  Hydrogen-induced pitting corrosion of metallic is a common phenomenon that
damages the integrity and durability of the materials. Its numerical simulation
is still a challenge due to many complex mechanisms, especially solid-solid
phase transformation and mechanical interaction, leading to the anisotropic
growth of hydride and inducing some bulges on the metal surface. In our work,
we propose a phase-field model and numerical technique for simulation of
hydrogen-induced pitting corrosion, and apply it to the system of
$\alpha$-Uranium. In our model, the elastic strain energy is introduced to
approximate the anisotropic pit morphology induced by the mechanical
interaction between metal and hydride. For the numerical technique, the free
boundary condition based on the finite element method is adopted to introduce
the bulges of the metal surface. By the application of our model and numerical
technique, the anisotropic pit morphology with a bulge on the metal surface in
agreement with experiments of $\alpha$-Uranium is obtained. Moreover, the
compression of $\alpha$-Uranium and the dilation of its hydride are discovered,
which develops the deep understanding of hydrogen-induced pitting corrosion.
This model is expected to be applied to the health detection of
hydrogen-induced pitting corrosion of metal in the industry.
