Issue 20

R. Brighenti et alii, Frattura ed Integrità Strutturale, 20 (2012) 6-16; DOI: 10.3221/IGF-ESIS.20.01 14 Element volume fraction Mass density Young modulus Poisson’s ratio Thermal expansion coeff.  [%]  [kg/m 3 ] E [Gpa]   [K -1 ] Iron Fe ~ 98.00 7870 200 0.29 1.20E-05 Molibden Mb ~ 1.05 10220 330 0.38 5.35E-06 Cromium Cr ~ 1.05 7190 248 0.30 6.20E-06 Table 1 : Physical and mechanical parameters of the main elements in a carbon steel D6ac. Element volume fraction Mass density Young modulus Poisson’s ratio Thermal expansion coeff.  [%]  [kg/m 3 ] E [GPa]   [K -1 ] Base material Fe ~ 98.00 7870 200 0.29 1.20E-05 Equivalent inclusion -- ~ 2.10 8705 289 0.34 5.78E-06 Table 2 : Mean physical and mechanical parameters of the base material and the equivalent inclusion in a carbon steel D6ac. Now consider an infinite plane under remote uniform tensile stress 0 y  , containing an initial straight crack normal to the applied stress. By adopting the equivalent inclusion volume fraction (Tab. 2) and considering an average inclusion diameter equal to about 20 m  (e.g. see Ref. [16]), an inclusion spacing d equal to about 234 m  can be computed for a regular hexagonal distribution of inclusions (Fig. 3). The static crack extension is determined by applying the above described criteria (the Erdogan-Sih criterion and the R-criterion) on the crack growth direction. The mixed mode SIFs are computed by taking into account only the remote stress 0 y  (the local fluctuation of the stress component y  is negligible, as is shown in Fig. 4) and the micro shear stress fluctuations   . In Fig. 9, the crack path predicted for an initially straight crack developing at half distance between two horizontal lines of inclusions (see Fig. 4a, with 0 / 0.0026 a y     ) is represented. The crack path evaluated by the Erdogan-Sih criterion is similar to that determined by the R-criterion (Fig. 9). Nevertheless, it can be observed that the R-criterion produces a slight crack path deviation since the plastic zone shape is influenced in a complex way by the Mode I and Mode II SIFs which continuously change during the whole process of crack propagation. (a) (b) Figure 9 : (a) Path of an initially straight crack developing at half distance between two lines of inclusions in an infinite plane under remote uniform tensile stress y 0  . (b) Detail of the crack path at the microscale where the distribution of inclusions is shown.