PSI - Issue 13

Lapin V.N. et al. / Procedia Structural Integrity 13 (2018) 1171–1176 Lapin V.N. and Cherny S.G. / Structural Integrity Procedia 00 (2018) 000–000

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Рис. 5. (a) Fracture path computed at β = 0 . 5 , ∆ R = 0 . 001 m ; (b) Fracture trajectories computed at β = 0 . 5 (up): 1 – ∆ R = 0 . 0005 m ; 2 – ∆ R = 0 . 001 m ; 3 – ∆ R = 0 . 002 m and at ∆ R = 0 . 001 m (down): 1 – β = 0 ; 2 – β = 0 . 25 ; 3 – β = 0 . 75 .

see that the influence of the fracture increment or the weight parameter is quite small at least for considered problem.

4. Conclusion

The implicit criterion of the fracture propagation proposed by Cherny at al. (2016) as the part of 3D hydraulic fracture model has been verified and compared with global type criteria proposed by Lazarus et al. (2008). The kinking angle distribution obtained from the implicit criterion is close enough to the experiment values as well as global type criteria. The criteria of Lazarus et al. (2008) use the analytical representation of stress intensity factors and can not be applied without modification to general cases. In contrast to them the implicit criterion is based on the values of stress intensity factors that are calculated numerically for the stress state after the fracture propagation and so can be applied for any problem. Although it is necessary to consider a few possible fracture propagation directions the numerical experiments have shown that 5-6 iterations provide the converged solution. Buchholz F.-G., Chergui A., Richard H.A., 2004., Fracture analyses and experimental results of crack growth under general mixed mode loading conditions. Engineering Fracture Mechanics 71(4), 455 - 468. Cherny S., Lapin V., Esipov D., Kuranakov D., Avdyushenko A., Lyutov A., Karnakov P., 2016, Simulating fully 3D non-planar evolution of hydraulic fractures. International Journal of Fracture 201(2), 181–211. Cooke M.L., Pollard D.D., 1996 Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate. Journal of Geophysical Research 101 (B2), 3387–3400. Erdogan,F. and Sih,G.C., 1963, On the Crack Extension in Plates Under Plane Loading and Transverse Shear Journal of Basic Engineering 85 (4), 519-525 Lazarus. V., Buchholz F.-G., Fulland M., Wiebesiek J., 2008., Comparison of predictions by mode ii or mode iii criteria on crack front twisting in three or four point bending experiments. International Journal of Fracture 153(2), 141–151. Richard H.A., Fulland M., Sander M., Theoretical crack path prediction. Fatigue Fracture of Engineering Materials and Structures 28 (1-2), 3–12. Schollmann M., Richard H.A., Kullmer G., Fulland M., 2002., A new criterion for the prediction of crack development in multiaxially loaded structures. International Journal of Fracture 117(2), 129–141. Shokin Yu., Cherny S., Esipov D., Lapin V., Lyutov A., Kuranakov D., 2015., Three-dimensional model of fracture propagation from the cavity caused by quasi-static load or viscous fluid pumping. In: Danaev N., Shokin Y., Darkhan AZ. (eds) Mathematical Modeling of Technological Processes. CITech 2015. Communications in Computer and Information Science, vol 549. Springer, Cham, 143–157. Sih G. C., 1974, Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture, 10(3), 305–321. References