ОЦЕНКА НАПРЯЖЕНИЙ, СОПУТСТВУЮЩИХ ОБРАБОТКЕ ПОДВИЖНЫМ ИСТОЧНИКОМ ЭНЕРГИИ ТОНКОГО СЛОЯ, РАСПОЛОЖЕННОГО НА ПЛОСКОЙ ПОДЛОЖКЕ

Князева, А.Г.; Смолин, И.Ю.

doi:10.15593/perm.mech/2025.5.04

ОЦЕНКА НАПРЯЖЕНИЙ, СОПУТСТВУЮЩИХ ОБРАБОТКЕ ПОДВИЖНЫМ ИСТОЧНИКОМ ЭНЕРГИИ ТОНКОГО СЛОЯ, РАСПОЛОЖЕННОГО НА ПЛОСКОЙ ПОДЛОЖКЕ

А.Г. Князева, И.Ю. Смолин

Сведения об авторах

А.Г. Князева
Институт физики прочности и материаловедения Сибирского отделения Российской академии наук, Томск, Российская Федерация
И.Ю. Смолин
Институт физики прочности и материаловедения Сибирского отделения Российской академии наук, Томск, Российская Федерация

https://doi.org/10.15593/perm.mech/2025.5.04

Взаимодействие полей разной природы (тепловых, химических и механических) в современных технологиях синтеза и обработки материалов привлекает все большее внимание. Это обусловлено необходимостью прогнозирования поведения и свойств новых материалов и изделий в зависимости от условий их создания. Настоящая работа посвящена постановке и решению плоских задач термохемоупругости, которые описывают, например, сплавление слоя порошка на тонкой подложке при лазерном или электронно-лучевом воздействии. В этом случае внешний источник тепла перемещается по поверхности с определенной скоростью и по заданной траектории, вызывая существенное повышение температуры и в общем случае химические реакции. Это приводит к необходимости учета температурной зависимости свойств материала, которые становятся в рассматриваемом случае функциями и координат. Двумерные уравнения модели получены осреднением трехмерных уравнений термохемоупругости по слоям реагирующего слоя порошка и подложки. При этом в результате осреднения получены и выражения для эффективных характеристик двумерной среды. Выведена новая формулировка механической части задачи в напряжениях для случая плоского напряженного состояния, обусловленная неоднородными характеристиками среды при объединении уравнений равновесия, условий совместности деформаций и соотношений Дюамеля – Неймана. Эволюция температурного поля описывается нелинейным уравнением теплопроводности. При численном решении задач использован неявный конечно-разностный метод с расщеплением по координатам для уравнения теплопроводности и конечно-разностный метод последовательной верхней релаксации с чебышевским ускорением для уравнений в напряжениях. Приведены результаты численного моделирования обработки лазерным лучом смеси порошков титана и алюминия на железной подложке. Показано, что свойства подложки в значительной степени определяют величину максимальной температуры и сопутствующих напряжений, что следует учитывать при моделировании явным образом.

Ключевые слова

поле температурытемпературные напряжениятемпературно-зависимые свойстваподвижный источник теплачисленное моделированиелазерная обработкааддитивные технологиислой порошкаматематическая модельплоское напряженное состояние.

Evaluation of stresses associated with the processing of a thin layer located on a flat substrate by a moving energy source

The interaction of fields of different natures (thermal, chemical, and mechanical) in modern technologies of synthesis and processing of materials attracts increasing attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. This paper is devoted to the formulation and solution of plane problems of thermochemoelasticity, which describe, for example, the fusion of a powder layer on a thin substrate under laser or electron-beam action. In this case, an external heat source moves along the surface at a certain speed and along a given trajectory, causing a significant increase in temperature and, in general, chemical reactions. This drives the need for taking into consideration the temperature dependence of the material properties, which in this case become functions of coordinates as well. Two-dimensional equations of the model are obtained by averaging three-dimensional equations of thermochemoelasticity over the reacting powder layer and the substrate. In this case, as a result of averaging, expressions for the effective characteristics of the two-dimensional medium are also obtained. A new stress-based formulation of the mechanical part of the problem for the case of a plane stress state is derived, caused by the inhomogeneous characteristics of the medium when combining the equilibrium equation, Duhamel – Neumann law, and the strain-compatibility equation. The evolution of the temperature field is described by the nonlinear heat conduction equation. An implicit finite-difference scheme with coordinate splitting for the heat conduction equation and a finite-difference method of successive over-relaxation with Chebyshev acceleration for the stress-based equations are used for the numerical solution of the problems. The results of numerical modeling of laser beam processing of a mixture of titanium and aluminum powders on an iron substrate are presented. It is shown that the properties of the substrate largely determine the magnitude of the maximum temperature and associated stresses, which should be taken into account when modeling explicitly.

Keywords

temperature fieldthermal stresstemperature-dependent propertiesmoving heat sourcenumerical simulationlaser processingadditive manufacturingpowder bedmathematical modeling and simulationplane stress state.

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Опубликована: 17.12.2025
В выпуске: 17.12.2025
Выпуск: № 5 (2025)

ОЦЕНКА НАПРЯЖЕНИЙ, СОПУТСТВУЮЩИХ ОБРАБОТКЕ ПОДВИЖНЫМ ИСТОЧНИКОМ ЭНЕРГИИ ТОНКОГО СЛОЯ, РАСПОЛОЖЕННОГО НА ПЛОСКОЙ ПОДЛОЖКЕ

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Evaluation of stresses associated with the processing of a thin layer located on a flat substrate by a moving energy source

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