PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1291–1298 Toribio and Kharin / Structural Integrity Procedia 00 (2017) 000 – 000

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2.1. Gas phase flow

The phase of environmental transport of hydrogenous substance towards the proximities of eventual FPZs in solids culminates in particle collisions with metal surface, which are characterized by the frequency  of particle surface touches per unit area. In the case of static gas under pressure p it reads (O’Hanlon (2003)): p zp  ( )  , (1) B and absolute temperature T , and m M is the molecule mass. Concerning HEAF under static gas that has unrestricted access to metal surface near potential FPZ, as it is proper to solids with rather smooth geometry, the molecular impingement rate  is defined by the global pressure p , and the issue of gas phase transport is then resolved. where )   2 /( M m z  is the Knudsen collision factor, in which  = ( k B T ) – 1 includes the Boltzmann constant k

Fig. 1. Sequential transport steps and potential trace for hydrogen on its way towards fracture site in the course of HEAF process. The hatched band indicates the location of the surface. Different states (sites) passed by hydrogen on its way, as well as their key energy characteristics that control the rates of thermally activated hydrogen migration in a system between different sites are indicated. See text for details. However, this may fail for a crack having a micrometer-scale height, which narrowness limits the substance conductance to the crack tip (CT), see, e.g., Lu et al. (1981) or Gao and Wei (1985). Sinking of hydrogen from a crack into metal (hydrogen uptake in metal) depends there on the impingement rate (1) at local pressure p CT at the CT, whereas the pressure drop along the crack  p = p – p CT drives the in-crack gas-phase flow of molecules towards the CT. The unified description of such flow is radically complicated, but the flow physics (O’Hanlon (2003), Karniadakis et al. (2005)) provides particular solutions and approximations for certain flow regimes distinguished basing on the Knudsen number Kn =  / b , which relates the crack height b and the gas particle mean free path ) /(    d p M 2 1 2  , where d M is the molecule diameter. These regimes are the next (Karniadakis et al. (2005)): ( i ) the Knudsen flow at Kn > ~ 10, ( ii ) the transition regime at ~ 0.1 < Kn < ~ 10, ( iii ) the slip-flow at ~ 0.01 < Kn < ~ 0.1, and ( iv ) the Poiseuille one at Kn < ~ 0.01. For H 2 gas ( 2 H d = 0.27 nm) at standard temperature T º = 273 K and pressure p º = 101.3 kPa, it is  º = 0.11  m. The crack height in a solid under load ) /( Y b K E  2 I  , where K I is the stress intensity factor, E is the Young modulus and  Y is the yield strength, depends on both the material and the load level in a given HEAF case. It may vary from b  1  m (high strength brittle alloys manifesting HEAF under low K I ) to b  10 2  m (ductile metals supporting higher K I values). This yields  10 – 3 p º/ p < Kn <  10 – 1 p º/ p for cracks under HEAF at the reference temperature T º, i.e., different flow regimes can occur in particular HEAF cases. For rectangular channel with impermeable flanks that has the height b , length L and cross-section width B , the molecule number flow per unit cross-section area g * , where * is a wildcard of the flow regime identificator, can be defined according to Karniadakis et al. (2005) as follows. For the Knudsen flow ( Kn > 10) in a duct it reads: