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.

1. Introduction	1
2. The Basics of Fracture Mechanics	5
2.1 Introduction	5
2.2 Brittle Fracture	6
2.3 Ductile Fracture	7
2.4 Fatigue Fracture	9
2.5 High Temperatures and Creep Fracture	10
2.6 Dynamic Fracture	11
3. The Main Fracture Parameters	13
3.1 Introduction	13
3.2 The Griffith Criterion	13
3.3 General Crack Tip Geometry	16
3.4 Modes at the Crack Tip	17
3.5 Elastic Stress Fields around the Crack Tip	18
3.6 The Westergaard Equations	18
3.6.1 Stresses	19
3.6.2 Displacements	19
3.7 Potential Energy Release Rate	21
3.8 Relationship Between G and K	21
3.9 The J-Integral	22
3.10 Elastic-Plastic Fracture Mechanics	24
3.10.1 The EPFM Potential Energy Release Rate: G* or J	24
3.10.2 The EPFM CTOD: The Crack Opening Displacement	25
3.10.3 The Behaviour of G* with Increasing Loads	26
3.10.4 The HRR model	28
3.11 Fatigue Crack Growth	29
3.12 Creep Crack Growth	30
3.13 The T-Stress Constraint Parameter	30
4. How To Calculate the Fracture Parameters with Finite Elements	33
4.1 Introduction	33
4.2 Finite Element Considerations	33
4.2.1 Elements and Numerical Integration	33
4.2.2 Special Crack Tip Elements	34
4.3 How To Calculate the K Values	36
4.4 Substitution Methods	36
4.5 Energy Methods	38
4.6 Energy Difference Technique	39
4.7 Virtual Crack Extension Methods	40
4.7.1 Discrete VCE Methods	40
4.7.2 Continuum VCE Methods	42
4.8 The J-Integral Method	44
4.9 The Crack Closure/Opening Work Methods	44
4.10 Other Methods	46
4.11 Accuracy	46
4.12 Fracture Parameters for Fatigue	47
4.13 Fracture Parameters for EPFM	49
4.13.1 Potential Energy Release Rate Methods for EPFM	49
4.13.2 CTOD for EPFM	51
5. Examples of Fracture Mechanics	53
5.1 Introduction	53
5.2 A Look at Near Tip Fields	55
5.3 A Note on VCE Methods	58
5.4 Centre-Cracked Plate in Tension	60
5.5 An Example of Fatigue Crack Growth in Gear Teeth	62
6. Concluding Remarks	67
7. References	69
Glossary	73

Document Details

Reference	HT18
Author	Hellen. T
Language	English
Audience	Analyst
Type	Publication
Date	1st January 2001
Region	Global

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