PSI - Issue 48

Štěpán Major / Procedia Structural Integrity 48 (2023) 230 – 237 Major / Structural Integrity Procedia 00 (2019) 000 – 000

232

3

model is obviously only usable for the reverse simulation of the process i.e., for its use it is necessary to know the maximum dimensions of inclusions and other inhomogeneities in the material. 2. Model of hydrogen affected fatigue crack initiated on the subsurface inclusion 2.1. Subsurface crack and inclusion diameter We will now look at a model of a crack formed on a subsurface inclusion that was affected by hydrogen embrittlement. We usually encounter this phenomenon mainly in the area of gigacycle fatigue, but if we have components that are in an environment with a high concentration of hydrogen, such as, for example, pipelines with compressed hydrogen, this phenomenon occurs with a much smaller number of load cycles. The relevant cycles can be represented, for example, by the periodically changing g value of the pressure in the pipeline. In this case, hydrogen will diffuse through the metal and hydrogen will accumulate in microcavities such as those around non-metallic inclusions. At the same time, it is possible to assume a higher concentration (of these inclusions) in the weld area than in the surrounding material. The increasing pressure of the accumulated hydrogen in the microcavity will lead to the generation of a bias stress. The presence of this stress results in a decrease in the necessary stress intensity K around the inclusion, which is needed for crack growth to occur. When we will calculate critical diameter of inclusion with the use of fracture mechanics (it is therefore a sufficiently large diameter of the inclusion on which a subsurface crack can be formed), we would find that the diameter of these inclusions is an order of magnitude larger than what we actually encounter. This fact is precisely the cause of the fact that we commonly encounter fatigue cracks formed on the surface of the component. Subsurface cracks then occur where hydrogen has enough time to diffuse into the cracks of these microcavities (hydrogen traps). In the case of gigacycle fatigue, hydrogen, normally found in small concentrations in the environment, has enough time to accumulate in the vicinity of the inclusion and affect the formation of cracks known as fisheyes. However, if the device works in an environment with a high hydrogen content, this phenomenon will occur much earlier. 2.2. Hydrogen transport in steel In the literature we can find various models describing the transport of hydrogen in steel, see Krom (1999) and Hagi (1979). In this work, we decided to use the method proposed by Sofronis and McMeeking (1989). These authors created a hydrogen transport model with the aim of simulating hydrogen on hydrostatic stress and trapping of hydrogen atoms. Hydrogen embrittlement generally requires localization of hydrogen atoms, which can occur at trap sites such as dislocations, grain boundaries, interfaces between different phases, voids or cracks. These authors assume that the diffusing hydrogen atoms settle in the place of the traps that are thus filled. Even in the eighties of the twentieth century, it was possible to carry out permeation tests, which demonstrated the finding that the intensity of hydrogen trapping depends on the degree of plastic strain. These experiments were carried out by Kumnick and Johnson (1980). Diffusion of hydrogen atoms to the trap sites is driven by the plastic deformation but it is not only reason of its concentration on the trap sites. Other influences are also at play here. Localization of hydrogen can also occur through the effect of hydrostatic stress on chemical potential. Hydrogen transport can be described by equation in form

t   







0

L S C C dV J n dS      T



(1)

V

Where C L is hydrogen concentration in lattice and C T is hydrogen concentration at trap sites. Vector J is hydrogen flux and n is outward pointing unit normal vector. Hydrogen flux vector is defined as

L L L J M C   

(2)

where M L is mobility of hydrogen atoms in lattice and μ L is chemical potential of the hydrogen in the lattice. The hydrogen concentrations are first related to the number of sites