Special Features of Fracture by Spalling

The calculation results confirm the sufficiently high accuracy of the numerical methods used. Consequently, they can be used to examine the problem of controlling

FIGURE 10.30 Profiles of stresses G_zz on the axis of symmetry (modeling of experiments), 1) t = 0.035 x 10"⁶ second; 2) I = 0.070 x 10'⁶ second; and 3. 4) t = 0.123 x 10"⁶ second (line 5 is the calculation without taking the fracture into account).

fracture and optimizing it during of spallation of the DSO by laser pulses and elimination of space debris. For it is necessary to construct a quite detailed picture of various variants of spallation fracture for different pulse energies. Let us consider two variants of pulsed irradiation which gives a sufficiently detailed picture of possible fracture mechanisms if they will be studied together with the experimentally recorded variant (variant C, see Section 10.5.3).

We shall examine two variants of calculating irradiation of an aluminum plate differing only in the surface density of the energy pulse: In variant A, Q = 1.27 x 10^-2 J/m², and in variant B, Q = 1.91 x 10^-2 J/m². The geometrical parameters of the calculations are as follows: R = 0.6 mm, h = 1.0 mm, and /?, = 0.6 mm. In addition, in comparison with variant C, we selected irradiation with a shorter wavelength, L = 150,000 m^-1. In these calculations, the distribution of the pulse energy in the depth was assumed as (10.75). The number of calculation cells in the plate along the axis of symmetry was 10 and along the diameter 12.

Variant A. Only the disk-shaped spallation was realized in the variant. Figure 10.31 A shows the corresponding configuration of the target at time t = 16 ns.

The mechanism of formation of tension and compression zones, causing spallation at first moments, is shown in Figure 10.32 which illustrates the profiles of the axial stresses along the axis of symmetry of the plate (its cylindrical volume). The general form of the stress waves resembles that shown in Figure 10.30, but the level of the tensile stresses is not reduced by the recoil pulse of the jet of the vapors.

The amplitude of the tensile wave is almost equal to the amplitude of the compression wave. A tensile pulse appears during the departure of the stress wave from the free surface. This tension may be enough to form external spallation [35] (see Sections 10.1.4, 10.2, and 10.3). However, the stress wave attenuates while moving through the material. When this wave reaches the rear surface, its amplitude does not reach the critical tension of the material. Thus, there is no rear spallation. Front spallation takes place almost without evaporation.

Variant B. Figure 10.31B shows the configuration of the cross section of the loaded plate at time t = 22 ns for the second variant B. Two types of spallation are detected in this case: rear and front. Neither of them are strictly in disk-like shape. The front spallation has the form of a toroidal crack. In other words, the material at the axis of symmetry in the vicinity of the front surface is not fractured. It should be mentioned that the formation of a ring spallation cannot be detected in

FIGURE 10.31 Configuration of the calculation mesh after spallation: variant A - only external spallation, t = 16 ns; variant В - external and rear spallation, t = 22 ns.

FIGURE 10.32 Profiles of stresses <7_a (GPa) on the axis of symmetry for external spallation: 1) t = 5.4 ns, 2) / = 8.1 ns, 3) t = 13.6 ns, and 4) t = 16.3 ns (dashed line is the surface of external spallation).

unidimensional calculations. Observation of this type of fracture in experiments at present is associated with difficulties because laboratory lasers usually have a relatively long wavelength (in the vicinity of the optical range) and, correspondingly, relatively thin spallation sheets (of the order of tens of micrometers). In addition, the external spallation is formed in a relatively narrow range of the intensities.

The formation of the ring-like crack is caused by the stress state which is highly heterogeneous along the radius. In the vicinity of the center of the target, it is close to variant C as a result of extensive evaporation. External spallation does not take place in this case. At the periphery of the irradiation zone, the stress state is close to variant A. The external spallation can take place as a result of a low counter pressure of the vapors.

The rear spallation is not disk-shaped but rather semi-lens facing the rear side of the target by the convex center. This is also associated with the operation of two- dimensional effects: distortion of the edges of the flat wave as a result of lateral unloading.

The mechanism of formation of the tensile and compression zones for variant В for the cylindrical surface having the radius 0.3 mm is shown in Figure 10.33. This calculation was carried out in order to show the surfaces of both spallation fractures. The general form of the stress waves resembles that shown in Figure 10.32. The amplitude of the tensile wave is sufficient to initiate a front spallation although the magnitude of the tensile stresses is partially suppressed by the recoil pulse of the jet of the outgoing vapors. At the same time, attenuation of the wave in the material weakens this wave insufficiently so that rear spallation is also possible.

FIGURE 10.33 Profiles of stresses a~ (GPa) along the direction of the axial coordinate at the distance 0.3 mm from the axis of symmetry. Cases of the external and rear spallation: 1) t = 5.4 ns, 2) t = 10.9 ns, 3)t = 16.3 ns, and 4) / = 21.7 ns (dashed lines are surfaces of spallation).

It should be mentioned that there is no the spallation in the vicinity of the external surface if the initial pulse energy is lower than that in variant A.