Abstract
Within the framework of a discrete model of the nuclei of linear and planar defects, the variational principles of sliding in translational and rotational plasticity, fracture by separation (cleavage) and shear (shearing) in crystalline materials are considered. The analysis of mass transfer fluxes near structural kinetic transitions of slip bands into cells, cells into fragments of deformation origin, destruction by separation and shear for fractal spaces using fractional Riemann-Liouville derivatives, local and global criteria of destruction is carried out. One of the possible schemes of the crack initiation and growth mechanism in metals is disclosed. It is shown that the discrete model of plasticity and fracture does not contradict the known dislocation models of fracture and makes it possible to abandon the kinetic concept of thermofluctuation rupture of interatomic bonds at low temperatures.
Highlights
The analysis of works [1] [2] [3] shows that during the generation of nuclei of linear and planar defects, two subsystems of electrons arise: photoelectrons knocked out of cations by an intermittent field, and intrinsic electrons of a solid
It is shown that the discrete model of plasticity and fracture does not contradict the known dislocation models of fracture and makes it possible to abandon the kinetic concept of thermofluctuation rupture of interatomic bonds at low temperatures
These are conduction electrons; in dielectrics and semiconductors, they are injected into the volumes of shock waves under the influence of external strong electric fields, and arise when impurity donor atoms are introduced into the material
Summary
The analysis of works [1] [2] [3] shows that during the generation of nuclei of linear and planar defects, two subsystems of electrons arise: photoelectrons knocked out of cations by an intermittent field, and intrinsic electrons of a solid. At large plastic deformations leading to the formation of stable fragmented structures up to critical ones, the average electron densities nep and nphe and the corresponding plasma frequencies Ωep and Ω phe are quantities of the same order, which leads to a fundamentally new distribution of the dielectric constant tensor εαβ (ω, k ) both in space and in time In this case, a new branch of the spectrum associated with the presence of beams is added to the main branch of the spectrum of longitudinal oscillations of the intrinsic plasma, where Ωep reflects the collective natural oscillations, and Ω phe -oscillations and rotations in the additional potential relief of the nuclei of linear and plane defects. The aim of this work is to build a physical and mathematical discrete model of structural kinetic transitions taking into account the fractality of deformation processes
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