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How To Undertake Fracture Mechanics Analysis with Finite Elements

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

1. Introduction1
2. The Basics of Fracture Mechanics5
2.1 Introduction5
2.2 Brittle Fracture6
2.3 Ductile Fracture7
2.4 Fatigue Fracture9
2.5 High Temperatures and Creep Fracture10
2.6 Dynamic Fracture11
3. The Main Fracture Parameters13
3.1 Introduction13
3.2 The Griffith Criterion13
3.3 General Crack Tip Geometry16
3.4 Modes at the Crack Tip17
3.5 Elastic Stress Fields around the Crack Tip18
3.6 The Westergaard Equations18
3.6.1 Stresses19
3.6.2 Displacements19
3.7 Potential Energy Release Rate21
3.8 Relationship Between G and K21
3.9 The J-Integral22
3.10 Elastic-Plastic Fracture Mechanics24
3.10.1 The EPFM Potential Energy Release Rate: G* or J24
3.10.2 The EPFM CTOD: The Crack Opening Displacement25
3.10.3 The Behaviour of G* with Increasing Loads26
3.10.4 The HRR model28
3.11 Fatigue Crack Growth29
3.12 Creep Crack Growth30
3.13 The T-Stress Constraint Parameter30
4. How To Calculate the Fracture Parameters with Finite Elements33
4.1 Introduction33
4.2 Finite Element Considerations33
4.2.1 Elements and Numerical Integration33
4.2.2 Special Crack Tip Elements34
4.3 How To Calculate the K Values36
4.4 Substitution Methods36
4.5 Energy Methods38
4.6 Energy Difference Technique39
4.7 Virtual Crack Extension Methods40
4.7.1 Discrete VCE Methods40
4.7.2 Continuum VCE Methods42
4.8 The J-Integral Method44
4.9 The Crack Closure/Opening Work Methods44
4.10 Other Methods46
4.11 Accuracy46
4.12 Fracture Parameters for Fatigue47
4.13 Fracture Parameters for EPFM49
4.13.1 Potential Energy Release Rate Methods for EPFM49
4.13.2 CTOD for EPFM51
5. Examples of Fracture Mechanics53
5.1 Introduction53
5.2 A Look at Near Tip Fields55
5.3 A Note on VCE Methods58
5.4 Centre-Cracked Plate in Tension60
5.5 An Example of Fatigue Crack Growth in Gear Teeth62
6. Concluding Remarks67
7. References69
Glossary73

Document Details

ReferenceHT18
AuthorHellen. T
LanguageEnglish
AudienceAnalyst
TypePublication
Date 1st January 2001
RegionGlobal

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Member Price £20.00 | $26.35 | €23.89
Non-member Price £90.00 | $118.55 | €107.49

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