Phase field modeling of flaw-induced hydride precipitation kinetics in metals

Sammanfattning: Hydrogen embrittlement can manifest itself as hydride formation in structures when in contact with hydrogen-rich environments, e.g. in space and nuclear power applications. To supplant experimentation, modeling of such phenomena is beneficial to make life prediction reduce cost and increase the understanding.

In the present work, two different approaches based on phase field theory are employed to study the precipitation kinetics of a second phase in a metal, with a special focus on the application of hydride formation in hexagonal close-packed metals. For both presented models, a single component of the non-conserved order parameter is utilized to represent the microstructural evolution. Throughout the modelling the total free energy of the system is minimized through the time-dependent Ginzburg-Landau equation, which includes a sixth order Landau potential in the first model, whereas one of fourth order is used for the second model. The first model implicitly incorporates the stress field emanating from a sharp crack through the usage of linear elastic fracture mechanics and the governing equation is solved numerically for both isotropic and anisotropic bodies by usage of the finite volume method. The second model is applied to plate and notched cantilever geometries, and it includes an anisotropic expansion of the hydrides that is caused by the hydride precipitation. For this approach, the mechanical and phase transformation aspects are coupled and solved simultaneously for an isotropic material using the finite element method.

Depending on the Landau potential coefficients and the crack-induced hydrostatic stress, for the first model the second-phase is found to form in a confined region around the crack tip or in the whole material depending on the material properties. From the pilot results obtained with the second model, it is shown that the applied stress and considered anisotropic swelling induces hydride formation in preferential directions and it is localized in high stress concentration areas. The results successfully demonstrate the ability of both approaches to model second-phase formation kinetics that is triggered by flaw-induced stresses and their capability to reproduce experimentally observed hydride characteristics such as precipitation location, shape and direction.