Mathematical Model of the Formation of a Crystallographic Shear Band in fcc Metals Taking Account for Elastic Interaction of Dislocations

Petelin, Alexander; Samokhina, Svetlana I.; Kolupaeva, S. N.

doi:10.1007/s11182-013-0123-4

Cited by 6 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It shall be noted that the results of the performed computational experiment are consistent with experimental data [11] and calculations carried out using a mathematical model which takes into account the force of elastic interaction among all dislocations of the forming dislocation cluster [14,15].…”

Section: Results Of the Computational Experimentssupporting

confidence: 72%

The Impact of the Dislocation Density, Lattice and Impurity Friction on the Dynamics of Expansion of a Dislocation Loop in FCC Metals

Petelina

Kolupaeva

Kayuda

et al. 2016

KEM

View full text Add to dashboard Cite

The study of the role of various factors in plastic behavior of materials is carried out using a mathematical model that takes into account fundamental properties of deformation defects in a crystal lattice based on the continuum theory of dislocations. Calculations were performed for copper, nickel, aluminum, and lead using a specialized software system Dislocation Dynamics of Crystallographic Slip. It has been shown that a decrease in the density of dislocations from 1012 m-2 to 1011 m-2 leads to an increase in the dislocation path in 10−16 times, and the maximum velocity in 1.5−2 times in copper and nickel, by nearly 20% in aluminum, and practically remains unchanged in lead. A decrease in the lattice and impurity friction from 2 MPa to 0.1 MPa leads to a linear increase in the path and the maximum velocity of the dislocation by 10−25%.

show abstract

Section: Results Of the Computational Experimentssupporting

confidence: 72%

The Impact of the Dislocation Density, Lattice and Impurity Friction on the Dynamics of Expansion of a Dislocation Loop in FCC Metals

Petelina

Kolupaeva

Kayuda

et al. 2016

KEM

View full text Add to dashboard Cite

show abstract

“…3, c). The mean value of the dislocation velocity calculated in [9] is approximately by an order of magnitude lower than its maximum value.…”

Section: Resultsmentioning

confidence: 69%

“…In [9], using the continuum theory of dislocations [10], a mathematical model of expansion of the closed dislocation loop and formation of the crystallographic shear zone was written. The model was written in the form of a system of ordinary differential equations of the following form:…”

Section: Methodsmentioning

confidence: 99%

Influence of the Dislocation Density on the Expansion Dynamics of the Crystallographic Slip Zone along Screw Orientations in Aluminum and Copper

Petelina

Kolupaeva

Polosukhin

et al. 2016

KEM

View full text Add to dashboard Cite

Crystallographic slip is one of key mechanisms determining plastic form change of crystalline solids. Despite a large amount of works done on the subject, crystallographic slip is a very difficult subject to study. Significant progress in the study of the crystallographic slip process is possible only with the use of a set of different methods: experimental methods, methods of mathematical modeling and simulation. The paper presents a modification mathematical expansion model of closed dislocations emitted by one dislocation source with takes into account the elastic interaction force among all dislocations of the forming dislocation pile-up. The model takes into account the Peach-Koehler forces, lattice, impurity, and dislocation friction, linear tension, viscous deceleration, and the intensity of generation of point defects beyond jogs on the dislocation, as well as the elastic interaction force among all dislocations of the forming dislocation pile-up. The analysis of the study results on the expansion dynamics of the dislocation loop along the screw orientation on copper and aluminum with varying of the dislocation density from 3×1011 m−2 to 1012 m−2 is carried out. It is established that the length and the path time of the screw dislocation, as well as the number of dislocations emitted by the dislocation source, essentially depend on the density of dislocations. The dependence of the current radius, velocity, and kinetic energy of the screw dislocation on the path time and the dependence of the current velocity and the kinetic energy of the first screw dislocation emitted by the dislocation source on its current radius are described.

show abstract

“…The methods of simulation are very effective, but at the same time extremely laborious. Alternative methods are methods of mathematical modeling [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Mott [10], the first mathematical models of the dislocations dynamics were presented and investigated, which later on were developed in the works of V. D. Natsik and K. A. Chishko [11], N. A. Tyapunina [12], L. E. Popov and S. N. Kolupaeva [13], A. E. Petelin [15], [16] and others.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Plastic Deformation in FCC Metals

Ryumkin¹,

Petelin²,

Kolupaeva³

et al. 2018

J. Sib. Fed. Univ., Math. phys.

View full text Add to dashboard Cite

show abstract

Mathematical Model of the Formation of a Crystallographic Shear Band in fcc Metals Taking Account for Elastic Interaction of Dislocations

Cited by 6 publications

References 5 publications

The Impact of the Dislocation Density, Lattice and Impurity Friction on the Dynamics of Expansion of a Dislocation Loop in FCC Metals

The Impact of the Dislocation Density, Lattice and Impurity Friction on the Dynamics of Expansion of a Dislocation Loop in FCC Metals

Influence of the Dislocation Density on the Expansion Dynamics of the Crystallographic Slip Zone along Screw Orientations in Aluminum and Copper

Mathematical Modeling of Plastic Deformation in FCC Metals

Contact Info

Product

Resources

About