6 Figure 2: Dynamic energy versus static energy required for fragmentation of sphere (after Chau et al. [2]) CONCLUSION The present paper summarizes a new theoretical approach to consider the dynamic stress within a sphere under double dynamic test. The application of this tensile stress to dynamic fracture in the sphere is also outlined. More elaborated numerical analysis remains to be done and will be presented at a later time. Nevertheless, the present framework should be very useful to investigate the dynamic fragmentation problem of spheres under dynamic compressions. ACKNOWLEDGMENTS The work was supported by the Research Grants Council of the Hong Kong SAR government with a CERG Grant No. PolyU 5044/99E to The Hong Kong Polytechnic University through KTC, by the PolyU studentship Project G-V946 to SZW, and by Post-doctoral Project No. G-YW39 to XXW. REFERENCES 1. Valanis K.C. (1966). J. Appl. Mech. 33, 888. 2. Chau, K.T., Wei X.X., Wong R.H.C. and Yu T.X. (2000). Mech. Mat. 32, 543. 3. Chau, K.T., Wong, R.H.C. and Lee, C.F. (1998). Int. J. Rock Mech. Min. Sci.35(4-5), 662, Paper No. 007. 4. Chau, K.T., Wong, R.H.C., Liu, J., Wu, J.J. and Lee, C.F. (1999). In: The 9th International Congress on Rock Mechanics, Vol. 1, pp.541-544. 5. Chau, K.T., Liu J., Chan, T.C.P., Yu, T.X. and Chen, X.W. (1999). In: Sixth Pan American Congress of Applied Mechanics (PACAM VI), pp. 967-970. 6. Darvell, B.W. (1990). J. Mat. Sci. 25, 757. 7. Hiramatsu, Y. and Oka, Y., (1966). Int. J. Rock Mech. Min. Sci 3, 89. 8. Freund L.B. (1989). Dynamic Fracture Mechanics, Cambridge University Press, Cambridge. 9. Chau, K.T. and Wei, X.X. (1999). Int. J. Solids Struct.36, 4473. 10. Wei, X.X. and Chau, K.T. (1998). Int. J. Rock Mech. Min. Sci.35(4-5), 623, Paper No. 006. Wd = 1.52 Ws R2 = 0.7439 0 2 4 6 8 10 12 14 0 5 10 Static energy (J) Dynamic energy (J)
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