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.

The formation of brittle compounds in metals operating in corrosive environments can be a tremendous source of embrittlement for industrial structures and such phenomenon is commonly enhanced in presence of stresses. To study this type of microstructural change modeling is preferred to experiment to reduce costs and prevent undesirable environmental impacts. This thesis aims at developing an engineering approach to model stress-induced precipitation, especially near stress concentrators, e.g. crack tips, for multi-phase and polycrystalline metals, with numerical efficiency.

In this thesis, four phase-field models are developed and applied on stress-induced hydride precipitation in zirconium and titanium alloys. The energy of the system is minimized through the time-dependent Ginzburg-Landau equation, which provides insights to the kinetics of the phenomenon. In these models, the driving force for precipitation is the coupling between the applied stress and the phase transformation-induced dilatation of the system. Models 1-3 implicitly incorporate near crack-tip stress fields by using linear elastic fracture mechanics so that only the phase-field equation is solved numerically with the finite volume method, reducing the computational costs. Phase transformation is investigated for intragranular, intergranular and interphase cracks in single- and two-phase materials by considering isotropy and some degrees of anisotropy, grain/phase boundary energy, different transition orders and solid solubility limit. Model 4 allows representing anisotropy connected to lattice mismatch and the orientation of the precipitates influenced by the applied stress. The model is employed through the finite element program Abaqus, where the fully coupled thermo-mechanical solving method is applied to the coupled mechanical/phase-field problem. Hydride growth is observed to follow the near-crack tip hydrostatic stress contours and can reach a steady state for specific conditions. The relation between hydride formation kinetics and material properties, and stress relaxation are well-reflected in the results.

With the presented approaches, precipitation kinetics including different kinds of defects, multi-phase microstructures, phase/grain boundaries, order transitions and loading modes can be successfully captured with low computational costs. They could therefore contribute to the numerical efficiency of multi-scale environment-assisted embrittlement prediction schemes within commercial software serving engineering projects.