13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- each other (Fig. 4); they depend on the strain rate of tension in the rarefaction wave and on the metal temperature in the layer. When the volume fraction of vapor exceeds the volume fraction of the liquid phase, the consolidation of bubbles begins in the layer; the liquid phase is destructed on the drops (Fig. 5). Gradually the liquid phase fracture takes place in all area, in which the bubbles were generated by the tension. Further evolution of the two-phase medium is reduced to the expansion of droplets accompanied by the droplets coalescence due to the Brownian motion. Figure 5. Time evolution of the average diameters of the drops: 1 – average on the number of drops, 2 – average on the drops surface areas, and 3 – average on the mass of the drops. The first drops are formed approximately 200 ns after the irradiation beginning in the layer with the maximal concentration of the vapor bubbles. A sharp increase of the average diameters is observed during the first 1 s, it is connected with the gradual fracture of the liquid layers with lower concentration and, consequently, with the higher diameters of the vapor bubbles. 3. Conclusions The mathematical model is proposed and the numerical investigation is performed of the metal fracture and fragmentation in the energy-release zone under the action of the high-current electron beam. The beam heats the metal and converts it in the metastable liquid state, which is destructed under the action of rarefaction wave propagating from the free (irradiated) surface of the metal. The tensile stresses of the value of about 2.5 GPa initiate the generation and growth of vapor bubbles. The following merging of the bubbles results in fragmentation of the simply connected liquid phase on the drops. Under the investigated conditions, the formation of the vapor bubbles begins 30 ns after the end of irradiation pulse. Concentration of the bubbles depends on the metal temperature and on the strain rate of tension in the rarefaction wave. This concentration determines the diameter of the resulting liquid drops, which varies from several tens up to several hundreds of nanometers in different parts of the energy release zone. Existence of the metastable state of expanded liquid results in propagation of the rarefaction wave with negative pressure of the value up to 2.5 GPa behind the shock wave in the deeper solid layers of the irradiated metal, which can substantially influence on the spallation of back surface in solid state as well.
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