Hydrogen Induced Fracture Near the Surface

Abstract

We consider fracture growth controlled by fluid diffusion into the fracture. If the fluid is accumulated inside the fracture, after some incubation period, it starts growing under the pressure of the accumulated fluid. An important example is given by hydrogen induced cracking. Hydrogen absorbed by a metal is typically dissolved in the lattice in the proton form. Some of the protons reach the surface of a pre-existing or freshly created crack where they recombine with electrons and form molecular hydrogen in the crack cavity. Because the molecular form of hydrogen usually is thermodynamically more stable, this process leads to accumulation of gas hydrogen inside the crack. Then the fracture can propagate even in the absence of any external loading, that is, only under the excessive hydrogen pressure. Another example is given by the heating of water saturated rock. If due to the heat, the water evaporates or boils inside the crack, the pressure exerted by the vapor can cause the cracks to propagate, increasing the crack size by orders of magnitude. This mechanism underlies the process of phreatic eruptions, which involves the transfer of magmatic heat to groundwater and subsequent eruption of steam and rock fragments, often without any eruption of magma. In this work we consider several important cases of diffusion-controlled fracture growth. We consider an axisymmetric crack (1) in the infinite space, (2) in the half-space, and (3) in the layer/plate. By implementing asymptotic analysis, we obtain in the closed form simple and robust expressions for the corresponding dependencies of the fracture size upon time. The results reveal some intriguing features worth checking experimentally. For example, although the driving pressures for identical axisymmetric fractures located far and close to the half-space boundary are very different, the expressions for their radii and velocities are exactly the same (i.e., within the accuracy of the higher-order terms with respect to the distance between the fracture and the free-surface). In a fluid-saturated layer (plate) an axisymmetric fracture located in the middle plane first depletes the region around itself but then starts growing towards the saturated regions. The process manifests itself as if the fracture were “sucked” into the saturated zone. This example shows, for example, that hydrogen-induced cracking may occur at very low hydrogen concentrations even if the crack (e.g., mechanical part) is no longer in the hydrogen-rich environment and only residual hydrogen is present. The developed model gives the time to failure and its dependence upon the concentration of diffusing fluid.