13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- where ( )/ ( ) P t k k C t N LT L TL T = + , Q t k N C t N LT T L( )/ ( ) = , and 0 0 = = T t TC C is the initial condition. Substitution of the expression (23) into the first of Eqs. (22) reduces the problem to the sole integrodifferential-equation with respect to CL. Its computational implementation, e.g., via available finite element routines [4-6], requires modification only of calculation of concentration capacity matrices. 5. Summation: Suitability of Models for HAF Analysis The system of equations of diffusion with trapping, which is derived here from kinetics principles, provides generalisation of pertinent previously suggested models, as well as it retrieves special ones typically either raised on the thermodynamics bases or postulated partially from microscopic arguments. This way, simpler equations of specialised models gain clarification of involved approximations and, respectively, of the requisites of their applicability. This allows reasoned pondering of their advantages and limitations to select optimal models for HAF-case analyses. Demonstrated relation of general kinetics-based equations of trapping-affected diffusion with thermodynamics-grounded variable-solubility model visualises the incorporation of traps in this latter. However, its solid thermodynamics foundation makes it capable of accounting of wider variety of factors that influence hydrogen diffusion in metals, but are not amenable to incorporation in kinetics analysis. These are phase transformations under loading (e.g., γ→α transition in steels), variable alloy composition, thermodiffusion, and all microstructural features, such as inclusions, grain boundaries or dislocations, which, strictly speaking, can hardly be treated as point-wise lattice irregularities that the majority of kinetics-based models deal with. With variable solubility model, numerous factors of H behaviour in metals can be incorporated in HAF analyses and simulations through macro-level determined, i.e., apparent or measurable, diffusivities and solubilities dependent on microstructure, cold working, etc. It is the advantage of this model in addition to its linearity, which substantially streamlines computations. However, the prominent deficiency of this model is inability to describe dissymmetry between hydrogenation and dehydrogenation kinetics. Meanwhile, the significance of this fault for HAF analysis seems to be case-dependent, e.g., it may be irrelevant whenever only monotonic hydrogenation occurs, but can be substantial under load or hydrogenation cycling. As well, this model discounts the lattice/trap exchange kinetics, which may be desired in particular HAF analyses. The importance of these deficiencies is also case-dependent, as far as HAF involves definite diffusion distances towards fracture sites xcr, and corresponding diffusion times tdif ∼ xcr 2/(4D), which may be short or long compared with the characteristic time of approaching trap-lattice equilibrium tT-L ∼ kTL + kLTCL/N according to the solution (23). E.g., the role of trap-filling kinetics may be noticeable for hydrogen assisted crack growth in high-strength or brittle materials, where sub-micrometer diffusion distances of the order of crack-tip opening displacement are involved [1,5], and it can be irrelevant otherwise. Concerning diffusion models that account for trapping explicitly, they lack of the majority of attractions of the preceding one, as far as they cannot account for a series of cited diffusioninfluencing factors. In return, they describe hydrogenation-degassing dissymmetry and a series of other trap-related abnormalities of diffusion. However, this improvement raises computational expenses of managing non-linear partial-differential or integro-differential equations. These models
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