Longitudinal and lateral stress measurements in shock-loaded gabbro and granite

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1 JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 8 15 APRIL 2000 Longitudinal and lateral stress measurements in shock-loaded gabbro and granite J. C. F. Millett a) and K. Tsembelis Physics and Chemistry of Solids, Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, United Kingdom N. K. Bourne Royal Military College of Science, Cranfield University, Swindon, SN6 8LA, United Kingdom Received 25 October 1999; accepted for publication 17 January 2000 Plate impact experiments have been performed on two igneous rocks of different grain size. Shock stresses have been measured using embedded manganin stress gauges, up to 12 GPa. In the coarser grained material data was obtained by impacting rock flyer plates onto previously characterized targets. Results are compared and contrasted to the existing data for other geological materials. In the finer-grained material lateral stress was also measured. In combination with the longitudinal stresses, these results have been used to obtain the materials shear strength under shock loading conditions. Results suggest that the material is deforming in an inelastic manner American Institute of Physics. S I. INTRODUCTION The shock properties of geological materials have long been a source of interest. Traditionally, the main driving forces have been planetary impact and geological research. 1 3 Recently, there has been a growing interest in the shock properties of concrete, 4,5 where geological materials are added as aggregates. A large number of geological materials have been investigated using a number of different techniques. Boslough and Ahrens 3 used particle velocity gauges to investigate anorthosite and gabbro, while Furnish 6 used velocity interferometry system for any reflector VISAR to examine a range of materials including slate and granite. Manganin stress gauges were used by Nakazawa et al. 7 in basalt and Takazawa et al. 8 used high-speed photography to investigate jadeite. The dynamic failure of brittle materials has become increasingly important over the past few years, in particular the presence of the so called failure wave. This feature was first observed by Razorenov et al. 9 who noted small reload signals superimposed on rear surface velocity traces taken in glass. These were interpreted as the release from the rear surface interacting with a moving front behind the shock, which reduced the dynamic impedance. Thus the release would be partially reflected as a compressive pulse. This appeared to give experimental backing to the earlier work of Nikolaevskii 10 who had proposed such a mechanism. Subsequent studies by Brar et al. 11 provided further confirmation of this, showing that the spall strength of soda-lime glass reduced to zero behind the failure wave and that shear strength also underwent a significant reduction. Bourne et al. 12 were also able to visualize failure waves in soda-lime a Present address: Royal Military College of Science, Cranfield University, Swindon, SN6 8LA, United Kingdom; electronic mail: j.millett@rmcs.cranfield.ac.uk glass using high-speed photography. Subsequently, failure waves have also been detected in polycrystalline ceramics such as silicon carbide and alumina. 13 In this article we examine the shock properties of another class of brittle materials, namely igneous rocks, and the possibility that they may display delayed shock-induced failure. II. EXPERIMENT Plate impact experiments were carried out on a 50 mm bore, 5 m long, single stage gas gun. 14 Flyer plate velocities were measured by the shorting of sequentially mounted pairs of pins. The specimens were aligned to better than 1 milliradian by an adjustable specimen mount. To measure the Hugoniot of the gabbro, manganin stress gauges MicroMeasurements type LM-SS-125CH-048 were embedded between tiles 4 6 mm thick. All were cut from a single block and lapped flat to five optical fringes using 15 m silicon carbide grit. The voltage data was reduced using the calibration data of Rosenberg et al. 15 One sample was prepared with the stress gauge supported on the rear surface with a block of polymethylmethacrylate PMMA. In this configuration the gauge now has increased temporal resolution due to the near impedance match of the PMMA, epoxy adhesive, and gauge backing, and becomes sensitive to the shape of the shock pulse as it arrives at the gauge location. Specimens for lateral gauge experiments were cut from the same original block. These were 23 mm thick by 45 mm 45 mm. Each sample was sectioned in two, and commercial stress gauges MicroMeasurements type J2M-SS-580SF-025 were introduced 2 and 6 mm from the impact surface of each sample. Samples were then reassembled using a low viscosity epoxy with a curing time of approximately 12 h. Lateral gauge data was reduced using the analysis of Rosenberg and Partom. 16 Longitudinal stress specimens were shot with 6 mm copper or 5 mm tungsten flyer plates at such velocities so as to induce stresses in the range of 6 12 GPa. Lateral stress /2000/87(8)/3678/5/$ American Institute of Physics

2 J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Millet et al TABLE I. Materials properties of Swedish gabbro and Loughborough granite. Material c L mm s 1 c T mm s 1 0 gcm 3 Grain size Gabbro m Granite mm 5 MHz transducer connected to a Panametrics 5052PR pulse receiver. III. MATERIALS DATA The relevant properties of the Swedish gabbro and the Loughborough granite are presented in Table I. FIG. 1. Specimen configurations showing gauge mounting configurations. a Longitudinal orientation, b lateral orientation. specimens were impacted with either 10 mm copper, or 5 mm tungsten flyers using the same velocities to induce the same longitudinal stresses. Specimen configurations are presented in Fig. 1. The granite was taken as a 75-mm-diam core from Loughborough, United Kingdom. 17 This material had a very large grain size 2 3 mm, similar to the dimensions of the stress gauge. Thus it was felt unlikely that the gauge would give meaningful information about the bulk properties, especially if the properties of each grain are dependent upon orientation. Thus 50 mm granite flyers of thickness 5 6 mm were taken from the core and impacted onto targets made from dural aluminum alloy 6082-T6, copper or tungsten, whose shock properties are well characterized. 18 Impact velocities were such that stresses were in the range of 2 12 GPa. Stress gauges were embedded between tiles of the target material in the way discussed above. Gauges were placed greater than twice the grain size from the impact face. If the gauge is of similar dimensions to the grains in the granite, and the individual grains have mechanical properties determined by orientation, then the gauge reading will be local, and not representative of the bulk if placed too near the impact face. Longitudinal sound speeds were measured using a IV. RESULTS AND DISCUSSION Stress-time histories from embedded manganin gauges in longitudinal orientation are presented below in Fig. 2. These traces are typical of the embedded gauge configuration in a wide range of materials. Note that the relatively long rise time of the traces of the order of 200 ns is due to the stress ringing up in the layer of epoxy adhesive that surrounds the gauge. The dip that appears in the trace labeled 6 mm Cu, 882 m s 1 is likely to be an artifact due to an interaction between the gauge and the epoxy layer. It is unlikely to reflect a genuine material response in the gabbro. The steady values of stress from each trace have been reduced to in-material values to present as Hugoniot points. These impedance matching techniques use the known Hugoniots of copper and tungsten. The results are shown in Fig. 3. As a comparison we have included the data of Boslough and Ahrens. 3 It may be observed that the agreement between our data and the published data is good. However, it should be realized that these two materials come from different geographical locations, and thus material characteristics will be different. For example, our material has a grain size in the range of m compared to a grain size of 1 2 mm in the other material. We have fitted our data with the elastic impedance of the material such that the longitudinal stress, x, x 0 u p c L, 1 where 0, u p, and c L are the ambient density, particle velocity, and ambient longitudinal sound velocity, respectively. FIG. 2. Longitudinal gauge traces in Swedish gabbro.

3 3680 J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Millet et al. FIG. 3. Shock Hugoniot of Swedish gabbro stress-particle velocity space. Straight line fit is according to Eq. 1. FIG. 5. Stress gauge traces in dural, copper and tungsten, impacted with granite flyers. The agreement with this fit is excellent and suggests that the material is behaving elastically under all impact conditions in this investigation. Also note that this figure includes a datum point calculated from stress measured in the back surface configuration, that is where the gauge is supported on the rear surface of the target with a block of PMMA. The results are shown below in Fig. 4. In this figure it can be seen that there is no evidence of a clear elastic precursor. The measured stress in the PMMA ( p ) can be converted to stress in the gabbro ( g ) through the well-known relation g Z g Z p 2Z p, 2 p where Z g and Z p are the shock impedances of the gabbro and PMMA, respectively. In this case we have assumed that the impedance of the gabbro appears elastic, and thus may be calculated from the ambient density and longitudinal sound speed as seen in Eq. 1. Note from Fig. 3 that this calculated point lies on both on the measured Hugoniot and the calculated elastic Hugoniot and again suggests that this material is behaving elastically. It would appear that no data are available in the literature concerning the Hugoniot elastic limit HEL although Hughes and McQueen 19 quote a phase transition at around 15 GPa. However, HELs for other igneous geological materials have been quoted, for example basalt 7 has a HEL in the region of 5 GPa, while jadeite has a quoted HEL 8 in the range of GPa. Thus it can be seen that geological materials can possess quite high HELs, and thus it is possible that the back-surface shot in gabbro at a stress of 6.4 GPa is actually below the materials HEL. It is also possible that the elastic and shock impedances of gabbro are similar, and thus if true would make resolution of the change in slope at the HEL in stress-particle velocity space difficult to resolve. A final possibility is that the shock has been over driven, that is the shock velocity is greater than the longitudinal sound speed. Embedded gauge traces from known metallic targets impacted with granite flyers are shown in Fig. 5. In this material, it was not possible to obtain meaningful stress data using available commercial stress gauges. The most likely reason is that the large grain size 2 3 mm is on a similar scale to the size of the stress gauges. Thus if the gauge is placed across one or two grain boundaries, and differently orientated grains have differing responses, the resultant gauge trace could be difficult to interpret. In the case of the gabbro with its much finer grain size approximately 200 m, the gauge will be sampling a much larger number of grains, and thus the effects of each individual grain will be averaged out. Therefore, if it is assumed that during plate impact the stresses in the flyer and the target are the same, the Hugoniot can be obtained by impacting the material of interest onto a target made from a material with known characteristics. The resultant Hugoniot is presented in Fig. 6. As with the gabbro, the present work is compared with that of others, 6,18 where it can be seen that a high degree of agreement exists. A straight line fit according to Eq. 1 has been put through the data, suggesting that the material is FIG. 4. Back surface gauge trace in Swedish gabbro. 10 mm copper flyer at 528 m s 1. Specimen is 6.8 mm thick. FIG. 6. Shock Hugoniot of Loughborough granite stress-particle velocity space. Straight line fit is according to Eq. 1.

4 J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Millet et al TABLE II. Longitudinal stress data for Swedish gabbro and Loughborough granite. Material Flyer Velocity ms 1 u D mm s 1 X GPa 2% Gabbro Cu, 6 mm Gabbro Cu, 6 mm Gabbro Cu, 6 mm Gabbro W, 5 mm Gabbro a Cu, 6 mm Granite b Dural, 4 mm Granite b Cu, 6 mm Granite b Cu, 6 mm Granite b Cu, 1.45 mm Granite b Cu, 6 mm Granite b W, 5 mm a Stress calculated from back surface configuration using transmission coefficient calculated from elastic impedance of gabbro and shock impedance of PMMA. b Shots carried out in reverse impact configuration. Flyer thickness refers to thickness of metallic target. elastic up to 12 GPa. This is in contrast to the work of Furnish, 6 who has placed the HEL of granite at 2.8 GPa. Thus if this were true for our material, it might be expected that there be a change in slope at this point in the Hugoniot data. Therefore it is possible that the situation previously discussed in the gabbro may apply here. Also, in a previous article 20 we showed that two glasses, when shocked above their HELs, could give differing stresses depending upon whether the measurement was made in the glass using a known flyer plate material, or in a known target material using a glass flyer. In that work, it was demonstrated that in the reverse impact situation, the elastic portion of the glass Hugoniot extended above the supposed HEL. Since the Hugoniot data for the Loughborough granite were obtained using this technique, the same effects may operate here. Longitudinal stress data for both materials is summarized in Table II. Manganin stress gauges have been used to measure the lateral component of stress in the Swedish gabbro, during plate impact Table III. Representative traces are presented in Fig. 7. Gauges have been placed 2 and 6 mm from the impact face. At both stress levels shown, the traces rise to a constant lateral stress level 3 GPa at a longitudinal stress of 6.1 and 8 GPa at a longitudinal stress of 11.7 GPa before releasing. The differences in arrival time of the shock at the 6 mm position between the two shock levels is believed to be due to experimental variation in positioning the gauges. In the case of the 2 mm gauge at 11.7 GPa, the signal rises in rather a noisy fashion approximately 2 s after the arrival of the TABLE III. Lateral stress and shear strength of Swedish gabbro. Flyer Velocity ms 1 X GPa 2% Y GPa 2% 2 GPa 4% Cu, 10 mm Cu, 10 mm Cu, 10 mm W, 5 mm FIG. 7. Lateral gauge traces at 6.1 and 11.7 GPa in Swedish gabbro. Gauge positions are 2 and 6 mm from impact. main shock. This we interpret as failure in the gauge itself, and not as a result of the materials behavior. In none of the gauges traces shown or indeed at the stresses between the two extremes shown is a secondary rise in lateral stress sometime after the arrival of the main shock that is characteristic of failure waves observed. However, it is not possible to say with certainty that they are not present. In polycrystalline ceramics such as silicon carbide and alumina 13 it has been shown that the failure wave slows as it moves into the target, and in fact beyond a certain distance does not penetrate at all. Here it was suggested that grain boundaries would impede the progress of failure until it eventually stopped. However, in those materials, it was shown that failure wave could penetrate at least 4 mm into the target. If grain boundaries impede the passage of the failure wave in gabbro, they must do so with even greater efficiency than in either silicon carbide or alumina since no sign of failure is noted even 2 mm from the impact face. The shear strength of a material under onedimensional shock loading can be calculated through knowledge of the longitudinal and lateral stresses ( y ), through the relation, 2 x y. 3 In turn, both lateral stress and shear strength can be related to the impact stress assuming of course that the impact stress is elastic by the Poisson s ratio,, y 1 x, x, where In Fig. 8, shear stress data calculated from Eq. 3, is plotted against longitudinal stress. As a comparison, the data are also fitted to the assumed elastic behavior given by Eq. 4. Observe that the measured values of shear strength lie significantly below the calculated values assuming purely elastic behavior. This would seem to indicate that the material is not responding elastically at all, but some inelastic process such as fracture in the shock front is reducing the strength. It is interesting to note that Schock and Heard 21 observed that the effective Poisson s ratio of granite increases with pressure, which as can be seen from Eq. 4 would have the effect of reducing the shear strength away from the calculated elastic values. An increasing Poisson s 4

5 3682 J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Millet et al. We are grateful to Dr. A. Pullen of Imperial College, London for supplying the granite used in this work. We acknowledge Dr. J. Sheridan and Dr. C. O Carrell of DERA Farnborough and Dr. P. Church of DERA Ft. Halstead. We would like to thank D. L. A. Cross and R. P. Flaxman for valuable technical support. Finally, we acknowledge Professor J. E. Field and Dr. Z. Rosenberg for many helpful discussions and encouragement. FIG. 8. Shear strength of Swedish gabbro vs longitudinal stress. Straight line fit is according to Eq. 4. ratio indicates a reduction in a materials ability to resist shear. Increasing damage levels with pressure would have this effect and thus may explain the results in Fig. 8. V. CONCLUSIONS Plate impact experiments have been performed on two igneous rocks, a Swedish gabbro and a granite from Loughborough, UK. Longitudinal stress measurements from embedded stress gauges suggest that both materials are behaving elastically even up to 12 GPa. However, other workers quote rather lower HELs. It would seem possible that similarities between the accoustic and shock impedances would make resolution of a break in slope at the HEL difficult. Lateral stress gauges have been placed in the Swedish gabbro. Failure waves were not observed although their presence cannot be discounted, given that they may only penetrate a small distance. Measurements of shear strength are lower than expected assuming purely elastic behavior. An increase in Poisson s ratio, caused by damage in the shock front has been suggested as a possible cause. ACKNOWLEDGMENTS 1 M. B. Boslough and T. J. Ahrens, Particle Velocity Experiments in Anorthosite and Gabbro, in Shock Compression of Condensed Matter, edited by J. R. Asay, R. A. Graham, and G. K. Staub North Holland, Santa Fe, NM, 1984, pp M. A. Lange, T. J. Ahrens, and M. B. Boslough, Icarus 58, M. B. Boslough and T. J. Ahrens, J. Geophys. Res. B 90, C. A. Hall, L. C. Chhabildas, and W. D. Reinhart, Shock Hugoniot and Release States in Concrete Mixtures With Different Aggregate Sizes From 3 to 23 GPa, in Shock Compression of Condensed Matter, edited by S. C. Schmidt, D. P. Dandekar, and J. W. Forbes AIP, Amherst, MA, 1998, pp K. Tsembelis, J. C. F. Millett, W. G. Proud, and J. E. Field, The Shock Hugoniot in a Cement Paste From 0.5 GPa to 5.0 GPa, in Shock Compression of Condensed Matter, edited by M. D. Furnish AIP, Snowbird, Utah, M. D. Furnish, Measuring the dynamic compression and release behavior of rocks associated with HYDROPLUS Part II, Sandia National Laboratory, SAND , UC-703 unpublished. 7 S. Nakazawa, S. Watanabe, M. Kato, Y. Iijima, T. Kobayashi, and T. Sekine, Planet. Space Sci. 45, E. Takazawa, T. Sekine, T. Kobayashi, and Y. Zhu, J. Geophys. Res. B 103, S. V. Razorenov, G. I. Kanel, V. E. Fortov, and M. M. Abasemov, High Press. Res. 6, V. N. Nikolaevskii, Int. J. Eng. Sci. 19, N. S. Brar, Z. Rosenberg, and S. J. Bless, J. Phys. IV C3, N. K. Bourne, Z. Rosenberg, and J. E. Field, J. Appl. Phys. 78, N. Bourne, J. Millett, N. Murray, and Z. Rosenberg, J. Mech. Phys. Solids 46, N. K. Bourne, Z. Rosenberg, D. J. Johnson, J. E. Field, A. E. Timbs, and R. P. Flaxman, Meas. Sci. Technol. 6, Z. Rosenberg, D. Yaziv, and Y. Partom, J. Appl. Phys. 51, Z. Rosenberg and Y. Partom, J. Appl. Phys. 58, A. Pullen private communication. 18 S. P. Marsh, LASL Shock Hugoniot Data University of California Press, Los Angeles, D. S. Hughes and R. G. McQueen, Trans. Am. Geophys. Union 39, J. Millett, N. Bourne, and Z. Rosenberg, J. Appl. Phys. 84, R. N. Schock and H. C. Heard, J. Geophys. Res. 79,

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