13th International Conference on Fracture June 16–21, 2013, Beijing, China 8 In summary, the relationship between fracture toughness KIC and parameters of micromechanism of cleavage fracture Xf, σf , and σy of a C-Mn normalized steel can be generally described by the formula ( ) ( ) ( ) [ ] N N y N N f f N IC X K 1 /2 1 /2 1 /2 1/2 / − + − + = σ σ β , (2) Here the work hardening exponent N is taken as 0.21, and the amplitude of HRR crack tip stress singularity β is about 6.14. As shown in Fig.1, the measured values of KIC exhibit a linear pattern of distribution against the term F=Xf 1/2[σf (1+N)/2N/σy (1-N)/2N] with a slope content of 1/3. The total scatter of KIC reaches 102MPam-1/2 and at a fixed F value it reaches 55.8 MPam-1/2. The scatters in KIC caused by the micro-parameters in micromechanism of cleavage fracture are summarized as follows: Xf, variation from 17μm to 175μm at fixed σf produce scatter of 96.3 MPam-1/2 accounting for 95% in total scatter of 102MPam-1/2 σf, variation from 1391MPa to 1875MPa at fixed Xf produce scatter 21.7 MPam-1/2 accounting for 21% in total scatter of 102MPam-1/2 εpc, variation from 0.0035 to 0.1829 at fixed σf produce scatter 34.1 MPam-1/2 accounting for 34% in total scatter of 102MPam-1/2 Among these three main micro-parameters, the Xf is the major significant factor in production of scatter in measured values of KIC. Thus, in a statistical model, the variation of Xf should be taken into account as the main factor firstly. The effect of εpc present in moving the Xf. In case the variation of Xf, (including on both left and right sides) has been taken as the main factor, the effect of εpc is diminished. In common cases, the σf is a stable parameter and its scatter is within ±10%, which causes about 20% of the scatter of KIC so its effect is minor. Therefore, it is unreasonable to take the distribution of σf as the main event in a statistic model. Acknowledgements This work was financially supported by National Nature Science Foundation of China (No. 51035004 and 51265028). References [1] J. H. Chen, G. Z. Wang, On scattering of measured values of fracture toughness parameters. Inter. J. Fract, 94(1998)33-49. [2] D. A. Curry, Cleavage micromechanisms of crack extension in steels. Metal. Sci, 14(1980)319326. [3] J. W. Hutchinson, Plastic stress and strain field at a crack tip. J. Mech. Phys. Solids, 16(1968)1331. [4] J. R. Rice, G. R. Rosengren, Plain strain deformation near a crack tip in a power-law hardening material. J. Mech.Phys. Solids, 16(1968)1-12. [5] R.O. Ritchie, J. F. Knott, J. R. Rice, On the relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids, 21(1973) 395-410. [6] A. Pineau and B. Tanguy, Advances in cleavage fracture modeling in steels:Micromechanical, numerical and multiscale aspects, Comptes Rendus Physique, 11, (2010) 316-325
RkJQdWJsaXNoZXIy MjM0NDE=