Crack Propagation in Rock Plates Loaded by Projectile Impact ' A p p a r e n t ' s u p e r v e l o c i t y c r a c k s w e r e o b s e r v e d in r o c k p l a t e s u s i n g t h e m e t h o d s of d y n a m i c p h o t o e l a s t i c i t y

by L.A. Glenn and H. Jaun

ABSTRACT--Photoelastic coatings were bonded to limestone and granite plates which were then struck on edge with a steel projectile. The resulting fracture zone growth was observed with a reflecting polariscope and recorded with an image converter camera. It is shown that the maximum velocity at which cracks propagate under these circumstances is very much higher than predicted by quasi-steady theories. 'Apparent' supervelocity cracks can be generated by shock reflection from bounding interfaces, producing tensile waves of sufficient amplitude to activate and join isolated flaws. Photoelastic coatings are also shown to very much enhance surface-crack visualization subsequent to impact.

Introduction If the speed at which cracks propagate in a medium is small in comparison to the speed at which 'information' is transferred from one region to another (wave speed), the problem of determining the crack energetics is uncoupled from that of determining the stress field. Polariscope observation of the developing isochromaticfringe pattern in impacted glass plates suggests that such uncoupling may not be possible for brittle materials under intense impulsive loading.' There is evidence, in fact, that the fracture-zone growth rate in bulk glass, loaded in this manner, may exceed the previously observed 'maximum' fracture velocity. 2 To be sure, Schardin 3 has described the appearance of cracks in glass traveling faster than the maximum velocity; these he showed to be the result of the continuous initiation of secondary fractures ahead of the main crack. The mechanism is quite simple. All that is required is a tensile wave of sufficient amplitude to activate disconnected intrinsic flaws in the material. An example is illustrated in Fig. 1 in which a 100 • 100 x 6-mm glass plate has been struck midway on its upper edge by a 15mm-diam • 30-mm steel projectile at 100 m/s. The plate

L.A. Glenn is presently a member o f the Technical Staff at Lawrence Livermore Laboratory, Livermore, CA; was formerly Senior Staff Scientist, Applied Mechanics Department, Institute CERAC, S.A., Ecublens, Switzerland. 1-1. Jaun is Engineer, Applied Mechanics Department, Institute CERAC, S.A. Original manuscript submitted : March 1, 1977. Final version received : July 18, 1977.

was backsurface coated with a mirror and is viewed in reflected light with an image converter camera at a framing rate of 2 x 105 s-' ; the first frame is at approximately 22 from impact. It is to be noted that the fracture development is not by continuous extension or bifurcation but mainly by the linking of isolated crack elements as evidenced, for example, by the crack array formed along the impact axis. The presence of the bounding surfaces is of obvious importance in the case of the plate since it is by reflection from these that tensile waves are created. Even in the absence of interfaces, however, it should be possible to produce supervelocity cracks (Schardin's term); for example, in the tensile tail of diverging cylindrical or spherical shocks. Moreover, as in s i t u rock formations invariably contain numerous faults, joints or interfaces, it was of interest to know whether rock media behaved in similar manner to glass. It is the object of the present report to summarize the results of a series of experiments in which thin plates of German (Solenhofen) limestone and Swedish red (Bohus) granite were struck on edge by steel projectiles, and observation recorded of the resulting fracture-zone growth. The method employed to observe the temporal behavior is similar to that described by Daniel and Rowlands,' i.e., photoelastic coatings were bonded to the plate surface and the events following impact were studied with a reflecting polariscope. The measurement of fracture speed made in this way was compared with an alternate technique in which an array of electrically conducting paint stripes was arranged on the rock surface so as to signal an open circuit on crack arrival. Finally, it is demonstrated that prebonding photoelastic sheet to a rock surface can markedly enhance the identification of surface cracks subsequent to loading.

Experimental Setup and Procedure All rock specimens employed were cut to the same dimensions, 100 x 100 • 6 ram. The properties of Solenhofen limestone are well documented in the literature. '-7 Bohus granite is a red, medium-grained (1-3 ram) granite found in the western part of Sweden, north of Gothenburg.

Experimental Mechanics 9 35

Fig. 1--15-mm-diam x 30-mm steel projectile impact on 100 x 100 x 6-mm backsurface-coated glass mirror at 100 m/s

Its nominal composition is 55-percent alkali feldspar, 26percent quartz, 12-percent plagioclase and 7-percent mica. Nominal density, bulk modulus and Poisson's ratio are, respectively, 2640 kg/m 3, 355.3 kb (35.53 GPa) and 0.25. The measured static tensile strength ranges from 0.083 kb (8.3 MPa) with the pinch test to 0.114 kb (11.4 MPa) with the Brazilian. The dynamic behavior of this rock under impact loading has recently been reported? Several different photoelastic materials were tried. All were produced by Photolastic Inc. (Malvern, PA). The most effective is designated PS 3-C by the manufacturer. Its thickness, Young's modulus and photoelastic coefficient are, respectively 1.0 mm, 2.0 kb (200 MPa) and 0.02. The photoelastic sheet stock was bonded to the rock face with PC-6 aluminized epoxy cement in accordance with the instructions from the manufacturer, except that the cement-layer thickness was reduced to approximately 0.25 mm. For testing, each specimen was mounted vertically on a rubber absorber and positioned by means of 2 plastic spacers 25 mm from the barrel of a 15-mm-diam vertical gas gun (Fig. 2). The steel projectile was nominally 15-mm diameter x 30 mm long and all tests Were performed at a commercially interesting impact speed, i.e., 25 m/s. The optical system is illustrated in Fig. 3. It consisted of a flash light source, plane polarizer, 88 plate, target with l~hotoelastic coating, 88 plate, analyzer, lens and camera. The camera used was a model HE 700 Ima-Con image converter manufactured by Hadland Photonics Ltd (Bovingdon, U.K.); the flash was a Microflash type HL 150, also supplied by this company. The framing rate used throughout was 2 • l0 s s-', except for one experiment conducted at 1 x 105 with a newer camera. The flash duration was approximately 200 p.s. Triggering of the flash to synchronize with the camera sequencing was accomplished by allowing the projectile to interrupt a He-Ne laser beam, positioned a precise distance above the impact surface, and targeted on a photocell. The photocell output, passed through a delay leg set for the predetermined projectile velocity (the latter was measured for each test

36 9 January 1978

with an electromagnetic gage built into the gun), triggered the flash and then the camera. As shown in the lower sketches in Fig. 3, the setup was slightly modified in a few tests wherein both sides of the target were observed simultaneously. When electrically conducting paint was used to measure crack speed, it was applied in parallel stripes, normal to the impact axis. The paint used, Elecolit 350, had an acrylic base and contained 1-2 percent silver, according to the manufacturer, 3M. The stripes were nominally 0.5 mm wide and 20-40 mm long; after application, the paint was

"ILE~

I

SHEET

Fig. 2--Arrangement of rock-plate target and

gun barrel

EXPERIMENTALSETUPFOR ONE--SiDEDPHOTOGRAPH IMPACT

AB

FLASH

~. ~L~

~~'-'~

IMA--CON CAMERA

/U "PHOTOELASTICSHEET TARGET FLASH j ~ IMPACT AB

A B ~ ~ /

EXPERIMENTAL SETUPFOR (TWDO-vS E ' IDwE)DPHOTOGRAPH

HE--NE LASER

MIRROR ~

/

. ~

"4q- 1

PHOTODIODE WITHAMPLIFIER

./// ..j-

~

9~

NL:

,

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PHOTOELASTIC SHEET

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TABLE 1--SOLENHOFEN-LIMESTONE TEST DETAILS Test No.

Side 1 Preparation

Side 2 Preparation

57 59

PC* PC

Nothing Nothing

61 62 63

PC PC PC

-10 conducting stripes, q 10 mm apart, beginning| 5 mm from impact plane_]

64 I C + 5 conducting stripes nder coating, 20 mm 65 part, beginning 10 mm 66 om impact plane / 67

5 conducting stripes aq identical locations with I stripes under coating | side _[

68 - l lconductingstripes q g stripes, 15 mm apart I, /at identical locations| 69 70 eginning 5 mm from I ~with stripes on | 71 ~mpact plane _~ ~pposite side _J

f~ocoating;7conduct

80 81 82

PC (no conducting stripes) PC (no conducting stripes) PC (no conducting stripes) PC (no conducting stripes) PC (no conducting stripes) PC (no conducting stripes)

CAMERA

* PC = p h o t o e l a s t i c c o a t i n g

PROJECTILEIMPACT

A-1/4-WAVE PLATE S-- PLANEPOLARIZER OR ANALYZER

Fig. 3--Schematic illustration of optical system

cured for 50 min at 80~ A separate bridge was formed for each stripe with 0.2-mm copper wire contacts soldered to each end of a stripe. A 5-V signal was applied across each bridge and each was normally monitored on a

All tests: Nominal initial projectile speed-25m/s Steel projectile 15-mm diameter x 30 mm long Camera framing interval - 5 ms (10#s for test No. 81)

separate channel of a Biomation (Cupertino, CA) model 810-D digital logic recorder. Separation of any stripe by a crack opened that leg and reduced the corresponding signal to zero; crack reclosure restored the applied voltage. The sampling rate was 0.5 #s and the total measurement duration was normally 128/~s.

Fig9 4--Illustrating the development of a running crack in Solenhofen limestone9Crack has a maximum speed between 3.2 and 3.4 mm/~s

Experimental Mechanics 9 37

Results Sixteen tests were made with the limestone targets; the important details are given in Table 1. The first two tests employed target specimens with one side bare and the

Fig. 5--Fracture-zone growth in Bohus granite

other with a coating. Figure 4 shows the result for the first test, No. 57. An expanding wavefront is visible from the first frame, at 3 #s from impact. The speed of this front is more or less constant until Frame 4, after which the fringe pattern is controlled by wave reflections. The maximum wavefront speed, ~ , for this test was measured to be 3.22 mm//~s. The average value of ~ for all the limestone tests with the PS 3-C coating was 3.85 mm//zs, with a standard deviation of 0.62. This can be compared with the elastic values,* CE = 4.63 mm//zs and C s = 2.9-3.1 mm//~s. The leading fringe in Fig. 4 thus appears to be the longitudinal wave, attenuated somewhat by the coating a n d / o r the cement. Polariscopic views of impacted glass plates (without coating) confirm that the leading fringe coincides with CE. Moreover, for the seven tests made with Bohus granite, the average value of ~ was 4.36 mm/#s with a standard deviation of 0.25. This compares very well with the value of CE for this rock, 4.49 mm/#s. The coating appears to adhere better to the granite surface, perhaps a result of the increased roughness or graininess of the latter. Two cracks, identified as [1] and [2] are visible already in Frame 3 at 13/~s from impact. The angular crack, [2], was typically observed in all tests with the limestone; its speed was found to be roughly 2 m m / ~ . Crack [1], running along the impact axis, was less common. Its speed was measured at between 3.2 and 3.4 mm/#s until crack arrest occurred, somewhere between Frames 6 and 7, at approximately 68 mm from the impact plane. Note that the time for a longitudinal wave, originating at the

* CE = speed o f longitudinal waves in plane stress (E/o) 1/2 Cs = speed o f shear waves (G/O) 1/2

Fig. 6--Illustrating supervelocity crack in Solenhofen limestone. Extension rate of crack between frames 4 and 5 is in excess of 10.8 mm/# s

38 9

January 1978

impact plane, to reflect off the bottom free surface and arrive at the 68-ram location is precisely 28.5/~s, i.e., just corresponding with Frame 6. Crack [1] thus seems to be arrested by this reflection. The bottom surface reflection produces a tensile region in its wake which is augmented by reflection of longitudinal and shear waves off the lateral boundaries. The time for the elastic precursor to reflect off the bottom corners and reach the plate center at the bottom edge is 35.0 ~s, i.e., between Frames 7 and 8. This coincides with a new crack (seen first in Frame 8), issuing from this edge and traveling along the impact axis, eventually connecting with crack [1]. Below the 10 Ima-Con frames in Fig. 4 are two views of the target specimen subsequent to the experiment. The left-hand view is of the rock face; the main cracks are easily visible. The right-hand picture is of the coating face, viewed through a polaroid sheet (plane polarizer + 88 plate). If the polaroid sheet is removed, all the cracks disappear from view. More interesting perhaps is that many more cracks are visible in the coating than in the rock face. That these are indeed cracks and not mere illusion could be easily verified by viewing the rock face when the specimen was bent along a crack axis. Moreover, most of the cracks observed in the coating after the experiment can also be observed during the experiment. The effect is even more dramatic with the granite plates. Figure 5 shows a granite specimen in the first 28 #s after impact, along with the posttest photographs. With this material, it is much more difficult to see cracks in the rock face, but easier to identify them in the coating. (Note that the circular region in the lower left-hand part of the photos is a blemish imparted to the coating during assembly.) The crack marked [I] in Fig. 5 is extending at a rate of 4.7 mm/#s through Frame 6 of the Ima-Con sequence; in subsequent frames (not shown) the cracks are somewhat obscured by the fringe pattern resulting from wave reflections. The choice of the photoelastic material is important in this regard. Materials with higher photoelastic coefficient tended to either produce too many fringes and thereby wash out the cracks or to separate too easily from the crack face, with the same result. The use of conducting-paint stripes on the limestone face opposite the coating was an attempt to obtain independent verification of the crack presence. Instead, the paint stripe data were radically at odds with those from the coating. Figure 6 shows the photoelastic sequence, as well as the stripe arrangement for test No. 61 (cf., Table 1). Angular cracks [1] and [2] are formed as in test No. 57 (Fig. 4), but there is no running crack along the impact axis. This time, however, the crack connected to the bottom center of the plate appears suddenly, between Frames 4 and 5, i.e., 24-29 #s from impact. This crack, identified with the numeral [3], appears in Frame 5 to be growing in two directions--the upper tip towards the impact plane and the lower tip towards the bottom edge. Note that it is not until Frame 6 (34/~s) that waves reflected from the bottom corners arrive at the bottom center. The crack separation at this point is then amplified. The apparent speed of crack [3], between Frames 4 and 5 is more than 10.8 mm//~s, more than double the longitudinal wave speed. Of course, crack [3] is not a 'running crack' in the usual fracture-mechanics sense. On the other hand, as shown by the posttest views in the lower part of Fig. 6, such a crack is indistinguishable from any other. The conducting-paint-stripe results were highly erratic but, in all cases, indicated the presence of a crack at a

specific location only after (and in many cases, long after) the crack was apparent in the coating. When three tests (Nos. 61-63) produced similar results, four target specimens were prepared with conducting-paint stripes on both sides--underneath the cement on the coating side (the cement, although 'aluminized', was nonconductive). The experiments with these specimens did little to clarify the discrepancy. In the seven tests (61-67), not a single example was found of a crack detected by a paint stripe before its appearance at the corresponding position on the opposite coating face. The average time lag, based on 31 samples, was 36 /zs and the standard error exceeded the mean. Moreover, the set of paint stripes under the coating was obviously affected by the presence of the latter; most of the time the electrical circuits on this side never opened during the experiment and remained closed even thereafter. To eliminate coating interference, four new specimens were prepared with paint stripes on both sides, but without coating on either. The results o f testing these (tests No. 68-71)showed the existence of a significant time lag between the appearance of a crack at a given distance from the impact plane on one side and its appearance at the same position on the other. Based on 25 samples, the average time lag was 15 #s (the time for waves to traverse the plate thickness 10 times) and the standard error again exceeded the mean. When a given circuit did open, multiple opening and reclosure was t h e rule. The period varied from the sampling rate (0.5 /~s) to 70 #s. Crack opening and reclosure was also evident in the photoelastic coatings and

Fig. 7--Simultaneous view of both sides of an impacted backsurface-coated glass mirror. Framing rate is 2 x 10 ~ s-'

Experimental Mechanics 9 39

crack observed on one side was not necessarily 'through' on the other. Three specimens were therefore prepared with photoelastic coating applied to both sides. Figure 8 illustrates the record from test No. 81. For this test, an Ima-Con 790 camera was used, instead of the 700 and the framing rate was halved to 105 s-l; the 790 has the output phosphor on the image tube coated on a fiber-optic end plate, instead of the normal glass window and gives better resolution than does the 700. The remarkable symmetry in Fig. 8 is striking evidence of through cracks. These results were confirmed in tests 80 and 82.

Conclusions

Fig. 8--Simultaneous view of both sides of an impacted Solenhofen-limestone plate. Framing rate is 10 s s-'

has previously been observed, and indeed predicted, when bulk glass is subjected to projectile impact. ~.2 An explanation for the failure of the conducting-paint stripes to confirm the photoelastic results can perhaps be found in the ductility of the paint. It was observed earlier in our experiments with backsurface-coated glass mirrors that the glass fractured long before the mirror surface showed any sign of a crack. Specifically, these mirrors were struck as in Fig. 2, but both sides were viewed simultaneously, with the optical setup similar to that in the lower part of Fig. 3. Figure 7 illustrates that the glass is entirely shattered before any indication is seen in the mirror. Furthermore, subsequent examination of the fragments (each several square centimeters in size) showed that, on each of these, the mirror side was free of cracks whereas multiple cracks were in evidence in the glass backing, We hypothesize that the paint stripes behaved in like fashion and that cracks were detected with this method only after the crack had opened to a rather large extent in comparison to the opening required for photoelastic detection. The authors have been advised that the discrepancy between the two methods could have been avoided by using thinner stripes (possibly vacuum deposited), but we are unable to cite specific references wherein the required response time ( - 1/~s) has been attained. Notwithstanding the insensitivity of the conductingpaint method, tests 68-71 suggested at least the possibility that the cracks observed in the limestone plates were asymmetric with respect to the plate thickness, i.e., a

40 9 January 1978

The results of our experiments suggest that the maximum speed at which cracks can propagate in rock media, loaded by projectile impact, is much higher than the Rayleigh wave limit derived from quasi-steady energybalance ideas. 9 It appears likely that the limiting speed is governed by the time for isolated flaws or defects to 'activate' and connect to form a finite array. The physical appearance of such a crack may be indistinguishable from a conventional running crack. Moreover the orientation of such crack arrays is intimately connected with the mechanics of wave propagation within the medium, particularly reflection from bounding interfaces and, of course, from neighboring nascent cracks. Our results imply further that the concept of a characteristic crack speed under these circumstances is valid only in a stochastic sense, i.e., the distribution of crack speeds can vary from near zero to values at least several times the wave speed. It has been shown that surface-crack visualization on impulsively loaded rock targets is much enhanced when photoelastic coatings are employed. This is especially useful f o r materials like concrete or granite where it is often very difficult to detect cracks subsequent to loading. We infer, from experiments with glass targets, with and without coatings, that the extent to which the coatings influence the crack development is small. The wave-speed measurements support the converse as well, i.e., that crack motion observed with the coating is not much attenuated thereby. In this connection, we note finally, that crack-velocity measurements with this method most likely represent a lower bound; it is hard to see how cracks could propagate faster in the coating than in the base rock.

References 1. Glenn, L.A., "'The Mechanical Response of Brittle Materials to Intense Impulsive Loading," Proc. Colloq. Numerical Methods o f Analysis, Swiss Federal Inst. Tech., Lausanne, Oct. 11-13, 1976; Int. Series o f Num. Math. (ISNM), Birkhliuser Press, Basel, 37 (1977). 2. Glenn, L.A., "'The Fracture o f a Glass Half-Space by Projectile Impact, "" J. Mech. Phys. Solids, 24, 93-106 (1976). 3. Schardin, H., "'Velocity Effects in Fracture, "" Fracture (Proc. Int. Conf. Atomic Mechanisms o f Fracture, Swapscott, UK, Apr. 12-16, 1959), Auerbach, B.L. et al. eds., M I T Press (1959). 4. Daniel, LM. and Rowlands, R.E., "'On Wave and Fracture Propagation in Rock Media," EXPERIMENTALMECHANICS, 15 (12), 449-457 (1975). 5. La Mori, P.N,, "'Compressibility o f Three Rocks . . . . '" Defense Atomic Support Agency Report D A S A 2151, Battelle Memorial Institute (Aug. 1968). 6. Jones, A.H. and Froula, N.H., "'Uniaxial Strain Behavior o f Four Geological Materials to 50 kilobars, "" Defense Atomic Support Agency Report D A S A 2209, General Motors Mads & Struct. Lab. (Mar. 1969). 7. Mogi, K., "'Effect o f the Intermediate Principal Stress on Rock Failure, "" J. Geophys. Res., 72, 5117 (1967). 8. Glenn, L.A. and Janach, W., "'Failure o f Granite Cylinders under Impact Loading, "" Int. Jr. Fract., 13 (3) (,fun. 1977). 9. Erdogan, F., "'Crack Propagation Theories, '" Fracture, A n Advanced Treatise, I1, Ch. 5, H. Liebowitz, ed., Academic Press (1968).