The Relationship between Fugacity and Stress Intensity Factor for Corrosive Environment in Presence of Hydrogen Embrittlement
Hydrogen diffusion is the main problem for corrosion fatigue in corrosive environment. In order to analyze the phenomenon, it is needed to understand their behaviors specially the hydrogen behavior during the diffusion. So, Hydrogen embrittlement and prediction its behavior as a main corrosive part of the fractions, needed to solve combinations of different equations mathematically. The main point to obtain the equation, having knowledge about the source of causing diffusion and running the atoms into materials, called driving force. This is produced by either gradient of electrical or chemical potential. In this work, we consider the gradient of chemical potential to obtain the property equation. In diffusion of atoms, some of them may be trapped but, it could be ignorable in some conditions. According to the phenomenon of hydrogen embrittlement, the thermodynamic and chemical properties of hydrogen are considered to justify and relate them to fracture mechanics. It is very important to get a stress intensity factor by using fugacity as a property of hydrogen or other gases. Although, the diffusive behavior and embrittlement event are common and the same for other gases but, for making it more clear, we describe it for hydrogen. This considering on the definite gas and describing it helps us to understand better the importance of this relation.
[1] J. O. M. Bockris, P. K. Subramanyan, A thermodynamic analysis of
hydrogen in metals in the presence of an applied stress field, Acta
Metallurgica, Vol. 19, No. 4, 1971, pp. 1205-1208.
[2] A. T. Yokobori, J. R. T. Nemoto, K. Satoh, T. Yamada, Numerical
analysis on hydrogen diffusion and concentration in solid with emission
around the crack tip, Engineering Fracture Mechanics, Vol. 55, No. 1,
1996, pp. 47-60.
[3] D. M. Symons, A comparison of internal hydrogen embrittlement and
hydrogen environment embrittlement of X-750, Engineering Fracture
Mechanics, Vol. 68, No. 6, 2001, pp. 751-771.
[4] G. Muller, M. Uhlemann, A. Ulbricht, J. Bohmert, Influence of
hydrogen on toughness of irradiated reactor pressure vessel steels,
Journal of nuclear materials, Vol. 359, No. 1-2, 2006, pp. 114-121.
[5] N. Takeichi, H. Senoh, T. Yokota, H. Tsuruta, K. Hamada, H. T.
Takeshita, H. Tanaka, T. Kiyobayashi, T. Takano, N. Kkuriyama,
Hybrid hydrogen storage vessel, a novel high pressure hydrogen storage
vessel combined with hydrogen storage material, International Journal
of Hydrogen Energy, Vol. 28, No. 10, 2003, pp. 1121-1129.
[6] A. T. Yokobori, J. R. T. Nemoto, K. Satoh, T. Yamada, The
characteristic of hydrogen diffusion and concentration around a crack tip
concerned with hydrogen embrittlement, Corrosion Science, Vol. 44,
No. 3, 2001, pp. 407-424.
[7] H. P. V. Leeuwen, The kinetics of hydrogen embrittlement: A
quantitative diffusion model, Engineering Fracture Mechanics, Vol. 6,
No.1, 1974, pp. 141-161.
[8] A. Turnbull, D. H. Ferriss, H. Anzai, Modeling of hydrogen distribution
at a crack tip, Materials Science and Engineering, Vol. 206, No. 1, 1996,
pp. 1-13.
[9] J. Toribio, The role of crack tip strain rate in hydrogen assisted cracking,
Corrosio Science, Vol. 39, No. 9, 1997, pp. 1687-1697.
[10] B. Z. Margolin, V. I. Kostylev, Analysis of biaxial loading effect on
fracture toughness of reactor pressure vessel steels, International
Journal of Pressure Vessels and Piping, Vol. 75, No. 8, 1998, pp. 589-
601.
[11] Y. Kim, Y. J. Chao, M. J. Pechersky, M. J. Morgan, On the effect of
hydrogen on fracture toughness of steel, International Journal of
Fracture, Vol. 134, No. 3-4, 2005, pp. 339-347.
[12] H. P. V. Leeuwen, A failure criterion for internal hydrogen
embrittlement, Fracture Mechanics, Vol. 9, No. 2, 1997, pp. 291-296.
[13] M. A. Guerrero, C. Betegon, J. Belzunce, Fracture analysis of a pressure
vessel madeof high strength steel (HSS), Engineering Failure Analysis,
Vol. 15, No. 3, 2008, pp. 208-219.
[14] B. S. Lee, M. C. Kim, M. W. Kim, J. H. Yoon, J. H. Hong, Master curve
techniques to evaluate an irradiation embrittlement of nuclear reactor
pressure vessels for along-term operation, International Journal of
Pressure Vessels and Piping, Vol. 85, No. 9, 2008, pp. 593-599.
[15] S. N. Choi, J. S. Kim, J. B. Choi, Y. J. Kim, Effect of cladding on the
stress intensity factors in the reactor pressure vessel, Nuclear
Engineering and Design, Vol. 199, No. 1-2, 2000, pp. 101-111.
[16] S. A. J. Jahromi, M. Najmi, Embrittlement evaluation and lifetime
assessment of hydrocracking pressure vessel made of 3Cr-1Mo lowalloy
steel, Engineering Failure Analysis, Vol. 14, No. 1, 2007, pp. 164-
169.
[17] G. Karzov, B. Margolin, E. Rivkin, Analysis of structure integrity of
RPV on the basis of brittle criterion: new approaches, International
Journal of Pressure Vessels and Piping, Vol. 81, No. 8, 2004, pp. 651-
656.
[18] H. W. Liu, L. Fang, Effects of surface diffusion and resolved shear stress
intensity factor on environmentally assisted cracking, Theoretical and
applied fracture mechanics, Vol. 25, No. 1, 1996, pp. 31-42.
[19] C. J. McMahon Jr., hydrogen-induced intergranular fracture of steels,
Engineering Fracture Mechanics, Vol. 68, No. 1, 2001, pp. 773-788.
[20] S. Serebrinsky, E. A. Carter, M. Ortiz, A quantum-mechanically
informed continuum model of hydrogen embrittlement, Journal of
Mechanics and Physics of Solids, Vol. 52, No. 10, 2004, pp. 2403-2430.
[21] I. Ohanaka, Mathematical analysis of solute redistribution during
solidification with diffusion in solid phase, Journal archive, Vol. 26, No.
1, 1986, pp. 1048-1050.
[22] U. Krupp, Fatigue crack propagation in metals and alloys:
microstructure aspects and modelling concepts" WILEY-VCH Verlag
GmbH & Co. KGaA, Germany; 2007.
[23] J. M. Smith, H. C. V. Ness, Introduction to chemical engineering
thermodynamics, McGraw-Hill Inc., Fourth Edition, New York; 1916.
[24] J. M. Prausnitz, R. N. Lichtenthaler, E. G. de Azevedo, Molecular
thermodynamics of fluid-phase equilibria, Prentice Hall International
Series in the Physical and Chemical Engineering Sciences, Third
Edition; 1998.
[1] J. O. M. Bockris, P. K. Subramanyan, A thermodynamic analysis of
hydrogen in metals in the presence of an applied stress field, Acta
Metallurgica, Vol. 19, No. 4, 1971, pp. 1205-1208.
[2] A. T. Yokobori, J. R. T. Nemoto, K. Satoh, T. Yamada, Numerical
analysis on hydrogen diffusion and concentration in solid with emission
around the crack tip, Engineering Fracture Mechanics, Vol. 55, No. 1,
1996, pp. 47-60.
[3] D. M. Symons, A comparison of internal hydrogen embrittlement and
hydrogen environment embrittlement of X-750, Engineering Fracture
Mechanics, Vol. 68, No. 6, 2001, pp. 751-771.
[4] G. Muller, M. Uhlemann, A. Ulbricht, J. Bohmert, Influence of
hydrogen on toughness of irradiated reactor pressure vessel steels,
Journal of nuclear materials, Vol. 359, No. 1-2, 2006, pp. 114-121.
[5] N. Takeichi, H. Senoh, T. Yokota, H. Tsuruta, K. Hamada, H. T.
Takeshita, H. Tanaka, T. Kiyobayashi, T. Takano, N. Kkuriyama,
Hybrid hydrogen storage vessel, a novel high pressure hydrogen storage
vessel combined with hydrogen storage material, International Journal
of Hydrogen Energy, Vol. 28, No. 10, 2003, pp. 1121-1129.
[6] A. T. Yokobori, J. R. T. Nemoto, K. Satoh, T. Yamada, The
characteristic of hydrogen diffusion and concentration around a crack tip
concerned with hydrogen embrittlement, Corrosion Science, Vol. 44,
No. 3, 2001, pp. 407-424.
[7] H. P. V. Leeuwen, The kinetics of hydrogen embrittlement: A
quantitative diffusion model, Engineering Fracture Mechanics, Vol. 6,
No.1, 1974, pp. 141-161.
[8] A. Turnbull, D. H. Ferriss, H. Anzai, Modeling of hydrogen distribution
at a crack tip, Materials Science and Engineering, Vol. 206, No. 1, 1996,
pp. 1-13.
[9] J. Toribio, The role of crack tip strain rate in hydrogen assisted cracking,
Corrosio Science, Vol. 39, No. 9, 1997, pp. 1687-1697.
[10] B. Z. Margolin, V. I. Kostylev, Analysis of biaxial loading effect on
fracture toughness of reactor pressure vessel steels, International
Journal of Pressure Vessels and Piping, Vol. 75, No. 8, 1998, pp. 589-
601.
[11] Y. Kim, Y. J. Chao, M. J. Pechersky, M. J. Morgan, On the effect of
hydrogen on fracture toughness of steel, International Journal of
Fracture, Vol. 134, No. 3-4, 2005, pp. 339-347.
[12] H. P. V. Leeuwen, A failure criterion for internal hydrogen
embrittlement, Fracture Mechanics, Vol. 9, No. 2, 1997, pp. 291-296.
[13] M. A. Guerrero, C. Betegon, J. Belzunce, Fracture analysis of a pressure
vessel madeof high strength steel (HSS), Engineering Failure Analysis,
Vol. 15, No. 3, 2008, pp. 208-219.
[14] B. S. Lee, M. C. Kim, M. W. Kim, J. H. Yoon, J. H. Hong, Master curve
techniques to evaluate an irradiation embrittlement of nuclear reactor
pressure vessels for along-term operation, International Journal of
Pressure Vessels and Piping, Vol. 85, No. 9, 2008, pp. 593-599.
[15] S. N. Choi, J. S. Kim, J. B. Choi, Y. J. Kim, Effect of cladding on the
stress intensity factors in the reactor pressure vessel, Nuclear
Engineering and Design, Vol. 199, No. 1-2, 2000, pp. 101-111.
[16] S. A. J. Jahromi, M. Najmi, Embrittlement evaluation and lifetime
assessment of hydrocracking pressure vessel made of 3Cr-1Mo lowalloy
steel, Engineering Failure Analysis, Vol. 14, No. 1, 2007, pp. 164-
169.
[17] G. Karzov, B. Margolin, E. Rivkin, Analysis of structure integrity of
RPV on the basis of brittle criterion: new approaches, International
Journal of Pressure Vessels and Piping, Vol. 81, No. 8, 2004, pp. 651-
656.
[18] H. W. Liu, L. Fang, Effects of surface diffusion and resolved shear stress
intensity factor on environmentally assisted cracking, Theoretical and
applied fracture mechanics, Vol. 25, No. 1, 1996, pp. 31-42.
[19] C. J. McMahon Jr., hydrogen-induced intergranular fracture of steels,
Engineering Fracture Mechanics, Vol. 68, No. 1, 2001, pp. 773-788.
[20] S. Serebrinsky, E. A. Carter, M. Ortiz, A quantum-mechanically
informed continuum model of hydrogen embrittlement, Journal of
Mechanics and Physics of Solids, Vol. 52, No. 10, 2004, pp. 2403-2430.
[21] I. Ohanaka, Mathematical analysis of solute redistribution during
solidification with diffusion in solid phase, Journal archive, Vol. 26, No.
1, 1986, pp. 1048-1050.
[22] U. Krupp, Fatigue crack propagation in metals and alloys:
microstructure aspects and modelling concepts" WILEY-VCH Verlag
GmbH & Co. KGaA, Germany; 2007.
[23] J. M. Smith, H. C. V. Ness, Introduction to chemical engineering
thermodynamics, McGraw-Hill Inc., Fourth Edition, New York; 1916.
[24] J. M. Prausnitz, R. N. Lichtenthaler, E. G. de Azevedo, Molecular
thermodynamics of fluid-phase equilibria, Prentice Hall International
Series in the Physical and Chemical Engineering Sciences, Third
Edition; 1998.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64962", author = "A. R. Shahani and E. Mahdavi and M. Amidpour", title = "The Relationship between Fugacity and Stress Intensity Factor for Corrosive Environment in Presence of Hydrogen Embrittlement", abstract = "Hydrogen diffusion is the main problem for corrosion fatigue in corrosive environment. In order to analyze the phenomenon, it is needed to understand their behaviors specially the hydrogen behavior during the diffusion. So, Hydrogen embrittlement and prediction its behavior as a main corrosive part of the fractions, needed to solve combinations of different equations mathematically. The main point to obtain the equation, having knowledge about the source of causing diffusion and running the atoms into materials, called driving force. This is produced by either gradient of electrical or chemical potential. In this work, we consider the gradient of chemical potential to obtain the property equation. In diffusion of atoms, some of them may be trapped but, it could be ignorable in some conditions. According to the phenomenon of hydrogen embrittlement, the thermodynamic and chemical properties of hydrogen are considered to justify and relate them to fracture mechanics. It is very important to get a stress intensity factor by using fugacity as a property of hydrogen or other gases. Although, the diffusive behavior and embrittlement event are common and the same for other gases but, for making it more clear, we describe it for hydrogen. This considering on the definite gas and describing it helps us to understand better the importance of this relation.
", keywords = "Hydrogen embrittlement, Fracture mechanics,
Thermodynamic, Stress intensity factor.", volume = "3", number = "3", pages = "330-5", }
