13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- c d d v w dt z , (4) d d d v w dt z , (5) c c c c d v J w dt z , (6) d d d c d J w dt , (7) c c c c dU v P w Q dt z , (8) d d d c dU P w Q dt . (9) In the Eqs (4)-(9) w is the growth rate of the dispersed phase volume in a unit volume of the medium; it can be expressed as that follows: 2 3 4 4 /3 cr w n R R R n , (10) where n is the concentration of the dispersed particles (bubbles or drops) in the medium, and R is radius of this particles; cr R is the radius of critical (nucleating) bubbles. In the Eq. (6), Eq. (7) J is the growth rate of the dispersed phase mass in a unit volume of substance: 3 1 4 /3 cr v J n m g R n , (11) where 1m is the mass of one atom of the substance; g is a number of atoms in the bubble (or in the drop); v is a saturated vapor density. And, finally, the value Q characterizes the heat exchange between the phases, which tends to equal temperatures of the phases. The next equation describes the bubbles growth in the liquid at the stage b) and a size change of the liquid drops at the stage c): 2 2 3 2 1 8 2 3 d c c R R R P P A B R R R R , (12) where s is the surface tension and h is viscosity of the liquid metal; A and B are the numerical factors: 1 A B = = at the stage b), and 5 A= , 1,25 B= at the stage c). Critical radius of the vapor bubble is equal to 2 cr v c R P P , (13) where vP is a saturated vapor pressure. The bubbles nucleation rate is 4 exp 2 cr c cr W c n kT R , (14) where c is a sound speed in liquid metal, cT is a temperature, k is the Boltzmann constant, and is the formation work of the critical bubble: 3 2 16 3 cr v c W P P . (15) In the case of liquid drops, the condition 0 n has been supposed to hold, but the drops can
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