toughness in tensile mode fracture by three-point bending (ASTM, 1972). In the past 30 years, many investigations dealing with crack propagation in brittle rock ...
Rock Mech. Rock Engng. (1997) 30 (1), 59-64
Rock Mechanics and Rock Engineering
9 Springer-Verlag1997 Printed in Austria
Technical Notes Influence of Pressure on the Crack Propagation Under Mode I Loading in Anisotropic Gneiss By
B. V~isfirhelyi Department of Engineering Geology, Technical University of Budapest, Hungary
1. Introduction Recently, fracture mechanics has been applied in the solution of rock engineering problems, especially for competent brittle rocks under hydrostatic pressure of dynamic loading. Fracture toughness is one of the basic parameters in fracture mechanics indicating the ability of rock to resist fracturing, i.e. the initiation and propagation of cracks. Although a number of authors have paid more and more attention to the investigation of fracture toughness of rocks, most of them have conducted their research with tensile loading. The standard testing procedure was proposed for determination of toughness in tensile mode fracture by three-point bending (ASTM, 1972). In the past 30 years, many investigations dealing with crack propagation in brittle rock have employed the well-founded discipline of linear elastic fracture mechanics, LEFM, with great success. Although this theory is based on linear elasticity and it is directly related to the Griffith theory (Griffith, 1924), plastic flow and other non-linear behaviour can occur on a small scale without affecting its predictive success. Purely brittle behaviour is not required and only when the size of the zone of non-linear behaviour at a crack tip cannot be considered small when compared to the crack length, does recourse to fracture theories such as the J-integral (Rice, 1968) become necessary. Recent investigations have measured the fracture toughness, Kc, of the orthotropic gneiss. Moreover, Schmidt and Huddle (1977) and Abou-Sayed (1977) indicated that the apparent fracture toughness of Indiana limestone increases with increased confining pressure. The anisotropic rocks were examined by Afassi (1991). The main objective of the present paper is to show the influence of the confining pressure and the anisotropy on the propagation of crack under mode I.
2. Material Description The object of this research was a rock having anisotropic properties. Gneiss was chosen
60
B. Vfis~irhelyi
for this purpose. The metamorphic rock consists of smali grains and during the metamorphosis the minerals deform in one direction which can be seen with unaided eye. Table 1 shows the physical properties of the rock. Table 1. The physico-mechanical properties of the gneiss Physico-mechanical properties
Index
Modulus of elasticity
E1 E2 = vtz = vzl = v--z3= ol Oz =
Poissou's ratio
Maximal stress
E3
Unit
Result
GPa GPa
41.69 70.05 0.166 9262 0.247 238 267
v13
--
v3~ ~'32
MPa MPa
03
3. Specimen Preparation Extensive specimen preparation is necessary for performing confined fracture toughness tests. This includes initial specimen machining, fatigue pre-cracking, final machining, instrumenting and jacketing. For the best result the specimens were cut from one block. Forty notched three-point bend specimens of gneiss were &y-machined to dimensions in accordance with ASTM standard (ASTM, 1972) (Fig. 1). All experiments were performed on 2 specimens.
~
ti~
I
L =4H
O • i
Fig. 1. Three-point bend specimen configuration used for fatigue pre-cracking
All specimens were 15 (+0.1) mm thick (B) and 25 (-+0.1) mm wide (H) and were machined in the divider geometry in which the crack front is perpendicular to the bedding planes of the material. It was used in the initial phase of the tests in order to facilitate fatigue pre=cracking. It should be noted that all tests were performed on specimens of equal size with nearly equal crack lengths (a) (5 (-+0.1) mm long). However, the size criterion often used for 'valid' tests of Kic requires the crack length to be larger than 2 . 5 (KIc/Gy)2. The measurements were elaborated in cases of anisotropy in the directions 0; 30; 45; 60 and 90 degrees to the horizontal line.
Influence of Pressure on Crack Propagation
61
To perform tests under confining pressure, the specimens had to be jacketed with flexible material that would cover all machined surfaces including the notch, but not enter the crack.
4. Test Equipment The experimental measurements were performed at the rock mechanical laboratories of the Technical University of Lorraine in Nancy, France under the leadership of Prof. F. Homand. The pressure vessel used was specifically designed for confined fracture toughness tests (Fig. 2).
Fig. 2. Schematictest configuration The test chamber is 15 cm in diameter and 30 cm long with a working pressure of 100 MPa. The confining pressure was supplied and controlled using 0, 10, 30 and 60 MPa servo-controlled intensifier. A light hydraulic oil was used as the pressurising medium. The load was controlled by an electric instrument made for this purpose. The instrument was located between the head and the specimen, and due to its deformation all the measurements had to be calibrated. Static loading was chosen and the loading velocity was 0.3/~m/s.
5. Test Procedure First, the jacketed and instrumented specimen was fastened inside the pressure vessel. Confining pressure was applied to the specimen while maintaining a slight tensile load on the external load cell. The specimen was then loaded to failure at a constant rate of increase in crack opening displacement.
62
B. V~s~irhelyi
The apparent fracture toughness, KQO was determined from each test by using the following expression (Srawley, 1976):
3PS a
W 1.09 - (1 - a)(2.15 - 3.93a + 2.7a 2) f(a) =
(1)
(1 + 2c~)(1 - 003/2
where P was the maximum load measured. 6. Results and Discussion The increase in fracture toughness of gneiss with increased confining pressure is shown in Fig. 3 and Table 2. 80 70 60 50 40 3020 10 0
I
I
I
~
I
/
10
20
:30
40
50
60
p IMF~]
Fig. 3. Fracture toughness in function of the confiningpressure The equations are shown below in function of the confining pressure with the variances 0r): 0~ (a = 2.663) K~c = 8.551 § 1.084P 30~
Kxc = 9.819 + 1.078P
(or = 3.374)
45~
KIC
=
10.288 + 1.070P
(a = 0.642)
60~
Klc= 6.964 + 1.124P
(o = 0.514)
K~c = 8.048 + 1.048P
(or = 1.756)
90~
Influence of Pressure on Crack Propagation
63
Table 2. Experimental data Direction 0~
Press• [MPa]
[NIKlCmm312 [ / ]
0 10 30 60
6.63, 18.95, 45.98, 73.77,
Average [N/ram3/2]
7.03 18.21 45.68 68.91
6.83 • 18.58 • 45.83 • 71.34 +
0.20 0.37 0.15 2.43
10 30 60
10.03, 9.34 15.43, 19.44 47.96, 47.37 71.43, 73.04
9.69 • 17.44 • 47.67 • 72.23 •
0.35 2.00 0.30 0.80
45~
0 10 30 60
11.18. 10.07 21.33, 18.81 42.92, 43.55 71.10, 77.29
10.62 • 20.07 • 43.23 • 74.20 •
0.55 1.24 0.22 3.10
60~
0 10 30 60
6.39, 5.85 18.47, 19.97 38.56, 42.79 75.65, 72.80
6.12 • 19.22 • 40.68 • 74.22 •
0.27 0.75 2.11 1.43
90~
0 10 30 60
7.39, 6.87 19.78, 17.67 44.36, 41.82 65.55, 74.13
7.13 • 18.73 • 43.09 • 69.84 i
0.26 1.05 1.27 4.29
30~
0
I suppose that the c o n n e c t i o n b e t w e e n the toughness intensity factor and the hydrostatic pressure is linear. This assumption is supported by m y investigations. A c c o r d i n g to m y tests there are not large differences a m o n g the tangents ( 1 . 0 5 1.12) of the lines. T h e a v e r a g e v a l u e and the v a r i a n c e are 1.081 and 0.024, respectively (V~sfirhelyi, 1995). The direction o f anisotropy does not influence the slope of the line. S i m i l a r e x p e r i m e n t s w e r e done by S c h m i d t and H u d d l e (1977) on Indiana limestone and by Terrien et al. (1984) on sandstone. E x a m i n i n g their published results of FortT~
[kN]
P = 60 MPa
#~ \~ 4-
1
/~
P = 10 M P a /
~
-
0.5
P = 30 MPa
1
I "! i I i 1.5 2 displacement [ram]
Fig. 4. Force - displacement diagrams at different confining pressures
I 2.5
64
B. Vfis~rhelyi: Influence of Pressure on Crack Propagation
experiments I have found that the line defined above can be fitted very closely and the value of the slope characterises the rocks. As confining pressure increases, toughness increases and in the post critical domain the yield strength is expected to decrease. The measure of decrease is in strong connection with the confining pressure. This fact can be seen on the force-displacement diagrams (Fig. 4).
Acknowledgements The author is indebted to Madame F. Homand for her expert help in performing the experiments. The work has been made possible through a grant of the French Government Scholarship (Bourse du Gouvernement Fran~ais - BGF).
References Abou-Sayed, A. S. (1977): Fracture toughness KIC of triaxially loaded Indiana limestone: In: Proc. 17th U.S. Symp. Rock Mechanics, Keystone, Colorado, 2 A3-1-2 A3-8. Afassi, F. (1991): Caract6risation de la R6sistance/t la propagation des fissures dans une roche anisotrope: le schiste. Thbse de Doctorat; Universit6 des Sciences et Techniques de Lille. ASTM, American Society for Testing and Materials (1972): Tentative method of test for plane strain fracture toughness of metallic materials. ASTM Designation E399 72T, Annual Book of Standards, Part 31. Griffith, A. (1924): Theory of rupture; In: Proc., 1st. Int. Congress Appl. Mech., Delft, 55-63. Rice, J. R. (1968): A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379. Schmidt, R. A., Huddle, C. W. (1977): Effect of confining pressure on fracture toughness of Indiana limestone. Int. J. Rock. Mech. Min. Sci. 14, 289-293. Srawley, J. E. (1976): Wide range stress intensity factor expression for ASTM E399 standard fracture toughness specimens. Int. J. Fract. Mech. 12, 475-476. Terrien, M., Sadra, J. P., Chaye D'Albissin, M., Bergues, J. (1984): Experimental study of the anisotropy of a sandstone and a marble. Coll. CNRS, Villard de Lans. Vfisfirhelyi, B. (1995): l~tude de l'influence de la pression de confinement et de l'orientation de la foliation sur la propagation des fissures dans un gneiss. Rapport de Stage, INPL, ENSG, Nancy. Authors' address: B. V~sfirhelyi, Department of Engineering Geology, Technical University of Budapest, Kiss J. alt. u. 34, H-1124 Budapest, Hungary.
