# HFIR-Vessel Probabalistic Fracture Mechanics Analysis

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Da. ( 3 3 ) ]n(l + a/2K)~" The integral can be expressed in terms of exponential integrals, but must be evaluated numerically. The asymptotic values for large and small K are given by t ^ l + iK^K»1' ,0 8 Wo t *~16KHl/2K)^K«1- M The large K asymptotic value for t* is accurate to within less than one per cent for K > 1. Some calculated values of t* are shown in Table 1. It should be noted Table 1. The lifetime of a drop for C

To demonstrate the significant features of the solution of this model problem, it is sufficient to treat the special case of zero Bond number. The initial conditions are given in Eq. (7). In the outer region, the height profile of the drop can be written as h = hc + Ch1} hc = — (a2 - r2) , 0app = —, y = - / , (18) where the last equation represents the global mass balance (6). After one integration, the evolution equation (4) gives dr \ dr2 rdr J a3 dt J \ 2a2 The solution of this equation subject to the boundary conditions can easily be determined.

Michalland, Euro. J. Mech. B/Fluids 10, 253 (1991). 20. H. Z. Cummins, L. Fourtune, and M. Rabaud, Phys. Rev. E 47, 1727 (1993). 21. S. Michalland and M. Rabaud, Physica D 61, 197 (1992). 22. S. Michalland, M. Rabaud, and Y. Couder, Europhys. Lett. 22, 17 (1993). 23. V. Hakim, M. Rabaud, H. Thome, and Y. Couder, Proc. NATO Adv. Workshop in New Trends in Nonlinear Dynamics and Pattern Forming Phenomena: the Geometry of Nonequilibrium, Cargese, France (1988). 24. A. M. McEwan and G. I. Taylor, J.