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- Fatigue & Fracture Mechanics in Finite Element Analysis

Fatigue failure occurs when a material is subjected to repeated loading and unloading cycles. The level of stresses present to cause failure may be well below values considered safe for a single static load application. The critical fatigue initiation is usually at a very localized site and may be a result of additional factors such as stress concentration due to component shape, surface finish or corrosion pitting.

Fatigue has been cited as one of the major causes of in-service failure throughout engineering history. The earliest application of rotating machinery with its attendant cyclic nature produced documented fatigue failures. Textile loom machinery, pumping machinery and above all steam railway operations were beset by a mode of failure that was not understood. The early railway axle failures and mining equipment failures prompted fundamental testing and research. The theories on which much of modern fatigue analysis is based on were developed all through the industrial revolution and into the 1920’s.

The advent of more complex structures with more complex loading histories was typified by the introduction of the first jet powered airliners. Sadly new fatigue lessons had to be learned in the period from 1954 as a result of the DH Comet crashes.

The nature and prediction of fatigue is much more understood, and is a requirement for most design products today. However the application of fatigue analysis is not easy and a good background is essential to be able to use the powerful FEA method as a basis for fatigue analysis.

Much of the terminology used in setting up the fatigue problem through a modern GUI is confusing and the choice of options is not always clear.

**The objective of this course is to break down the fatigue analysis process into clearly defined steps, give an overview of the physics involved and show how to successfully implement practical solutions using Finite Element Analysis.**

All attendees on the course will be able to download a fully functioning Fatigue Life Calculator. As well as forming a useful tool for many of the homework tasks set, attendees will be able to explore the implications of both High Cycle and Low Cycle Fatigue as discussed in the class.

A tutorial guide is also available for download. Basic Material Data and Strain Life Material data is input, or derived from fundamentals. Neuber notch and Plastic material intersection points are found allowing a hysteresis cycle to be plotted. The strain life curve is plotted and the number of cycles to failure is calculated.

The Calculator has been steadily developed over the last few years of delivering this course and attendees will be entitled to future upgrades.

Each topic in the class is treated as a building block and is presented using an overview of the physics and theory involved. The math is kept simple and the emphasis is on practical examples from real life to illustrate the topic. The mapping to Finite Element analysis techniques is shown with numerous workshops.

**Who Should Attend?**

This course is aimed at practicing engineers who wish to learn more about how to apply finite element techniques to fatigue analysis in the most effective manner. Ideally a student should have some experience of FEA analysis, but this is not essential. The material that is presented is independent of any particular software package, making it ideally suited to current and potential users of all commercial finite element software systems. This course is a must for all engineers aiming to use FEA as a reliable predictive tool for fatigue analysis.

- Introduction to Fatigue
- High Cycle Fatigue Methods
- Mean Stress Effects
- Fatigue Correction Factors
- Loading Environment
- Low Cycle Fatigue Overview
- FEA Application of Fatigue

- Notch Effects in High Cycle Fatigue
- Notch effects Low Cycle Fatigue
- Low Cycle Fatigue - Overview
- Low Cycle Fatigue - Mean Stress
- Low Cycle Fatigue - Data
- Cycle Counting Methods

- More FEA implications
- Stress Concentrations
- Multi Axial Fatigue

- Background to Random Analysis
- The PSD specification
- Vibration Fatigue Analysis
- Examples

- Introduction to Fracture
- FEA Implementations
- Fatigue in Composites

ID |
Competence Statement |

FATkn1 | List the conditions necessary for fatigue failure. |

FATkn2 | List the possible sources of cyclic loading in your company products. |

FATkn3 | List potential sites for fatigue in your company products. |

FATkn4 | Sketch a sinusoidal stress variation and show the maximum stress, minimum stress, mean stress, alternating stress (or stress amplitude), stress range and stress ratio. |

FATkn5 | List a common source of harmful tensile residual stress in your company products. |

FATkn6 | List ways of inducing beneficial compressive stresses in your company products. |

FATkn7 | Sketch a fatigue diagram, showing the Modified Goodman, Gerber, Soderberg and Langer/Yield lines. |

FATkn8 | Sketch typical welds, highlighting features detrimental to fatigue performance. |

FATkn11 | Define the terms Nominal stress, Notch stress, Equivalent stress and Weld-Throat stress. |

FATco1 | Discuss the initiation, propagation and fast fracture stages of Fatigue in metallic materials. |

FATco2 | Describe how the data used to construct an S-N curve are obtained. |

FATco3 | Discuss the term high cycle fatigue, highlighting a common source in your company products. |

FATco4 | Discuss the statistical nature of fatigue and explain how this is handled in relevant design standards and codes of practice. |

FATco5 | Discuss the salient features of an S-N diagram for steels and explain the terms endurance limit, infinite life and low cycle fatigue. |

FATco6 | Discuss the typical appearance of a fatigue failure surface in a metallic component and explain how the source of the fatigue failure is commonly identified. |

FATco7 | Discuss the observed relationship between endurance limit and static tensile strength for steels and explain why this relationship does not hold for welded steels. |

FATco8 | Discuss the philosophy of Safe Life Design. |

FATco9 | Explain the term Damage Tolerant Design. |

FATco10 | Contrast the Stress-Life and Strain Life / Manson-Coffin approaches to fatigue assessment. |

FATco11 | Explain the use of Endurance Limit Modifying Factors in Stress-Life based fatigue assessment. |

FATco13 | Discuss the effects of corrosion on fatigue life and highlight how this is typically handled in relevant standards and codes of practice. |

FATco14 | Discuss the term Fatigue Strength Reduction Factor in relation to stress concentrations and explain how this has traditionally been handled in relevant design standards and codes of practice. |

FATco15 | Discuss the concept of cumulative damage and explain how this is commonly handled. |

FATco16 | Explain why a multiaxial stress field can complicate an analysis and discuss approaches to handling this. |

FATco17 | Discuss the significance of the choice of equivalent stress used in the fatigue assessment of welded joints |

FATco18 | Outline a conservative approach to situations where the directions of principal stresses vary during a stress cycle. |

FATco21 | Discuss why weld toe grinding can be beneficial and explain how a design standards and codes of practice will typically allow for this improvement. |

FATco25 | Reflect on why fatigue is such a long-standing and persistent cause of failure. |

FATco26 | Discuss the nature of and typical locations for, stress singularities in a finite element model and explain how they would typically be handled in a fatigue analysis. |

FATco27 | Describe the approximations inherent in a plate/ shell idealisation of welded joints and how these could influence fatigue assessment. |

FATco28 | Discuss the term Effective Notch Stress and Nominal Stress. |

FATco29 | Explain how a Cyclic Stress-Strain Curve is constructed and used. |

FATco30 | Explain Neuber's Rule and its limitations and why corrections to the elastic strain range from an elastic analysis may be necessary. |

FATco31 | Discuss the term Local Plastic Strain Amplification Coefficient and Elastic Follow-Up. |

FATco33 | Explain why corrections for mean strain are often unnecessary for low cycle fatigue. |

FATco35 | Discuss the term endurance limit for many non-ferrous metals, steels in a corrosive environment and the possible effects of load sequencing. |

FATco37 | Reflect on how variable amplitude load sequencing can affect the prediction of damage accumulation and fatigue life. |

FATap1 | Employ a fatigue diagram, consisting of Modified Goodman and Langer lines, to assess fatigue performance of components. |

FATap2 | Carry out elastic fatigue assessment using design standards and code guidelines for components and structures including any special procedures for ancillary components such as bolts, |

FATap5 | Use Reservoir Counting / Rainflow Method or similar to specify the necessary stress ranges, number of cycles and loading history for any component to be analysed. |

FATap6 | Employ a finite element analysis system for the fatigue analysis of a component or structure. |

FATap7 | Use hot spot stress techniques (extrapolation and/ or linearization) to determine structural stresses for fatigue assessment. |

FATsy1 | Prepare a fatigue analysis specification, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties. |

FATsy2 | Plan a fatigue analysis, specifying necessary resources and timescale. |

FATsy3 | Prepare quality assurance procedures for fatigue analysis activities within an organisation. |

FATsy4 | Specify whether a Fracture Mechanics approach is more appropriate. |

FATev1 | Assess the significance of neglecting any feature or detail in any idealisation being used for fatigue assessment. |

FATev2 | Assess the fatigue significance of simplifying geometry, material models, loads or boundary conditions. |

FAFMkn1 | Give an overview of the historical development of fracture mechanics |

FAFMkn2 | Summarise the scope of fracture mechanics for the different types of cracks and material situations |

FAFMkn3 | Define stress intensity factor and state the relationships between G and KI, KII and KIII for plane stress and plane strain crack tip conditions |

FAFMco1 | Explain the Griffith criterion and the significance of the toughness parameter Gc |

FAFMco3 | Identify the key field variables (displacement, strain, stress and principal stress) relevant to a general 3D crack profile and sketch their components. |

FAFMco6 | Describe the significance of the strain energy release rate G |

FAFMco8 | Describe a range of solutions to the more common geometrical configurations in both 2D and 3D, the latter having both straight, elliptical and circular crack profiles |

FAFMco9 | Explain how a pre-existing crack propagates in a new loading field that exhibits both mode I and II behaviour at the crack tip, and discuss FE techniques useful for predicting the new crack propagation direction |

FAFMco10 | Discuss the main components required of a FE model to represent the main features of a cracked structure, to include the discrete crack geometry, material properties and mechanical/thermal loads |

FAFMco11 | Describe, from the results of a FE analysis, how it is possible to calculate K and/or G at any position along a crack profile; explain the difference between substitution and energy methods |

FAFMco12 | Describe how the following energy methods work, their applicability, and limitations: the potential energy difference technique, the virtual crack extension method, J-integral (both as line and domain integrals), and crack closure work |

FAFMco13 | Describe how special finite elements are use to represent the crack tip singularity and the availability in user's FE software |

FAFMco15 | Describe the mechanism of plasticity in the context of its existence around a crack tip |

FAFMco21 | Describe how cracks grow under fatigue conditions and the factors that affect this growth |

FAFMco22 | Explain why there is a tendency for fatigue crack growth to be under LEFM conditions, the relevance of stress intensity factor; and the Paris law to describe growth rates |

FAFMco23 | Describe how FE analysis can be used to calculate both the growing crack length and direction change from an initially cracked geometry under mixed mode conditions |

FAFMap1 | Determine the meshing requirements for any FM approach being employed. |

FAFMap2 | Employ an analysis system effectively for LEFM and use the Westergaard Equations (displacement or stress) to determine Stress Intensity Factors in components. |

FAFMap6 | Use documented solutions for standard stress intensity factors to check FEA results or to benchmark FEA procedures. |

BMPSap2 | Employ appropriate techniques to retrieve hot-spot and other stress quantities for the assessment of welds. |

MASco8 | Explain, in metallurgical terms, how fatigue cracks form and grow in metallic materials. |

MASco11 | Discuss the terms elastic-perfectly plastic, kinematic hardening, isotropic hardening, Bauschinger effect, hysteresis loop. |

MASco19 | Discuss common material characteristics and typical manufacturing related flaws in welding. |

MASco20 | Discuss common material characteristics and typical manufacturing related flaws in hot and cold rolled plate and tubes. |

MASco21 | Discuss common material characteristics and typical manufacturing related flaws in forgings. |

MASco22 | Discuss common material characteristics and typical manufacturing related flaws in castings. |

MASap2 | Determine whether any allowance needs to be made to the material data for the effects of environment and variability. |

PLASco33 | Explain Neuber's Rule. |

**Please complete this form if you are interested in scheduling an on-site training session, or if you would like to be notified of the next public course session.**

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