PSI - Issue 5
Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1291–1298
1294
Toribio and Kharin / Structural Integrity Procedia 00 (2017) 000 – 000
4
m k T b B b L b 2 ( / , / )
p
g
,
(2)
Kn
L
B
M
where is the transmission probability, for which experimental and molecular-dynamics solution data are available. This flow regime at standard temperature corresponds to . º º p pb ~ 0 1 , i.e., it rather can occur in HEAF under rarefied hydrogen-containing gases and when cracks are narrow. Indeed, in experiments with high-strength steels under low-pressure gases described by Lu et al. (1981) and Gao and Wei (1985), the temperature dependence of the hydrogen induced crack growth rate manifested the same T – 1/2 -pattern, as the gas transport rate (2) does. For the transition and slip flows ( ~ 0.1 < Kn < ~ 10 and ~ 0.01 < Kn < ~ 0.1), specific models and empirical fits are available. As well, the entire range ~ 0.01 < Kn < ~ 10 of booth them is covered by the unified flow model, which renders the next suitable approximation:
Kn m YY b r
5 2 16
Kn
p
g
,
(3)
1 6 2
UF
L
Kn
1
M
b / and is
( , / ) Y Y Kn b B r r are the geometry and rarefaction factors, respectively,
Kn
where Y = Y ( b / B ) and
the mean free path (1) at the average pressure , and is the tangential momentum accommodation coefficient. Difficult to obtain, parameters of the relation (3) are available for certain gas-metal systems (Karniadakis et al. (2005), Shen (2005)), although the data for H 2 -metal cases are scarce. At standard temperature, this flow regime corresponds to º º . º º p pb p ~100 ~ 0 1 (or 10 – 1 < b/ ( p ) < 10 2 ), i.e., it may be appropriate for HEAF in the range of sub- and about-atmospheric gas pressures depending on the crack height b , which is determined by the material and load level. Finally, the Poiseuille flow ( Kn < ~ 0.01, i.e., º º p pb ~100 at T = T º) in long ( L >> b , B ) ducts (cracks) yields: 2 ) / ( CT p p p
2
p
( / )
º
k T g Y b B b T B Pois º 3 / 2
p p p 2 1
,
(4)
L
where Y ( b/B ) is the geometry factor available in the literature (O’Hanlon (2003), Karniadakis et al. (2005)), and º is the gas viscosity at standard temperature T º. Unlike other flow regimes relying solely on p , this one can provide sufficient hydrogen supply to the CT at small relative pressure drop p / p <<1, i.e., at p CT p . In this flow, which occurs when b > 100 ( p ), the in-crack molecular transport turns out to be irrelevant for the kinetics of hydrogen delivery to FPZ, i.e., the gas can be considered stationary and having the same pressure everywhere, p CT = p . Hydrogen, which arrives at the CT by in-crack flow, enters there the metal via the surface phase of the overall transport process. These consecutive stages of transport should be linked by means of the condition of mass conservation of hydrogen in the near-surface gas layer having representative thickness ~ , where it must balance hydrogen delivery to the CT by gas-phase flow and its uptake by metal depending on p CT . At the proximities of metal surface, hydrogen migrates among the states of gaseous H 2 ( G ), molecular ( ) and dissociative ( ) adsorption (physi- and chemisorption), and of interstitial solute in a crystal surface layer (Christmann (1988), Pisarev and Ogorodnikova (1997)), see Fig. 1. As well as metal bulk, its surface provides a variety of different sites (potential wells) to accommodate adsorbed hydrogen (Morris et al. (1984), Christmann (1988)). To abbreviate the analysis, only one site kind is assumed for each surface state, i.e., the physisorption sites and chemisorption sites that have respective number concentrations N and N species migration along the surface is ignored. Besides, although the moves of hydrogen along the energy landscape (Fig. 1) between the listed states can go successively gas solute and taking various by-passing ways (Morris et al. (1984), Pisarev and Ogorodnikova (1997)), present description limits to consider consecutive steps, 2.2. Hydrogen at the gas-metal interface
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