Development of the method with enhanced accuracy for solving problems from the theory of thermo-pseudoelastic-plasticity

Petrov, Alexander; Chernyakov, Yuriy; Steblyanko, P.; Demichev, Konstantin; Haydurov, Vladislav

doi:10.15587/1729-4061.2018.131644

Cited by 9 publications

(9 citation statements)

References 8 publications

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“…It is shown that the phase boundary moves at a constant speed for the selected temperature. It has been established that classical material diagrams represent a curve, bending the family of material diagrams at a point, which is constructed for certain laws of change of the deformation gap front velocity [2].…”

Section: Experimental/theoretical Detailsmentioning

confidence: 99%

“…The value of the yield tooth is modelled separately and compared with experimental data. At the same time, it is necessary to solve the thermal conductivity equations separately and determine additional strain and stress values based on temperature differences [2]. In fact, the flow tooth diagram is a projection of a trajectory that follows an instantaneous thermo-mechanical surface.…”

Section: Experimental/theoretical Detailsmentioning

confidence: 99%

See 1 more Smart Citation

Behaviour Modelling of the Pseudo-Elastic-Plastic Material at Non-Stationary Loading

Steblyanko¹,

Domichev²,

Petrov³

2021

Metallofiz. Noveishie Tekhnol.

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The article is devoted to studying the behaviour of pseudo-elastic-plastic materials under significant deformations. The study of the behaviour of bodies from pseudo-elastic-plastic materials requires the development of special algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at a point is represented as the sum of the elastic component, the jump of deformation during a phase transition, plastic deformation and deformation caused by temperature changes. A numerical method of increased accuracy based on the use of two-dimensional spline functions for solving multidimensional non-stationary problems of the theory of thermo-elasticity for bodies made of pseudo-elastic plastic materials at large deformations is proposed. A phenomenological model is constructed to describe the properties of thermo-elasticity in a point with consideration of heat generated during phase transition in geometrically nonlinear formulation. Basic equations describing the behaviour of pseudo-elastic plastic materials at significant deformations and consisting of the equation of thermal conductivity, motion, physical and geometric relations are written. Numerical examples are considered.

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Section: Experimental/theoretical Detailsmentioning

confidence: 99%

Section: Experimental/theoretical Detailsmentioning

confidence: 99%

Behaviour Modelling of the Pseudo-Elastic-Plastic Material at Non-Stationary Loading

Steblyanko¹,

Domichev²,

Petrov³

2021

Metallofiz. Noveishie Tekhnol.

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“…In the general case, the magnitudes of deformation are functions of the process of stresses and temperature differences, which are determined by the characteristics of the entire previous process of changes in physical factors, and not just the current values. Detailed information on this issue can be found in [2].…”

Section: Solving the Problemmentioning

confidence: 99%

Modeling the Behavior of the Physical and Geometric Non-Linear Functional Heterogeneous Materials

Domichev

2021

ISMS

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The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions

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“…Processing of experimental data of work [5] . Under active load, the total thermo-mechanical surface consists of three separate surfaces.…”

Section: Experimental Substantiation Of the Modelmentioning

confidence: 99%

“…To do this, use the equations of motion, geometric and physical equations, as well as the equation of thermal conductivity. The temperature field at any point in the body in the presence of heat sources and in the case of heat, which is released during its deformation, is determined by solving the equation of thermal conductivity under certain initial and boundary conditions[2, 3].After determining the temperature field for different points in time, the components of the velocity vector and the components of stress and strain tensors satisfying three differential equations of motion, six geometric equations and six physical equations are searched. These equations are solved under certain initial and boundary conditions.…”

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confidence: 99%

Phenomenological Modeling of Volume Nanomaterials With Form Memory

Steblyanko

Domichev²,

Petrov

2020

ISMS

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The paper presents a phenomenological approach to modeling bulk memory nanomaterials form. A phenomenological model has been proposed that can be applied to model the behavior of nanomaterials with shape memory properties. The study of shape memory alloys as functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity is presented. The phenomenological model is confirmed by experimental data. Tables of diagrams for different temperatures of alloys with shape memory are given.Key words: modeling, functionally inhomogeneous materials, nanomaterials, phenomenological approach, large deformations

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Development of the method with enhanced accuracy for solving problems from the theory of thermo-pseudoelastic-plasticity

Abstract: Alloys possessing shape memory (ASM) constitute a special group of alloys with the capability to restore previous shape even after rather large deformations. If ASM is deformed plastically at low temperatures, this deformation

Cited by 9 publications

References 8 publications

Behaviour Modelling of the Pseudo-Elastic-Plastic Material at Non-Stationary Loading

Behaviour Modelling of the Pseudo-Elastic-Plastic Material at Non-Stationary Loading

Modeling the Behavior of the Physical and Geometric Non-Linear Functional Heterogeneous Materials

Phenomenological Modeling of Volume Nanomaterials With Form Memory

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