The influence of mobility of dissolved hydrogen on the elastic response of a metal

Abstract

The general principles of the mechanics of materials are used to describe the effect of interstitial mobile hydrogen on the linear elastic behavior of metals and alloys. The linear field equations reveal that during transient hydrogen diffusion the Laplacian of the hydrostatic stress is related to the Laplacian of the hydrogen concentration in the lattice, and it is not zero, as has often been assumed in calculations involving stress-driven diffusion of hydrogen under plane strain conditions. When the hydrogen reaches equilibrium with the local stress and diffusion terminates, the linear elastic constitutive response of the solid accounting for the hydrogen effect can be described by the standard Hooke's law of infinitesimal elasticity in which the stiffness moduli are termed moduli at fixed solute chemical potential and are calculated in terms of the moduli at fixed solute composition, the nominal hydrogen concentration, and the material parameters of the system. These moduli at fixed solute chemical potential can be viewed as the counterparts of those characterizing the drained deformation at constant pressure of fluid-infiltrated porous geomaterials, or the adiabatic deformation of thermoelastic materials. Next the linear transient field equations are solved in the case of a dislocation and a line force in an infinite medium under plane strain conditions by using analytic function theory. The range of validity of the solution to the linear field equations for an isolated edge dislocation is investigated for specific materials. Lastly, the implications of the constitutive behavior of the hydrogen-metal binary system on the fracture and dislocation behavior are discussed when the hydrogen is in equilibrium with local stress.