Mathematical modeling of work hardening of heterophase materials with nanosized strengthening particles

Kovalevskaya, Т. А.; Kolupaeva, S. N.; Daneyko, O. I.; Semenov, Mikhail; Kulaeva, N. A.

doi:10.1134/s0036029511100089

Cited by 5 publications

(12 citation statements)

References 2 publications

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“…The model takes into account the basic processes of generation, annihilation, and relaxation transformation of dislocations of various types and point defects [8][9][10]. In the processes of deformation and subsequent relaxation, mutual transformations are possible between the structural elements.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The mathematical model [15] includes the balance equations of the shear-forming dislocations (their density is denoted as ρ m ), prismatic dislocation loops of interstitial ( p ρ i ) and vacancy ( p ρ v ) types, dislocations in the dipole configurations ( d ρ v ) and of interstitial type ( d ρ i ), interstitial atoms (we denote their concentration as c i ), monovacancies (c 1 v) and bivacancies (c 2 v). The system of differential balance equations of deformation defects is presented in the following form [2, 3]:…”

Section: Mathematical Modelmentioning

confidence: 99%

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Investigation of Thermal Hardening of the FCC Material Containing Strengthening Particles with an L12 Superstructure

et al. 2015

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A mathematical model of plastic deformation of dispersion-hardened materials with an fcc matrix containing strengthening particles with an L1 2 superstructure having a coherent relationship with the matrix is presented. The model is based on the balance equations of deformation defects of different types with taking into account their transformation during plastic deformation. The influence of scale characteristics of the hardening phase, temperature, and deformation rate on the evolution of the dislocation subsystem and strain hardening of an alloy with an fcc matrix hardened by particles with an L1 2 superstructure is studied. A temperature anomaly of mechanical properties is found for the materials with different fcc matrices (Al, Cu, Ni). It is shown that the temperature anomaly is more pronounced for the material with larger volume fraction of the hardening phase. INTRODUCTIONIn material science, the use of composites based on a metal matrix hardened by the second phase to improve the mechanical properties of materials for various purposes remains of current interest. In almost any area of research, a convenient and universal instrument is mathematical modeling that allows widely vary the characteristics of the material and the impacts on the material. The modeling allows to precede and, perhaps, even to replace the experimental studies. This paper presents a mathematical model of plastic deformation in the dispersion-hardened materials with the fcc matrix containing the hardening particles with an L1 2 superstructure having a coherent relationship with the matrix.In preparation and investigation of materials for various purposes, mathematical modeling allows to accelerate the processes of analysis and implementation of the results, to explore the fundamental properties, mechanisms and processes that determine the strength and plastic properties of materials. Varying the composition of the matrix and filler and their ratio, we can get a wide range of the dispersion-hardened materials with the desired set of properties. The aim of this study is to investigate the effect of the deformation temperature on the hardening of material with a variety of scale characteristics of the hardening phase in a wide range of external influences. MATHEMATICAL MODELIntroduction of a coherent phase ordered by an L1 2 type into an fcc metal matrix brings a number of features in the accumulation of dislocations and strain hardening of the material [1-4]. Dislocations interact with coherent particles, whose number is assumed to be equal to N = 1/Λ p . It is the number of the hardening particles per unit length of the dislocation and Λ р is an average distance between the centers of the particles.The moving dislocations can cut through a coherent particle of an ordered phase shifting it to a distance equal

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Investigation of Thermal Hardening of the FCC Material Containing Strengthening Particles with an L12 Superstructure

et al. 2015

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“…Sinks for point defects are dislocations of different types. We also consider the mutual annihilation of interstitial atoms with vacancies and take into account thermodynamic equilibrium point defects [25]. We note that when two vacancies meet in their random walk then bivacancy is formed; a meeting of bivacancy and interstitial atom leads to formation of the monovacancy.…”

Section: -2mentioning

confidence: 99%

“…The particles, in which the Kear-Wilsdorf barrier is formed, become not slit for dislocations, whereby dislocation overcomes such particles on mechanism Orowan leaving on them Orowan rings and prismatic loops. This entails an increase in the total dislocation density and excess stress dyn , which increases the generation of point defects [28].…”

Section: -4mentioning

confidence: 99%

“…The system of equations of the model also includes an equation relating the strain rate with the applied force and the density of dislocations in a deformable material [25]: Where B is the parameter determined by the probability of formation of the dislocation barriers limiting the shear zone, is the fraction of the forest dislocations, r is the fraction of the reacting forest dislocations, is an average length of the free dislocation segment, and is the applied stress. It was assumed in calculations that the deformation of the crystal occurs at a constant strain rate a a .…”

Section: -2mentioning

confidence: 99%

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Influence of the scale characteristics of the hardening phase with L12 superstructure on the evolution of deformation point defects

Kovalevskaya

Daneyko

Kulaeva

et al. 2016

AIP Conference Proceedings

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Abstract. The linear density and the concentration of point defects in heterophase alloy with nickel matrix and strengthening particles with superstructure L1 2 ( -phase) is obtained by methods of mathematical modeling. The influence of dispersion of the particles of -phase on the behavior of deformation defects is analyzed. The model includes mechanisms for braking the motion of dislocations in the cutting -phase, which are the cause of the anomalous behavior of the material with increasing temperature.

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Plastic Behavior of Heterophase Alloys with a Fcc Matrix Hardened by Particles with an L12 Superstructure

et al. 2015

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Using a mathematical model of plastic deformation of dispersion-hardened materials, the effect of the scale characteristics of the hardening phase with an L1 2 superstructure on the temperature dependence of the flow stress and evolution of the dislocation subsystem of heterophase alloys with the fcc matrix is studied. It is found that in materials with a nanoscale hardening phase, more intensive strain hardening and more severe temperature anomaly of mechanical properties is observed, than in materials containing larger particles at the same volume fraction of the hardening phase.

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Mathematical modeling of work hardening of heterophase materials with nanosized strengthening particles

Cited by 5 publications

References 2 publications

Investigation of Thermal Hardening of the FCC Material Containing Strengthening Particles with an L12 Superstructure

Investigation of Thermal Hardening of the FCC Material Containing Strengthening Particles with an L12 Superstructure

Influence of the scale characteristics of the hardening phase with L12 superstructure on the evolution of deformation point defects

Plastic Behavior of Heterophase Alloys with a Fcc Matrix Hardened by Particles with an L12 Superstructure

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