13th International Conference on Fracture June 16–21, 2013, Beijing, China 4 For investigating the effect of σf on the scatter of measured values of KIC, Fig.2 is drawn, which shows the plots of KIC against the square root of the fracture distance, Xf 1/2, using the data of Table 1. Then Fig.2 is compared with Fig.1 where the KIC is plotted against F= Xf 1/2[σf (1+N)/2N/ σy (1-N)/2N]. Because in Fig.1, the product of Xf 1/2 and σf (in the term of [σf (1+N)/2N/ σy (1-N)/2N]) is fixed at an abscissa value, the effects of the variations of Xf 1/2 and σf on the KIC values offset to each other, the effect of the variation of σf alone is minor. While in Fig.2 at a fixed Xf 1/2, only the σf is varied, thus the difference of scatters presented between Fig.1 and Fig.2 at a fixed abscissa is attributed to the scatters of the σf. The scatter of KIC at a fixed Xf 1/2 reaches 77. 5MPam-1/2 in Fig.2. Comparing this value with the scatter of 55.8MPam-1/2 at a fixed F in Fig.1, the total scatter of σf from 1391MPa to 1875MPa (demonstrated in the Table 1) causes about 21.7MPam-1/2 in the scatter of KIC, which accounts for about 28% of the scatter of 77. 5MPa m-1/2 at a fixed Xf 1/2 and only 21% in whole scatter of 102MPam-1/2 measured at -100oC for the 42 specimens of the normalized C-Mn steel. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 40 80 120 160 KIC(MPam-1/2) Xf 1/2(mm1/2) Figure 2. KIC plotted against Xf 1/2for a normalized C-Mn steel ● for Xf on left side of DMS ○ for Xf on right side of DMS, (Chen, 1998) For further analyses, in Fig.2 one median line is also drawn, which divides the KIC-distributing zone to two areas: in the upper area all points ● represent the crack initiation site (Xf) locating at the left side of DMS and have higher KIC. The scatter in this area (the vertical distance between the upper and median lines) of measured values of KIC reaches about 34.1MPam-1/2 at a fixed Xf which is almost the same in Fig.1. It means that the scatter of σf has little influence on the scatter of KIC in the upper area. In the lower area, all points ○ represent the crack initiation site (Xf) locating at right side of DMS and have lower KIC. The scatter in this lower area (the vertical distance between the lower and median lines) of measured values of KIC accounts for about 43.4MPam-1/2 which is 21.7 MPam-1/2 larger than that in Fig.1 and the difference is considered to be caused by variation of the σf in term of [σf (1+N)/2N/ σy (1-N)/2N]at a fixed Xf. In summary, the effects of the variation of σf from 1391MPa to 1875MPa at a fixed Xf induce 21.7 MPam-1/2 i.e. only 20% increase in scatter of KIC and manifests itself in the lower area where the normal stress predominates the cleavage fracture process. Therefore it is not reasonable for a statistical model to be based on the statistical distribution of the local fracture stress σf i.e. on the
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