Busov, V.L. (2020) On the Relationship of the Discrete Model of the Nuclei of Linear and Planar Defects and the Continuum Models of Defects in Crystalline Materials. Applied Mathematics, 11, 862-875.
https://doi.org/10.4236/am.2020.119056

has been cited by the following article:

• TITLE: Discrete Model of Plasticity and Failure of Crystalline Materials

  AUTHORS: V. L. Busov

  KEYWORDS: Variational Principles of Plasticity and Destruction, Photoelectrons, Conduction Electrons, Injected Electrons, Fractal Space, Fracture Criteria

  JOURNAL NAME: Applied Mathematics, Vol.12 No.3, March 12, 2021

  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.