Creep & Stress, Part 1 | Reliability Insights Beyond FEA

Image concept depicting the structural integrity of material

To engineer the best-performing products, we test material for creep & stress relaxation. By subjecting the material to prolonged stress at high temperatures, we can predict long-term performance and reliability. Though we start with a finite element analysis (FEA), rigorous testing for the effects of material creep and stress reveals a more accurate expected service life. These insights guide our material selection and design decisions for improved product durability and safety.

Calculating Creep & Stress, Realistically

Image of Dan Faulkner, AC Principal Mechanical Engineer

Dan Faulkner, AC Principal Mechanical Engineer

Creep and stress relaxation are easy to ignore… until they become a problem. As product design engineers, we focus on the short-term performance properties of materials. Yet, it’s crucial to consider that materials behave very differently over long spans of time. 

Rote material engineering teaches that materials follow a simple stress-strain equation:

σ/ε = E

This formula is derived from the relationship between stress (), strain (), and the modulus of elasticity (), often called Young’s modulus.

But, in reality, the stress-strain relationship is much more complicated:

σ/ε = f (material, time, temperature, etc.)

Instead of considering just the elastic modulus (E), we also need to think about time, temperature, material structure, and a whole host of other variables (f).

Most importantly, when materials are exposed to long-term loads, they have larger deflections, lower apparent stiffness, and lower ultimate strength. When temperatures are elevated, all of this happens more rapidly. Long-term loads can cause permanent deflection or rupture, even when the material is well below its yield point. These time- and temperature-dependent behaviors are present in all materials to some degree.

In materials science, creep (sometimes called cold flow) is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material.

Creep & Stress Relaxation: Related, But Different

Let’s take a look at two examples that illustrate the two related, but different behaviors of creep and stress relaxation:

CREEP​

Creep is the time-dependent and permanent deformation of materials under a constant-stress load.

σ = constant

h decreases with time

STRESS RELAXATION

Stress relaxation is the decrease in stress under a constant-strain load over time.

 

h = constant
σ decreases with time

As time →∞, σ→0

Factors influencing creep and stress relaxation:

  • Higher temperatures facilitate a faster rate of creep and stress relaxation.
  • Higher stress levels can accelerate deformation.
  • Longer durations allow more significant stress relaxation.
  • The material’s grain size, phase distribution, and presence of precipitates can significantly affect creep resistance.

Analyzing Creep & Stress | Why Does it Matter?

Creep is a primary consideration for designers of engines, combustion equipment, and other high-temperature metal systems. It can also occur in structural materials like concrete. In this post, we’ll focus on polymers, although these lessons and general principles also apply to other materials.

Water Tank Wall Deflection: A Constant Stress-Load

Consider, for example, a square polypropylene tank filled with water.

1.0m x 1.0m x 1.0m, 19mm wall, open top

In this example, our design requires us to keep wall deflections to less than 8mm when the tank is full.

We run a quick FEA simulation and find that the maximum deflection is 6.4mm. So, everything is OK, right?

Well… the next step is to analyze the creep data for polypropylene.

Suddenly, as shown in the following graph, we find a very different situation when we account for time and temperature.

Increased maximum deflection at temperatures over time

Of significance, after just one hour under load, the tank is predicted to have a deflection larger than 8mm. If this tank were continuously used for ten years, the predicted deflection would be around 34mm! And that’s just at room temperature. If the tank holds hot water, the situation would be much worse: deflections of 55mm or more. Clearly, the standard stress-strain equation does not give us the whole picture.

This tank problem is an example of creep, which occurs when materials are subjected to a constant-stress load. The hydrostatic pressure of the water always pushes on the walls of the tank equally. So, the stresses don’t change. But over time, the walls slowly deform due to creep.

Spring Arm Clamping Force: A Constant Strain-Load

Next, let’s look at an injection-molded part with a spring arm.

  • The arm is intended to push on the red ABS block and clamp it in place.
  • The product requirements stipulate that the clamping force should never drop below 6N over a ten-year life.


In the graph below, the FEA simulation predicts that the spring force will start out at around 10N, but then decay to 6N after ten years. It just barely meets our force requirement. Yet, we have no safety factor, and we’ve only calculated for room temperature.

What if this device also has heat-generating electronics or is exposed to warm summer days? The spring force will decay faster.

Clearly, it’s crucial that we know the long-term material behaviors of a product.

Decreased spring force at temperatures over time

This spring arm problem demonstrates the effects of stress relaxation, which happens with constant-strain loads. The arm deflection doesn’t change over time, but the internal stresses continue to dissipate over the years. If we could somehow wait for an infinite span of time, we’d find that the stress has decayed to zero.

This result proves that no unusual conditions or unique materials are required to generate creep and stress effects on a material’s performance. Any time a polymer part is under a continuous load, it will experience some of these behaviors to some extent. The higher the load and temperature, the more pronounced the impact will be.

What's Creeping Inside? Long-Term Structural Shifts

So, what’s going on here? Why do materials behave so differently when times are long and temperatures are elevated? The simplest explanation is that long-term loads cause the material’s structure to shift. In plastics, the polymer chains start to slip, stretch, and disentangle. Other materials undergo similar kinds of structural rearrangement.

Visualizing Short- & Long-Term Creep Behavior

One way to think about it is using the simple spring-dashpot model:

  • The spring on the right represents the short-term behavior, which follows the standard equation: σ/ε = E.
  • The section on the left represents the long-term behavior. It has another spring in parallel with a dashpot, which adds a time-dependent element.

 

When the material is first subjected to a load, the spring on the right stretches immediately. However, the section on the left hardly moves at all. Over time, though, the dashpot slowly begins to slide, adding to the overall deflection.

Real materials are more complex than this, but this illustration serves as a rough model to visualize what’s going on.

The Necessity of Testing & Empirical Data

Unfortunately, creep and stress relaxation mechanisms can be very complicated, and there is still active research in this area. To fully understand them, we would need to consider a host of variables, including these and many more:

  • Geometry
  • Stress magnitude and distribution
  • Strain rate
  • Cyclic loads
  • Temperature and humidity
  • Chemical environment
  • Material batch differences
  • Material aging
  • Manufacturing process

No simple equation can predict these behaviors under all possible conditions. We need to rely on empirical data gathered through rigorous testing for practical engineering work.

Understanding Creep Testing, Isochronous Curves, & the Creep Modulus Slope

Before using empirical creep data, it’s helpful to know how the testing was done. Most published creep data comes from long-term tensile testing.

  • In these tests, identical samples of material are loaded with various constant stresses (σ1, σ2, σ3, σ4, σ5).
 
  • Changes in length are measured over time and translated into strains (ε1, ε2, ε3, ε4, ε5).
 
  • At each time interval (1, 10, 100, 1000 hours, etc.) they plot (σ1, σ2, σ3, σ4, σ5) vs. (ε1, ε2, ε3, ε4, ε5).
 

Typically, these tests are run at various temperatures, resulting in a family of curves that describe the material’s behavior under long-term loads. These are called “isochronous” (equal time) curves. 

Tensile Creep example published by Covestro

When designing, we often consider the material’s elastic modulus (E), which is the slope of the short-term stress-strain curve. When considering creep or stress relaxation, we can use an analogous property called the creep modulus (E_creep) which is simply the slope of an isochronous curve. The creep modulus changes over time, so material datasheets often list more than one value, measured after different load durations (more on this later).

Because E_creep is always smaller than E, it’s tempting to think that the material has become less stiff over time. But E_creep is only valid for long-duration loads. The short-term modulus (E) doesn’t really change much over time (except in extreme cases).

Let’s think about the creep modulus with our earlier spring-dashpot model: 

  • If we suddenly increase the force after a long-duration load, the spring on the right will immediately stretch with the same spring rate it’s had from the beginning.
 
  • This means that the new short-term load will be controlled by E, not E_creep, and the material has not truly become less stiff.

While the creep modulus provides valuable insights into the material’s behavior under long-term loading conditions, it is crucial to recognize that its inherent stiffness, characterized by the elastic modulus, remains largely unaffected over time. This understanding is essential for accurate predictions and designs, particularly when dealing with short-term or transient loading scenarios.

In the next Part 2 of this series on Material Creep & Stress, we’ll examine how to use creep data to make better product design decisions. Check back soon!

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