A METHOD
OF M E A S U R I N G
IN A R O C K
SPECIMEN
V. V.
Smirnov
THE
UNDER
CRACK
IMPACT
PROPAGATION
VELOCITY
LOAD UDC 622.831.6+622.831.32
The fragmentation of rocks b y various kinds of m e c h a n i c a l action, including shock loading, is a process which takes time. Since t i m e plays an important part in rock strength phenomena, we have to study the kinetics of the formation of l o c a l fragmentation zones and their propagation through the whole specimen. The fragmentation of rocks by impact (shock) loads is a process in which brittle fractures form and grow. A study of the velocity of growth of fractures from the m o m e n t of a p p l i c a t i o n of the i m p a c t load to the c o m p l e t e fragmentation of a specimen of any composition or structure is therefore of undoubted interest for developing the theory of rock fragmentation and for d e signing percussive-type machines. Methods of measuring the rate of fragmentation of m a t e r i a l s can be divided into three groups: high-speed photography, and ultrasonic and e l e c t r i c a l methods. High-speed photography by cameras with repeated spark illumination, in conjunction with t h e T b p l e r shadow method and the method of double reflection of light from the fracture surface [1,2], enables us not only to measure the crack propagation rate in o p t i c a l l y transparent materials, but also to investigate internal stresses at the front of a spreading crack. Various authors [3,4] mention the possibility of also studying nontransparent m a t e r i a l s with the aid of light reflected from the plane polished surface of a specimen. Preliminary research r e v e a l e d that the separation of the walls at the apex of a crack is only 0.02 ram, and, even with the highest-quality polishing of the surface of a rock specimen, it is impossible to discern the crack w i t h out high magnification. Developments in ultrasonic defectoscopy enable us to use ultrasonic methods to measure the dimensions of cracks in rocks. However, it is difficult to use the ultrasonic method to study the d e v e l o p m e n t of cracks during fragmentation by i m p a c t , because it is p r a c t i c a l l y impossible to ensure contact between brittle emitters and the specimen or to use immersion liquid baths if the fragments fly apart at a considerable speed. To study the fragmentation v e l o c i t y incrystals and rocks, e l e c t r i c a l methods [5-8] have been suggested: cur~ rent-conducting lines are fixed to the specimen surface, and give a signal at the moment when they are broken by the passage of the crack vertex. As these "signal lines" we use wires or foils glued on to the specimen [6,7], a layer of m e t a l produced by vacuum sputtering [5,8], or Aquadag [8]. Measurement of the crack propagation v e l o c i t y by means of signal lines is c l e a r l y the only feasible method, and shows great promise for research on rock fragmentation by i m p a c t . However, existing systems of measurement have a number of shortcomings which have sometimes led authors to incorrect conclusions [7], and require c r i t i c a l analysis of the possible types of signal lines and recording apparatus. The accuracy and r e l i a b i l i t y of measurements of fragmentation v e l o c i t y are governed primarily by the properties of the materials of the signal lines; considering that the strengths of some rocks are sensitive to moisture and temperature, these materials must satisfy the following requirements: 1) m i n i m u m inertia (i.e., c a p a c i t y to react precisely at the moment when the apex of the growing crack passes). This determines the principal properties of the line m a t e r i a l - h i g h a d h e s i v e c a p a c i t y and brittleness, and low strength. 2) The technology of a p p l i c a t i o n of the signal lines must not alter the properties of the rock. Signal lines obtained by depositing m e t a l on a specimen in a vacuum chamber have given good results with crystals. However, the use of this method in research on rocks involves the use of c o m p l i c a t e d equipment, and high vacuums affect the properties of rocks, reduce their i m p a c t strength, and cause large random errors.
Institute of Mining, Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 64-70, May-lune, 1968. Original article submitted May 16, 1967.
260
Fig. 1
TABLE 1 Material Flint glass Carbon steel LiF crystal Slate Hornblend Quartz Limestone
Fig. 2
Crack speed,
m/see
7506303502500 2070 2200 2000-
2155 1170 1000
2150
Source
[:3] [3] [5] [8] [82 [3] [8]
The use of fine wires or foils as signal lines involves keeping the specimen at a high temperature to get a h i g h quality glued joint. In addition, the glued joint is not sufficiently brittle; the signal line is joined to the rock by a viscous layer of glue, and may break, not at the apex of the developing crack, but at a distance from it as the walls of the crack separate. To verify this hypothesis, we studied the rupture of signal lines made of constantan wire, a l u m i num foil, and VKGS-0 colloidal graphite ( T U - 3 5 - X I I - 3 2 9 61). The crack initiated by the impact of a sharp wedge spread to the center of the specimen, enabling us to study the rupture of lines at the crack apex.
Figure I shows photomicrographs of parts of a specimen (x 60) of siltstone with signal lines of 0.05 m m d i a m eter wire. When the walls are 0.12 m m apart (Fig. la), the insulation breaks but not the wire; when the crack width is 0.06 m m (Fig. lb), the wire has a break which was preceded by considerable plastic deformation; closer to the apex of the crack the signal line is not ruptured (Fig. lc, crack width 0.03 mm). Experiments with lines made of a l u m i n u m foil gave the same results. Clearly, signal lines made of wire or foil cannot give exact information on the time of passage of the crack apex.
261
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Signal lines of finely-dispersed graphite preparations are the best for research on the fragJ,,- B / m t t ~ t l l ~ m e n t a t i o n rates of rocks. These preparations have good adhesion properties, and, after b r i e f drying-out at room temperature, lines m a d e of Fig. 3 them and deposited on the s p e c i m e n surface have low strength and high brittleness. The p h o t o micrograph in Fig. 2 of a part of a specimen near the apex of a crack (wall separation 0.015 ram, m a g n i f i c a t i o n 185) quite convincingly illustrates the virtues of this m a t e r i a l as a signal line. The advantages of graphite m a t e r i a l s also include low cost and e l e m e n t a r y deposition technique for lines of the required thickness on any surface.
3,75,
I
In measurements of the rate of propagation of cracks in rocks, the feasibility of using any particular type of recording device is governed by the probable speed of the crack, the characteristic dimensions of the specimen, and the a t t a i n a b l e rapidity with which the d e v i c e will record the process. The fracture speeds of some solids, including rocks, are listed in T a b l e 1. When the specimen dimensions are 10-20 em the t i m e required for the passage of a crack is c l e a r l y 50-200 ~sec, and it is not possible to use oscillographs of the MPO-2 type, as described in [6,7]. From an analysis of various types of signal lines and measuring equipment, in developing a method of m e a s u r ing the rate of propagation of a crack we used the following: Material of current-carrying signal lines, VKGS-0 c o l loidal graphite preparation; recording apparatus, CR oscillographs with the required sweep times; there must be a large number of signal lines so as to measure the speed and a c c l e r a t i o n of the crack front along its entire path. Our method of measurement was based on a de h a l f - b r i d g e circuit of which the measurement arm was the signal lines in parallel. Rupture of the lines by the apex of the advancing crack l e a d to a stepwise growth of the v o l t age at the input to the oscillograph. Preliminary experiments r e v e a l e d that for accurate measurement of the moment of rupture of the line the h a l f - b r i d g e must be fed by a voltage of order 6-10 V. With higher voltages the arcs formed on rupture of the lines greatly reduced the accuracy of the t i m e measurements. A circuit constructed on the above principles is suitable for work with any high-sensitivity oscillograph, and requires only the d e v e l o p m e n t of a sufficiently reliable circuit for triggering the sweep. Measurement Circuit with OK-17m Oscillograph. Since the h a l f - b r i d g e is fed with a low voltage, it is not convenient to trigger the sweep from the measured signal, in view of the large a m p l i t u d e of the a u t o m a t i c trigger
Fig. 5
262
signal of the device. Triggering of the oscillograph from an external source with closing of the contacts of the t r i g get circuit by the failing weight is also i m p r a c t i c a b l e , because the t i m e between the sweep trigger and the m o m e n t of formation of the crack m a y be much longer than the t i m e required for the crack to traverse the specimen. To trigger the oscillograph at the m o m e n t of initiation of the crack, we developed a circuit acting on the c i r c u i t - b r e a k e r principle. When the growing crack breaks a line of graphite, the small signal from the external source is a m p l i f i e d by a pulse a m p l i f i e r and fed to the trigger terminals of the OK-17m. The final measurement circuit is shown in Fig. 3: A denotes the signal lines, B the trigger sensor. By varying resistances RI* and R2* we select the b e a m deflections with the signal lines switched in and out (thus m o d e l i n g rupture of the lines) so that they fall within the linear part of the a m p l i t u d e characteristic. The t r i g g e r - s i g n a l pulse a n a l y z e r is based on a 6Zh9P pentode. With this circuit, the rate of propagation of the cracks can be measured with various different ways of breaking the specimen and with any type of CR0 which has a h i g h - l e v e l trigger signal and signal v o l t a g e of up to 50 V with independent triggering. Measurement Circuit with S l - 1 9 b Oscillograph. The $1-19b CR0 has a number of advantages over the OK-17m: it has greater (up to 50 ram) vertical beam deflection within the linea r part of the a m p l i t u d e characteristic, p e r m i t ting the use of a greater number of signal lines and a greater accuracy of measurement; it also has a lower trigger signal level for a u t o m a t i c triggering. This p e r m i t s us to dispense with the independent trigger system, increase the r e l i a b i l i t y of the measurement circuit, and move the signal lines closer to the zone of contact of the instrument with the specimen. It also has a much wider range of de a m p l i f i c a t i o n , allowing a lower voltage to be fed to the h a l f bridge, and thus improving the accuracy of measurement. In view of the operating characteristics of the $1-19b oscillograph we m o d i f i e d the circuit described above; this is now (Fig. 4) very simple and r e l i a b l e . In Fig. 4, A denotes the signal lines. Their resistance varies from s p e c i men to specimen, and therefore in simulating rupture of the lines the v a r i a b l e 2.2 k~ resistor is used to keep the 9 beam deflection within the linear range of the a m p l i t u d e characteristic. A sample trace of the rupture of the lines by the passage of a crack, recorded by the $1-19b oscillograph, is shown in Fig. 5. CONCLUSIONS 1. On the basis of the requirements for the m a t e r i a l of signal lines in e l e c t r i c a l methods of measurement and of microscopic investigations of the nature of the rupture of these lines by an advancing crack, the authors show that m e t a l wires and foils are unsuitable for measuring the rate of fracture of a rock. 2. Reliable data on the crack v e l o c i t y in rock specimens can be obtained by using finely-dispersed graphite preparations as line materials. 3. Circuits are developed which can be used to get highly accurate and r e l i a b l e measurements of the d e v e l o p ment of cracks in rock specimens. LITERATURE 1.
CITED
H. Schardin and W. Struth, Neurere Ergebnisse der Funkenkinematographie, Zeitschr. Techn. Physic., No. 18
(1937). 2. 3. 4. 5. 6.
7.
8.
Proceedings of Conference on High-Speed Photograph and Kinematography (Leningrad, 12-15 November, 1957), "Progress in Scientific "Photography;' Vol. 6 [in Russian], Izd. AN SSSR, Moscow-Leningrad (1957). Kh. Shardin, "Research on fracture v e l o c i t y , " in: The Atomic Mechanism of Fracture [in Russian], M e t a l l u r g i z dat, Moscow (1963). A . M . Bueche and A. V. White, Kinematographic Study of Tensile Fracture in Polymers, I. Appl. Physics, 27, No. 9 (1956). I . I . Gilman, C. Knudsen, and W. P. Walsh, " C l e a v a g e cracks and dislocations in LiF crystals," I. Appl. Physics, 29, No. 4 (1958). Yu. V. Gaek, M. F. Drukovanyi, and V. V. Mishin, "The rate of propagation of cracks in rocks and solids, and methods of measuring it," in: Blasting [in Russian], No. 51/8 (1963). P.S. Danchev, Ya. M. Puchkov, and V. A. Vetluzhskikh, "The rate of propagation of cracks in a strong m e d i u m during blasting," Proceedings of Institute of Mining, "Problems in Fragmentation of Rocks by Blasting" [in Russian], Sverdlovsk (1963). V . A . Lagunov and Sh, A. Mambetov, "The rate of propagation of cracks in rock specimens," PMTF, No. 6
(1965).
263