Extended finite element method for crack propagation / Sylvie Pommier [and others].
- Published:
- London, UK : ISTE ; Hoboken, NJ : Wiley, 2011.
- Physical Description:
- xxiv, 254 pages : illustrations ; 24 cm
- Additional Creators:
- Pommier, Sylvie
- Contents:
- Machine generated contents note: 1.1.Introduction -- 1.2.Superposition principle -- 1.3.Modes of crack straining -- 1.4.Singular fields at cracking point -- 1.4.1.Asymptotic solutions in Mode I -- 1.4.2.Asymptotic solutions in Mode II -- 1.4.3.Asymptotic solutions in Mode III -- 1.4.4.Conclusions -- 1.5.Crack propagation criteria -- 1.5.1.Local criterion -- 1.5.2.Energy criterion -- 1.5.2.1.Energy release rate G -- 1.5.2.2.Relationship between G and stress intensity factors -- 1.5.2.3.How the crack is propagated -- 1.5.2.4.Propagation velocity -- 1.5.2.5.Direction of crack propagation -- 2.1.Geometric representation of a crack: a scale problem -- 2.1.1.Link between the geometric representation of the crack and the crack model -- 2.1.2.Link between the geometric representation of the crack and the numerical method used for crack growth simulation -- 2.2.Crack representation by level sets -- 2.2.1.Introduction -- 2.2.2.Definition of level sets -- 2.2.3.Level sets discretization -- 2.2.4.Initialization of level sets -- 2.3.Simulation of the geometric propagation of a crack -- 2.3.1.Some examples of strategies for crack propagation simulation -- 2.3.2.Crack propagation modeled by level sets -- 2.3.3.Numerical methods dedicated to level set propagation -- 2.4.Prospects of the geometric representation of cracks -- 3.1.Introduction -- 3.2.Going back to discretization methods -- 3.2.1.Formulation of the problem and notations -- 3.2.2.The Rayleigh-Ritz approximation -- 3.2.3.Finite element method -- 3.2.4.Meshless methods -- 3.2.5.The partition of unity -- 3.3.X-FEM discontinuity modeling -- 3.3.1.Introduction, case of a cracked bar -- 3.3.1.1.Case a: crack positioned on a node -- 3.3.1.2.Case b: crack between two nodes -- 3.3.2.Variants -- 3.3.3.Extension to two-dimensional and three-dimensional cases -- 3.3.4.Level sets within the framework of the eXtended finite element method -- 3.4.Technical and mathematical aspects -- 3.4.1.Integration -- 3.4.2.Conditioning -- 3.5.Evaluation of the stress intensity factors -- 3.5.1.The Eshelby tensor and the J integral -- 3.5.2.Interaction integrals -- 3.5.3.Considering volumic forces -- 3.5.4.Considering thermal loading -- 4.1.Introduction -- 4.2.Fatigue and non-linear fracture mechanics -- 4.2.1.Mechanisms of crack growth by fatigue -- 4.2.1.1.Crack growth mechanism at low AK -- 4.2.1.2.Crack growth mechanisms at average or high AK! -- 4.2.1.3.Macroscopic crack growth rate and striation formation -- 4.2.1.4.Fatigue crack growth rate of long cracks, Paris law -- 4.2.1.5.Brief conclusions -- 4.2.2.Confined plasticity and consequences for crack growth -- 4.2.2.1.Irwin's plastic zones -- 4.2.2.2.Role of the T stress -- 4.2.2.3.Role of material hardening -- 4.2.2.4.Cyclic plasticity -- 4.2.2.5.Effect of residual stress on crack propagation -- 4.3.eXtended constitutive law -- 4.3.1.Scale-up method for fatigue crack growth -- 4.3.1.1.Procedure -- 4.3.1.2.Scaling -- 4.3.1.3.Assessment -- 4.3.2.eXtended constitutive law -- 4.3.2.1.Damage law -- 4.3.2.2.Plasticity threshold -- 4.3.2.3.Plastic flow rule -- 4.3.2.4.Evolution law of the center of the elastic domain -- 4.3.2.5.Model parameters -- 4.3.2.6.Comparisons -- 4.4.Applications -- 4.4.1.Mode I crack growth under variable loading -- 4.4.2.Effect of the T stress -- 5.1.Energy conservation: an essential ingredient -- 5.1.1.Proof of energy conservation -- 5.1.1.1.X-FEM approach -- 5.1.1.2.Cohesive zone models -- 5.1.1.3.Energy conservation for adaptive cohesive zones -- 5.1.2.Case where the material behavior depends on history -- 5.2.Examples of crack growth by fatigue simulations -- 5.2.1.Calculation of linear fatigue crack growth simulation -- 5.2.2.Two-dimensional fatigue tests -- 5.2.2.1.Test-piece CTS: crack growth in mode 1 -- 5.2.2.2.Arcan test piece: crack growth in mixed mode -- 5.2.3.Three-dimensional fatigue cracks. Propavanfiss project -- 5.2.3.1.Internal crack growth rate -- 5.2.4.Propagation of corner cracks -- 5.3.Dynamic fracture simulation -- 5.3.1.Effects of crack speed a and crack growth criteria -- 5.3.2.Analytical solution: rectilinear crack propagation on a reference problem -- 5.3.3.Kalthoff experiment -- 5.3.4.Tests on test pieces CCS of Maigre-Rittel -- 5.3.5.Réthoré, Gregoire and Maigre tests -- 5.3.6.X-FEM method in explicit dynamics -- 5.4.Simulation of ductile fracture -- 5.4.1.Characteristics of material 16MND5 -- 5.4.1.1.Dynamic characterization of the material -- 5.4.1.2.Fracture tests -- 5.4.1.3.Crack advancement measurement device -- 5.4.1.4.Description of tests on CT test pieces -- 5.4.1.5.Numerical simulation -- 5.4.2.Ring test and interpretation -- 5.4.2.1.Geometry, mesh, and loading -- 5.4.2.2.Interpretation of the test in Mode I -- 5.4.2.3.Interpretation of the test in mixed mode.
- Subject(s):
- ISBN:
- 9781848212091
1848212097 - Bibliography Note:
- Includes bibliographical references and index.
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