PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 206–213 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

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With F1 the fracture phenomenon is modelled as a damage process spatially localized, whereas F2 and F3 imply a time localization of damage/fracture. Although the initiation of fracture is really a progressive process, it is assumed that the specimen remains unaffected until a crack of depth xc is created (space localization), the moment at which it propagates in an unstable manner up to the final fracture (time localization). This implies that initiation and fracture criteria are equivalent and that there is no subcritical crack growth. The environmentally-assisted fracture criterion includes environmental factors (critical hydrogen concentration) and mechanical parameters (critical size for initiation). Hydrogen transport by stress-assisted diffusion is computed in an uncracked cylinder (prior to any kind of damage). When the critical hydrogen concentration is reached over a critical distance, suddenly a crack appears and the unstable fracture happens. Thus, the depth xc can be calculated on the basis of linear elastic fracture mechanics (LEFM) assumptions, and is a decreasing function of the applied stress. The solution requires the knowledge of the time to failure or critical time t c at which the hydrogen reaches a critical concentration c c over a critical distance x c . The initiation/fracture criterion is based on the stress intensity factor (SIF): where K IHE is the threshold SIF for the hydrogen environment (another material property);  ap is the externally applied stress, and M is a dimensionless factor dependent on the geometry of the cracked body (a part-through crack of depth x in a cylindrical bar). The factor M is a function of three dimensionless variables M = M (x/a, x/b,  /  o ) representing the crack depth (x/a, where x is the crack depth and a the cylinder radius), the crack shape (x/b, where b is the second parameter defining the crack line, e.g the major axis in an elliptic crack, x being the minor axis), and the considered point on the 3D – crack line (  /  o , where  is a curvilinear coordinate representing the position on the crack curve, and  o the coordinate of a reference point, e.g. the intersection between the crack and the surface). From the fracture condition (9), the critical depth of the embrittled zone (xc) can be obtained: K I = M  ap  x = K IHE (9) The critical hydrogen concentration c c can be expressed in dimensionless form by relating it to the concentration at the boundary co*, given by (3): c c co* = c c / c o exp [s ap V*/RT] (11) where s ap  is the externally-applied hydrostatic stress, since a smooth (uncracked) cylinder subjected to a uniform axial load has a uniform stress state, and the hydrostatic stress at the boundary is given by its constant value (externally applied). The ratio c c /co is a constant characteristic of the specific couple material-environment, since the critical concentration cc is a material property and co is the equilibrium concentration of hydrogen for the material free of stress (thermodynamic equilibrium conditions). Equation (11) can also be expressed in terms of axial stresses in the main axis direction of the cylinder: c c co* = c c / c o exp [  ap V*/3RT] (12) where  ap  is the externally-applied axial stress. The final aim is to determine the time to fracture of the structural member in the hydrogen atmosphere produced by the external hostile environment. To achieve this, it is necessary to calculate the evolution of the hydrogen x c = 1        K IHE M  ap 2 (10)