This book presents a description of the collective behavior of dislocation ensembles based on a continuous description using the powerful tools of the mathematical theory of partial differential equations. Because, in contrast with conventional theories of the plasticity, it features the relevant interaction mechanisms between the participating crystal defects, the theory is able to describe the emergence of dislocation structures. Examples show the intermittent and self-organized character of plastic activity, the effects of sample size on the plastic behavior, and the impact of complex loading paths on the material work hardening.
1. Continuous representation of dislocations
Lattice incompatibility. Burgers vector. Incompatibility equations.
Continuous distributions ofdislocations. Continuity conditions a interfaces.
Incompatibility and curvature of the crystalline lattice.
2. Field Equations and evolution equations
Determination of internal stresses. Plastic distortion rate.
Resolution length scale. Evolution equations for the dislocation densities.
Constitutive assumtions. Rate form of the continuity conditions at interfaces.
Governing equations in a field theory of dislocations.
Boundary conditions aux limites. Resolution algorithms.
Incremental form of the field equations.
Example : plane dislocations .
3. Constitutive laws
Fields of dislocations et constitutive laws. Dissipation. Incompressibility.
Viscoplasticity. Compatible and incompatible dislocation fields.
4. Intermittency, size effects and complex loading paths
Applicability of field dislocation mechanics.
Intermittency of plasticity. Effets of size on plastic activity. Complex loading paths.
Glossary, definitions, notations