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Crack Propagation Modelling

This book started out as a continuation of the “How and Why…” sets of booklets published by NAFEMS, designed to guide both new and experienced analysts in a range of problem types. Along the editing process, the anticipated publication gained both critical mass in content and increasing traction from the Finite Element Analysis (FEA) community, and finally matured to become a fully-blown NAFEMS text book. We recommend reading the NAFEMS booklet on How to Undertake Fracture Mechanics Analysis as a precursor for this book on Crack Propagation Modelling.

In the last decades, linear FEA has become a widely used numerical design tool in many engineering fields such as the construction, automotive, aerospace, nuclear and offshore oil and gas sectors. FEA is an integral part of the design cycle in most engineering companies.

In the meantime, advances in both computing power and commercially available Finite Element (FE) codes have paved the way for the introduction of non-linear FEA to simulate e.g. complex material behaviour, contact problems or geometric non-linearity.

More recently, the use of finite elements to solve fracture mechanics problems has developed and is finding its way to among others the pipeline and pressure vessel industry, the nuclear sector, biomedical engineering, etc. Nowadays, defects such as sharp cracks can be easily included in FE models and analysed using the relevant linear or non-linear solution processes. In addition to the usual FE outputs, special quantities which are of relevance to fracture mechanics can also be calculated, to indicate the conditions due to the presence of defects.

This book aims to explain how to model crack propagation using FEA. The book aims at a graduate-level industrial user who is familiar with basic linear FEA, but is inexperienced in advanced FE simulations. Hence, this book assumes little or no prior knowledge of fracture mechanics theory or FE modelling of cracks.

This publication starts by covering the essentials of fracture mechanics and crack propagation theory. Then, it covers the most commonly used constitutive material models which can be used to simulate crack propagation. After that, different FE methods (such as crack tip elements, cohesive zone models, virtual crack closure techniques and the extended finite element method or XFEM) are covered. Several practical engineering examples are reviewed to demonstrate the added value of fracture mechanics and crack propagation modelling for different industry sectors. The last chapter covers a series of well-defined test cases and benchmarks on crack propagation modelling. At the end of the book, a glossary and a list of abbreviations and acronyms has been included to guide the reader through the FEA and fracture mechanics jargon. A list of Professional Simulation Engineer (PSE) competencies addressed in this book is provided as well.


SectionPage Number
1.Introduction to Fracture Mechanics1
1.1Overview on Fracture Mechanics1
1.2Theory of Linear Elastic Fracture Mechanics12
1.3Elastic-Plastic Fracture Mechanics (EPFM)26
1.4Summary of Important Fracture Parameters37
1.5Notions on Time Dependent Fracture38
1.6Other Sources of Information about Fracture Mechanics44
2Crack Propagation Theory51
2.1Mechanisms of Crack Initiation and Propagation51
2.2Criteria for Direction of Crack Growth62
2.3Fatigue Crack Propagation70
3Material Modelling to Simulate Crack Propagation87
3.1Primer on Constitutive Material Modelling87
3.2Gurson-Tvergaard-Needleman (GTN) Model100
3.3Modified Bai-Wierzbicki (MBW) Model113
3.4Other Models to Simulate Progressive Damage and Failure127
4Finite Element Methods to Simulate Crack Propagation139
4.1Crack Tip Elements139
4.2Cohesive Zone Models (CZM)147
4.3Virtual Crack Closure Techniques (VCCT)157
4.4Extended Finite Element Method (XFEM)167
5Engineering Examples of Crack Propagation Modelling175
5.1Crack Growth in a Three Point Bend (3PB) Specimen175
5.2Computational Fracture Mechanics to Ensure Pipeline Integrity183
5.3Practical Use of XFEM in Engineering Applications199
5.4Fatigue Crack Propagation in Airframe Structures211
6FEA Benchmarks on Crack Propagation221
6.1Fracture Mechanics Benchmarks221
6.2Extended Finite Element Method (XFEM) Benchmarks240
6.3Debonding of a Double Cantilever Beam252
6.4Verification of Crack Propagation261
7.1Introduction to Fracture Mechanics269
7.2Crack Propagation Theory275
7.3Material Modelling to Simulate Crack Propagation281
7.4Finite Element Methods to Simulate Crack Propagation290
7.5Engineering Examples of Crack Propagation Modelling299
7.6FEA Benchmarks on Crack Propagation308
9Abbreviations and Acronyms327
10Professional Simulation Engineer Competencies329
10.1Flaw Assessment and Fracture Mechanics330
10.3Materials for Analysis and Simulation336
10.4Mechanics, Elasticity and Strength of Materials337
10.5Finite Element Analysis338


Document Details

AuthorVan den Abeele. F
Date 21st February 2022


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Non-member Price £120.00 | $147.24 | €139.91

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Order RefR0130 Book
Member Price £25.00 | $30.68 | €29.15
Non-member Price £120.00 | $147.24 | €139.91

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