# Welcome to ME036004 - Introduction to Fracture Mechanics¶

## Overview¶

Over the years Fracture mechanics ha evolved from a theoretical framework to a practical approach for design and reliability assessment. The aim of this introductory class is to present the basic concepts of fracture mechanics for undergraduate & graduate students, which are interested in broadening their understanding of design principles originating from solid mechanics and materials science.
We will start by laying the required foundations for understanding **Linear Elastic Fracture Mechanics** and the concept of **Small Scale Yielding** . Building upon these foundations, the role of a material’s **microstructure** on its ability to resist crack growth will be discussed. Next, we will discover how the concepts learned so far relate to the phenomena of **Fatigue** which in turn accounts for ~25% of structural failure in engineering components and more than **50%** of failures in aircraft components 1.

## Reading Materials¶

Links within the lecture notes and Moodle course website.

Anderson, T.L., 2017. Fracture mechanics: fundamentals and applications. CRC press.

Dharan, C.K.H. and Kang, B.S., 2016. Finnie’s Notes on Fracture Mechanics.

François, D., Pineau, A. and Zaoui, A., 2012. Mechanical behaviour of materials: volume ii: fracture mechanics and damage (Vol. 191). Springer Science & Business Media.

## Communication¶

Course email: ME036004@gmail.com.

Lecture notes: Course Website.

Announcments: Moodle course website.

Reception hours: Wednesday 12:45 to 13:35

## Assignments and grading¶

The final grade will be combined of 30% homework assignments, 15% project proposal (5-10 minutes presentation), 60% project evaluation (oral presentation + written report).

### Homework assignments¶

A total of 3 assignments will be given during the semester. All homework assignments are to be submitted in order to pass the course.

HW1 - 5%(+3%); HW2 - 8%(+3%); HW3(+3%) - 8%

The HWs will be published two weeks before the submission date.

The HW grading is binary and the HWs will be peer-reviewed. A week after each submission deadline, each group will present a short review of another group’s submitted assignment.

### Course project¶

The projects can be of computational, theoretical or experimental nature.

At week 8 of the semester each student/group (up to 2 students) will present their project while emphasizing:

The theoretical background of the project.

The problem to be solved.

The solution approach.

What will be considered as a success of the project.

Important dates

Date |
Task |
Submision Format |
---|---|---|

24.11 |
HW1 |
Moodle |

1.12 |
HW1 review |
Oral presentation |

15.12 |
HW2 |
Moodle |

22.12 |
HW2 review |
Oral presentation |

29.12 |
Project proposal |
Oral presentation |

12.1 |
HW3 |
Moodle |

19.1 |
HW3 review |
Oral presentation |

26.1 |
Project presentation |
Oral presentation |

24.2 |
Project report |
Moodle |

## Table of Contents¶

- Elasticity - A Reminder
- Airy’s Stress Functions
- Kirsch’s Infinite Plate
- Inglis Solution
- Fracture on the Atomic Scale
- Griffith’s Energy Balance
- The Energy Release Rate
- Stress Intensity Factors
- Stress Intensity Factors II
- More on Stress Intensity Factors
- Crack Tip Plasticity
- Plane Strain Fracture
- Testing for Toughness
- Mixed Mode Fracture

- Using FENICS to solve simple problems in mechanics
- Getting Started
- Installing FEniCS directly in WSL
- Installing using Conda (miniconda)
- Install required packages (option 1)
- Using FENICS to solve simple problems in mechanics
- Getting Started
- Install Conda (miniconda)
- Install required packages (option 1)
- A few more opensource FE frameworks which are relatively easy to get started with
- FEniCS example - Kirsch’s problem

- 1
Why aircraft fail. Materialstoday, Vol. 5 p.18-25, 2002.