On the Relationship of the Discrete Model of the Nuclei of Linear and Planar Defects and the Continuum Models of Defects in Crystalline Materials

• 作者: V. L. Busov
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Maxwell Stress Tensor of an Alternating (Intermittent) Field Equation of Evolution of Internal Stresses Autocorrelation Function of the Speed of Photoelectrons and Cations
• 年，卷（期）: 2020,（9）
• 页码范围: 862-875
• 页数: 14页
• 分类号: O17

摘要

A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor <span><i>σ</i></span>^<i>if</i><sub style="margin-left:-15px;"> <i>αβ</i></sub> are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses <span><i>σ</i></span>^<i>if</i><sub style="margin-left:-15px;"> <i>αβ</i></sub> in the defect core and the elastic stresses <span><i>σ</i></span>^<i>el</i><sub style="margin-left:-9px;"><i>ik</i></sub> in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons <span>Ψ</span>^<i>β</i><sub style="margin-left:-6px;">⊥</sub>(<i>β</i>) and cations <img src="Edit_e2d8e074-eb94-44dc-8ab6-6644bbf74f9c.bmp" alt="" /> , which transforms into linear spectra as <i>T</i> → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.