chambers using two single-stage light gas guns at the Cavendish Laboratory. Impact velocities, measured to an accuracy of 1 %, ranged from 0.18 to Ikms"1.
THE EFFECT OF STRUCTURE ON FAILURE FRONT VELOCITIES IN GLASS RODS D.D. Radford*, G.R. Willmott and J.E. Field PCS Group, Cavendish Laboratory, Madingley Road, Cambridge, CB3 OHE, UK * Currently at University of Cambridge, Department of Engineering, Cambridge, CB2 1PZ, UK Abstract. Symmetric Taylor and reverse ballistics tests were used in conjunction with high-speed photography to examine the characteristics of failure in fused silica rods. Experiments were performed at impact velocities up to 800 m s"1 yielding impact pressures to approximately 7 GPa. Failure front velocities were strongly dependent on impact pressure consistent with results for borosilicate and soda-lime glasses [1]. One-dimensional strain waves were observed in some experiments before a one-dimensional stress regime was reached. For high impact pressures (> 2 GPa) the failure fronts followed almost immediately behind the incident shocks at a velocity near V? cs for fused silica, borosilicate and soda-lime glasses.
The aim of the current study is to investigate failure in the silica based glass denoted "fused quartz" or "fused silica". This glass is the most open structured of the silica glasses, meaning that the spaces between interlocking SiO2 tetrahedra are devoid of additives. As a result, fused quartz has a lower density than both borosilicate and soda-lime glasses. High-speed photography from Taylor impact experiments are used to determine the characteristics of failure in fused quartz and the results are compared to previous data for borosilicate and soda-lime glasses.
INTRODUCTION Since Kanel [2] first introduced the idea of the so-called "failure wave" in shock loaded glass, there has been a significant number of studies into the failure of glasses and other brittle materials [312]. These investigations have generally involved examination of the failure process in a state of 1-D strain, as obtained in plate impact experiments. Recently, the failure of glasses has been investigated for materials in a state of 1-D stress using the well-known Taylor impact test method [1,13-15]. In these studies, failure was observed in both the classic [16] and symmetric [17] Taylor test configurations using high-speed photography, stress and strain gauges, and VISAR. Results for borosilicate and soda-lime glasses have shown that failure front velocities increase for increasing impact pressure, approaching the elastic wave speeds above ca. 2 GPa. The time dependent nature of the failure process in brittle materials is consistent in 1-D strain [12] and 1-D stress [1], indicating that the physical mechanism of failure is related to the material structure.
EXPERIMENTAL METHOD In the current investigation, classic and symmetric Taylor impact experiments were performed on fused quartz rods in evacuated chambers using two single-stage light gas guns at the Cavendish Laboratory. Impact velocities, measured to an accuracy of 1 %, ranged from 0.18 to Ikms" 1 . The pressures induced at the impact plane were calculated by matching impedances, using the well-known shock responses of the materials.
CP706, Shock Compression of Condensed Matter - 2003, edited by M. D. Furnish, Y. M. Gupta, and J. W. Forbes © 2004 American Institute of Physics 0-7354-0181-0/04/$22.00
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TABLE 1. Material properties of the glasses studied. Wave velocities are for material in a state of 1-D stress. E Glass Type V CL cs P P 3 (GPa) (GPa) (± 0.01 mm us"1) (± 0.01 mm us"1) (± 0.01 g cm' ) 0.17 5.74 Fused Quartz 72.5 30.9 3.61 2.20 30.4 0.20 73.1 5.72 Borosilicate 3.49 2.23 29.8 0.23 Soda-Lime 73.3 5.43 3.22 2.49
In the classic configuration, the rod was impacted against the flat, polished surface of a hardened steel anvil with a measured hardness of 58.4 ±0.7 (Rockwell C). In the symmetric configuration, the target and projectile were identical rods. In both configurations, the target was carefully aligned to ensure an axially symmetric impact. The specimens were cut from industrystandard, high purity fused silica rods. Table 1 summarizes the material properties of the rods used in this investigation and the properties of borosilicate and soda-lime glasses used previously.
Each cylindrical rod used in these experiments had a diameter of 10 or 25 mm and a length-todiameter ratio of 10. The flat ends of each rod were polished. The sabots and supports used for alignment did not significantly affect observations of the failure front. High-speed photographic sequences of the impacts were taken using a programmable imageconverter camera (either a Hadland Ultra-8 or an Imacon Ulrranac 501). Each impact was photographed over a sequence of between 8 and 15 frames. The exposure time for each frame was between 100 and 250ns and inter-frame times ranged from 1 to 3 us. The images were spatially calibrated using fiducial markers. RESULTS AND DISCUSSION
Figure 1 shows a high-speed photographic sequence for a symmetric impact of 25 mm diameter rods. The flyer rod was travelling from the left to the right. The wide horizontal lines along the edges of the specimen are due to the refraction of light through the curved surface of the rods. In the first frame (0.3 us after impact), two vertical dark lines are observed. The line to the left is the impact face and the line to the right is the shock wave. The shock can be seen propagating into the rod ahead of other features in subsequent frames. Another front, first observed in the frames labelled 1.5 jus and 1.8 us, has become the failure front by 2.1 us after impact. As in plate impact experiments, a 1-D state of strain exists until release waves from the outer edges converge along the axis of the specimen, so that there is a transition to a 1-D stress state. Several effects of this transition are observed. Firstly, the incident shock slows from a velocity approximately equal to the 1-D strain longitudinal wave speed in fused quartz (5.96 mm us"1) during the initial 2.1 us after impact, to 5.3 ± 0.3 mm us"1 after 3.9 us. Secondly, the incident shock wave is not visible in later
FIGURE 1. High-speed photographic sequence of a symmetric Taylor impact test using 25 mm diameter fused quartz rods (impact velocity is 534 m s"1). Time (in microseconds) after impact is indicated in each frame.
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frames because the pressure gradient across the shock front decreases in the 1-D stress state. Finally, frames from 1.5 jus onwards clearly show that the advancement of the radial expansion corresponds with the leading edge of the failure front. Similar observations were made in other experiments in this study and by Willmott and Radford [1] for borosilicate and soda-lime glasses. Figure 2 is a sequence showing a symmetric impact performed using 10 mm diameter rods. The projectile was travelling from the right to the left. 3 (is after impact, the failure front (dark portion of the rod) has moved into the target rod. Subsequent frames show further propagation of the failure front and the lateral expansion of the failed material. Following the technique described in [1], the failure front velocity in the rod was measured to be 4.51 ±0.03 mm jus"1. Figure 3 shows the calculated failure front velocity as a function of impact pressure for all of the experiments performed on fused quartz rods in this investigation. Included in the figure are the longitudinal wave speed (CL) and A/2 times the shear wave speed (^2 c$). The failure front velocity
'a
g LL Q)
2
= "CO LL
1
0
1
2
3
4
5
6
7
Impact Pressure (GPa)
FIGURE 3. Measured failure front velocities as a function of impact pressure for fused quartz rods.
increases rapidly as the impact pressure increases from 1 GPa, and then asymptotically approaches a maximum value near A/? cs. Classical fracture theories predict that the limiting velocity of a single mode I or II crack in an infinite medium is the surface (Rayleigh) wave speed (CR), approximately 90% of the shear wave velocity. Rosakis et al. [18] have suggested that single shear cracks may propagate at speeds close to A/2 of the shear wave speed. In practice, mode I cracks typically bifurcate at a velocity of approximately 0.5 CR [19]. At impact pressures > 2 GPa, the average failure front velocity for the fused quartz is 5.1 ±0.3 mm us'1, which is within experimental error of A/2 cs. Table 2 compares the data for fused quartz with combined data for borosilicate and soda-lime glasses [1,15] at impact pressures between 3.5 and 4 GPa. Trends in the failure front velocity are similar in all three materials. In practice, single cracks do not propagate faster than the shear wave speed [19], so the observed fracture pattern is caused by the nucleation of multiple cracks within uncomminuted glass behind the incident shock. It appears that under severe impact conditions, ensembles of cracks can approach group velocities near A/2 cs independent of the material.
FIGURE 2. High-speed photographic sequence of a symmetric Taylor impact test using 10mm diameter fused quartz rods (impact velocity is 306 m s"1). Time (in microseconds) after impact is indicated in each frame.
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TABLE 2. Experimentally determined failure front velocities for three silica-based glasses. Glass Type Failure Front V2Cs Velocity (mm us"1) (mm us"1) Fused Quartz 5.11 5.110.3 Borosilicate 4.94 4.8 ±0.5 Soda-Lime 4.55 4.55 ±0.5
5. Radford, D.D., and Tsembelis, K., (to be published), (2003). 6. Brar, N.S., and Bless, S.J., High Pressure Research 10, 773-784 (1992). 7. Clifton, R.J., Appl Mech. Rev. 46, 540-546 (1993). 8. Grady, D.E., "Dynamic Properties of Ceramic Materials," Sandia National Laboratories SAND943266 (1995). 9. Espinosa, H.D., Xu, Y., and Brar, N.S., J. Am. Ceram. Soc. 80, 2061-2073 (1997). 10. Kondaurov, V.I., J. Appl. Maths Mechs 62, 657-663 (1998). 11. Kanel, G.I., Bogatch, A.A., Razorenov, S.V., and Chen, Z., J. Appl. Phys 92, 5045-5052 (2002). 12. Radford, D.D., Proud, W.G., and Field, J.E, "The Deviatoric Response of Three Dense Glasses Under Shock Loading Conditions" in Shock Compression of Condensed Matter - 2001, edited by M.D. Furnish et al., AIP Conference Proceedings 620, New York, 2001, pp. 807-810. 13. Bless, S.J., Brar, N.S. and Rosenberg, Z., "Failure of Ceramic and Glass Rods Under Dynamic Compression" in Shock Compression of Condensed Matter - 1989, edited by S.C. Schmidt et al., Elsevier, Amsterdam, 1990, pp. 939-942. 14. Bless, S.J., and Brar, N.S., High-Pressure Science and Technology, 1813-1816 (1994). 15. Murray, N.H., Bourne, N.K., Field, J.E, and Rosenberg, Z, "Symmetrical Taylor Impact of Glass Bars", in Shock Compression of Condensed Matter - 1997, edited by S. C. Schmidt et al, AIP Conference Proceedings 429, pp. 533-536. 16. Taylor, G.I, J. Inst. Civil Engrs. 26, 486-519 (1946). 17. Erlich, D.C, Shockey, D.A, and Seaman, L, "Symmetric Rod Impact Technique for Dynamic Yield Determination" in Shock Waves in Condensed Matter - 1981, edited by WJ. Nellis et al, American Physical Society, New York, 1982, pp. 402-406. 18. Rosakis, A.J, Samudrala, O, and Coker, D, Science 284, 1337-1340 (1999). 19. Field, J.E, Contemp. Phys. 12, 1-31 (1971).
CONCLUSIONS
Recent results from Taylor impact tests on borosilicate and soda-lime glasses and those presented in this paper for fused quartz show that failure front propagation in rods is irregular and the structure of the failure is material dependent. The results for fused quartz further demonstrate the dependence of the failure front velocity on impact pressure. It is believed that dynamic failure of glasses is not due to a continuous boundary sweeping through the material (failure wave), but is a time dependent process that evolves from inelastic deformation and subsequent nucleation of microcracks due to shear failure. ACKNOWLEDGEMENTS
We acknowledge financial support of Qinetiq and are grateful to T. Andrews, P.D. Church, B. Goldthorpe, and I.G. Cullis for continued encouragement. We also thank J.M. Burley and W.G. Proud for assistance with experimentation. D.L.A. Cross and R.P. Flaxman provided valuable technical support.
REFERENCES 1. Willmott, G.R., and Radford, D.D., Proc. R. Soc. Loud., submitted for review (June 2003). 2. Kanel, G.I., Rasorenov, S.V., and Fortov, V.E., "The Failure Waves and Spallations in Homogeneous Brittle Materials", in Shock Compression of Condensed Matter - 1991, edited by S.C. Schmidt et al., Elsevier, Amsterdam, 1992, pp. 451-454. 3. Bourne, N.K., Rosenberg, Z, Mebar, Y., Obara, T., and Field, I.E., J. Phys. IV France 4, C8-635C8-640 (1994). 4. Bourne, N.K., Millett, J.C.F., and Rosenberg, Z, J. Appl Phys. 81, 6670-6674 (1997).
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