PSI - Issue 5

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

1298

Toribio and Kharin / Structural Integrity Procedia 00 (2017) 000 – 000

8

(the classical Sieverts law is recuperated from (16) when for all site types  A << 1, A   ). Besides, the equalities between the rates of forward and backward diffuser jumping A  B within d 3 x for all pairs of site types A , B   yield then the habitual equilibrium distributions of the species between dissimilar interstitial positions (Hirth (1980))



  e   



G G 

/

C

  C C N  B A

A B



 

  e   







G G 

B A B

A

or

,

(17)

/

/

/

1

1



B   







A B





B

A B

B

B



  e   



G G 

/

N

C

1 



A B

A

A B

A

which allows to transform the DE system (15) into the sole diffusion equation for C L (Toribio and Kharin (2015)):

    

    

   

      

  

         A A Y C ln 

( )

 C C C L

t C

N C

 t N





 



 B L B  





d C Y

U

1

B L

L

B

A

 





.

(18)

BA B A



B A ,

   A L B B B L , , 

;







A

As it has been shown by Toribio and Kharin (2015), when small relative concentration of traps,  { T } N T << N , strong trapping,  ( G L – G T ) >>1 ( T   ), and small lattice site occupancy,  L << 1, concur in a system, equation (18) converts into the standard Oriani-theory equation of diffusion and trapping under local equilibrium, whereas in the limit of small occupancies of all type sites,  A << 1 ( A   ), it transforms further into the known phenomenological equation of stress-strain assisted diffusion. Regardless of the local equilibriums, a series of other known diffusion trapping models (e.g., the McNabb-Foster theory among others) may be retrieved as special cases of the presented generalised theory as well, by way of skipping in the present model definite terms that may be insignificant under specific circumstances. This way, developed generalised model of hydrogen transport can be used to clarify the applicability of the specialised models for analyses of definite HEAF cases. Acknowledgements A part of this work was accomplished within the EU 7FP Project “MultiHy” under Grant 263335 . Christmann, K., 1988. Interaction of Hydrogen With Solid Surfaces. Surface Science Reports 9, 1. Gao, M., Wei, R. P., 1985. A "Hydrogen Partitioning" Model for Hydrogen Assisted Crack Growth. Metallurgical Transactions 16A, 2039. Hirth, J. P., 1980. Effects of Hydrogen on the Properties of Iron and Steel. Metallurgical Transactions 11A, 861. Karniadakis, G., Beskok, A., Aluru, N., 2005. Microflows and Nanoflows: Fundamentals and Simulation. Springer, New York. Kharin, V. S., 1987. Crack Growth in Deformed Metals under the Action of Hydrogen. Soviet Materials Science 23, 349. Kompaniets, T., Kurdyumov, A., 1984. Surface Processes in Hydrogen Permeation Through Metal Membranes. Progress in Surface Science 17, 75. Lu, M., Pao, P. S., Weir, T. W., Simmons, G. W., Wei, R. P., 1981. Rate Controlling Processes for Crack Growth in Hydrogen Sulfide for an AISI 4340 Steel. Metallurgical Transactions 12A, 805. Morris, M., Bowker, M., King, D., 1984. Kinetics of Adsorption, Desorption and Diffusion at Metal Surfaces, in “ Simple Processes at the Gas Solid Interface. Comprehensive Chemical Kinetics ”. In: Bamford, C.H., Tipper, C.F.H., Compton R.G. (Eds.). Elsevier, Amsterdam, p. 2. Nelson, H. G., 1983. Hydrogen Embrittlement, in “ Embrittlement of Engineering Alloys ” . In: Briant, C., Banerji, S. (Eds.). Academic Press, New York, p. 275. O’Hanlon, G. H., 2003. A User's Guide to Vacuum Technology. John Wiley & Sons, Hoboken. Pasco, R. W., Ficalora, P. J., 1983. A Work Function-chemisorption Study of Hydrogen on Iron: Kinetics and Strain Effects. Acta metallurgica 31, 541. Pisarev, A. A., Ogorodnikova, O. V., 1997. Elementary Processes near the Interface between Hydrogen Gas and Solid. Journal of Nuclear Materials 248, 52. Shanabarger, M. R., 1985. The Isothermal Kinetics of Hydrogen Adsorption onto Iron Films Observed With the Chemisorption-induced Resistance Change. Surface Science 150, 451. Shen, C., 2005. Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows. Springer, Berlin. Toribio, J., Kharin, V., 2015. A Generalised Model of Hydrogen Diffusion in Metals with Multiple Trap Types. Philosophical Magazine 95, 3429. Williams, D. P., Nelson, H. G., 1970. Embrittlement of 4130 Steel by Low-Pressure Gaseous Hydrogen. Metallurgical Transactions 1, 63. References