Crack Growth Rate for Ideal and Non-Ideal Sink for Hydrogen Diffusion Model

Abstract

In this study, we model a non-ideal sink of hydrogen diffusion into a crack and its consequential growth in metal over time. First, we study how the crack grows in an ideal-sink approximation, which is when we don’t take into account that hydrogen inside the crack can diffuse back into the material. In both cases, we start with the equation of state for the ideal gas, PV = mRT, and sequentially derive the gas pressure P, the crack volume V, and the gas mass m. For the gas mass m, we calculate the gas flux through the crack, Q(t). To obtain a result when a non-ideal sink is taken into account, we come up with a different method of calculating the gas flux, Q(t), to include the loss of hydrogen inside the crack. After formulating the integral equation for the crack radius, we then differentiate both sides to reduce it to a differential equation. After solving the differential equation, we finally obtain a closed form solution how the radius of the crack depends on time.