A Chemo-Damage-Mechanical Coupled Phase-Field Model for Three-Dimensional Hydrogen-Assisted Dynamic Cracking

Abstract

This study develops a chemo-damage-mechanical coupled phase-field method for modeling two-dimensional and/or three-dimensional hydrogen-assisted transient dynamic cracking in metallic materials. In this method, hydrogen diffusion in solids is described by the evolution of bulk hydrogen concentration governed by the diffusion equation with an extended Fick's law. The hydrogen concentration and the inertial force of solids are incorporated into the governing equations of a non-standard quasi-brittle phase-field model (known as the phase-field regularized cohesive zone model, PF-CZM) capable of modeling complicated multiple crack nucleation, initiation, and propagation with insensitivity to mesh size and length scale. The resultant displacement-damage-hydrogen concentration coupled three-field equation is derived by the finite element Galerkin method and solved using a staggered Newton–Raphson iteration algorithm with an unconditionally stable implicit Newmark integration scheme. The new method was verified by four benchmark examples with hydrogen-free numerical/experimental results for comparison, including quasi-static/dynamic fracture of a notched plate under uniaxial tension, a dynamic crack branching experiment under constant traction, the Kalthoff-Winkler impact fracture experiment, and dynamic fragmentation of a cylinder under internal pressures, with the effects of loading velocity, initial bulk hydrogen concentration, and diffusion time on crack propagation investigated in detail. It is found that the present method is capable of modeling complex 2D and 3D hydrogen-assisted dynamic crack propagation and bifurcation under impact or internal pressure loadings, and thus holds the potential to be used for the structural design of hydrogen storage.