Some Thoughts on Accelerated Durability Testing

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Siemens Valued Contributor

Got a standard fatigue test that is always run for your product?  Does it perfectly replicate the desired customer usage, down to the hours and hours the product should last?

 

Who has time to wait for a fatigue test to finish?  The pressure is on! We want to know now: will the latest product design last or not? The quicker the results the better!

 

Fortunately, there are methods to accelerate a fatigue test. The most common methods (Figure 1) include:

  1. Increase the load level
  2. Apply cycles more quickly
  3. Omit non/low damaging events from the test profile

accelerated_testing_options.pngFigure 1: How can I make my durability test go faster? Increase the speed? Increase the amplitude? Something else?

Great! But which method should be used?  What are the pros and cons? Each of these different methods are discussed in more detail in the following sections.

 

Load Level

 

Perhaps to make the test finish quicker, all I have to do is turn up the amplifier to the shaker a little bit!  Or maybe a lot?  The higher the shaking forces, the quicker the test, right?

 

Unfortunately, it is not that easy.  Increase the shaking force level too much, and it will break in a way that it would never fail during actual customer usage.  How much of an increase is too much?  How much can the test time be reduced?

 

For many materials, there is a logarithmic relationship between load and the number of fatigue cycles (see material curve in Figure 2).  Increase the test level a small amount, for example 15%, and the fatigue life will be reduced by 50%. 

 

cycles_vs_load.pngFigure 2: For a material curve with a slope of k=5, a 15% change in load level changes the test time by 50%.

This means a relatively small increase in load can reduce the test time significantly. To learn more about a material property curve, see the SN-Curve knowledge base article.

 

The slope of the SN-Curve is different depending on the material used to make the product.  The slope, expressed as a k-factor, is typically 5 for many steels.  However, the k-factor can differ depending on the material used.  For example, most aluminums have a k-factor of 7, which leads to a 60% reduction in life (versus 50% for steel) for a 15% increase in load. 

 

key_small_load_big_life.png

 

Why not double the load level, rather than increasing it by a measly 15%?  Consider the classic SN curve (Stress versus Number of Cycles) shown in Figure 3:

  • The ultimate tensile strength point is the load where one cycle fails the material.
  • The yield strength separates the plastic and elastic region (see Figure 3) of the material. The failure mechanisms are different in the two regions.
  • If all loads are in the infinite life region (see Figure 3), below the endurance limit, no failure can occur.

For many steels, the ratio of the ultimate tensile strength and the endurance limit is about 2 to 1.

 

double_load.pngFigure 3 – The ultimate strength of a typical SN curve for steel is two times the endurance limit. Unwisely doubling the stress levels can lead to unrepresentative failures in the fatigue life verification test.

The red and orange dots in Figure 3 shows a very simplified example of how to not accelerate a fatigue test.  

 

The current test, represented by the orange dot, takes 100,000 cycles to complete.   Perhaps that is a long time to wait to verify that the current product design will live up to the expected life.  So your manager may say “Hey, crank up the amplitude of that test!  Double it!” in order to not have to wait for all 100,000 cycles to complete.

 

Unbeknownst to the manager, by doubling the stress level, the product will fail in one cycle (red dot in Figure 3)! This would not be the best way to accelerate the test!

 

key_double_load.png

 

When increasing the load levels of the test, it is desirable to keep the amplitude of the stress cycles within the same region of the SN-curve as shown in Figure 4.

 

sn_curve_regions.pngFigure 4 – The SN curve of a typical metal has three regions: plastic, elastic, and infinite life. Load levels in an accelerated test should not change regions in which they operate.

The fatigue failure mechanism in the elastic region is different than that of the plastic region.  If the loads were increased in level from the elastic region to the plastic region, a different type of failure is induced.  This failure would not occur in real product usage where the loads operate only in the elastic region.

 

key_acceleration_same_region.png

 

If loads for a test only occurred in the infinite life region (which is a pretty long test!), increasing the levels into the elastic region would cause failures, whereas none would occur on the original test.

 

Note: It is always a good practice to understand the maximum load relative to the endurance limit and where it will be after the scaling operation.  The level of the cycles in an endurance test can be determined by using the rainflow counting method to analyze the loads.

 

If the load levels and SN-curve material properties are already known, why run the test at all?  The material property is not the only factor governing the fatigue life of a product.  The geometry of the part is also an influence, so the test needs to be run to ensure the part will last.  For example, a part made with sharp corners creates ‘stress concentration’ areas that can lead to shorter fatigue life.  These stress concentrations can be reduced by making the part with rounded corners.

 

Apply Cycles More Quickly

 

Faster! Faster!

 

Can’t the speed of the test be increased simply by applying the cycles more quickly?  Fatigue is not a frequency dependent phenomenon, correct?

 

For example, if the test machine applies 8 cycles per second, I can just increase it to 16 cycles per second to halve my test time. Right?

 

There are two factors that should be considered before running a test faster: heat buildup and natural frequency behavior.

 

Heat

 

A test can be sped up, but if it goes too fast, heat will build up in the part which cannot be dissipated quickly.  This heat would cause a pre-mature failure that would not occur during the original test. A general rule of thumb is that the temperature of the part should not increase by more than 10 degrees Fahrenheit (~6 degrees Celsius) from the original test.

 

Natural Frequency

 

The frequency content is a consideration, especially in a test where exciting a resonant frequency could create higher than expected deformations (see Figure 5).

 

natural_frequency.pngFigure 5 – Comparison of load time history and power spectral density of original test (red) and increased speed test (green). Increasing the speed of the test (left graph) causes the test to excite a natural frequency which was not excited previously (right graph).

In particular, the frequency content of the loads should not be increased so that it excites a resonance of the part or product that was not previously being excited.  In Figure 5, the spectrum (original in red, accelerated in green) is shifted in frequency by performing the same test schedule (left graph) at a faster rate. 

 

The shape in the frequency domain is the same (red and green curves in right graph).  Looking at the power spectral density spectrums, notice the shape of both curves are identical. The green curve is just stretched over a wider frequency range than the red curve.  Think of a recording of a voice that is played back at triple speed – you can still make out the words, but the voice has a much higher pitch!

 

If there was a resonance in the product (represented by the purple line), it would not be excited in the original test (red spectrum), but would be excited by the accelerated test (green spectrum).

 

key_resonance.png

  

This will cause the structure to experience higher deformations in the accelerated test, which can cause the part to fail earlier than it would on the original test.

 

Omit Non-Damaging or Low Damage Cycles

 

Many cyclic fatigue tests consist of a variety of cycles, differing in amplitude and number of occurrences.

 

The cycle information is typically contained in a rainflow matrix (Figure 6) which shows:

  • Cycle Amplitudes: The cycle amplitude is the difference of the from load level and to load level values on the X and Y axis.
  • Number of Cycles: The number of cycles (indicated by the color key) at a given from and to value.

 

rainflow_high_low_damage.pngFigure 6 – The rainflow diagram contains the number of fatigue cycles and their amplitudes for a fatigue test. Some cycles create little damage (denoted in green) while others create higher damage (denoted in red).

The cycles contained along the diagonal area of the rainflow diagram are of low amplitude, and do not create much damage.  These cycles go to and from very similar load levels, hence the cycles appear on the diagonal of the rainflow matrix.

 

The highest amplitude load cycles go to and from very different load levels, and are indicated in red on the rainflow diagram.

 

In this fatigue test, indicated by the rainflow diagram, 7% of the cycles (outlined in red) account for 99.5% of the fatigue damage. 

 

To accelerate the test, the low damage cycles can be removed from the diagonal area of the rainflow diagram. An equivalent reduced time history can then be written out from the modified rainflow data (Figure 7).

 

time_history_modification.pngFigure 7: A reduced time history with 99.5% of the damage of the original test is created by removing the appropriate cycles along the diagonal of the rainflow diagram.

This reduced time history is shorter than the original time history.  The amount of reduction depends on the number of cycles removed.

 

This reduction method can be done while still preserving key attributes of the original test durability.  For example, the frequency content can be preserved, and not altered, as shown in Figure 8.

 

shorter_test_with_spectral_content_preserved.pngFigure 8 – Time data is reduced (red – original, green – reduced) in the test (upper graph), but frequency content (bottom left) and damage content (bottom right) are preserved.

Another important aspect when doing a durability test reduction is to preserve any multi-axial loading relationships.  Data can exist on multiple load measurement channels that have related phase as shown in Figure 9.

 

uni_vs_mult_axial.pngFigure 9: Left – Uniaxial load time history can be compressed without phase concerns, Right – Multiaxial loading must take phasing into account when doing compression.

Sometimes the phasing of multiple channels should be kept intact when the durability test time is reduced.  To preserve multiaxial phasing, common time segments are kept across different channels.  As a result, the reduction in test time will not be as large as if the phase preservation was not required.

 

key_omit.png

 

One benefit of removing low or non-damaging events to reduce test times is that the amplitude does not need to be increased. Increasing the amplitude can lead to causing unrepresentative failures in the accelerated tests, as previously discussed.

 

Conclusions

 

When looking to accelerate a durability test, there are several key items to keep in mind:

  • Load levels should not be increased such that they create un-representative failures by moving into different region of material curve.
  • The rate at which loads are applied should not be increased such that temperature is raised too much, or a natural frequency is excited that would not normally.
  • Low damage cycles can be omitted to accelerate a test without increasing load level. This can be done with regard to frequency content preservation and/or multi-axial loading considerations.

There are many other considerations and methods for accelerating tests which were not covered in this article, including frequency based fatigue using Power Spectral Density functions (through mission synthesis) and block cycle testing.

 

Need to accelerate your durability test?  Tools like Simcenter Testlab Neo from Siemens can be used to acquire, analyze, and design your test.

 

Questions or other thoughts?  Email john.hiatt@siemens.com or download the Simcenter Testlab Fatigue and Load Data Analysis Solution Brief.

 

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