## Citation

Liu, Cangli
(1999)
*I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation.*
Dissertation (Ph.D.), California Institute of Technology.
http://resolver.caltech.edu/CaltechTHESIS:04232013-084302487

## Abstract

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10^{5} g. The technique includes bar-coded projectile, sabot-projectile separation,
detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10^{5} g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_{max}, is linearly scaled with initial projectile energy per unit cross-section area, e_{s} , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_{max}(mm) 1.15e_{s} (J/mm^{2} ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_{max}, increases slowly with e_{s} and does not depend on projectile radius approximately, the dependence of t_{max} on projectile length is suggested to be described by t_{max}(μs) = 2.08e_{s} (J/mm^{2} + 349.0 x m/(πR^{2}), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10^{4}, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_{max}, and normalized penetration time, t/t_{max}, as P/P_{max} = f(t/t_{max}, where f is a function of t/t_{max}. After f(t/t_{max} is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_{f}/σ^{0}_{f} = exp(0.0905(log(έ/έ_0) ^{1.14}, in the strain rate range of 10^{-7}/s to 10^{3}/s (σ^{0}_{f} and έ are reference compressive strength and strain rate, respectively). The non-dispersive
Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO_{2} were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO_{2} to planar shock loading
can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ_{0} = 3.655 gj cm^{3} . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge^{+4} with O^{-2} in vitreous GeO_{2} occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for
fused SiO_{2} to that on vitreous GeO_{2} demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO_{2} and fused SiO_{2} are found to coincide approximately if pressure in fused SiO_{2} is scaled by the ratio of fused SiO_{2}to vitreous GeO_{2} density. This result, as well as the same structure, provides the basis for considering vitreous Ge0_{2} as an analogous material to fused SiO_{2} under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO_{2} decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO_{2} decays faster than a linear elastic wave; (2) In vitreous GeO_{2} , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^{-3.35} , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO_{2} and vitreous GeO_{2} is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||||
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Subject Keywords: | Geophysics | ||||||||

Degree Grantor: | California Institute of Technology | ||||||||

Division: | Geological and Planetary Sciences | ||||||||

Major Option: | Geophysics | ||||||||

Thesis Availability: | Restricted to Caltech community only | ||||||||

Research Advisor(s): | - Ahrens, Thomas J. (advisor)
- Stock, Joann M. (advisor)
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Thesis Committee: | - Unknown, Unknown
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Defense Date: | 17 May 1999 | ||||||||

Funders: |
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Record Number: | CaltechTHESIS:04232013-084302487 | ||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechTHESIS:04232013-084302487 | ||||||||

Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||

ID Code: | 7626 | ||||||||

Collection: | CaltechTHESIS | ||||||||

Deposited By: | Benjamin Perez | ||||||||

Deposited On: | 23 Apr 2013 17:16 | ||||||||

Last Modified: | 02 May 2016 19:17 |

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