This series of articles is designed to help molders understand how a few analytical tools can help diagnose a part failure. Michael Sepe is our analyst and author. He is the technical director at Dickten & Masch Mfg., a molder of thermoset and thermoplastic materials in Nashotah, WI. Mike has provided analytical services to material suppliers, molders, and end users for 15-plus years.

The devastating combination of time and temperature can introduce stress and creep into your part.

In the last article, we discussed the interaction between an application’s temperature and time-to-failure as it relates to the chemical effects of long-term elevated temperature exposure. However, there is a second aspect to this time-temperature relationship that acts on materials even when they are not used at temperatures high enough to cause oxidative degradation. This is a mechanical process that manifests as creep or stress relaxation.

Creep denotes the time-dependent strain that accumulates in a design feature when a stress is continuously applied. Stress relaxation manifests as a reduction in the stress required to maintain a constant strain. Both of these can be expressed as plots of apparent modulus vs. time. These parameters are usually plotted on logarithmic scales.

Low Temp=Slow; High Temp=Fast

This mechanical response to stress exhibits an equivalence between time and temperature. Therefore, a certain creep strain that occurs in a short period at, for example, 90°C, also occurs at a lower temperature, like 70°C; but it takes longer. The lower the temperature, the longer it takes to reach a particular strain. The higher the temperature, the less time it takes. If we were to view the results of two creep experiments and we did not have access to a clock or a thermometer, we would not be able to distinguish between a part exposed to an elevated temperature for a short period of time and a part exposed to the lower temperature for a longer period of time. The hard part is quantifying this relationship between time and temperature. How much longer can the part sustain a given load if the temperature is reduced by 20 deg C? Or, more importantly, how much less time will it take for the part to reach some critical strain if the temperature is increased by 20 deg C?

The simplest materials to model for this type of behavior are amorphous resins that are not crosslinked, such as ABS and polycarbonate. We can use dynamic mechanical analysis (DMA), the same technique that provides us with information on the temperature-dependent behavior of a material, to arrive quickly at an evaluation of how time and temperature together affect material performance.

Operating in either the constant stress or constant strain mode, we can conduct a series of short-term tests that measure apparent modulus as a function of time. We can then use the equivalence of time and temperature to make a prediction about the long-term behavior of the material at lower temperatures by observing the short-term behavior at higher temperatures.

Long-Term Behavior

Figure 1 shows a plot that contains a series of short-term creep tests for a vinyl ester composite. The experiments begin at 100°C and are conducted in increments of 5 deg C up to a temperature of 135°C. Note that this small temperature range involves a relatively large change in elastic modulus. The vertical axis covers an order of magnitude, so the change in modulus from the lowest temperature to the highest is almost 90%.

It can be observed that each temperature increase of 5 deg C produces a decline in the initial modulus of each experimental step. However, it is also obvious that sustaining a stress for even a short period of time at a constant temperature appears to have the same effect.

The equivalence between time and temperature can be quantified for this material by performing an operation known as time-temperature superpositioning. This technique involves selecting the lowest temperature in the data set as a reference and then shifting all of the results obtained at higher temperatures until they lie on the line described by the set of points associated with the lowest temperature. This involves moving the data points to the right. Since the x-axis plots time, movement to the right is the same as extending the curve to longer times. The resulting master curve should represent the long-term behavior of the material at the reference temperature without requiring that we actually run the long-term test. Figure 2 (previous page) shows the resulting creep master curve with some key values annotated. The curve extends to more than 100,000 hours, or approximately 12 years, based on data that was generated in less than 8 hours using this principle. There is a significant incentive for performing these types of characterizations, particularly in today’s time-compressed market where few have the patience to run an actual creep test for 100,000 hours or even 5000 hours. This technique allows us to model multiple temperatures from one experiment, provided that we have enough data at elevated temperatures to produce a meaningful extension of the short-term data. When we engage in this exercise, we find some surprising effects of temperature on the time-dependent behavior of a polymer.

Elastic Modulus and the Glass Transition

Figure 3 shows the results of a temperature sweep on a 20% glass-fiber-reinforced polycarbonate. As is typical with amorphous materials, the elastic (flex storage) modulus is relatively constant as a function of temperature until the material reaches the glass transition temperature. (We have discussed the practical significance of the glass transition in a previous article: “Frequently Asked Questions (Part 2)—Glass and the Glass Transition,” August 2003 IMM, immnet.com/articles/2003/ August/2192.) At approximately 140°C, the elastic modulus begins to decline rapidly. Over an interval of only 25 deg C, it declines by more than two orders of magnitude, or 99%.

This plot contains two other curves. One of these is associated with a property known as the loss modulus. This is a measure of the tendency of the material to exhibit viscous flow when placed under load. Viscous flow is not recoverable and therefore is related to creep. This results in permanent deformation. The tendency for viscous flow is very small when the temperature is lower and the elastic modulus is high. But as the polymer begins to undergo the relaxation process associated with the glass transition, this property rises rapidly to a local maximum. The temperature at the peak of this curve is often referred to as the glass transition temperature (Tg), even though this transition is actually a process that spans a temperature range. In this sample, we would report the Tg at 153.7°C, which is a typical value for polycarbonate.

The third plot illustrates a property known as tan delta. A thorough discussion of the significance of tan delta is beyond the scope of this article. However, it represents a ratio of the loss modulus to the elastic modulus and can be thought of as a sort of viscoelastic index. When tan delta values are high, the material is compliant; it deforms rapidly under load and much of that deformation is not recoverable. When tan delta values are low, deformations are small and largely recoverable. But if the effects of time and temperature are equivalent when it comes to relaxation processes such as the glass transition, then it follows that the steep decline in elastic modulus that all amorphous materials exhibit will also occur at lower temperatures if given enough time. The crucial question is, what does that time-temperature relationship look like? The answer is that right now we do not have enough data to make a definitive statement about this behavior. However, enough experiments have been done to suggest striking patterns.

Small Temperature Increases are Big Trouble

Figure 4 shows a family of creep master curves for the same glass-reinforced polycarbonate referred to in Figure 3. These curves cover behavior at 40°C, 60°C, and 85°C. We already know that the effect of temperature on the elastic modulus of this material is negligible. This is confirmed by the starting point for each of these creep curves. But as we extend out to longer times, the prediction calls for a significant divergence in behavior. This is illustrated by the horizontal line connecting the end of the 40°C master curve to the y-axis. The 10,000-hour prediction at 40°C calls for a reduction in apparent modulus from 4804 MPa (696,800 psi) to 3335 MPa (483,700 psi).

The stiffness of the material does not really decline; this is a mathematical construct for expressing the increasing strain associated with the sustained application of a load. This is why it is called the apparent modulus. If we find the point on the elastic modulus curve in Figure 3 where we reach a modulus of 3335 MPa, we find it at approximately 150°C. In other words, at 40°C the equivalence between time and temperature is 10,000 hours equals 110°C.

However, this equivalence changes as we approach the glass transition. The horizontal line drawn through the three master curves shows that the same degree of deformation that occurs in 10,000 hours at 40°C takes place in approximately 1000 hours at 60°C and in about 100 hours at 85°C. In addition, the apparent modulus of the material after 10,000 hours at 85°C is only 1276 MPa.

This looks like quite a reduction from the result at 40°C, and it is. But if we go back to our temperature-dependent results, we find that the temperature increase required to produce this same decline is only 6 deg C! In other words, the effect of a glass transition occurring at a particular temperature can be measured at much lower temperatures as an acceleration in the creep process.

The effect is dramatic; for every temperature rise of 20 deg C, the rate increases by an order of magnitude and the relationship is exponential. More importantly, this occurs in a region where temperature has no short-term effect on properties.

Don’t be Afraid to Ask

The available data is not substantial enough at this point to turn this into anything resembling a law. However, this pattern appears in a number of creep experiments performed on noncrosslinked amorphous polymers. It almost certainly requires adjustments for crosslinked materials and semicrystalline thermoplastics, but it points out the importance of understanding more than just the short-term effects of temperature on mechanical properties. It also suggests that the accelerating effects of temperature on the physical performance of a material are much greater than those that govern chemical changes due to oxidation.

Finally, if we extend this modeling to the deflection temperature under load (DTUL), we can see the folly of trying to use this property as a gauge of anything approaching mechanical performance. Figure 5 (opposite) shows a creep master curve for a 10% glass-fiber-reinforced polycarbonate at 135°C. This temperature is still 7 deg C below the DTUL at 264 psi. And at this temperature the material is still quite rigid with an initial modulus of 3107 MPa (450,600 psi), or about 90% of its room-temperature value. However, in 1 hour the apparent modulus has declined by nearly 70%. This is approximately the same change that occurred in 10,000 hours at 85°C.

So when the continuous-use temperature of a material is provided on a data sheet, consider the dual influences of chemical and mechanical effects on long-term performance and inquire about the time scale and the stresses used when this property was measured. It is more work for everyone, but that’s why we call it engineering. If we are going to continue to push plastics into applications that have historically been the domain of metals and ceramics, we have a lot of work to do to satisfy engineers who are accustomed to a much greater degree of certainty than we in the plastics industry can currently offer.

Contact information Dickten & Masch Mfg. Co., Nashotah, WI Michael Sepe; (262) 369-5555, ext. 572 dmlab@execpc.com www.dicktenplastics.com