PSI - Issue 14

Rakesh Kumar et al. / Procedia Structural Integrity 14 (2019) 668–675 Author name / Structural Integrity Procedia 00 (2018) 000–000

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2.2. Hydrogen transport model The hydrogen in material is categorised based on its occurrence at two sites namely normal lattice interstitial sites (NILS) giving hydrogen concentration � and trapping sites like dislocation core, vacancies, micro-pores, grain boundaries, phase boundaries etc. In this model, however, dislocations are the considered as the only trapping sites. The total hydrogen in material is sum of both these contributions. � can be expressed using total available lattice sites for hydrogen atom in lattice of host metal �� � � , and occupancy of hydrogen atoms � in these sites as L L L C N   (10) where is number of lattice sites for solute atoms per lattice site. Lattice and trap hydrogen has an equilibrium established between each other which is formulated by Oriani R.A (1970). According to Oriani’s theory, the trapped hydrogen concentration � � � is related to the hydrogen occupancies at lattice sites � � � , total available trap sites �� � � at the material point and equilibrium constant � . Therefore, the trapped hydrogen concentration resolved along slip systems can be defined as   1 L T T T L T L N K C K         (11) where, � � ���� � / � , � is trap binding energy, R is gas constant and T is temperature. Considering the mass conservation, the rate of change of total hydrogen concentration at any material point is equal to the flux through the boundaries of the volume element considered. Defining � as lattice hydrogen diffusivity, � partial molar volume of hydrogen, the HTM can be defined as     1 1 (1 ) . . 0 N L T T T N L L L H L L H T L C C C D C V D C C t RT N                                                   (12) The standard HTM considers the effects of trapping and hydrostatic stress gradients and was first described by Sofronis and McMeecking (1989), whereas the plastic strain-rate factor in HTM was introduced by Krom et al. (1999), but the depiction of the last term in (12) in the present form is introduced for first time to consider the effect of slip-rates along slip systems and make more suitability of HTM with the dislocation density based crystal plasticity formulations. Hydrogen transport model takes care of concentration gradient, hydrostatic stress gradient, plastic slip-rate and dislocations as the only trapping sites along the slip systems. 3. Fatigue indicator parameter To investigate the role of various factors e.g. elastic and plastic anisotropy, grain boundary normal stress and hydrogen concentration on fatigue crack initiation a fatigue indicator parameter (FIP) is developed. The proposed FIP considers the effect of various terms affecting the fatigue initiation as discussed above and replaces them with a scalar value. Thus, the scalar parameter FIP provides the combined effect of various parameters on the local damage of the material and critical value of FIP signifies the crack initiation. Proposed FIP is modified Fatemi and Socie (1988) parameter with additional consideration of hydrogen concentration as an equivalent factor responsible for crack nucleation. The FIP is formulated as (13) where �� � defines grain-boundary normal stress, � is reference stress, � is total hydrogen concentration � � � � �, � is reference hydrogen concentration and p, the accumulated plastic strain at each material point is sum of equivalent plastic strain over the total time T as 2 : 3 p p T p L L dt           (14) 0  0 0 0 0 0 1 n n n GB     GB GB H H H C C C C C FIP p C            