Numerical analysis of hydrogen transport near a blunting crack tip

TLDR: In this paper, Oriani's equilibrium theory is used to relate the hydrogen in traps (micro-structural defects) to concentration in normal interstitial lattice sites (NILS), and the resulting non-linear transient hydrogen diffusion equations are integrated using a modified backward Euler method.

Abstract: T he hydrogen transport problem is studied in conjunction with large deformation elastic—plastic behavior of a material. Oriani's equilibrium theory is used to relate the hydrogen in traps (micro-structural defects) to concentration in normal interstitial lattice sites (NILS). The resulting non-linear transient hydrogen diffusion equations are integrated using a modified backward Euler method. Coupled diffusion and plastic straining is analysed with this numerical procedure in the area around a blunting crack tip. A uniform NILS concentration as dictated by Sievert's law at the pressure and temperature of interest is used as initial condition throughout the body. The crack is initially blunted by plane strain mode I (tensile) loading. The finite element results show that hydrogen residing at NILS is generally very small in comparison with the population that develops in trapping sites near the crack surface. That is, lattice diffusion delivers the hydrogen but it is predominantly the trapping that determines its distribution at temperatures of interest. The predominance of trapped hydrogen over lattice concentration prevails even in the case when hydrogen migrates under steady state conditions. Hence, the hydrostatic stress effect is less important than traps created by plastic straining as far as the creation of high total hydrogen concentration is concerned. The trapping site locations and the temperature determine the amounts and locations of high hydrogen concentrations. Consequently, ahead of a blunting crack tip, the total hydrogen concentration and plastic strain diminish with distance from the crack tip whereas the hydrostatic stress rises. This would seem to have significant consequences for fractures induced by the presence of hydrogen.