13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Results and Discussion For the explanation of the difference in threshold energy behavior between both cases the following should be marked. The problems of the penetration with spherical and cylindrical indenters are fundamentally different. In case of the cylindrical particle, the contact area is a constant value during the penetration process, whereas for spherical particle, the contact area is a variable quantity. Also, in cylindrical case the points belonging to contact area border are singular and the stresses take out infinity in these points. But sphere indentation is attended with the finite values of stresses in all points of the contact region. The fact that the energy is zero for the zero impact duration and radius in the cylindrical case (Fig. 2) can be explained by the fact that the problem of penetration of a cylinder into a half-space is an idealized problem. When considering small particles, it is impossible to neglect the roundedness of the cylinder angles near the basis, and this model becomes unsuitable. Acknowledgements This work was financially supported with President of Russian Federation grant for young scientists. References [1] K.L. Johnson // Contact Mechanics, Cambridge University Press, 1987. [2] Akbari J., Borzoie H., Mamduhi M.H. Study of Ultrasonic Vibration Effects on Grinding Process of Alumina Ceramic (Al2O3) // World Academy of Science, Engineering and Technology. 2008. N 17. P. 785–790. [3] Li Z.C., Pei Z.J., Sisco T. et al. // In: Proceedings of the ASPE 2007 Spring Topical Meeting on Vibration Assisted Machining Technology, Chapel Hill, NC, USA, 2007. P. 52–57. [4] Yu. V. Petrov, “On the ‘Quantum’ Nature of Dynamic Fracture of Brittle Solids,” Dokl. Akad. Nauk USSR 321 (1), 66–68 (1991) [Sov.Math. Dokl. (Engl. Transl.)]. [5] Yu. V. Petrov, “Incubation Time Criterion and the Pulsed Strength of Continua: Fracture, Cavitation, and Electrical Breakdown,”Dokl.Ross. Akad. Nauk 395 (5), 621–625 (2004) [Dokl. Phys. (Engl. Transl.) 49 (4), 246–248 (2004)]. Petrov Y.V. // Doklady Physics. 2004. Vol. 49. N 4. P. 246–249. [6] Petrov Y., Morozov N. // ASME Journal of Applied Mechanics. 1994. Vol. 61. Issue 3. P. 710–712. Petrov Y.V., Morozov N.F., Smirnov V.I. // Fatigue and Fracture of Engineering Materials & Structures. 2003. Vol. 26. N 4. P. 363–372. [7] Morozov N., Petrov Y. Dynamics of Fracture. Berlin–Hidelberg–NewYork: Springer–Verlag, 2000. 170 p.
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