# How To Undertake Fracture Mechanics Analysis with Finite Elements

Linear finite element analysis has for many years been widely used in the civil and mechanical engineering fields and, in particular, in the construction, automotive, aerospace, and offshore sectors. Finite element analysis is an integral part of the design cycle in many companies.

Finite element programs that have the capability to solve non-linear problems have also been available for many years, although they were originally used in the more specialised industries typified by nuclear and aerospace engineering. However, the application of non-linear finite element analysis to more general engineering has been growing rapidly, using commercially available packages of high quality and reliability.

The use of finite elements to solve fracture mechanics problems has also developed in parallel with this improving technology. Defects such as sharp cracks can be included in finite element models and analysed using the relevant linear or non-linear solution processes. In addition to the usual finite element outputs, special quantities can also be calculated which are of relevance to fracture mechanics, to indicate the conditions due to the presence of the defects.

This book aims to describe the background to fracture mechanics, and how the main fracture results can be calculated from the different types of finite element analysis. Discussion is included on how to use finite elements effectively, and several examples illustrate the concepts and potential accuracy that can be achieved.

## Contents

### IntroductionThe Basics Of Fracture Mechanics

• Introduction
• Brittle Fracture
• Ductile Fracture
• Fatigue Fracture
• High Temperature and Creep Fracture
• Dynamic Fracture

### The Main Fracture Parameters

• Introduction
• The Griffith Criterion
• General Crack Tip Geometry
• Modes at the Crack Tip
• Elastic Stress Fields around the Crack Tip
• The Westergaard Equations
• Stresses
• Displacements
• Potential Energy Release Rate
• Relationship Between G and K
• The J-Integral
• Elastic-Plastic Fracture Mechanics
• The EPFM Potential Energy Release Rate: G or J
• The EPFM CTOD: The Crack Opening Displacement
• The Behaviour of G with Increasing Loads
• The HRR model
• Fatigue Crack Growth
• Creep Crack Growth
• The T-Stress Constraint Parameter

### How To Calculate the Fracture Parameters with Finite Elements

• Introduction
• Finite Element Considerations
• How To Calculate the K Values
• Substitution Methods
• Energy Methods
• Energy Difference Techniques
• Virtual Crack Extension Methods
• The J-Integral Method
• The Crack Closure/Opening Work Methods
• Other Methods
• Accuracy
• Fracture Parameters for Fatigue
• Fracture Parameters for EPFM

### Examples of Fracture Mechanics

• Introduction
• A Look at Near Tip Fields
• A Note on VCE Methods
• Centre-Cracked Plate in Tension
• An Example of Fatigue Crack Growth in Gear Teeth

### Product Details

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