ANALYSIS OF ELASTIC DEFORMATIONS INDUCED BY HYDRIDE TRANSFORMATION IN MAGNESIUM WITHIN THE GRADIENT THEORY OF ELASTICITY

Valery N. Aptukov, Nataliya E. Skryabina, Daniel Fruchart

Author details

Valery N. Aptukov
Perm State University, Perm, Russian Federation
Nataliya E. Skryabina
Perm State University, Perm, Russian Federation
Daniel Fruchart
Université Grenoble Alpes &CNRS, Grenoble, France

https://doi.org/10.15593/perm.mech/2025.3.02

One of main sustainable development principles is associated with changing the energy bal- ance in favor of renewable energy sources. In the future, this means replacing traditional fossil fuels by new fuels characterized by lower levels of gas pollution. Hydrogen, as an alternative to carbonaceous resources, constitutes an ideal clean fuel. Its storage as metal hydrides is one of the best solutions in terms of safety and disposal. Magnesium hydride is more particularly advantageous for both its volumetric capacity and energy balance. However, the implementation of its use faces some difficulties, including the kinetics of hydride formation. The rate and completeness of magnesium to magnesium hydride conversion depends on several parameters. For example, the formation of hydride corresponds to a marked change of volume, reaching up to 30 % from Mg to MgH2. Consequently, the volume increase initiates the occurrence of stresses in the vicinity of the hydride/matrix interface. The stresses caused by de- formations of the initial matrix lead to different effects on penetration of hydrogen: tensile stresses contribute but compressive stresses inhibit this process. Although experimental studies were based on hydride nucleation modeling, the presence of grain boundaries was not taken into account in the theoretical models. In theoretical models, this is a classical interpretation of the development of stresses at the interface between two phases. In the present investigation, the calculations are based on a gradient field theory model. The gradient field theory is particularly suitable to describe the elastic behavior of materials at the microscale, where the dimension parameters are on the same level as the characteristic parameter e.g. of the grain size. In the present study, the major results make it possible to conclude that the distribution of strains (stresses) is not restricted to the near vicinity of the hydride core, but it exhibits a long- range character. Furthermore, it is shown that the rapid formation of isolated MgH2 nuclei is re- placed by a slowdown of this process during the nucleus coalescence process. Local and discre- tized hydride formation is only energetically favorable for a specific value of the nucleus volume. As its volume increases, the energy balance changes and the hydride-matrix system transits to a new state with a new level of energy balance. In practice, this means that the growing kinetics of the hydride phase is not steady as it depends on the volume of the converted phase.

Keywords

magnesiummagnesium hydridephase transformationgradient theory of elasticityenergy relationships.

АНАЛИЗ УПРУГИХ ДЕФОРМАЦИЙ, ИНДУЦИРОВАННЫХ ГИДРИДНЫМ ПРЕВРАЩЕНИЕМ В МАГНИИ, В РАМКАХ ГРАДИЕНТНОЙ ТЕОРИИ УПРУГОСТИ

Один из принципов устойчивого развития связан с изменением энергетического баланса в пользу возобновляемых источников энергии. В перспективе это означает замену традиционного ископаемого топлива на новое, которые характеризуется меньшим содержанием вредных выбросов. Альтернативой углеводородному сырью может служить водород, который является идеальным энергоносителем. Для его безопасного использования и транспортировки часто предлагается металлогидридный способ хранения, например, в виде гидрида магния. На пути практической реализации этой идеи существует ряд трудностей, одна из которых – кинетика гидридного превращения. Скорость и полнота превращения «магний – гидрид магния» зависит от многих параметров. Например, фазовый переход, обусловленный гидридным превращением, сопровождается локальным изменением объема и достигает значительных величин (в магнии до 30 %). В свою очередь изменение объема инициирует появление напряжений вблизи границы раздела «гидрид – матрица». Напряжения, обусловленные деформацией исходного материала, по-разному влияют на интенсивность проникновения водорода: растягивающие напряжения способствуют, а сжимающие препятствуют этому процессу. Существующие модели зарождения гидридной фазы в магнии не учитывают наличие межкристаллитных границ. В теоретических моделях – это классическая интерпретация возникновения напряжений на границе раздела двух фаз. Расчеты, проведенные в настоящем исследовании, основаны на теории градиентного поля. Считается, что градиентная теория более подходит для описания упругого поведения материалов на микроуровне, где размерный параметр имеет порядок характерного параметра объекта, например, зерна. Полученные в данном исследовании результаты позволяют сделать принципиально важный вывод: распределение деформации (напряжений) вблизи зародыша гидрида носит не локальный, а дальнодействующий характер. Более того, показано, что быстрое изолированное образование MgH2 сменяется замедлением этого процесса в процессе слияния зародышей. Локальное образование гидрида энергетически выгодно только при некотором определенном объеме гидрида. По мере увеличения его объема энергетический выигрыш исчерпывается, и система «гидрид – матрица» переходит в новое энергетическое состояние. На практике это означает, что кинетика роста гидридной фазы неравномерна и зависит от объёма превращенной фазы.

Ключевые слова

магнийгидрид магнияфазовое превращениеградиентная теория упругостиэнергетические соотношения.

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Article information

Published: 8 September 2025
Issue date: 8 September 2025
Issue: No. 3 (2025)