Theoretical study on mathematical model of hydride-introduced steady-state crack growth in metals

The present paper is focused on the theoretical approach to building a mathematical model of delayed hydride crack developed in hydride-forming metals due to the precipitation at the crack tip under the conditions of constant temperature and crack velocity,plane strain and insignificant hydride.As is necessary,the model has to be built by taking into account the coupling of the operating physical processes of hydrogen diffusion,hydride precipitation of the nonmechanical energy flux and material deformation so as to derive analytically the terminal solid solubility of hydrogen in a stressed metal to describe any hydride with different elastic properties and geometrical shapes,in which hydride and the metallic phases concerned are both assumed to take full anisotropic properties.The experimental results of the paper indicate that a hydrostatic stress plateau may develop in the area of hydride precipitation near the crack tip,when the crack propagates under the conditions approaching hydrogen chemical equilibrium,or,near to the stress intensity threshold.Though the plateau hydrostatic stress is strongly dependent on the remote hydrogen concentration and temperature,it has,on the contrary,hardly anything to do with the yield stress and the hardening of the metal.Almost the same hydrostatic stress would develop behind the crack tip in the presence of hydride.Luckily enough,the characteristics of the near-tip field can be used for estimating the critical remote hydrogen concentrations,below which no hydride precipitation will occur,neither will the threshold stress intensity factor.It is also shown that,when the normalized stress intensity factor tends to be zero,the crack-tip field may result in near the threshold stress intensity factor,which is characterized by a constant hydrostatic stress in the hydride precipitation area.As the value of the normalized stress intensity factor increases,the evolution will be followed of the near-tip field for the crack propagation from stage-I to stage-II regime.That is to say,with the decrease of the actual size of the hydride precipitation zone,the hydrostatic stress is increasing,deviating from the level of the plateau.And the neartip field turns to be that of a hydrogen-free metal.In such a situation,the field depends strongly on the hydrogen concentration,far away from the crack tip. And,in turn,the stage-II crack growth velocity can be predicted with the experimentally observed effect of metal yield stress and temperature on crack velocity being confirmed.Thus,it can be seen that the theoretical estimates prove to be favorable for experimental measurements.