Соболев В.В., Шиман Л.Н. Высокоэнергетическая обработка материалов. Сборник научных трудов

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Measurements were carried out on the stand presented in Fig.1. Pictures

were taken using streak camera coupled with pulse flash. The projectile hits the

target at the angle of 45° while camera axis is rectangular to the target surface.

The following symbols are used in description of records: K – is the expo-

sure time (frame width), P – is the time interval between frames, D – is the target

thickness. The size of square targets was 50x50 mm while diameter of circular tar-

gets was 50 mm. The muzzle velocity of the steel ball was 250 m/s in all

experiments. In Fig. 2 exemplary pictures are presented.

Fig.1. Diagram of the measurement stand

Fig.2. Sodium glass target. D = 6 mm, K = 100 ns, P = 2.5 μs

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Fig.3. Sodium glass target. D = 4 mm, K = 100 ns, P = 2.0 μs

Fig.4. Target made of BK7 glass. D = 4 mm, K = 100 ns, P = 2.0 μs

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Fig.5. Silica glass target. D = 4 mm, K = 100 ns, P = 2.0 μs

3. Comparative theoretical-experimental analyses based on dynamic tests

In general, during experimental tests with electro-optic camera it is difficult

to hit precisely the center of the target due to large distance between the target and

the projectile launcher. Moreover, in experiments with electro-optic camera the

projectile hits the target not at the right angle but at 45°. Exemplary results of

modelling for sodium glass are presented in Figs. 6-8. The variants W1-W10 vary

in test values for modified Mohr-Coulomb model:

Y=Y

+α

p for p<0

Y=Y

+α

p for p>0

where Y – is the elastic limit for glass, p – is the pressure. Values for test material

constants are shown in Table 1.

Table 1

Model coefficient values for destruction of glass

for simulation variants analyzed in a test series

Variant No

GPa Variant No

GPa

W1 …3.5 ..3.5 ..0.15 W6 ..5 ..5 0.1

W2 5 5 ..0.15 W7 ..7 ..7 ..0.15

W3 5 5 ..0.15 W8 10 10 0.3

W4 5 5 0.1 W9 ..7 ..7 0.1

W5 …3.5 ..3.5 0.1 W10 …3.5 …3.5 0.1

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Fig.6. Exemplary results for computer simulation of a process of a glass

plate penetration by steel ball for variants W1-W4. Plate images obtained after re-

moval of destructed areas

Fig.7. Exemplary results for computer simulation of a process of a glass

plate penetration by steel ball for variants W5-W8. Plate images obtained after re-

moval of destructed areas

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Fig.8. Exemplary results for computer simulation of a process of a glass

plate penetration by steel ball for variants W9-W10. Plate images obtained after

removal of destructed areas

Analysis of the performed simulations showed that

- search for optimal combination of coefficients describing strength proper-

ties of glass in order to obtain better conformance between theory and experiment

(based on the frame and after-shot pictures) is necessary,

- occurrence of a qualitative correspondence between experiment and results

of modeling non-central, skew projectile impacts on glass plate (3D spatial variant)

– the most frequent instance – is confirmed.

4. Experimental verification of qualitative and quantitative modeling results

Analysis of the solutions allowed a selection of the optimal parameters de-

scribing destruction processes of the glass target thus assuring conformance of the

theoretical and experimental results. This conformance concerns both dynamic

phase of cracks propagation and target shape after the shot. For the set of material

constants close to optimal ones simulations performed for sodium glass are pre-

sented in Figs. 9-13. The statement of these constants is shown in Table 2.

Temporal sequences of a development of a glass plate cracking after the im-

pact of a steel ball hitting the plate at the angle of 45º with 250 m/s velocity are

presented in Fig.1. For better presentation of simulation results for each time in-

stant the process development is shown in three projections. The first projection

(left column) presents a view from the plate front side, while the second (central

column) and third (column on the right) ones show a view from the rear side. In

order to show destruction areas inside the plate, some calculation points are re-

moved from the results presented in the left and central columns (a quadrant of the

plate was cut out). In the next figures simulations of a temporal development of the

cracking process are compared with pictures taken with the electro-optic camera.

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Table 2

Values of modeling coefficients for analyzed variants

Variant No

, GPa

W1 3 1 0.05

W2 3 2 0.05

W3 3 3 0.05

W4 5 1 0.05

W5 5 2 0.05

W6 5 4 0.05

W7 7 1 0.05

W8 7 2 0.05

W9 7 4 0.05

0 μs

11 μs

70 μs

Fig.9. Exemplary temporal sequences of a process evolution of a glass plate

cracking

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Experiment

Fig.10. A comparison of a temporal sequence of pictures taken with electro-

optic camera with computer simulations for various combinations of parameters

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Experiment

Fig.11. A comparison of a temporal sequence of pictures taken with electro-optic

camera with computer simulations for various combinations of material constants

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Experiment

Fig.12. A comparison of a temporal sequence of pictures taken with electro-

optic camera with computer simulations for various combinations of material con-

stants

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Experiment

W1 W2

Fig.13. A comparison of computer simulation results (final stage for variants W1-

W9) with experimental results (target recovered after shot, picture of the plate front)