Strain Gradient Plasticity-Based Modeling of Damage and Fracture (eBook)

Supervisor’s Foreword 7
PublicationsParts of this thesis have been published in the following articles:Martínez-Pañeda, E., Natarajan, S., Bordas, S., 2016. Gradient plasticity crack tip characterization by means of the extended finite element method. Computational Mechanics 59, 831–842.Martínez-Pañeda, E., Niordson, C.F., Gangloff, R.P., 2016. Strain gradient plasticity-based modeling of hydrogen environment assisted cracking. Acta Materialia 117, 321–332.Martínez-Pañeda, E., Niordson, C.F., Bardella, L., 2016. A finite element framework for distortion gradient plasticity with applications to bending of thin foils. International Journal of Solids and Structures 96, 288–299.Martínez-Pañeda, E., del Busto, S., Niordson, C.F., Betegón, C., 2016. Strain gradient plasticity modeling of hydrogen diffusion to the crack tip. International Journal of Hydrogen Energy 41, 10265–10274.Martínez-Pañeda, E., Niordson, C.F., 2016. On fracture in finite strain gradient plasticity. International Journal of Plasticity 80, 154–167.Martínez-Pañeda, E., Betegón, C., 2015. Modeling damage and fracture within strain-gradient plasticity. International Journal of Solids and Structures 59, 208–215. 9
Acknowledgements 10
Contents 12
Acronyms 15
Part I Numerical Framework 16
1 Introduction 17
1.1 Background 17
1.2 Objectives 22
1.3 Thesis Outline 23
References 24
2 Gradient Plasticity Formulations 26
2.1 Mechanism-Based Gradient Plasticity 27
2.2 Fleck-Hutchinson 2001 Theory 29
2.2.1 Infinitesimal Deformation Framework 29
2.2.2 Finite Deformation Framework 32
2.3 Advanced Gradient Plasticity Theories 33
2.3.1 Principle of Virtual Work and Governing Equations 34
2.3.2 Thermodynamically Consistent Constitutive Equations 35
2.4 Distortion Gradient Plasticity 38
2.4.1 Variational Principles and Balance Equations 38
2.4.2 Energetic Contributions 40
2.4.3 Dissipative Contributions 41
References 42
3 Numerical Implementation 45
3.1 CMSG Plasticity: FEM and X-FEM 45
3.1.1 Finite Element Implementation 46
3.1.2 A Novel X-FEM Scheme 53
3.2 Phenomenological Higher Order SGP 60
3.2.1 Numerical Method 60
3.2.2 Verification 62
3.3 Numerical Modeling of Energetic and Dissipative Size Effects 64
3.3.1 Minimum Principles 65
3.3.2 Numerical Implementation 65
3.3.3 Verification 67
3.4 A Finite Element Basis for DGP 71
3.4.1 Minimum Principles 71
3.4.2 Numerical Formulation and Solution Procedure 72
3.4.3 Verification 75
References 76
Part II Results 79
4 Mechanism-Based Crack Tip Characterization 80
4.1 Introduction 80
4.2 Crack Tip Fields with Infinitesimal Strains 81
4.3 Crack Tip Fields with Finite Strains 86
4.4 Discussion 90
4.5 Conclusions 91
References 91
5 On Fracture in Finite Strain Gradient Plasticity 93
5.1 Introduction 93
5.2 Numerical Results 94
5.2.1 Infinitesimal Deformation Theory 94
5.2.2 Finite Deformation Theory 96
5.3 Conclusions 103
References 104
6 The Role of Energetic and Dissipative Length Parameters 106
6.1 Introduction 106
6.2 Stationary Crack Tip Fields 107
6.3 Steady-State Crack Growth and Work of Fracture 111
6.4 Conclusions 118
References 119
7 Hydrogen Diffusion Towards the Fracture Process Zone 121
7.1 Introduction 121
7.2 Numerical Framework 122
7.3 Finite Element Results 123
7.3.1 Hydrogen Transport in Impure Iron 124
7.3.2 Crack Tip Blunting and Hydrogen Distribution in Duplex Stainless Steel 127
7.3.3 Crack Tip Hydrogen Concentration in X80 Pipeline Steel 129
7.4 The Role of Hydrogen Trapping 132
7.5 Conclusions 133
References 134
8 SGP-Based Modeling of HEAC 137
8.1 Introduction 137
8.2 Objective 139
8.3 Experimental Procedure 139
8.4 Modeling Procedure 140
8.4.1 Hydrogen Assisted-Cracking Modeling 140
8.4.2 Strain Gradient Plasticity Modeling 142
8.5 Results 144
8.5.1 Monel K-500 144
8.5.2 AerMetTM100 and FerriumTMM54 146
8.6 Discussion 151
8.6.1 SGP Impact on Hydrogen Cracking 151
8.6.2 FPZ Definition 152
8.6.3 Crack Growth Rate Modeling 152
8.6.4 SGP-HEAC Model Validation 153
8.7 Conclusions 157
References 158
9 Conclusions 162
9.1 Achievements 162
9.2 Concluding Remarks 163
9.3 Future Work 164
References 165
About the Author 166