A computational model of the subcritical growth of stress-corrosion cracks in metallic plates

Abstract

We construct a computational model for the evaluation of the period of subcritical growth of stress-corrosion cracks in metallic materials. The model is based on the deformation approach and fundamental concepts of fracture mechanics. We study the case of acid media whose interaction with the metal surfaces is accompanied by electrochemical reactions with hydrogen depolarization. It is assumed that the material is destroyed as a result of realization of the following two basic mechanisms: hydrogen-induced mechanical fracture and anodic dissolution of the metal. Therefore, the growth rate of a stress-corrosion crack is represented as the sum of two components: the rate of anodic dissolution of the material and the rate of its hydrogen-induced mechanical fracture. On the basis of this hypothesis, the results of mathematical description of the electrochemical reactions known from the literature, and some concepts of fracture mechanics, we deduce an equation for the description of the kinetics of propagation of stress-corrosion cracks. This equation, together with the corresponding initial and final conditions, forms a mathematical model for the evaluation of the period of subcritical growth of stress-corrosion cracks in the metals. The correctness of the accumulated analytic results is confirmed by the experimental data available in the literature.