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.