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Extra resources for Numerical methods for Laplace transform inversion - Program code only (2007)

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We define ζ more precisely in sec. 2. Obviously, ζ = 0 for the continuum dislocations. Two factors determine its value. In the case of the edge dislocation of fig. 5 the elastic energy of the crystal stored in the compressed upper atom row tends to increase ζ. Competing with this, the misfit energy due to the misalignment between the two atom rows decreases ζ. The mobility of a dislocation increases with increasing ζ. As the elastic energy is proportional to the elastic constants of the crystal, we expect wider dislocations in metals of simple crystal structure like fcc or hcp compared to homopolar crystals with strongly directed bonds like in diamond.

In the limit of small ε Hooke’s law (eq. 8)) is valid. • plastic flow regime (ε1 < ε < ε2 ): dislocations start to move and enable a large increase of strain with almost no increase of the external stress. The dislocation density increases as dislocation sources become activated. The deformation is no longer reversible: if the stresses are removed there remains plastic strain εpl . • work hardening regime (ε < ε2 ): a further increase of strain requires a large increase of external stress. The dislocations become immobile due to their mutual interaction.

When the dislocation reaches the right surface of the lattice the sample halves have slipped3 completely across the glide plane. Note that glide is a conservative process as it only involves the rearrangement of atoms. The term conservative means that the total number of atoms and lattice sites in the core is conserved. Imagine now that the lowest atom row of the extra half plane in fig. 2 were removed. This would correspond to an edge dislocation located one lattice constant above the former. Alternatively, we could think of an associated dislocation motion normal to the glide plane.

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