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Mechanics of Dislocation Fields,9781848213753
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Mechanics of Dislocation Fields



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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.

Table of Contents


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.

Transport waves.

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

