Mathematical Modeling of Hydrogen Cracks Growth Kinetics in Metallic Materials at High Hydrogen Parameters

This paper presents a mathematical model for analyzing local fractures in metal materials and structural elements induced by extremely high concentrations of hydrogen. Local fracture of materials is the initiation and propagation of crack-liked defects. Based on the deformation approach, a mathematical model has been developed to study the development of hydrogen cracks in metallic materials caused by high pressures and high concentrations of hydrogen. The model aims to determine the amount of hydrogen present in the crack. To determine the amount of hydrogen present in the crack, Fick’s laws of heat and mass transfer have been applied, and the corresponding diffusion problem has been formulated. The mathematical model was applied to study the process of deep cracking of oil in a bimetallic reactor. From the analysis of this mathematical model, which includes the corresponding differential equations, it was possible to determine the nature of fracture in the oil hydrocracking reactor vessel. The analysis revealed that the fracture occurs at the bimetal boundary due to the formation of hydrogen cracks, which are driven by high hydrogen pressures caused by the high hydrogen concentration at the bimetal boundary. Solving such an important technical problem was only made possible through the utilization of a mathematical model of the process.