Q: What happens when we attach a very heavy weight to a wire at relatively low temperature?
A: The wire snaps right away!
Q: What happens when we hang a lighter weight from the wire at a higher temperature?
A: At first, seemingly nothing—the weight just hangs there. Or does it? Under some circumstances, we may return several hours (…or several days… or several weeks…) later and find that the weight has gradually stretched the wire.
This deformation at elevated temperature under constant load is called creep. It depends on the wire material and the temperature of the room. Let's explore creep in more detail, and then look at the results of a real creep experiment. We will look at a fractured wire too!
Theory: Effect of Temperature on Deformation
In general, the response of our wire to an applied load will depend on the temperature and the amount of weight we use. When we talk about the temperature of a material, we are actually more interested in the absolute temperature (Tabs) of the material compared to the material's absolute melting temperature(TMPabs). We call this the homologous temperature and can designate it by the ratio (Tabs/TMPabs).
When we hang our weight on the wire at a low homologous temperature (Tabs/TMPabs < 0.4), the wire elongates. If that weight is relatively small, the wire stretches just a little. As soon as we remove it, the wire returns to its original length. This is an example of a reversible deformation, or an elastic deformation, like a spring.
When we hang a medium weight on the wire at low Tabs/TMPabs, it stretches more than before. When we remove the weight, it does not return to its original length. This permanent stretching of the wire is known as plastic deformation. If the weight is too heavy, the wire fractures.
If we raise the temperature so that Tabs/TMPabs > 0.4, and hang a weight on it that does not noticeably stretch the wire, it may initially appear that we have only elastically deformed the wire. At temperatures above about Tabs/TMPabs = 0.4, however, atoms begin to move about in the solid at significant rates. This atomic movement can lead to time dependent stretching of the wire under a load even when the weight is very small. If we observe the length of the wire over a long time (hours, days, or weeks), we notice that the wire very slowly elongating. This time dependent elongation of the wire is called creep.
Application: Why is Creep Deformation Important?
Creep is an important consideration in any application where a component must support a load at temperatures where Tabs/TMPabs > 0.4. A jet engine is one good example where a material operates at very high temperatures (about 1100 K, or Kelvin degrees). Because the engine temperatures are so high, the alloys used for the turbine blades operate at temperatures very close to their melting temperatures. They are called superalloys. In order to demonstrate creep in alloys without using very high temperatures, we can observe creep in low melting point alloys at temperatures near room temperature (about 300 K).
Left: Temperature variations across a turbojet engine.
Image courtesy of NASA, Glenn Research Center.
Sample Properties: Creep of 60/40
To demonstrate creep behavior at room temperature, we can use 60/40 solder that contains 60 wt% Sn (tin) and 40 wt% Pb (lead). The phase diagram for the Pb-Sn alloy system is shown below, and the composition of the solder is identified by the red vertical line at 40% Pb. One of the uses for a phase diagram is to determine the melting temperature of an alloy. The phase diagram indicates that the 60/40 solder melts at about 183°C = 456 K.
To determine the homologous temperature at room temperature (25°C), the calculation is as follows:
- Convert room temperature (25°C) to absolute temperature in Kelvins:
Tabs = 25 + 273 = 298 K
- Convert the melting temperature of the alloy (183°C) to absolute temperature in Kelvins:
TMPabs = 183 + 273 = 456 K
- The ratio of the absolute room temperature (298 K) to the absolute melting temperature
of the alloy (456 K) is the homologous temperature:
Tabs/TMPabs = (298 K) / (456 K) = 0.653
This means that room temperature corresponds to a homologous temperature of Tabs/TMPabs = 0.65 for the 60/40 solder. Because the solder is at a relatively high fraction of its melting temperature, we expect to observe creep deformation in solder at room temperature.
If we hang a small weight (4.8 kg = 10.6 lb) on a long 1/8” diameter wire made of 60/40 solder, at first we will not notice significant elongation. This load is well below that required to plastically deform the material rapidly, and only a very small amount of elastic elongation has occurred. The video below shows the experiment. (See a screenshot.) An indicator bar is attached to the bottom of the weight. A centimeter scale is shown in the background so that we can monitor the elongation of the wire over time.
Summary of Creep Test Conditions
- Wire Material: Solder = 60% Sn - 40% Pb
- Melting Temperature: 183°C = 456 K
- Wire Diameter: 1/8" = 0.125" = 3.175 mm
- Load: 4.8 kb = 10.6 lbs
The load applied to the wire (4.8 kg) is only about one tenth of the load required to get immediate plastic deformation. The experiment shows, however, that there is slow, continuous deformation (creep deformation) over a period of several days. The graph below shows a plot of the wire length versus time during the creep test. The wire is initially 30 cm long, but after more than 90 hours, it has stretched to around 140 cm.
- Original wire length: 12" = 1 ft = 30.5 cm
- Initial data indicator: 47 cm
- Final data indicator: 156 cm
- Final wire length: 54.9" = 4.5 ft = 139.5 cm
- Test temperature: 77°F
- Test duration: 90.8 hours = 3 days, 18 hours, 48 seconds
Time increases from zero to about 90 hours. The wire length increases slowly from 30 cm to about 50 cm over 60 hours, and then it increases rapidly to a length of about 140 cm.
Many complex processes are taking place inside the solder alloy during the creep test. The deformation observed is a result of the simultaneous application of a load (the 4.8 kg weight) and the atomic movement inside the alloy at elevated temperature. (In this case room temperature is an “elevated” temperature.) A creep curve such as the one shown above is often divided into three portions:
- Primary creep: This is the deformation that occurs just after the load is applied. In this region, the curve is downward. This means the deformation rate is decreasing. During primary creep, the internal structure of the alloy is changing in response to the applied load.
- Secondary creep: There is often a stage where the slope of the creep curve remains approximately constant, like a straight line. This is the period of secondary creep (also called steady state creep). During secondary creep, the internal structure of the alloy remains approximately constant.
- Tertiary creep: At the end of secondary creep, the plot begins to curve upward. This signals the onset of failure for the alloy and is called tertiary (third stage) creep. During this period, small cavities begin to form and grow inside the alloy. Growth and inter-linkage of these cavities eventually lead to failure of the alloy.
When materials scientists study creep of metals and alloys, much more sophisticated experiments are usually conducted. The alloys are precisely machined into test specimens, the testing temperature is fully controlled, and the elongation of the material is recorded in detail. In addition, the samples are usually analyzed before and after creep testing to better understand the relationship between creep deformation and the internal structure of the material.
This solder wire eventually fails by ductile fracture after a period of tertiary creep. This ductile fracture results from cavities that form inside the alloy as a result of creep deformation and atomic motion. The image sequence below shows the fracture surface of the solder at different zoom scales. The images were taken using a scanning electron microscope (SEM). Evidence of the internal cavities that formed and grew during tertiary creep can be seen in the final fracture. When the cavities get large enough, the material between them stretches out like saltwater taffy.
The creep experiment demonstrates the impact of the operational environment on a material's properties. This information is critical for assessing a component's service performance and for predicting whether a part will fail prematurely.
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