Thermodynamics of Dislocation Pattern Formation at the Mesoscale

Roman Gröger

doi:10.4028/www.scientific.net/KEM.592-593.79

Paper Titles

Comparison between Pile-Up Singularities and Stress Fields Induced by Thin Slip Bands. Application to the Prediction of Grain Boundary Microcrack Nucleation
p.61

Planar Defects and Dislocations in C40 and FCC Lattices
p.67

Thermally Activated Dislocation Motion in an AS21 Alloy and Alloy Reinforced with Short Ceramic Fibres Studied at Elevated Temperatures
p.71

Deformation and Fracture of a Magnesium Alloy at Elevated Temperatures
p.75

Thermodynamics of Dislocation Pattern Formation at the Mesoscale
p.79

Modeling and Experimental Study of Long Term Creep Damage in Austenitic Stainless Steels
p.83

3D Discrete Dislocation Dynamics Applied to a Motion of Low-Angle Tilt Boundaries
p.87

Lattice-Spring Modeling of Graphite Accounting for Pore Size Distribution
p.92

Non-Planar Dislocations in MoSi₂
p.96

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Thermodynamics of Dislocation Pattern Formation at the Mesoscale

Abstract:

We introduce a mesoscopic framework that is capable of simulating the evolution of dislocation networks and, at the same time, spatial variations of the stress, strain and displacement fields throughout the body. Within this model, dislocations are viewed as sources of incompatibility of strains. The free energy of a deformed solid is represented by the elastic strain energy that can be augmented by gradient terms to reproduce dispersive nature of acoustic phonons and thus set the length scale of the problem. The elastic strain field that is due to a known dislocation network is obtained by minimizing the strain energy subject to the corresponding field of incompatibility constraints. These stresses impose Peach-Koehler forces on all dislocations and thus drive the evolution of the dislocation network.