PSI - Issue 33

Jesús Toribio et al. / Procedia Structural Integrity 33 (2021) 1131–1138 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000–000

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It is important to state here that the computed values were obtained on the basis of the hypotheses of classical continuum mechanics, i.e., as if the process zone itself did not exist, which means that the microstructural damage (void growth in the MVC region) was not taken into account. Four approaches where considered to check which of them yields a universal critical parameter independent of the notch geometry and thus on the level of stress triaxiality (constraint) in the samples. All approaches consider a process zone size x c (measured from the notch tip) dependent on the geometry and related to the MVC depth (x MVC also measured from the notch tip). However, there are conceptual differences to model the initiation of the fracture process, as shown in Fig. 4: (i) The process zone is exactly the MVC region and the local value of the equivalent stress is calculated just at the border between the MVC (initiation) and the C (final fracture) domains. In this case x c = x MVC . (ii) The process zone is exactly the MVC region but the average value of the equivalent stress is calculated over this region in such a way that it is equivalent to compute the equivalent stress in the middle of the zone (x c = x MVC /2). (iii) Accounting for the fact that the fracture initiates by MVC but progresses by cleavage, the process zone size x c can be obtained by adding the size of a cleavage facet (x CL ) to the depth of the MVC region (x c = x MVC + x CL ). This means that the fracture instant takes place when the critical equivalent stress is achieved at the boundary between the first and the second cleavage facets after the MVC area. (iv) This approach also considers a mixed process zone size x c related to the size of a cleavage facet (x CL ) and to the depth of the MVC region, but in this case it is assumed that the final fracture takes place when the first cleavage facet fails after the MVC region, and then the equivalent stress has to be computed in the middle of such a facet (x c = x MVC + x CL /2). From the data of Table 3 (including the four fracture criteria), the best approaches are (iii) and (iv), i.e., those involving the average size of a cleavage facet (microstructural length for brittle fracture), apart from the extension of the process zone. The most adequate is the fourth, which indicates that the fracture takes place when a critical value of the equivalent stress is achieved in the center of the first cleavage facet after the process zone (MVC region). In the framework of this process zone approach, the characteristics of strength and microstructure (material parameters) are:  eff c = 1261 ± 7 MPa x c = x MVC + x CL / 2 where  eff c is the critical equivalent stress, xc the critical length (depth of the process zone), x MVC is a function of the geometry (see previous section of the paper) and x CL = 75 μm.

Table 3. Critical values at the fracture instant ___________________________________________

Geom. (iv) ___________________________________________ A 1317 1335 1206 1262 B 1299 1324 1250 1281 C 1255 1264 1246 1250 D 1251 1251 1251 1251 ___________________________________________ Average 1281±20 1294±20 1238±10 1261±7 Variation 5% 6% 3,5% 2% ___________________________________________ (i) (ii) (iii)