Modeling failure of metallic glasses due to hydrogen embrittlement in the absence of external loads

A model is developed to describe the expansion of high-pressure hydrogen bubbles and propagation of cracks between them in the absence of external loads. The focus is on cracks that form during electrochemical hydrogen charging of amorphous Fe₈₀B₁₁Si₉ ribbons. A coupled diffusion/fracture mechanics approach is developed, allowing determination of the time to failure. Finite element analyses are carried out to determine the values of the stress intensity factor for cracks of different lengths, assuming linear elasticity. In addition, the volume of a bubble with edge cracks is related to the internal pressure. The relation between critical pressure and crack length is obtained from an appropriate value of the fracture toughness, K_Ic. A criterion is proposed to obtain the pressure and volume as a function of the number of hydrogen moles within the bubble with edge cracks. Finite element analyses are also used to calculate the hydrogen concentration and hydrogen diffusion flux as a function of crack length and time. The time to failure as predicted from this model is of the same order of magnitude as that observed experimentally.