PSI - Issue 28

880 Alla V. Balueva et al. / Procedia Structural Integrity 28 (2020) 873–885 Author name / Structural Integrity Procedia 00 (2019) 000–000 where and are defined by (1.15). This analytical solution describes how the radius of the crack grows with respect to time, and the solution for a ( t ) is given implicitly. 2. Analysis of Results 1. The developed model will now be used for the analysis of Hydrogen Induced crack growth in metals and pipelines. Initial micro cracks may appear because of the local deformations. They may then grow considerably under the pressure of the molecular hydrogen accumulated inside these micro cracks. Let us first consider which experimental 8 Regarding values consistent with those found in real-world applications, there exists some estimations about the ranges of possible values for hydrogen concentration, diffusion rates, material toughness, and operating temperatures, among others. For example, hydrogen concentration in the medium have been known to vary drastically. A reasonable range of hydrogen concentration is between 10 -9 and 10 -5 mol/mm 3 (Eliaz et al. 2004; Zakroczymski et al., 2005; Addach et al., 2005). It is important to mention the equilibrium described by Oriani’s Theory for Hydrogen Concentration (Oriani 1970). It is understood that hydrogen may either dissolve into the Normal Interstitial Lattice Sites (NILS) or reversible trapping sites afforded by micro-structural voids in the metal. Oriani’s theory dictates that the two are always at equilibrium with each other. Hydrogen concentration is an important variable for several reasons. It is needed to find the initial yield stress for a given time t when hydrogen is present. Hydrogen also affects the rate of diffusion, dislocation velocity, and other factors. The diffusion coefficient, D , varies for steels in the range of 10  9  10  3 mm 2 /sec according to Beggs and Hahn , 1984 and Yokobori et al. , 1996. Grain-boundaries, junctions between multiple grains, and manufacturing defects have been identified as potential trapping sites for hydrogen. The trapping sites play a key role in HE. Hydrogen creates internal pressure in the metal as it accumulates in these sites, resulting in decohesion. Internal stress is described differently between models. Typical properties of steels operating in conditions of hydrogen embrittlement are given in Table 1. data about hydrogen embrittlement of pipeline are available in the literature. 2.1. Lifetime depending on Hydrogen Concentration and Diffusion Coefficient

Table 1. Typical properties of steel in the conditions of hydrogen embrittlement.

PROPERTIES

METAL / STEEL

10 11 Pa

Effective Young modulus, E /(1  v 2 )

Critical Stress Intensity Factor, K c

1  70 MPa  m

1/2

Diffusion coefficient, D

10  9  10  3 mm 2 /sec

The results (Tables 2) indicate that depending upon the hydrogen concentration, the lifetime of the metal constructions with cracks varies within many orders of magnitude, i.e., from years to thousands of years. In the presence of hydrogen for steel with the coefficient of diffusion D = 10  6 mm 2 /sec the lifetime is 0.96 years for c 0 = 10 -6 mol/mm 3 . whereas for c 0 = 10 -8 mol/mm 3 it is already 96 years (Table 2). This suggests that further and more detailed study of hydrogen concentration and diffusion mechanisms in steel is indeed required before any realistic lifetime predictions could be considered somewhat accurate and justified.