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AD752054 

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1972. Other requests shall be referred to 
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AD-752 054 


DYNAMIC TENSILE FAILURE IN ROCKS 
Donald A. Shockey 
Stanford Research Institute 


Prepared for: 

Bureau of Mines 

Defense Advanced Research Projects Agency 


30 October 1972 


DISTRIBUTED BY: 



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AD 75 20 54 


October 30, 1972 


Semiannual Technical Report 

Covering the Period April 15 to October 15, 1972 
DYNAMIC TENSILE FAILURE IN ROCKS 


By: Donald A. Shockey 


Prepared for: Bureau of Mines 

Twin Cities Mining Research Center 
Twin Cities, Minnesota 55111 

Attn: Dr. D. E. Siskind 

t 

SRI Project PYU-1793 



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hone Number: 

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1579, Amendment 2 
1F10 

Stanford Research Institute 
February 14, 1972 
February 13, 1973 
$59,598 
H0220053 

Dr. Carl F. Petersen 
(415) 326-6200, Ext. 4614 
Dr. Donald A. Shockey 
(415) 326-6200, Ext. 2587 
Dynamic Tensilt Failure in Rocks 


Sponsored by Defense Advanced Research Projects Agency 


Approved: 






George R. Abrahamson, Director 
Poulter Laboratory 
Physical Sciences Division 


The views and conclusions contained 
in th^s document are those of the 
authors and should not be interpreted 
as necessarily representing the official 
policies, either expressed or implied, 
of the Defense Advanced Research Projects 
Agency of the U. S. Government. 


Reproduced by 

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Unclassified 

Stanford Research Institute 
Menlo Park, California 94025 


3 REPORT TITLE 

DYNAMIC TENSILE FAILURE IN ROCKS 


A DESCRIPTIVE NOTES (Type of report and Indus rve dais) 

Semiannual Technical Report - April 15 to October 15. 1972 _ 

S au ThORiSI (First name, middle initial, last name) 

Donald A. Shockey 


6 REPOR T OATE 

October 30, 1972 


7a. TOTAL NO OP PAGES 


& 3 / 


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PYU-1793 

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this report) 

10 DISTRIBUTION STATEMENT Details of ftlU^rOtlOllS 

document may be bettor 
itudied on microfiche. 

11 SUPPLEMENT ATY NOTES 

12 SPONSORING MILH4R1 ACTIV Tv 

Director 

Defense Research Projects Agency 

Arlington, Virginia 22209 


13. ABSTRACT 


A fracture model is being developed based on the hypothesis that dynamic 
tensile failure in rocks occurs by the activation of preexisting flaws which propagate 
and may coalesce to produce fragments of various sizes. During the previous year the 
first two stages of the fracture process-flaw activation and crack growth—were 
treated quantitatively. The fracture model in its present stage of development allows 
us to predict the number of cracks, the total fracture surfac° area, and the energy 
absorbed by creation of new surface resulting from a known dynamic loading history. 

The objective of this second year is to treat quantitatively the final two stages of 
the fracture process-crack coalescence and fragmentation—to obtain the capability to 
predict fragment size, shape and location. 

Crack coalescence was studied and fragment size distributions were measured on 
Arkansas novaculite following dynamic loading experiments with a gas gun. Crack net¬ 
works as revealed on a polished section through the specimens yielded information on 
the size and shape of fragments as a function of position within the specimen, and 
hence as a function of stress history. Measured fragment size distributions of 
comminuted specimens are used to formulate and check the model. 

Although the model is not complete, procedures to generalize the fracture model t< 
ether rocks were initiated by examining petrographically specimens of Sioux quartzite, 
Westerly granite, and pink Tennessee marble to attempt to reveal and describe quanti¬ 
tatively their inherent flaw strictures. The distribution of preexisting flaws, an 


DD in°oI M ««1 473 {, ' AGE (continued) 

S N 0101.807.6801 


Security Classification 














UNCLASSIFIED 


Security Clasilficatlon 


Fracture in rocks 
Tensile failure 
Crack coalescence 
Fragmentation 
Novaculite 
Dynamic loading 


Abstract (concluded) 

important parameter in the fracture model, was 
found to be much more difficult to determine in 
these rocks than in novaculite because of the 
obscurity of the flaws. 


DD ,'”,“..1473 'sack, 

(page t 










CONTENTS 


ABSTRACT 11 

LIST OF ILLUSTRATIONS vii 

LIST OF TABLES vii 

I INTRODUCTION 1 

II THE DYNAMIC FRACTURE MODEL 3 

III FRAGMENTATION IN ARKANSAS NOVACULITE 5 

Target Design 5 

Dynamic Tensile Experiments 6 

In Situ Observations 9 

Fragment Size Distribution 9 

IV CHARACTERIZATION OF SIOUX QUARTZITE, WESTERLY GRANITE, 

AND PINK TENNESSEE MARBLE 15 

Microstructures 15 

Inherent Flaw Structures 15 

Quasi-static Tensile Strengths 19 

Stress History Measurements 20 

SUMMARY 23 

ACKNOWLEDGMENTS 25 

REFERENCES 27 


v 

Preceding pag(5blank 


ILLUSTRATIONS 


1 Target assembly used to study fragmentation of rock under 

dynamic terisile loads 7 

2 Polished cross sections of Arkansas novaculite specimens 

showing the extent of fracture damage produced at increasing 
levels of dynamic tensile stress 10 

3 Photomicrographs of various sized fragments from 

Experiment 33 12 

4 Fragment size distribution for Arkansas novaculite 

Specimen 53 14 

5 Microstructures of (a) Sioux Quartzite, (b) Westerly 

granite, and (c) pink Tennessee marble 16 

6 Experimental arrangement for measuring stress histories 21 


TABLES 

[ Uninstrumented Dynamic Tensile Experiments 8 

II Sieve Analysis Results for Arkansas Novaculite: 

Experiment 53 13 

III Measured Properties of Several Rocks 17 

IV Qua3i-static Tensile Tests on Sioux Quartzite 19 


vii 


Preceding page blank 


I INTRODUCTION 


Failure of rock by fracture under dynamic tensile loading conditions 
is more complex and considerably less well understood than fracture under 
quasi-static conditions. There is at present no satisfactory theoretical 
basis for predicting dynamic failure behavior, although the advantages 
of having such a basis are many. An understanding of rock failure under 
dynamic tensile loads would be most ut jful in the solution of practical 
mining and civil engineering problems. With such knowledge rapid 
excavation could be done more safely and economically, the stability of 
structures in rock could be designed and evaluated with more confidence, 
and the efficiency of rock disintegration processes could be improved. 

It is the objective of this three-year program to develop a model for 
rock fracture that can be used to predict failure behavior under dynamic 
tensile loading. This report summarizes the progress made during the 
first half of the second year. 

The program consists of three phases: 

Dynamic Measurements : Flat-plate impact experiments are performed 
on rock specimens, some of which are instrumented with in-material 
stress gages or particle velocity gages to determine stress histories 
in rock during tensile failure. 

Residual Measurements : Optical and scanning electron microscope 
techniques are used to examine the fracture damage in recovered rock 
specimens. 

Model Development : Based on our results and observations, a model 
for dynamic tensile failure of rock is developed and substantiated. 
Initially the model is to be applicable to Arkansas novaculite and 
Sioux quartzite, then later generalized to apply to Westerly granite 
and pink Tennessee marble (Holston limestone). 


1 



In the course of the first year significant progress was made in 

1 2 

understanding rock failure in tension. ’ The most encouraging result 
is that an approach has been developed that may lead to a capability 
for predicting fragment size distributions resulting from known stress 
pulses. 

Our observations during the first year’s work led us to hypothesize 
that dynamic tensile failure in rock occurred by the following sequence 
of events: (1) a number of preexisting flaws in the rock are activated 
by an applied stress pulse, (2) the activated cracks begin to grow 
radially outward on planes normal to the direction of maximum tension, 

(3) neighboring cracks begin to grow into each other and coalesce, and 

(4) coalescing cracks isolate integral fragments of rock and free them 
from the main body. In the first year a model based on this failure 
mechanism was proposed and the first two stages of the model, flaw 
activation and crack growth, were treated in some detail. In its present 
state, the model enables us to calculate the number of cracks, the 
total fracture surface area, and the energy absorbed in fracture for a 
known applied dynamic load. 

One of the two objectives this year is to obtain quantitative 
information on the final two stages of the failure process and extend 
the model to include fragmentation. The other objective is to test and 
to generalize the novaculite fracture model on other rock types. 

This semiannual technical report is presented in three parts: we 
first describe our model for dynamic tensile failure in rock; we then 
discuss the experiments and results from studies of crack coalescence 
and the fragmentation behavior in Arkansas novaculite; and finally we 
report the methods and results of the characterization work on Sioux 
quartzite, Westerly granite, and pink Tennessee marble with respect to 
microstructure, defect structure, quasi-static tensile strength, and 
response to stress waves. 


2 



II DYNAMIC FRACTURE MODEL 


We seek to develop a fracture model which relates loading parameters, 
rock properties, and geometry of specimen and load to permit calculation 
of fracture parameters. Fracture parameters of interest include number 
of cracks, total crack surface area, energy absorbed in fracture, shape 
of fragments, fragment size distribution, and fragment position distri¬ 
bution. 

The most important loading parameters are the peak stress and the 

duration of the stress pulse . We have measured directly the shape of the 

initial compressive pulse in gas gun experiments with ytterbium stress 

gages placed near the back surfaces of rock specimens. Computer codes 

have been used to compute the tensile stresses. In the more complex 

case in which fracture occurs and begins to relax the stresses, a 

3 

sophisticated code recently developed at SRI on another project is 
employed to compute the tensile stress history, and experimental 
measurements of the fracsure signal are used to check the computations. 

To simplify model development in the first year, the stress pulse was 
assumed to be square and hence describable by a constant stress level 
and a constant duration. 

The rock properties influential in fracture behavior are size distri¬ 
bution of preexisting flaws, plane strain fracture toughness, crack 
velocity, and specific fracture surface energy. These parameters must 
be determined and incorporated into the dynamic fracture model. Values 
for Arkansas novaculite were determined in the first year's work. Efforts 
to determine these parameters for other rock types are reported in Section 
IV. 

Specimen geometry and load geometry determine the stress and strain 
conditions under which fracture occurs and hence whether failure is tensile 
or shear. In this work we consider cylindrical specimens having a diameter 
to thickness ratio of about 5 loaded in uniaxial strain, an easily 
analyzable state which is suitable for model development. 


3 



Last year pulse shape and rock properties were related to provide 
the capability to predict the number of activated flaws, the total 
fracture surface area, and the energy absorbed in creating new surfaces 
by a known dynamic load in Arkansas novaculite in uniaxial strain. Our 
goal this year is to extend this predictive capability to include crack 
coalescence and fragmentation. Of particular interest are th* number and 
size of fragments. 

Simple thought experiments lead us to believe that the number of 
fragments resulting from a given shock load of duration sufficient for 
complete coalescence should be proportional to the number of cracks which 
are formed. (We expect additional fragments to be produced by crack 

branching events and as debris during the formation of large fragments.) 

1 2 

According to our fracture model ’ then, the number of fragments is 
determined mainly by the inherent flaw distribution, the plane strain 
fracture toughness of the rock, and the amplitude of the stress pulse. 

The extent to which coalescence proceeds is a function of pulse length, 
and hence for short term stress pulses the number of fragments will also 
depend on stress duration. 

The size of the fragments is also a function of inherent flaw 
structure, plane strain fracture toughness, and pulse shape. The pulse 
shape in a rock undergoing fracture varies strongly from position to 
position because of the stress relaxing effect of the cracks as they 
form and grow, and therefore the fragment size distribution also varies 
strongly. Specifically, the fragments which form in specimen zones 
where tension first appears are expected to be many in number and small 
in size; fewer and larger fragments should be produced at increasing 
distances from this zone. (This trend is exhibited in Figure 2d and 
indicates erosion of the stress amplitude by developing fracture damage.) 

At distances away from the zone of first tension where the stress amplitude 
is lower, fewer and more widely spaced flaws are activated. Stress 
duration becomes more important here, since the more widely-spaced 
activated flaws require more time to grow and coalesce. 



Ill FRAGMENTATION IN ARKANSAS NOVACULITE 


The experiments described in this section were designed to gain an 
understanding of crack coalescence and fragmentation, and to produce 
quantitative data to support the development of the dynamic fracture 
model. 

Gas gun experiments as described in the Annual Technical Report' 1 
were performed to attain dynamic tensile loads. Flat plexiglass flyer 
plates are accelerated down the evacuated barrel of a light gas gun 
upon sudden release of pressurized helium at the gun breech. When flat 
impact of the flyer plate with the specimen occurs, short-lived tensile 
pulses result in the rock specimen from the intersection of stress waves. 
If the stress level is sufficiently high, fracture can occur. Higher 
velocity recovery experiments than were performed in the first year are 
required to achieve stress levels sufficient to produce high degrees of 
crack coalescence and fragmentation. The target arrangement used in 
the previous work is unsuited for recovery of highly fractured and hence 
very fragile specimens or for recovering all of thefragments of polarized 
specimens. Therefore, a target arrangement was designed that allows in 
situ recovery of heavily damaged and even fragmented rock. 

Target Design 

The method for recovery of heavily damaged rock entails encasing 
the cylindrical rock specimens completely in a much tougher material of 
similar shock impedance. Aluminum was found to be a suitable jacket 
material, first because it does not undergo brittle fracture under the 
loading conditions of these experiments and therefore contains the 
cracking and fragmenting rock specimen, and second because its shock 
impedance is very similar to that of novaculite, so that disturbance of 
stress waves as they cross the specimen-encasement interface is minimal. 
The dimensions of the targets were designed to reduce edge effects. 


5 



As shown in Figure 1, specimens of Arkansas novaculite 12.7 mm in 
diameter by 6.35 mm thick were fit tightly in the center of an aluminum 
disk 50.8 mm in diameter and 9.53 mm thick. An epoxy was applied on the 
entire specimen surface to ensure intimate contact with the aluminum 
casing. An aluminum cover plate 50.8 mm in diameter by 3.18 mm thick was 
then placed over the exposed end of the specimen and held firmly to the 
disk with four equally spaced screws. This target assembly was then 
subjected to flat-plate impact with the gas gun. 

Dynamic Tensile Experiments 

Ten experiments were carried out; the details are given in Table 1. 

It was planned to subject Specimens 44, 45, and 46 to stresses a factor 
of about 2.0, 1.5, and 1.25 in excess of the dynamic tensile strengths in 
an attempt to obtain various degrees of crack coalescence leading to 
fragmentation. The resulting fracture damage is described in the next 
section. 

The next three experiments, 47, 48, and 49 were performed at stress 
levels near the dynamic tensile stre'gth to determine whether the aluminum 
encasement arrangement caused significant stress amplitude attenuation. 

If so,impact velocities sufficient to cause incipient spall fracture in 
unencased specimens would not result in damage when encased. Experiments 
47 and 49 performed at an impact velocity of 16,4 m/sec produced significant 
cracking, whereas Experiment 48 at 14.8 m/sec produced no damage. These 
results are in agreement with the damage threshold velocity of 15.1±0.6 m/sec 
established for unencased novaculite in the first annual report, 1 and so 
we conclude that the aluminum encasement had little attenuating effect on 
the stress. 


6 





UNINSTRUMENTED DYNAMIC TENSILE EXPERIMENTS 


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Specimens 50 and 51 were to be impacted at about 25 m/sec, in the 
velocity range of advanced stages of crack coalescence and incipient 
fragmentation (unfortunately much lowe^ velocities, about 17 m/sec, 
were attained and much less damage resulted than was desired). The final 
two specimens were shock loaded at significantly higher velocities to 
produce detached fragments. 

The recovered targets were prepared for fractographic observation 
and analysis in one of two ways. Either they were cut carefully on a 
diameter to reveal the cracking pattern on a cross section, or else the 
aluminum encasement was removed by carefully machining the periphery 
down to a few mils in a lathe and subsequently dissolving the remaining 
few mils of aluminum in a 50% HCL solution. 

In Situ Observations 

Specimens 45 through 52 were sectioned and polished to reveal the 
cracking patterns. The effect of stress level on the extent of cracking 
is illustrated in Figure 2, which shows cross sections of specimens 
impacted at various velocities. The characteristic dome-shaped crack 
pattern is evident. Damage is usually heaviest in the half nearer the 
impact surface. Fine particles seem to be produced at midthickness and 
in the zone encompassed by the dome cracks. Large fragments originate 
mainly near the flat surfaces. The free-surface side of the specimen is 
usually least damaged and is often recovered in one piece, even when the 
remainder of the specimen has fragmented. Free, uncoalesced crack tips 
are commonly observed in specimens impacted at high as well as at low 
stresses. 

Fragment Size Distribution 

We attempted to determine the fragment size distributions produced 
in Experiments 44, 45, and 53 by carefully removing the aluminum encase¬ 
ments. Specimen 44, however, fell apart in only a few large pieces and 


9 



Reproduced from 
best available copy. 





Id) EXPERIMENT 52 
138 x 10 6 PASCAL 


MP-1793-7 


FIGURE 2 POLISHED CROSS SECTIONS OF ARKANSAS 

NOVACULITE SPECIMENS SHOWING THE EXTENT 
OF FRACTURE DAMAGE PRODUCED AT 
INCREASING LEVELS OF DYNAMIC TENSILE STRESS 
(IMPACT DIRECTION WAS FROM TOP TO BOTTOM) 


10 





was vc uitable for a sieve analysis. Specimen 45 remained intact after 
removal of the aluminum and retained considerable strength (firm hand 
pressure was insufficient to break it up), so it was mounted in epoxy 
and sectioned as described in the previous discussion. 

The fragment size distribution for Specimen 53 was determined by 
placing the collected fragments in the top sieve of a series of U.S. 
sieves placed in the following order from top to bottom: No. 10, 14, 20, 
40, 50, 100, 200, and 400, and a pan to catch the fines. The system was 
vibrated for a short time, and the particles retained on each screen were 
counted and weighed. Figure 3 shows the shapes of the particles; the 
raw data are presented in Table 2 and in Figure 4. Such experimental 
fragmentation data will be used to develop and check the dynamic 
fracture model. 


11 





RADII QREATFR THAN 1000 microni 


RADII 74 TO 149 micron* 


3ADII 149 TO 210 micron* 


UNFRAGMENTED PORTION 


RADII 420 TO 1000 micron* RADII 37 TO 74 micron* 


RADII 210 TO 420 micron* RADII 18 TO 37 micron* 

MP-1793-8 

FIGURE 3 PHOTOMICROGRAPHS OF VARIOUS SIZED FRAGMENTS f-ROM EXPERIMENT 53 
















SIEVE ANALYSIS RESULTS FOR ARKANSAS NOVACULITE: EXPERIMENT 53 


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14 


FRAGMENT SIZE DISTRIBUTION FOR ARKANSAS NOVACULITE EXPERIMENT 53 



IV CHARACTERIZATION OF SIOUX QUARTZITE, WESTERLY GRANITE, 

AND PINK TENNESSEE MARBLE 

Microstructures 

One-inch cubes of Sioux quartzite, Westerly granite, and pink 
Tennessee marble were cut from the large blocks received from the 
Bureau of Mines and polished on three perpendicular sides in preparation 
for petrographic examination. Photomicrographs showing the grain structures 
of the three rock types are presented in Figure 5. 

The Sioux quartzite is relatively pure, dense, and homogeneous. 

Large cracks, pores, and faults are noticeably absent. The grains are 
equiaxed, randomly oriented, and about 30 times larger than those in 
Arkansas novaculite (average grain diameter is of the order of 300q,). 

As indicated by the pronounced relief of polished surfaces, Westerly 
granite consists of hard grains (quartz) in a softer matrix (microcline 
and plagioclaso). The quartz grains are generally irregular with diameters 
often exceeding lOOOq,. The dark biotite phase is randomly oriented. 

The grain size in the marble ranged from very small (~10p,) to very 
large (3000^) and was easily discernible in 3/4 polarized light. A large 
majority of the grains exhibited pronounced twinning. No preferred grain 
orientation was evident. 

Values of density and sound speeds which we measured on these rocks 
are presented in Table 3. Measured grain densities differed from the 
bulk densities by less than 1%, indicating that porosity was very low. 

Inherent Flaw Structures 

'Hie model for dynamic tensile failure in rock, which was proposed 
and partially developed in the course of last year's work, requires a 
knowledge of the inherent flaw structure of the rock. We were able to 
determine quantitatively the size distribution of preexisting flaws in 
Arkansas novaculite and thereby to use our fracture model to calculate 
the number of flaws activated by a given stress pulse. 




MP-1793-10 


FIGURE 5 MICROSTRUCTURES OF (a) SIOUX QUARTZITE 

(b) WESTERLY GRANITE, 

(c) PINK TENNESSEE MARBLE 








MEASURED PROPERTIES OF SEVERAL ROCKS 







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To apply this model to other rock types, one needs information 
about their inherent flaw structure also, and so this became one of the 
tasks in this second year. But whereas the flaw structure in novaculite 
was readily discernible and hence relatively easily described quanti atively, 
inherent flaws in Sioux quartzite, Westerly granite, and pink Tennessee 
marble were very difficult to see. 

Nearly all flaws in these latter rocks are associated with grain 
boundaries and could be detected only by focusing painstakingly up and 
down with the optical microscope at magnifications greater than 100X. 
Occasional transgranular cracks were observed in the feldspar grains of 
the Westerly granite. 

Special viewing and crack decoration techniques wc"e tried in attempt¬ 
ing to observe the flaw structure. Phase contrast photography and scanning 
electron microscopy proved ineffective; likewise swabbing polished rock 
surfaces with silver nitrate and vacuum impregnation with an organic 
fluorescing agent to decorate the microcracks was of little use. Thermal 
grooving was not attempted, but seems of doubtful value since the flaws 
are associated almost exclusively with grain boundaries which themselves 

should be attacked by the thermal grooving process. A procedure recently 

4 

reported by Brace, et al. which uses ion thinning to reveal cracks in 
Westerly granite and Rutland quartzite appears promising. 

Direct observation and measurement of the flaw structure in these 
rocks thus poses a difficult problem. Perhaps a more fruitful approach 
is to attempt to relate grain size or some other readily observable 
characterizing parameter of the grain boundaries to the number, sizes, 
and shapes of crack-like defects between the grains. This approach will 
be given more consideration in future work. 


18 


Quasi-static Tensile Strengths 


To predict gas gun flyer plate velocities necessary for dynamic 
fracture in rock specimens, the tensile strengths of the rocks of 
interest were determined quasi-statically. The quasi-static tensile 
strength also serves as a baseline for comparison of tensile strengths 
measured at the high strain rates attained in the gas gun experiments. 

The quasi-sta'^c tensile strength of Sioux quartzite was measured 

5 

using the expanding ring test. Nine ring-like specimens having inside 

diameters of 8.14 cm, 2.64-cm widths and various wall thicknesses were 

6 

stressed at the rate of 20.7 x 10 Pascal/sec (3000 psi/sec). The results 

are presented in Table 4 and indicate an average tensile strength of 
6 

18.3±2.28 x 10 Pascal (2660±230 psi). Average values of the quasi-static 

tensile strength of Westerly granite and pink Tennessee marble have been 

6 

reported by Wawersik and Brown to be 1575 psi and 1185 psi, respectively. 


Table 4 


QUASI-STATIC TENSILE TESTS ON SIOUX QUARTZITE 


Ring 

No. 

O.D. 

(cm) 

Wall Thickness 

(cm) 

* 

Pressure 

-6 

(Pascal x 10 ) 

* 

Tensile Strength 
(Pascal x 10 ) 

1 

10.10 

0.985 

3.81 

17.8 

2 

9.97 

0.921 

3.72 

18.4 

3 

9.42 

0.643 

2.30 

15.7 

4 

9.95 

0.901 

4.24 

21.4 

5 

9.85 

0.855 

3.46 

18.4 

6 

9.62 

0.746 

2.41 

14.5 

7 

9.75 

0.802 

3.13 

17.6 

8 

9.87 

0,868 

3.82 

20.0 

9 

9.42 

0.643 

3.04 

20.9 

* 

, 2 

-4 



Pasc 

al = 1 N/m 

= 1.45 x 10 psi . 




19 






Stress History Measurements 


The experimental arrangement depicted in Figure 6 is being used to 
measure the stress history experienced by rock specimens as they undergo 
fracture. An ytterbium grid sandwiched tightly between the specimen and 
a backing plexiglass plate acts as a piezoresistant stress gage and 
records the magnitude of the stress as a function of time. A signal 
from a conducting foil covering a small area of the impact surface 
determines the arrival time of the flyer plate. The stress history in 
the specimen is calculated by one-dimensional wave propagation codes 
from the information on the gage record. The stress gage located at 
the back surface of the- specimen is first loaded in compression by the 
initial shock wave and begins to unload as the wave reflects from the 
specimen-backing plate boundary. Before the gage is completely unloaded 
and begins to experience tension, recompressive waves emitted from the 
crack surfaces as they form and propagate impinge on the gage and reload 
it. This second peak is known as the spall signal and provides a 
quantitative measure of the dynamic tensile strength of the rock. 

Two experiments instrumented as indicated in Figure 6 were carried 

out on Westerly granite to determine the stress history and to record 

the spall signal. The gage records indicated that peak pressures of 75 x 10 
0 

and 338 x 10 Pascals,respectively,were attained, but because of excessive 
electrical noise, the fracture signals were unintelligible. Two 
additional specimens have been prepared and instrumented, and the 
experiments will be performed in the near future. 




SUMMARY 


This report has reviewed the technical progress achieved during the 
first six months of the second year of a program whose objective is to 
develop and substantiate a model for dynamic tensile failure of rock. 

The program consists of three phases: (1) flat plate impact experiments 
on rock specimens, some of which are instrumented with stress or particle 
velocity gages to measure stress histories during tensile failure, (2) 
microscopic examination of the fracture damage in recovered rock specimens, 
and (3) development of a quantitative model for predicting fracture 
behavior of rock under djuan.Xc tensile loads. Initially the model is to 
be applicable to Arkansas novaculi+e, then later generalized to other 
rock types. 

In the first year we hypothesized that fracture occurred by the 
activation of many preexisting flaws which propagated, coalesced and 
produced loose fragments of various sizes. The first two stages of the 
process, flaw activation and growth, were treated quantitatively last 
year. Our objectives this year are ;o (1) further develop the model by 
treating the final two stages—crack coalescence and fragmentation, and 
(2) begin to characterize other rock types to test and then generalize 
and novaculite model. The accomplishments of the first six months are 
summarized below. 

A target arrangement was designed to allow recovery of rock specimens 
which have been heavily damaged and fragmented under dynamic tensile loads 
in gas gun experiments. Using this arrangement ten experiments were 
performed at various stress levels on Arkansas novaculite and the extent 
of fracture damage was assessed. Information concerning the coalescence 
behavior of cracks was obtained from the cracking patterns as revealed 
on polished surfaces of section through the rock specimen, and the fragment 
size distribution resulting from a known dynamic stress history was 
determined quantitatively for one specimen. Additional crack coalescence 

23 

Preceding page blank 



and fragmentation information will be obtained in the next six months and 

used to further develop and extend the dynamic fracture model. 

Specimens of Sioux quartzite, Westerly granite, and pink Tennessee 

marble were examined petrographically and found to have more complex 

microstructures and less easily distinguishable flaw structures than 

Arkansas noveculite. The inaccessibility of the flaw structure is 

particularly distressing, because a quantitative description is a 

necessary parameter for the dynamic fracture model. The possibility of 

deducing this information from the grain structure is currently being 

explored. The quasi-static tensile strength of Sioux quartzite was 

6 

measured using the expanding ring test to be 18.3±2.28 x 10 Pascal 
(2660±230 psi). Efforts to measure the stress histories in specimens 
of Westerly granite undergoing fracture and fragmentation are continuing. 


) 



ACKNOWLEDGMENTS 


The author would like to thank Drs. C. F, Petersen and D. R. Curran 
for valuable consultation throughout the course of this work, 

J. T. Rosenberg and D. C. Erlich for performing the gas gun experiments, 
P. S. De Carli for his efforts to reveal Inherent flaws in the rocks 
and D. Petro for skillful fractographic work. 


25 




REFERENCES 


Shockey, D. A., C. F. Peterser,, D. R. Curran, and J, T. Rosenberg, 
"Dynamic Tensile Failure in Rocks," Annual Technical Report, DARPA 
Contract No. H0210018, prepared for the Bureau of Mines, Twin Cities 
Mining Research Center, Twin Cities, Minnesota, March 1972. 

Shockey, D. A., C. F. Petersen, D. R. Curran, and J. T. Rosenberg, 
Failure of Rock Under High Rate Tensile Loads," Proceedings of the 
14 Symposium on Rock Mechanics, Pennsylvania State University, 

June 12-14, 1972. 

Seaman, L., SRI PUFF 3 Computer Code for Stress Wave Propagation, 
Technical Report No. AFWL-TR-70-51, Air Force Weapons Laboratory, 
Kirtland AFB, New Mexico, September 1970. 

Brace, W. F., E. Silver, K. Hadley, and C. Goetze, "Cracks and Pores: 
A Closer Look," Science 178 , 162 (1972). 

Sedlacek, R , and F. A. Halden, "Method of Tensile Testing of Brittle 
Materials," Rev. Sci. Instr. 33, 298 (1962). 

Wawersik, W. R. and W. S. Brown, "Creep Fracture of Rock," Semi¬ 
annual Technical Report, DARPA Contract No. H0220007 prepared for 

the Bureau of Mines, Twin Cities Mining Research Center, Twin Cities, 
Minnesota, July 1972. 


27 


Preceding page blank 



Korin Di-liMU 

(Jinnp 19i<i' 


UNITED STATES 

DEPARTMENT OF THE INTERIOR 


Date October 1972 

SUMMARY REPORT OF INVENTIONS AND SUBCONTRACTS 


The follow ing report must be submitted in triplicate as part of the interim or final report as provided 
foi by the REPORTS and or PATENT ARTICLE in the grant or contract. 


Name of Contractor or Crantee 

Addreaa 

STANFORD RESEARCH INSTITUTE 

333 Ravenswood Avenue 

Menlo Park, California 94025 


Contract jr Grant No. 


(Check appropriate boxes) 


1. Type of Report: 


From . AP.rAl .1®...,19--.7? 

0 Interim 

To . October . 15.19.. 72 ... 


Q Final. 

2. Interim Report Data: 


A. Invention made Q, not made [x], during interval of (1). 

B. If invention(b) made, provide the following information: 

□ Previously fully disclosed in Invention Disclosures. Give dates submitted, and Contractor’s docket numbers. 


□ Invention Disclosures attached herewith. Give Contractor’s docket numbers. 




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