Understanding Fatigue Failure and S-N Curves

Summary

This video script delves into fatigue failure, a leading cause of mechanical engineering breakdowns globally. It explains the three stages of fatigue—crack initiation, growth, and fracture—highlighting the significance of S-N curves for predicting failure under cyclic stress. The script contrasts high cycle and low cycle fatigue, discusses variability in test results, and introduces methods like the Goodman diagram and Miner's rule for assessing complex loading conditions. It also touches on Linear Elastic Fracture Mechanics for existing cracks, offering a comprehensive guide to fatigue analysis in engineering.

Takeaways

• 🔧 Fatigue failure is a common cause of mechanical engineering failures worldwide, affecting components subjected to time-varying loads like bolts, crank arms, and pipelines.
• 💥 Fatigue failure is a three-stage process involving crack formation at stress concentrations, crack growth, and eventual fracture once the crack reaches a critical size.
• 📊 To predict fatigue failure, S-N curves are used, which plot the number of cycles to failure against the applied stress range, typically on a logarithmic scale.
• 📉 S-N curves for many materials are available in engineering codes, and for ferrous materials, they show an endurance limit where the material theoretically won't fail due to fatigue at stress ranges below this limit.
• 🔁 High cycle fatigue involves low stress levels and a large number of cycles, while low cycle fatigue involves higher stress levels and fewer cycles, with both elastic and plastic deformations.
• 📈 The variability in fatigue test data is significant, and published S-N curves are often adjusted downwards to reduce the probability of failure from 50% to a lower percentage, such as 1%.
• 🔄 Constant amplitude fully reversing cycles are used in fatigue tests, with terms like stress range, stress amplitude, and mean stress being key to understanding the test conditions.
• 📊 The Goodman diagram is a method to account for the effect of mean stress on fatigue life, providing a safe region below a plotted line for different mean stress values.
• 🌊 Complex loading conditions can be simplified using techniques like the Rainflow counting method and Miner's rule, which helps in calculating the cumulative fatigue damage from different stress ranges.
• 🚫 If a structure contains an existing crack, the S-N approach is not suitable, and Linear Elastic Fracture Mechanics should be used to determine the fatigue life based on crack growth.
• 👀 Understanding and applying these concepts is crucial for engineers to predict and prevent fatigue failure in mechanical components, ensuring safety and reliability in various applications.

Q & A

What is fatigue failure in mechanical engineering?

Fatigue failure occurs when components subjected to time-varying loads fail at stresses below the material's ultimate strength, typically due to the formation and propagation of cracks over time.

Why are bolts in an office chair, crank arms on a bicycle, and pressurized oil pipelines at risk of fatigue failure?

These components are at risk of fatigue failure because they are subjected to varying loads over time, which can lead to the initiation and growth of cracks, eventually causing failure.

What are the three stages of fatigue failure?

The three stages of fatigue failure are: 1) crack formation, usually at free surfaces and stress concentrations, 2) crack growth in size, and 3) fracture after the crack reaches a critical size.

How can S-N curves be used to predict fatigue failure?

S-N curves, which plot the number of cycles to failure (N) against the applied stress range (S), allow engineers to estimate the number of cycles a component can withstand before failing due to fatigue for a given stress range.

What is the significance of the endurance limit in S-N curves?

The endurance limit is the stress range below which a component could theoretically be cycled indefinitely without failing due to fatigue, making it a crucial parameter in fatigue design.

How do high cycle fatigue and low cycle fatigue differ?

High cycle fatigue occurs with low applied cyclical stresses and failure happens after a large number of cycles, typically over 10,000, involving only elastic deformation. Low cycle fatigue involves higher stresses, leading to failure after fewer cycles and includes both elastic and plastic deformation.

Why is there variability in fatigue test results even with identical test pieces?

Variability in fatigue test results is due to the complex nature of fatigue processes, including factors such as material inconsistencies, microscopic defects, and environmental conditions, which can all influence the outcome.

How are S-N curves adjusted to reduce the probability of failure?

S-N curves are adjusted by shifting the mean curve downward by a certain number of standard deviations to account for the variability in test results, thus reducing the probability of failure from 50% to a lower percentage, such as 1%.

What is the Goodman diagram and how is it used?

The Goodman diagram is a graphical method used to account for the effect of mean stress on fatigue life. It plots mean stress on the horizontal axis and stress amplitude on the vertical axis, with a line drawn between the endurance limit at zero mean stress and the material's ultimate tensile strength at zero stress amplitude.

How can complex stress spectra be simplified for fatigue analysis?

Complex stress spectra can be simplified using techniques like the Rainflow counting method, which breaks down the stress history into simpler constant amplitude cycles, allowing for more straightforward fatigue life prediction.

What is Miner's rule and how does it contribute to fatigue analysis?

Miner's rule is used to calculate the cumulative damage caused by different constant amplitude stress ranges in a complex stress spectrum. It sums the damage fractions for each stress range, where individual contributions are the ratio of cycles experienced to cycles to failure for that stress range.

Outlines

00:00

🔩 Fatigue Failure in Mechanical Engineering

This paragraph discusses the concept of fatigue failure, a leading cause of mechanical engineering failures worldwide. It explains that components like office chair bolts, bicycle crank arms, and oil pipelines can fail under varying loads, even at stresses below their ultimate strength. The process of fatigue failure involves crack formation at stress concentrations, crack growth, and eventual fracture once the crack reaches a critical size. To predict fatigue failure, S-N curves are used, which plot the relationship between the number of cycles to failure and the applied stress range. These curves are derived from fatigue tests and can estimate the lifespan of a component under specific stress conditions. The paragraph also introduces the endurance limit, a stress range below which a component could theoretically cycle indefinitely without failing due to fatigue.

05:02

📊 Advanced Fatigue Analysis Techniques

The second paragraph delves into more complex aspects of fatigue analysis. It begins by defining key terms such as stress range, stress amplitude, and mean stress, and explains how these factors can affect the fatigue life of a component. The paragraph highlights the impact of tensile mean stress on reducing fatigue life and introduces the Goodman diagram, a tool for adjusting the endurance limit to account for mean stress. The Goodman diagram is used to determine if a component will have an infinite life under certain loading conditions. The paragraph also addresses more complex real-world loading scenarios, introducing techniques like the Rainflow counting method and Miner's rule to simplify and calculate the cumulative damage from variable stress cycles. Finally, it mentions the Linear Elastic Fracture Mechanics approach for assessing the fatigue life of structures with existing cracks, which involves calculating a critical crack size and using a crack growth law to estimate the time to fracture.

Keywords

💡Fatigue Failure

Fatigue failure is the process by which a component or material fails under repeated cycles of stress that are below its ultimate strength. It is a critical concept in the video as it explains the primary cause of mechanical engineering failures worldwide. The script uses examples such as bolts in an office chair and pressurized oil pipelines to illustrate components at risk of this type of failure.

💡Crack Formation and Propagation

Crack formation and propagation are the stages in the fatigue failure process where cracks initiate at stress concentrations and grow over time. This concept is central to understanding how fatigue failure occurs, as it details the physical changes that lead to component failure. The video script describes this as a three-stage process, emphasizing the importance of monitoring and managing these stages to prevent failure.

💡S-N Curve

The S-N curve, or stress versus number of cycles to failure curve, is a graphical representation used to predict the fatigue life of a material under constant amplitude stress cycles. It is a key tool in the video for determining the likelihood of fatigue failure. The script explains how this curve is derived from fatigue tests and used to calculate the number of cycles until failure for a given stress range.

💡Endurance Limit

The endurance limit is the stress level below which a material can be cycled indefinitely without failing due to fatigue. It is highlighted in the video as an important fatigue design parameter, especially for ferrous materials. The script notes that the S-N curve becomes horizontal at a large number of cycles, indicating the endurance limit.

💡High Cycle Fatigue

High cycle fatigue refers to the failure of a material after a very large number of cycles, typically more than 10,000, under low applied cyclical stresses. The video script differentiates this from low cycle fatigue, noting that high cycle fatigue involves only elastic deformation and is a significant aspect of fatigue analysis.

💡Low Cycle Fatigue

Low cycle fatigue is characterized by failure after fewer cycles due to higher applied cyclical stresses. The video script explains that this type of fatigue involves both elastic and plastic deformation because the stresses are above the material's yield stress. It is contrasted with high cycle fatigue to illustrate different fatigue scenarios.

💡Coffin-Manson Relation

The Coffin-Manson relation is a strain-based approach used for predicting fatigue life, particularly in the context of low cycle fatigue. The video script mentions this relation as an alternative to the S-N curve approach when dealing with higher stresses that cause both elastic and plastic deformation.

💡Goodman Diagram

The Goodman diagram is a graphical method for estimating the fatigue strength of materials under variable stress conditions, taking into account the mean stress. The video script describes how this diagram is used to adjust the endurance limit for mean stress, providing a safety criterion for components subjected to non-zero mean stresses.

💡Rainflow Counting Method

The Rainflow counting method is a technique used to simplify complex stress spectra into simpler constant amplitude cycles. The video script introduces this method as a way to manage real-world cases where loading conditions are more complex than constant amplitude fully reversing cycles.

💡Miner's Rule

Miner's rule is a method for calculating the cumulative fatigue damage caused by different constant amplitude stress ranges. The video script explains that it sums the damage fractions for each stress range to determine if the total damage fraction exceeds one, indicating fatigue failure.

💡Linear Elastic Fracture Mechanics

Linear Elastic Fracture Mechanics (LEFM) is an approach used to determine the fatigue life of structures containing existing cracks. The video script mentions that if the dimensions of a crack are known, LEFM can be used to calculate the time required for the crack to grow to a critical size that would result in fracture.

Highlights

Fatigue failure, occurring at stresses below a material's ultimate strength, is a major cause of mechanical engineering failures globally.

Examples of components at risk of fatigue failure include bolts in office chairs, bicycle crank arms, and pressurized oil pipelines.

Fatigue failure is a three-stage process involving crack formation, growth, and eventual fracture.

Fatigue tests subject components to constant amplitude stress cycles to determine the number of cycles until fracture.

S-N curves graph the relationship between the number of cycles to failure and applied stress range, aiding in predicting fatigue life.

An S-N curve can predict component failure time, such as one year for a stress range of 100 MPa with one cycle per minute.

Published S-N curves for various materials in engineering codes provide a foundation for fatigue analysis without the need for individual testing.

The endurance limit on S-N curves represents the stress range below which a component could theoretically never fail due to fatigue.

High cycle fatigue involves low cyclical stresses and failure after over 10,000 cycles, dealing with only elastic deformation.

Low cycle fatigue features higher cyclical stresses, fewer cycles to failure, and involves both elastic and plastic deformation.

Variability in fatigue test results is common, necessitating the use of a best fit S-N curve and consideration of standard deviations.

Engineering codes often adjust S-N curves downward by two standard deviations to reduce the probability of failure to 1%.

Fatigue tests typically involve constant amplitude fully reversing cycles, defining specific terms like stress range, amplitude, and mean stress.

The Goodman diagram adjusts the endurance limit to account for mean stress, providing a method to ensure infinite fatigue life.

Rainflow counting method and Miner's rule are techniques for simplifying complex stress spectra and calculating cumulative fatigue damage.

If an existing crack is present, Linear Elastic Fracture Mechanics can be used to determine fatigue life instead of the S-N approach.

Fatigue analysis is crucial for predicting the lifespan and safety of mechanical components subjected to varying loads.

Transcripts

Components which are subjected to loading which varies with time can fail

at stresses well below the material's ultimate strength.

This is known as fatigue failure

and it accounts for the vast majority of mechanical engineering

failures worldwide.

The bolts in an office chair,

the crank arm on your bicycle,

and pressurized oil pipelines, are just a few examples of components

which are subjected to time varying loads, and may be at risk of fatigue failure.

Fatigue failure occurs due to the formation and propagation of cracks.

It is a three-stage process.

The first stage is crack formation. This usually

occurs at free surfaces and at stress concentrations.

In stage 2 the crack grows in size,

and in stage 3,

after the crack has grown to a critical size,

fracture occurs.

So how can we figure out whether a component is likely to fail due to fatigue?

One common approach is to run fatigue tests by subjecting a component

or test piece to a large number of constant amplitude stress cycles, and

counting the number of cycles until it fractures.

If we repeat this test a large

number of times with different applied stress ranges, we can plot the results on

a graph, with the number of cycles to failure N on the horizontal axis and the

applied stress range S on the vertical axis.

Because the number of cycles to

failure can be very large, a log scale is usually used for the horizontal axis.

By fitting a curve to the data points we obtain what is known as an S-N curve.

The S-N curve allows you to calculate the number of cycles until a component is

likely to fail for a given stress range. For example if we have a stress range of

100 MPa or 15 ksi this S-N curve tells us that the number of cycles to

failure is 500,000. If we know that our component is subjected to one cycle per

minute we could predict that our component will fail due to fatigue after

approximately one year.

Fortunately we don't have to perform these

time-consuming fatigue tests ourselves. S-N curves for many different materials

are already published in different engineering codes.

For some materials, and in particular for ferrous materials,

is important to note that the S-N curve

at a very large number of cycles becomes a horizontal line.

This is known as the endurance limit.

Theoretically the component could be cycled at stress

ranges below this level forever, and it will never fail due to fatigue.

This makes the endurance limit an important fatigue design parameter.

It is common to differentiate between high cycle and low cycle fatigue.

High cycle fatigue occurs when the applied cyclical stresses are low and failure

occurs after a very large number of cycles, typically more than 10,000 cycles.

Because the stresses are low we are only dealing with elastic deformation.

Low cycle fatigue involves higher applied cyclical stresses and failure occurs

after fewer cycles. Because the stresses involved are above the material yield

stress both elastic and plastic deformation occur.

In these cases a strain based approach, using for example the Coffin-Manson relation,

is usually preferred to the S-N curve approach.

If we return to the data from our fatigue tests, we can see that there is a

large amount of variability in the data. This is typical for fatigue tests even

when identical test pieces are used.

If we use a best fit S-N curve, as we have

done here, there is a significant possibility that our component will fail

at a much smaller number of cycles than the curve predicts.

This test piece for example failed at

a much lower number of cycles than predicted by our S-N curve.

For this reason S-N curves published in engineering codes are normally shifted

downwards by a certain number of standard deviations to give a reduced

probability of failure.

Here, by shifting the mean curve down on the vertical axis

by two standard deviations, we have reduced the probability of failure from 50% to 1%.

Fatigue tests are usually run for the constant amplitude fully reversing

cycles you can see here. The same stress magnitude is applied in tension

and in compression.

Let's define a few terms - the stress range is defined as the

difference between the maximum and minimum stresses.

The stress amplitude is defined as half of the stress range.

The mean stress is the average of the maximum and minimum stresses.

In this case the mean stress is zero.

But this is only one very specific type of loading.

In some cases we might have a mean

stress which is not equal to zero, as shown here.

This mean stress will have an effect on the fatigue life.

A tensile mean stress will typically result in a shorter fatigue life.

One way to account for a tensile mean stress is to use S-N

curves derived for specific values of mean stress.

But these are often not available,

or would be time consuming to obtain.

Another approach is to use the Goodman diagram,

which adjusts the endurance limit to account

for a mean stress.

Let's see how it works.

On a Goodman diagram the mean stress is shown

on the horizontal axis and the stress amplitude is shown on the vertical axis.

A straight line is drawn between the endurance limit at a mean stress of 0

and the material ultimate tensile strength at a stress amplitude of 0.

If our cyclic loading conditions are located below the Goodman line,

our component will be safe from fatigue failure.

There are a few different variations of this diagram,

as you can see here.

This approach can only be used to

determine whether a component will have an infinite life. It doesn't allow us to

calculate a fatigue life.

In many real-world cases the applied loading is

likely to be far more complex than what we have considered so far.

We can use techniques like the Rainflow counting method to simplify a complex stress

spectrum into a number of simpler constant amplitude cycles

Miner's rule allows us to account for the cumulative damage caused by each of

these different constant amplitude stress ranges.

It calculates the damage fraction D as the sum of the fatigue damage contributions for each stress

range. The individual contributions are calculated by dividing the number of

cycles by the number of cycles to failure for that stress range.

The damage contributions from all stress ranges are then summed.

If the total summed damaged fraction is greater than one

fatigue failure is considered to have occurred.

In this example the damage fraction D sums to 0.94. This is less

than 1, and so fatigue failure has not occurred.

If the structure we are assessing contains an existing crack,

the S-N approach is not suitable for

determining the fatigue life.

If the dimensions of the crack are known, we can

instead determine the fatigue life using a Linear Elastic Fracture Mechanics approach.

This involves calculating a critical crack size which would result in fracture,

and using a crack growth law to calculate

the time required for the crack to grow to this critical size.

But that's enough about fatigue for now.

Stay tuned for more engineering videos!