A Fast-Track Method for Fatigue Crack Growth Prediction with a Cohesive Zone Model A Thesis Submitted to the University of Manchester for the degree of PhD in the Faculty of Engineering and Physical Science 2013 HENDERY DAHLAN School of Mechanical, Aerospace and Civil Engineering A Fast-Track Method for Fatigue Crack Growth Prediction with a Cohesive Zone Model List of Content List of Content ......................................................................................................... 2 List of Figure ........................................................................................................... 7 List of Table ..........................................................................................................13 Abstract ..........................................................................................................16 Declaration ..........................................................................................................17 Copyright Statement ...............................................................................................18 Dedication ..........................................................................................................19 Acknowledgement ..................................................................................................20 Nomenclature .........................................................................................................21 List of Abbreviation ................................................................................................23 Chapter 1 Introduction ........................................................................................24 1.1. Background of Research ..............................................................................24 1.2. Research Objective ......................................................................................27 1.3. Research Contribution to Knowledge ..........................................................28 1.4. Outline of Research .....................................................................................29 Chapter 2 Literature Review ...............................................................................32 2.1. Introduction .................................................................................................32 2.2. Fatigue Crack Growth Prediction .................................................................32 2.3. Cohesive Zone Model ..................................................................................35 2.4. Overloading .................................................................................................37 2 A Fast-Track Method for Fatigue Crack Growth Prediction with a Cohesive Zone Model 2.5. Probabilistic and Statistical Prediction Fatigue Crack Growth ......................39 Chapter 3 Theoretical Review of Fracture Mechanics .........................................41 3.1. Introduction .................................................................................................41 3.2. Crack initiation ............................................................................................42 3.3. Crack growth ...............................................................................................43 3.4. Linear Elastic Crack Tip Stress Field ...........................................................45 3.5. Elastic-Plastic Crack Tip Stress Field ..........................................................47 3.5.1 Crack Tip Plastic Zone Size ...............................................................48 3.5.2 The Irwin Approximation ..................................................................49 3.5.3 The Dugdale Approximation ..............................................................50 3.6. Effect of Overloading ..................................................................................51 3.6.1 Retardation Models ............................................................................54 3.7. Energy Balance for Crack Growth ...............................................................56 Chapter 4 Energy Driven Force in Fracture Mechanics .......................................58 4.1. Introduction .................................................................................................58 4.2. General Transport Forms .............................................................................59 4.3. Entropy Transport Equation for Plastic Deformation: Reversible Approach .61 4.4. Entropy Transport Equation for Plastic Deformation: Irreversible Approach 63 4.5. Transport Equations for Fracture .................................................................64 4.6. Cohesive Approach .....................................................................................66 4.7. Practical Demonstrations .............................................................................68 4.7.1 Spring and Cohesive Element Combination .......................................69 4.7.1.1 The Calculation of Energy for Elastic Materials ...............70 4.7.1.2 Model Description ............................................................72 4.7.1.3 Results and Discussion .....................................................73 3 A Fast-Track Method for Fatigue Crack Growth Prediction with a Cohesive Zone Model 4.7.2 Sliding-Friction, Spring and Cohesive Element Combination .............75 4.7.2.1 The Calculation of Energy for Elastic Plastic Materials ....76 4.7.2.2 Material Properties ...........................................................79 4.7.2.3 Results and Discussion .....................................................79 4.8. Summary .....................................................................................................80 Chapter 5 Cohesive Zone Model .........................................................................82 5.1. Introduction .................................................................................................82 5.2. Cohesive Element Law ................................................................................88 5.3. Implementation of Cohesive Zone Model ....................................................96 5.3.1 Monotonic Loading ...........................................................................96 5.3.1.1 Model Description ............................................................96 5.3.1.2 Results and Discussion .....................................................98 5.3.2 Cyclic Loading ................................................................................ 102 5.3.2.1 Constant Amplitude Loading .......................................... 102 5.3.2.1.1 Model Description........................................ 102 5.3.2.1.2 Results and Discussion ................................. 103 5.3.2.2 Single Overloading ......................................................... 108 5.3.2.2.1 Model Description........................................ 109 5.3.2.2.2 Results and Discussion ................................. 109 5.3.2.3 The Effect of Critical Traction in Cohesive Law ............. 111 5.3.2.3.1 Model Description........................................ 112 5.3.2.3.2 Results and Discussion ................................. 112 5.4. Summary ................................................................................................... 113 Chapter 6 The Effect of Variable Toughness in Fatigue Crack Growth ............. 117 6.1. Introduction ............................................................................................... 117 4 A Fast-Track Method for Fatigue Crack Growth Prediction with a Cohesive Zone Model 6.2. Fatigue Crack Growth Model .................................................................... 118 6.3. Toughness in Cohesive Zone Model .......................................................... 120 6.3.1 Model Description ........................................................................... 122 6.3.2 Results and Discussion .................................................................... 124 6.4. Stress Distribution in Fatigue Crack Growth .............................................. 130 6.5. Energy Criteria in Fatigue Crack Growth ................................................... 132 6.5.1 Model Description ........................................................................... 135 6.5.2 Results and Discussion .................................................................... 135 6.6. Summary ................................................................................................... 136 Chapter 7 Fast Track Method for Fatigue Crack Growth ................................... 144 7.1. Introduction ............................................................................................... 144 7.2. Failure Assessment Diagram ..................................................................... 146 7.3. Method of Least Squares ........................................................................... 147 7.4. The Number of Cycles Estimation Strategy ............................................... 149 7.5. Model Description ..................................................................................... 150 7.5.1 Estimation of the Smallest Toughness .............................................. 150 7.6 Results and Discussion .............................................................................. 164 7.7 Summary ..................................................................................................