Analysis of Elastic Deformations Induced by Hydride Transformation in Magnesium within the Gradient Theory of Elasticity

One of main sustainable development principles is associated with changing the energy balance 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 deformations 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 longrange character. Furthermore, it is shown that the rapid formation of isolated MgH2 nuclei is replaced by a slowdown of this process during the nucleus coalescence process. Local and discretized 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.