Mechanics of Dislocation Fields.

Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Acknowledgements -- Introduction -- 1. Continuous Dislocation Modeling -- 1.1. Introduction -- 1.2. Lattice incompatibility -- 1.3. Burgers vector -- 1.4. Compatibility conditions -- 1.5. Dislocation fields -- 1.6. Tangential continuity at interfaces -- 1.7. Curvatures and rotational incompatibiliy -- 1.8. Incompatibility tensor -- 1.9. Conclusion -- 1.10. Problems -- 1.10.1. Discrete versus continuous modeling of crystal defects -- 1.10.2. Incompatibility in simple shear -- 1.10.3. Frank's relation -- 1.11. Solutions -- 1.11.1. Discrete versus continuous modeling of crystal defects -- 1.11.2. Incompatibility in simple shear -- 1.11.3. Frank's relation -- 2. Elasto-static Field Equations -- 2.1. Introduction -- 2.2. Elasto-static solution to field equations -- 2.2.1. Stokes-Helmholtz decomposition and Poisson-type equations -- 2.2.2. Navier-type equations for compatible elastic distortion fields -- 2.3. Straight screw dislocation in a linear isotropic elastic medium -- 2.4. Straight edge dislocation in a linear isotropic elastic medium -- 2.5. Conclusion -- 2.6. Problems -- 2.6.1. Screw dislocation -- 2.6.2. Twist boundary -- 2.6.3. Tilt boundary -- 2.6.4. Zero-stress everywhere dislocation fields -- 2.7. Solutions -- 2.7.1. Screw dislocation -- 2.7.2. Twist boundary -- 2.7.3. Tilt boundary -- 2.7.4. Zero-stress everywhere dislocation fields -- 3. Dislocation Transport -- 3.1. Introduction -- 3.2. Dislocation flux and plastic distortion rate -- 3.3. Coarse graining -- 3.4. Compatibility versus incompatibility of plasticity -- 3.5. Tangential continuity of plastic distortion rate -- 3.6. Transport equations -- 3.6.1. Small transformations -- 3.6.2. Finite transformations -- 3.7. Transport waves -- 3.7.1. Annihilation -- 3.7.2. Expansion of dislocation loops.

3.7.3. Initiation of a Frank-Read source -- 3.8. Numerical algorithms for dislocation transport -- 3.9. Conclusion -- 3.10. Problems -- 3.10.1. Propagation of a discontinuous dislocation density -- 3.10.2. Dislocation loop expansion -- 3.10.3. Stability / instability of homogeneous dislocation distributions -- 3.10.4. Dislocation nucleation -- 3.11. Solutions -- 3.11.1. Propagation of a discontinuous dislocation density -- 3.11.2. Expansion of dislocation loops -- 3.11.3. Stability / instability of homogeneous dislocation distributions -- 3.11.4. Dislocation nucleation -- 4. Constitutive Relations -- 4.1. Introduction -- 4.2. Dissipation -- 4.3. Pressure independence -- 4.4. Dislocation climb versus dislocation glide -- 4.5. Viscoplastic relationships -- 4.6. Coarse graining -- 4.7. Contact with conventional crystal plasticity -- 5. Elasto-plastic Field Equations -- 5.1. Introduction -- 5.2. Fundamental field equations -- 5.3. Boundary conditions -- 5.4. Coarse graining -- 5.5. Resolution algorithm -- 5.6. Reduced field equations -- 5.6.1. Plane dislocations -- 5.7. Augmented crystal plasticity -- 5.8. Dynamics of a twist boundary -- 5.9. Conclusion -- 5.10. Problems -- 5.10.1. Helical dislocations -- 5.11. Solutions -- 5.11.1. Helical dislocations -- 6. Case Studies -- 6.1. Introduction -- 6.2. Dislocation core structure -- 6.3. Piezoelectricity and dislocations -- 6.3.1. Coupling piezoelectricity, lattice incompatibility and transport -- 6.3.2. Piezoelectric polarization and dislocations in GaN layers -- 6.3.3. Dislocation transport and electric displacement in GaN layers -- 6.4. Intermittent plasticity -- 6.5. Effects of size on mechanical response -- 6.6. Complex loading paths -- 6.7. Strain localization -- 6.7.1. Experimental data in Al-Cu-Li alloys -- 6.7.2. Simulation results -- 7. Review and Conclusions.

7.1. Comparisons with conventional crystal plasticity -- 7.2. Alternative approaches -- 7.2.1. Peierls-Nabarro model -- 7.2.2. Atomistic simulations -- 7.2.3. Phase field methods -- 7.2.4. Discrete dislocation dynamics -- 7.3. Shortcomings and extensions -- 7.3.1. Fracture and disconnections -- 7.3.2. Rotational incompatibility and disclinations -- 7.3.3. Phase transformation and generalized disclinations -- 7.4. Final remarks -- Appendix: Complements -- A.1. Stokes' theorem -- A.2. Characterization of the compatibility of a tensor field -- A.3. Stokes-Helmholtz decomposition -- A.4. Second-order Riemann-Graves operator -- Bibliography -- Index -- Other titles from iSTE in Materials Science -- EULA.

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