PSI - Issue 39

Lucia Morales-Rivas et al. / Procedia Structural Integrity 39 (2022) 515–527 Author name / Structural Integrity Procedia 00 (2019) 000–000 7 Eq. 6 can be used in combination with the typical Δσ th equation for long cracks (Eq. 4), and resolved for = 10 0 2 , resulting in the hypothetical value for the transition to long-crack growth regime: √ = 10 0 0.65 2 = 440 μ m For the targeted short-crack dimension range (green dashed region in Fig. 1, as previously explained in the section Introduction), the characteristic crack dimension is at least one order of magnitude lower than the one defining the border between short cracks and long cracks. Therefore, as a first approximation, the parameter √ will be assigned a value one order of magnitude smaller: √ = 50 µm In order to tailor the dimension of the theoretically designed defect, the depth, , was fixed to 25-30 µm due to the practical setting optimization concerning the FIB defect manufacturing process. Thereafter, the following FIB defect length was determined as: = 50 2 µm ≈ 80 µm It is worth determining the th value for such a defect size based on Murakami´s theory for short cracks, using Eq. 7: th = 1.43 +120 �√ � 1 / 6 (7) It results in th = 536 , where the hardness, HV = 600 kgf/mm 2 , has been obtained from the results of the mentioned MECBAIN project [Sourmail, et al.(2016)]. This th value is considerably lower than σ 0_upp = 675 MPa , and therefore, the corresponding value for the √ of the FIB defect, 50 µm, will be considered as a good candidate at this stage to ensure a crack initiation and crack growth at the FIB defect. To further confirm if these selected FIB dimensions are appropriate to remain within the short-crack regime, it is vital to make use of a stress intensity factor solution in which the specimen dimensions are explicitly accommodated throughout the calculation of the desired defect dimension. Hence, the solution suggested by Anderson(2017) for a quarter elliptical corner crack in a flat plate was employed, denoted as: = � σ √ (8) where the term � is the shape factor, which is a function of the crack length and depth (in the present work, to be approximated as the FIB defect dimensions), along with the thickness and width of the specimen, and , respectively. A set of formulas by which the variables F and Q were calculated can be found in the section Appendix A, for = 0.5 mm and = 1 mm. Similarly as previously mentioned, stress and stress intensity factor values are substituted by their ranges, and threshold conditions for propagating/non-propagating long cracks are considered, which results in an equation with the form of Eq. 4. For a refined determination of the FIB defect dimensions, the shape factor of Anderson´s equation, Eq. 8, was solved for two conditions. These conditions are as follows (see also Fig. 4): (1) assuming the defect length and depth are identical (i.e. = 1), and the actual component geometry (blue line in Fig. 4). 521