s installment, linear elastic behavior is only obtained for a relatively small portion of the stress-strain curve up to a point known as the proportional limit. (As a side note, the proportional limit of a material would be an extremely useful property to have on a data sheet. But don’t strain your eyes looking for it; material suppliers do not provide it.)
Once the stresses are high enough to exceed the proportional limit, the application of the next increment of stress results in a strain that is larger than would be expected if we assumed perfectly elastic behavior. Because of this, we need to have a stress-strain curve for the material. And we cannot be content with a room-temperature stress-strain curve; it has to be generated at the same temperature as the one we are using to model creep behavior. As long as the predicted strains from the creep master curve remain at or below the proportional limit, we can use the values calculated directly from the Ea equation. Once the predicted strains exceed the proportional limit, we must correct for the calculation empirically using the actual value from the stress-strain curve.
Figure 5 gives an example of this transformation from predicted linear behavior to the actual response. This is a room-temperature stress-strain curve for an unfilled acetal copolymer, but the principle is the same for any material. The modulus line highlights the deviation of the curve from perfectly elastic behavior (red line). As the predicted strains from the master curve become greater, the correction factor becomes larger because the material deviates from linear behavior to an increasing degree. At a predicted 1% strain the actual strain is about 1.2%. But at a predicted strain of 1.5% the real strain is approximately 2.3%. And at a predicted strain of 2% the actual deformation will be more than twice the prediction at 4.65%.
We Have the Technology
So we have accounted for all three of the factors that determine the creep behavior of a material: temperature, time, and stress. Using these tools we can answer the tough questions about the behavior of a material under almost any constant loading conditions that can be imagined and we can do it in a reasonable time frame for a fraction of the cost of real-time testing.
In our last installment, we will illustrate the use of these tools in selecting a material for two applications in very different markets. In one case the analysis prevented the use of a material that was less expensive but would have failed. In the other, the analysis showed that a lower-cost material than the one originally selected could be used.
About
Michael Sepe Michael Sepe has worked in the plastics industry since 1975 in a variety of roles involving both manufacturing and research and development. He is an independent consultant based in Arizona with clients throughout North America. He assists clients with material selection, designing for manufacturability, process optimization, troubleshooting, and failure analysis. Learn
more about Michael Sepe.
