A Deep-Dive Into Fatigue Life Estimation for Product Development

In the previous article in this series, we briefly touched upon the basics of fatigue life estimation in simulation-driven product development. In part 2, we continue to explore this subject in more depth. Let's begin with a refresher.


Fatigue Life Estimation


For all the parameters mentioned above, your loads would pulsate. The graph plotted between 'Stress Amplitude' and 'Cycles to Failure' signifies that as the stress amplitude decreases, the number of cycles would rise.

We plot S-N curves typically via a Three-point beam bending, which involves zero mean. We have S-N curves for positive and negative mean as-well; however, S-N curves typically have zero mean. 

Let us consider the maximum stress and the minimum stress as +10 and -10. Since the formula for mean goes as the ratio of the sum of all values by the total number of these values, the ultimate answer here is zero.

Thus, zero-mean stress here implies that the mean would be zero. However, the amplitude would be ten as it is the height of the peak.

When amplitude plummets from 10 to 1, you will witness a significant improvement in Fatigue Life. Some materials like steel can make the S-N curve asymptotic.



According to this graph, the graph almost flattens after it hits a particular value of stress amplitude. 



In this graph, the blue line depicts steel, and the red one denotes aluminum. The curve for aluminum does not become parallel to the X-axis, implying that reduction in stress would not give you infinite life.

If aluminum meets 10^7 cycles, it might have a prolonged life; however, any value preceding that would not give you an infinite lifespan like in the case of steel.


Fatigue Life Estimation - S-N Curve Based (Stress Based) - Constant Amplitude

In this section, we would learn to estimate the fatigue life of materials.




According to this figure, we might assume that after hitting a cyclic stress value of 40000, steel has an indefinite life. However, we need to calculate the lifespan in Basquin's region. 




'Sr' here is defined as the equivalent stress amplitude. It is 'A' times to the number of cycles to failure to the power 'B'.

By taking log on both sides, we can calculate both constants 'A' and 'B'.



In this curve, all the fatigue calculations help estimate the life for crack nucleation. It does not provide you with the value of life for final failure but only for crack initiation. We calculate that value in the section of 'Fracture Mechanics'.


Fatigue Life Estimation - S-N Curve Based (Stress Based) - Constant Amplitude: Mean Stress Correction

Until now, we discussed the S-N curve for zero mean-stress. Now we consider the case when the mean is not zero. 




The middle graph depicts zero mean as the upper amplitude is equivalent to the lower amplitude below the X-axis. 

The first graph depicts the compression zone, which implies that the entire sketch is below the axis, and both the upper and lower amplitude is negative values.

The lowermost graph depicts the tensile zone, implying that the entire sketch is above the X-axis, and both the upper and lower amplitude are positive values.




As per this graph, as your mean stress rises, your tolerance decreases. If your mean is very low, you can absorb a massive value of stress amplitude.

With the rise in mean stress, the ability to absorb fatigue load decreases.



As per the Basquin's equation, you calculate the initial amplitude, for which we use the Goodman line.

We deduce the value of the stress amplitude and obtain the number of cycles by placing the magnitude of Sr in the Basquin's equation, as stated above.


Mean Stress Correction



Goodman or Modified-Goodman are most commonly used to calculate mean stress correction. Some might use the Gerber's relation as-well, which is less conservative as it allows a higher mean.

The Goodman relation might have you settle for a lower value of alternating stress, while Gerber relation allows you to increase its magnitude by a few leaps for the same figure of mean stress.

Goodman's line recedes more towards the origin as it becomes half of the initial limit and becomes more conservative, with the factor of safety being two, which is a high value.


Fatigue Life Estimation - S-N Curve Based (Stress Based): Variable Amplitude



So far, you might have observed that we have assumed graphs only with constant amplitudes for calculations. However, now you shall study the equations and calculations for varying amplitude.

You might observe fatigue loading from the engine of an automobile, presumably +10 to -10. With load vibrations adding on to the fatigue, the amplitude escalates to +15 to -15. Thus, fatigue life calculations become tedious in scenarios where parameters are mercurial.

Instead, you must calculate the damage for the fatigue life cycle with amplitude 10 and 20 separately. We do not consider average but segregate the calculations for more accuracy. 

After calculating individual damage values, the next step is to sum them collectively and equate them with one. 

If the factor of safety is not prevalent, then we automatically set the limit for damage to one. We call this rule the Minus Rule.


Improving Fatigue Life




As discussed earlier, negative mean increases life; and thus, you must devise ways to induce a negative mean. Negative mean implies inducing negative residual stresses. 

Here are some widely used methods -

  • Short-peening
  • Overloading (loading beyond yielding point) and unloading

Short-peening is a cold working process where the surface of the part gets bombarded with a small spherical media called shot. Each shot that strikes the facet acts as a tiny peening hammer, leaving a minute indentation. 

The net result is a layer of material in a state of residual compression. Cracks do not propagate in a compressively stressed zone. 


Fatigue Life Estimation - Strain Based Approach: Constant Amplitude



The stress-life approach applies to situations requiring primarily elastic deformation. Under these conditions, we expect the component to have a long lifetime. 

For situations dealing with high stresses, temperatures, or stress concentrations such as notches, where significant plasticity gets involved, the approach is not appropriate. Thus, we use the strain-based technique. 

As we have the curve between Stress Amplitude to the Number of Cycles, we assume that the high-cycle fatigue starts beyond the 10^6 cycles, and the low-cycle fatigue precedes this figure.

High-cycle fatigue is stress dominated because as long as the material is in the linear zone, the stress is directly proportional to strain. 

However, after entering the plastic zone, the stress does not show much increase while the strain keeps increasing. 

The entire high-cycle fatigue lies in the zone where stress increases with strain, and the low-cycle fatigue lies when the material enters the plastic domain. 

In the plastic zone, the factor of strain becomes the deciding criteria as stress varies diminutively. The algorithms that work in the plastic domain rely on the strain, while those in the low-cycle fatigue zone rely on stress.


Final Words

It is necessary to estimate the fatigue life of material under various conditions, especially in a realistic environment to test the limits of your product and ways to improve it.

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