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Figure 5. Hexahedral element showing the I-] - K convention of nodes[11]. The use of 2-D axial symmetry is a computationally efficient way to simulate the loading of a 3-D cylinder. However it does not show the complete solution of true dynamic fracture and fragmentation of specimens during and after the plasma blasting and full three-dimensional analysis is necessary to obtain the actual solution. The partial differential equations to be solved express the

Figure 5 Hexahedral element showing the I-] - K convention of nodes[11]. The use of 2-D axial symmetry is a computationally efficient way to simulate the loading of a 3-D cylinder. However it does not show the complete solution of true dynamic fracture and fragmentation of specimens during and after the plasma blasting and full three-dimensional analysis is necessary to obtain the actual solution. The partial differential equations to be solved express the

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Figure 1. Test setup characteristics of 24” dia. X 36” long, steel-reinforced concrete cylinder sample. After successfully blasting concrete specimens without any reinforcement we proceeded to test a set of samples to include the steel wire reinforcement and granite rocks with the purpose to emulate rocks and lunar soil. The steel wire mesh used was 2 wrapped layers of 0.125” steel wire welded mesh of 6” x 6” spacing. The test setup is shown in Figure 1. These blasting tests included the use of the blasting media of a non-Newtonian, dilatant fluid comprised of a water suspension of corn starch powder. The suspension was made with water-cornstarch contents approximately 50% by volume concentration to form a thin paste of smooth texture of low viscosity when measured with low shear force. This allows it to be easily poured into the blasting hole.
Figure 1. Test setup characteristics of 24” dia. X 36” long, steel-reinforced concrete cylinder sample. After successfully blasting concrete specimens without any reinforcement we proceeded to test a set of samples to include the steel wire reinforcement and granite rocks with the purpose to emulate rocks and lunar soil. The steel wire mesh used was 2 wrapped layers of 0.125” steel wire welded mesh of 6” x 6” spacing. The test setup is shown in Figure 1. These blasting tests included the use of the blasting media of a non-Newtonian, dilatant fluid comprised of a water suspension of corn starch powder. The suspension was made with water-cornstarch contents approximately 50% by volume concentration to form a thin paste of smooth texture of low viscosity when measured with low shear force. This allows it to be easily poured into the blasting hole.
but it is not as high as that of high explosive materials. However, is it is shown later, because the very high loading rate, the results of plasma blasting can be compared to those of high explosives, this is also true because performance is dependent on the velocity of detonation among other variables.
but it is not as high as that of high explosive materials. However, is it is shown later, because the very high loading rate, the results of plasma blasting can be compared to those of high explosives, this is also true because performance is dependent on the velocity of detonation among other variables.
Figure 3. Granite rock, before and after blast test shot with 12” Probe. Another test series corresponded to similarly sized steel-reinforced concrete cylinders, but now blasted using < short 6” plasma blasting probe. As can be observed in the bottom part of Figure 2, the effect had some surface spallation. This blast was characterized by a considerable zone of crushing around the borehole, in this case with cracks extending up to the walls of the cylinder. The number of radial cracks and cracks to the side walls also increased though the gaps in the cracks were smaller compared to those of the 12” blast probe test. Most of the side crack went down approximately 9.5”, or 3.5” lower than the blast probe implying an average lateral crack angle of approximately 16 degrees. The energy calculations from the time-history waveforms corresponding to this series of tests, can be found in previous work[8,9].
Figure 3. Granite rock, before and after blast test shot with 12” Probe. Another test series corresponded to similarly sized steel-reinforced concrete cylinders, but now blasted using < short 6” plasma blasting probe. As can be observed in the bottom part of Figure 2, the effect had some surface spallation. This blast was characterized by a considerable zone of crushing around the borehole, in this case with cracks extending up to the walls of the cylinder. The number of radial cracks and cracks to the side walls also increased though the gaps in the cracks were smaller compared to those of the 12” blast probe test. Most of the side crack went down approximately 9.5”, or 3.5” lower than the blast probe implying an average lateral crack angle of approximately 16 degrees. The energy calculations from the time-history waveforms corresponding to this series of tests, can be found in previous work[8,9].
We did more simulation varying the energy deposition pulse widths including Result af esull aller aps 50s, 60us, 75s, 100s, 125ps, 150s, 200s, 250us, and 300s and we could n in a steel- we ; d concrete sample. observe that the longer deposition time, the less damage immediately around the eposition rate 60ps blasting zone. However according to the simulations, the direction of cracks anc extension of damage varies. For lower times the damage is concentrated in the tion of the cylinder with cracks extending towards the top and bottom parts almost vertically in a shor ter some initial quasi radial direction. For slower (longer) pulses, or energy deposition pulse widths, the extended towards the exterior in a 45 degree pattem forming conic cracks up and down, appearing as ar ss-section. This suggests that the damage is greater in the top part than in the bottom with shorter pulse Sn nana never nnee eee ggg, ESA ny See aA Tn computer simulations we assume an initial energy charge of 53k]. The electrical basis for these simulations corresponds to the experimental sample blasted in a typical test where it was observed that the current pulse is delivered in approx. 60ps. This suggested the pulse or energy deposition interval to be used as a starting value for the simulations. Figure 4. Result after 300s simulation in a steel- reinforced concrete sample. Energy deposition rate 60p1s
We did more simulation varying the energy deposition pulse widths including Result af esull aller aps 50s, 60us, 75s, 100s, 125ps, 150s, 200s, 250us, and 300s and we could n in a steel- we ; d concrete sample. observe that the longer deposition time, the less damage immediately around the eposition rate 60ps blasting zone. However according to the simulations, the direction of cracks anc extension of damage varies. For lower times the damage is concentrated in the tion of the cylinder with cracks extending towards the top and bottom parts almost vertically in a shor ter some initial quasi radial direction. For slower (longer) pulses, or energy deposition pulse widths, the extended towards the exterior in a 45 degree pattem forming conic cracks up and down, appearing as ar ss-section. This suggests that the damage is greater in the top part than in the bottom with shorter pulse Sn nana never nnee eee ggg, ESA ny See aA Tn computer simulations we assume an initial energy charge of 53k]. The electrical basis for these simulations corresponds to the experimental sample blasted in a typical test where it was observed that the current pulse is delivered in approx. 60ps. This suggested the pulse or energy deposition interval to be used as a starting value for the simulations. Figure 4. Result after 300s simulation in a steel- reinforced concrete sample. Energy deposition rate 60p1s
i a Prager strength model which is a_pressure- Figure 6. Model with two joined concentric cylindrical dependent model for determining whether a parts. material has failed or undergone plastic yielding. It was determined that the Drucker-Prager criterion yave the best results for this application based upon previous physical observations of the plasma blasting 2x periment samples. The Drucker-Prager failure model, with a porous EOS was chosen as the best combination of ‘ailure model and equation of state for these simulations. The other options used were the RHT concrete model EOS and the Johnson-Cook failure mode. The RHT (Riedel, Heirmaier, and Thoma) concrete model EOS, which has its ywn associated RHT-failure model, produced results inconsistent with what was observed in our experimental plasma blasting. We had begun computer simulations with the RHT model, but once we worked through symmetry ssues, the RHT model produced anomalous results giving damage between 0.95 and 1 in greater than 50% of the sample which is obviously not what we see experimentally. Similar unacceptable results were obtained when using the Johnson-Cook failure mode. The porous EOS with Drucker-Prager failure model produced results very, very similar to what was actually seen in experimentation. ne — he se ne In this case the models were solved with Lagrangian solver and also could be solved : using the ALE solver. The dimensions of the cylinder are 36” long, 24” diameter with a borehole of 1” diameter. The solid model had a total of 260,344 nodes, the simulation solution time ended at 300ys, and the pressure loading condition was 600MPa with a pulse width of 60 ps to emulate the plasma blasting. This simulation took approximately 3 hrs to run using a dual core processor @ 2.2GHz, 2GB of RAM. Figure 6. Model with two joined concentric cylindrical parts.
i a Prager strength model which is a_pressure- Figure 6. Model with two joined concentric cylindrical dependent model for determining whether a parts. material has failed or undergone plastic yielding. It was determined that the Drucker-Prager criterion yave the best results for this application based upon previous physical observations of the plasma blasting 2x periment samples. The Drucker-Prager failure model, with a porous EOS was chosen as the best combination of ‘ailure model and equation of state for these simulations. The other options used were the RHT concrete model EOS and the Johnson-Cook failure mode. The RHT (Riedel, Heirmaier, and Thoma) concrete model EOS, which has its ywn associated RHT-failure model, produced results inconsistent with what was observed in our experimental plasma blasting. We had begun computer simulations with the RHT model, but once we worked through symmetry ssues, the RHT model produced anomalous results giving damage between 0.95 and 1 in greater than 50% of the sample which is obviously not what we see experimentally. Similar unacceptable results were obtained when using the Johnson-Cook failure mode. The porous EOS with Drucker-Prager failure model produced results very, very similar to what was actually seen in experimentation. ne — he se ne In this case the models were solved with Lagrangian solver and also could be solved : using the ALE solver. The dimensions of the cylinder are 36” long, 24” diameter with a borehole of 1” diameter. The solid model had a total of 260,344 nodes, the simulation solution time ended at 300ys, and the pressure loading condition was 600MPa with a pulse width of 60 ps to emulate the plasma blasting. This simulation took approximately 3 hrs to run using a dual core processor @ 2.2GHz, 2GB of RAM. Figure 6. Model with two joined concentric cylindrical parts.
Figure 7. Comparison of simulation and experiment of a blasted 24 in reinforced concrete cylinder. Highlighting the cracks on the picture and comparing side to side with the simulation, it can be observed that the simulation fairly well corresponds to this particular experimental concrete sample blasted with initial energy of 53kjJ, a total net energy used in blast of 26.7kJ, and a deposition in 60ys. At this point we could say that the simulation is reasonably validated with the experiment.
Figure 7. Comparison of simulation and experiment of a blasted 24 in reinforced concrete cylinder. Highlighting the cracks on the picture and comparing side to side with the simulation, it can be observed that the simulation fairly well corresponds to this particular experimental concrete sample blasted with initial energy of 53kjJ, a total net energy used in blast of 26.7kJ, and a deposition in 60ys. At this point we could say that the simulation is reasonably validated with the experiment.
The resulting crack propagation and damage after 300 simulation time is presented in Figure 9 and it is compare to the result of the 2-D simulation under same conditions The resulting red zones represent a fragment path witl material reduced to small rubble which has totally lost it strength. Yellowish lines emanating from the rubbled zone represent cracks. Figure 9 indicates that almost symmetrical crack growth occurs on both sides from the blasting hole, forming the “X” shaped crack pattern which also was observed in the 2-D simulations.
The resulting crack propagation and damage after 300 simulation time is presented in Figure 9 and it is compare to the result of the 2-D simulation under same conditions The resulting red zones represent a fragment path witl material reduced to small rubble which has totally lost it strength. Yellowish lines emanating from the rubbled zone represent cracks. Figure 9 indicates that almost symmetrical crack growth occurs on both sides from the blasting hole, forming the “X” shaped crack pattern which also was observed in the 2-D simulations.
IEEE IN The 3-D ‘solutions can be represented in cut-out sliced plane views along radial and longitudinal directions. This is useful to verify the symmetry (or lack of symmetry) of cracks and damage along different radial planes and longitudinal (transversal) planes. In Fig. 11 the slices of radial cut-out planes of the concrete sample blasted with 600MPa and 60ys pulse width are seen. The slices were taken each 15 degrees angular separation. As can be observed, those slices varied from one angle to the other, which at first view, is in concordance with the experiments. Note that for view separated each by 45 degrees, approximately repeated patterns are observed. A quasi horizontal fragment path develops passing through the center of the “X” shape. Cracks located at the mid length on each “leg” of the X shape developed in vertical direction, this trend was noticed in the 2-D simulations too. Note that in the 2D simulations the symmetry is perfect because the original simulation was for half of the model and the result is mirrored along vertical axis to complete the model. A eamianra nf Hma-hictnrn nf crackle and damanad zgnnac ic chhnwnin Bin 11)
IEEE IN The 3-D ‘solutions can be represented in cut-out sliced plane views along radial and longitudinal directions. This is useful to verify the symmetry (or lack of symmetry) of cracks and damage along different radial planes and longitudinal (transversal) planes. In Fig. 11 the slices of radial cut-out planes of the concrete sample blasted with 600MPa and 60ys pulse width are seen. The slices were taken each 15 degrees angular separation. As can be observed, those slices varied from one angle to the other, which at first view, is in concordance with the experiments. Note that for view separated each by 45 degrees, approximately repeated patterns are observed. A quasi horizontal fragment path develops passing through the center of the “X” shape. Cracks located at the mid length on each “leg” of the X shape developed in vertical direction, this trend was noticed in the 2-D simulations too. Note that in the 2D simulations the symmetry is perfect because the original simulation was for half of the model and the result is mirrored along vertical axis to complete the model. A eamianra nf Hma-hictnrn nf crackle and damanad zgnnac ic chhnwnin Bin 11)
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Space Plasma PhysicsLunar ScienceFracture MechanicsPulsed PowerLow Power DesignLunar Geology
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