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Ouchterlony F., SveBeFo, Lulea, Sweden. (finn.ouchterlony@svebefo.se)

Stephansson O., Royal Institute of Technology, Stockholm, Sweden. (Ove.Stephansson@t-online.de, ove@aom.kth.se)

Sun Z., South Central University, Changsha, China. (sunzongqi@sina.com)

It is found that under simple loading conditions, a crack is formed by crack propagation, bifurcation and looping. Bifurcation means that there is no more than two branches at any point on a crack, and looping means that two branches grow to meet each other at a point ahead. The bifurcation phenomenon may be due to the specific loading conditions in which two equal and opposing forces were applied. The crust of the earth is subject to firstly, such two simple east-west stresses due to the self-rotation around its north-south axis, and secondly, the slight pulling force in the north from outside the solar system. The combination of the two forces have caused all the continents of the earth to slowly drift towards the north pole, causing frictions between the continents. The observed crack growth patterns help explain why the Pacific and Atlantic oceans as well as the main valleys and rivers in America, such as the Mississippi River and the Rocky Mountain Divide, are orientated roughly in the north-south direction. For the Kallax gabbro, the fluorescent dye was confined within the crack and it penetrated to the very crack tip. But, for the Bjorka marble, the fluorescent dye permeated through the grain boundaries and even the grains themselves. The fracture toughness of gabbro is 2 to 3 times that of marble, and the Young’s modulus of gabbro is about 3 times that of marble. The acoustic emission count rate for the specimens of Kallax gabbro was about 10 times that of Bjorka marble. Thus, a tougher rock emits higher acoustic emission count rate. At unloading, the acoustic emission count rate disappeared quicker in the marble than in gabbro specimens.

The standard Short Rod Chevron Notched Core Specimen of rock specified in the ISRM suggested method for fracture toughness testing by the International Society for Rock Mechanics was employed in the investigation (Fig. 1). For the Kallax gabbro, cores were bored from large blocks of rock as shown in Fig. 2. Bjorka marble specimens of Series 3 were prepared from existing cores of marble obtained from the Bjorka mine in central Sweden. The Kallax gabbro is a black hard rock and the Bjorka marble is a white intermediate hard rock.

Two series of Kallax gabbro were made. Series 1 testing was a trial by which an appropriate experimental method was to be found for the other series of testing. The specimens in Series 1 were 71.4 mm diameter and were drilled from block A of Kallax gabbro whose composition is as follows:

In order to permit load application, aluminum alloy end plates were glued to the open end of a specimen as shown in Fig. 3. The two plates also served as fastening connection when the specimen was later sawed into slices after the testing. An Instron Model 1342 type stiff and servo-controlled testing machine with a loading capacity of 100 kN was used to obtain the complete load versus displacement curve. The tests were controlled by means of the crack mouth (notch mouth) opening displacement (CMOD). Load versus CMOD curves were plotted with pen plotters. A string was suspended from the cross head of the press to hold the specimen. The weight of a gabbro specimen was 1. 26 kg and that of a marble specimen was 1.36 kg.

The Dunegan/Endevco 3000 Series type of AE device was used (Fig. 3). A D9203 AE Transducer and a 80lP Pre-amplifier were utilized to receive the AE signals and a Model 301 Totalizer was used to measure the ring-down count rate of the AE signals.

In Series 3 tests, an additional AE parameter, the amplitude distribution, was recorded by utilizing the Model 920 Distribution Analyzer and the Model 921A Amplitude Detector.

The AE ring-down count rate is the number of waves whose amplitudes are greater than a reference value. Such an AE count rate is a relative value and its magnitude also depends on the gain (or magnification) of the measuring device with a preset reference value. In the Model 301 Totalizer, the reference value was set internally and cannot be adjusted. The AE instrumentation included the following components:

Multiplier: 100 for Series 1 and 2 gabbro specimens, and 10 for Series 3 marble specimens.

Filter: 0.3 - 1.0 MHz.

Plotting mode: MEM (Step plotting).

Gain: 40 dB (50 dB for Spec. 1-4).

Time Span: 1 Second.

From literature research, it is estimated an AE frequency range of 0.1 to 1.0 MHz was representative of AE signals emitted from crack growth in a rock material. This AE frequency range selected does not include the signals from the opening mode of micro-cracking, whose corresponding AE emission is of a lower frequency, but it does include those from the sliding mode of micro-cracking which follows the opening mode of micro-cracking. It also certainly includes the AE from crack coalescence that occurs in the segment of inter-locking cracks.

In the present investigation, a Filter Range of 0.3 to 1.0 MHz on the Totalizer was selected for crack growth detection. The transducer, having a greased contact face was attached and wrapped on to the back face of the specimen by tape (Fig. 3).

In tests on Series 1 gabbro specimens and Series 3 marble specimens, two recorders were used to record the test results. An X-Y recorder plotted the load and AE versus CMOD curves, and a Y-t recorder plotted the load and AE versus time curves. In Series 2 tests on gabbro specimens, however, only one X-Y recorder was used to plot the load and AE count rate versus CMOD curve. In Series 2 tests, the AE signals during reloading were separated from those during unloading by moving the plotting pen (Fig. 3.10).

Every specimen was loaded to a different load level whose position on the complete load F versus CMOD curve is indicated by the numbers shown in Fig. 4.

Figure 4. The unloading stages shown on a typical load versus crack mouth opening displacement curve, where (1) "Beginning" of non-linearity; (2) "Middle" of the non-linearity region; (3) "Peak" load; (4) Maximum AE point in the post peak region; and (5) "End" of the complete curve.

After the predetermined load was reached, a fluorescent dye penetrant (Penetrant ZL. 22A, ZYGLO) was injected into the notch and crack while the crack was open. Two methods of injecting the fluorescent penetrant had been tried and compared in Series 1 tests to find a suitable method for the next two series of tests.

In the first method, the control-module was transferred immediately from strain control to position control in which the mean level was adjusted continuously during the foregoing strain control. It was then possible to avoid load changes due to the transfer. In the second method an unloading-reloading cycle was performed before the transfer of the control module, so that the compliance of a specimen after a certain crack growth can be calculated from the unloading-reloading curve. After the control transfer, the fluorescent penetrant was injected into the notch from the pressure penetrant can sprayer with its long needle inserted into the notch.

After completing the Series 1 tests, it was found that with the second method, the fluorescent penetrant penetrated right to the crack tip. In tests of Series 2 and 3 specimens, the second method alone was adopted, but it failed in Series 3 marble specimens because the dye also diffused into the rock pores.

After the injection of the fluorescent penetrant, the specimen was removed from the test machine. With the sides of the notch sealed by a tape, an epoxy (HY 994, AW 136 H) mixed with a small quantity of fluorescent liquid was injected into the notch from the front face of the specimen. This precaution prevented further crack growth due to any disturbance before or during cutting. The use of additional fluorescent liquid made the notch visible under ultra-violet light.

An epoxy stabilized specimen was bolted to a thick steel plate through the aluminum alloy plates in order to be cut in a diamond wheel rock cutter (Fig. 5). Longitudinal slices perpendicular to the notch plane were first cut, then, the front end of the specimen was cut off to obtain the separate slices (Fig. 5). The width of the cutting was 2.5 mm. The thickness of the slices was between 4 and 8 mm (Fig. 6).

The positions of the slice surfaces in a specimen were determined by measuring the thickness of every slice after cutting. The accumulated error in surface position due to adding the thickness and the cutting width for all slices was less than 1 mm. This is acceptable compared to the precision of the crack length measurement, which was accurate within 1 mm. The "measured crack length (a)" on a surface is the measurable length of the crack projected to the notch plane, plus the corresponding notch length.

The slice surfaces were then examined and photographed under ultraviolet light which made the fluorescent penetrant appear bright blue. The surfaces of the slices were photographed on colour film by two methods in the Series 1 specimens. In the first

(b)

(c)

Figure 5. Slicing of a Kallax, where (a) shows the scheme, (b) the actual longitudinal cutting, and (c) the actual transverse cutting.

Figure 6. Slices of a Kallax gabbro specimen in a card box.

Figure 7. Setup for crack measurement under ultraviolet light, where the slice stand is on the left and the ultraviolet light lamp is on the right.

method, a standard camera was used (Fig. 7). In the second method, an optical microscope was used. In photos obtained from both methods, a transparent millimetre scale was placed on the slice surface along the crack.

The optical microscope has a maximum magnification of 50, but the photos were taken only with 6-fold magnification. A number of successive frames had to be taken to obtain the complete picture of the crack on a slice. By using the measurement scale, frames of a crack could be readily assembled. Higher magnifications of the microscope were occasionally applied to examine a crack in greater detail.

After crack length measurements for specimens of Series 1 had been completed, it was found that no significant difference in the measured crack length existed between the measurements from the photographs obtained by the two methods described above. In Series 2, measurements were therefore taken by using the first method (Fig. 7). Slides photographs were taken instead of prints so that measurements could be taken easier by using a slide projector.

The error in measured crack length was around 1 mm, or between 0.01 and 0.02 of the ratio of the crack length to specimen diameter (a/D). It may be larger if the tip positions were not clearly visible due to a thin fluorescent cloud at the crack tip. Such tip error was noted in taking the measurements.

The crack length (a), measured by the method described above, is therefore dependent on the penetrating ability of the fluorescent penetrant. It was certain that it reached further than human visibility under a microscope. It was believed that this length contains most, if not all of the damage zone (micro-cracking zone). The measured crack length in this work was therefore probably longer than that measured by Labuz et al. (1) in granite where a dye was not used.

The method of crack identification used in gabbro specimens, in which fluorescent penetrant was used, failed in the marble specimens. This was because both types of fluorescent dye had permeated through the rock surrounding the crack. The location of the crack tip could not therefore be determined under the ultra-violet light, see Fig. 8.

Despite our inability to measure the full crack length, we tried to measure the identifiable part, which was visible by naked eyes under normal light (Fig. 9) after spreading a film of water on the slice surface. This measurement is referred to as the "rough measurement". It should be mentioned that a microscope did not help to trace a crack tip longer on a rough surface than with the naked eyes.

It was found that by polishing the surface of a slice and by use of an optical microscope with normal light, the length of the crack could be traced a little further than was possible with the rough measurement. However, the presence of grain boundaries made the precise location of the crack tip difficult to determine. The error in the determination of crack tip location and thereby in crack length measurement may amount to 3 mm in the crack length or 0.04 of the ratio of the crack length to the specimen diameter (a/D). It should be noted that a crack on a marble surface was easier to trace than on a gabbro specimen under normal light.

The polishing was performed with grinding particles having mesh number 600 in the PM2 Precision Polishing Machine (LOGITECH LTD, Scotland). Because of the difficulty of surface polishing, only one face of a slice was polished and measured. The crack on a polished surface was examined carefully under a 6 to 100-fold magnification to locate a crack tip. A larger magnification did not help due to the presence of grain boundaries. It is believed that the crack length measured on a polished marble surface is probably similar to the one measured by Labuz et al. (1) in that it includes only a part of the fracture process zone (micro-cracking zone).

Figure 8. A marble slice under ultraviolet light.

Figure 9. A marble slice under normal light.

The rock mechanics laboratory had years of experience in preparing thin rock sections that have a thickness measured in micrometers. The thin sections had to be impregnated with a fluorescent dye for it to be observed under the microscope. This technique could not be used for granite and marble because the pores would be filled with the fluorescent dye such that the created cracks are not identifiable. The Kallax gabbro had basically no preexisting pores such that the fresh micro cracks were clearly visible under a microscope.

The thin section shown in Fig. 10 was prepared from Specimen 1-7 of Series 1. The specimen had been loaded to the post-peak regime before it was cut. This author did not participate in the preparation of the thin section. I selected one center slice of Specimen 1-7 and instructed to cut the thin section from face B at the created crack tip region where the fracture process zone could be examined. Since the thin section must not have a run-through crack, I also asked that the one side of the thin section should be the same as the back face of the specimen. This back face could be used as a reference line for crack positions. The thin section was about 36 mm in length along the crack.

Figure 10. Thin section of Kallax gabbro (about 36 mm in length), from bottom surface for Specimen 1-7 of Fig. 13. (Note that the black arch shape in the lower right corner is on the metal stand behind the thin section. This indicates that the thin section is transparent.)

The thin section was impregnated with fluorescent fluid in vacuum. The fluorescent fluid was composed of fluorescein sodium powder, alcohol and an epoxy of low viscosity (epo-tek, Sweden). It was then examined and photographed under a microscope with magnifications of 10 or 70, under ultra-violet and/or polarized light.

The ligament length from the crack tip that was located in a feldspar crystal (see Fig. 7-5B in Appendix 7), to the back face of the specimen was measured under the microscope. The length agreed well with that measured on the ordinary photo of the corresponding slice, see Fig. 7-2. The difference, was within 1 mm. We were therefore confident that the fluorescent penetrant injected into the notch during testing did reach the very crack tip. Since the specimens were placed in the upright position for the fluid to reach the crack tips under gravity prior to cutting, it was unknown how long it took to reach the crack tips.

Photographs of cracks on all slice surfaces for Specimen 2-1 of Series 2 tests are presented in Fig. 11. Crack length was measured with a plastic millimeter scale regardless of the crack waviness, but the maximum deviation from the notch plane was noted down. The curve connecting the crack tip positions measured on different slice surfaces of a specimen is called the crack front. Measured crack fronts in the six specimens of Series 2 gabbro specimens are presented in Fig. 12.

Figure 12. Crack front in gabbro specimens of Series 2.

Figure 13. Photographs of a few slice surfaces for Specimen 1-7 of Series 1 tests.

Figure 14. Surface 2A of slice 2 from Spec 1-7 of Fig. 12 with a larger magnification.

Figure 15. Center slice of Specimen 1-4 of Series 1 that was photographed under normal light. Note that the right hand portion of the plastic millimeter scale reflected light to appear in white color.

Photographs of a few slice surfaces for Specimen 1-7 of Series 1 are presented in Fig. 13. The surface 2A of Spec 1-7 (top of Fig. 13) was also photographed in a larger magnification (Fig. 14). Fig. 15 shows a center slice of Specimen 1-4 of Series 1 that was photographed under normal light. This specimen was loaded nearly to the end of the complete load-displacement curve. An open planar crack was clearly visible with the naked eyes, but a small ligament at the crack tip was not so. However, The fluorescent dye was visible in this ligament, and the crack front reached the free back face for the most part except for a small portion.

It can be seen from the photographs that the cracks in gabbro specimens are like rivers with lots of bifurcation. The fluorescent dye has a low viscosity and flowed to the crack tips that were not visible by naked eyes or in an ordinary optical microscope.

Detailed analysis and calculations of Series 1 and 2 gabbro specimens were performed by Yi (2,3). The main conclusions were as follows:

1. the crack length calculated from the unloading tangent compliance equals approximately the traction free crack length;
2. the crack length calculated from the secant tangent compliance equals approximately the entire crack length; and
3. the difference between the two equals approximately the fracture process zone length. The fracture process zone length in the 71.4 mm diameter Short Rod gabbro specimens was approximately 10 mm.

Crack fronts in the five specimens of Series 3 marble specimens are presented in Fig. 16. Data points for polished surfaces were only half as much as for the rough surfaces because only one face of a slice was polished. Although, cracks on polished faces could be traced 1 to 4 mm further than on rough faces in some cases, statistically, the two types of measurements were not significantly different from each other.

Unlike the case for gabbro specimens, the measured crack length for marble specimens equals approximately the crack length calculated from the unloading tangent compliance (3). In other words, the fracture process zone was not identifiable with this experimental technique. This could be due to either the different material properties or the different crack length measurement technique. It was also observed that the cracks in marble specimens deviated less from the notch plane than in gabbro specimens. This was probably due to less brittle or more ductile material property for marble.

(a)

(b)

Figure 16. Measured crack fronts in Bjorka marble specimens, where (a) on rough surfaces and (b) on polished surfaces.

The thin section as shown in Fig. 10 was made from the B face of one of the center slices of Spec.1-7 of Series 1 (Fig. 13). Fig. 17 focused on the last bifurcation point. It was approximately 12 mm from the back face of the specimen. There were plenty of crack bifurcation and looping. From observations of all specimens, it was clear that only one of the two major branches would reach the back face of the specimen if it were loaded further. Since the thin section was impregnated with fluorescent dye after it was made, micro-cracks that are not connected to the main crack are now visible. It is seen that the looping and the bifurcation did not occur on grain boundaries, instead, they occurred within the grains. It was estimated that 99% of the crack ran through the grains, and only a small proportion of crack ran along grain boundaries.

Fig. 18(top) shows that the single crack also had some minor bifurcation, and (bottom) shows that the loop before the big bifurcation point had a small loop in it. The fact that bifurcation rather than multi-branching occurred at a certain point remains to be explained. It may be a result of the fundamental laws of nature (like the bifurcation of living cells). It may also have something to do with the binary loading method (i.e. specimen was loaded by two equal and opposing forces).

In Figs. 17 and 18, we find that to the crack mouth side, there is a dominant crack despite the looping and bifurcation, while near the crack tip, after the last big bifurcation point, a dominant crack has not yet formed. The last 12 mm length might account for the fracture process zone. Fig. 19 shows the last major bifurcation point of Fig. 17 in higher magnifications. Fig. 20 shows the very tips of the last two major branches.

Microscopic observation of a marble slice under ultra-violet light and ordinary transmitted light was performed on some of the polished marble slice surfaces at a magnification of up to 150. It could be seen that the fluorescent dye had permeated through the grain boundaries as well as most of the grains in the surrounding of the crack and notch. It has been observed that on a polished surface of marble under the transmitted light, very few cracks could be seen on the grain boundaries. This is true even though more fluorescent dye appears on the grain boundaries than inside the grains themselves. This implies that dye spreading is not due to the presence of micro-cracks but due to the inherent property of the material.

Figure 17. The last big bifurcation of the crack, where the top picture was photographed with polarized light and the bottom picture with transmission ultra-violet light, both Mag. 10. Note that the specimen back face is situated in the north of the pictures, and the notch plane is situated to the east of the cracks.

Figure 18. Further magnified segments from Fig. 17 (bottom photo) with reflected ultra-violet light, where the top picture shows the single crack located below the large loop, and the bottom picture shows the segment at the big bifurcation point; Mag. 70.

Figure 19. Magnified segments of the crack under both polarized and ultra-violet light, where the top picture shows the two major branches immediately after the big bifurcation point in Fig. 17, and the bottom picture shows the loop before the big bifurcation point; Mag. 70.

Figure 20. The very tips of the two major branches under both polarized and ultra-violet light, where the top picture for the left branch of Fig. 17, and the bottom picture for the right branch; Mag. 70.

Figure 21. Load versus CMOD and AE count rate curves for Specimen 2-1 of Series 2 tests.

Fig. 21 shows the plots from Specimen 2-1 of Series 2 testing. The acoustic emission parameters are explained as follows:

"F( iAE)" is the load at AE initiation, at which the first AE signal, whether small or large, appears. In the Series 2 tests, it was observed that after initiation of AE, there was normally a period of 20 seconds of AE silence, after which AE increases continuously. We define the end of the period of AE silence as the substantial AE point, whose load level is denoted "F(AE)".

Once unloading begins, the AE count rate decreases suddenly to a small magnitude that lasts for a very short period of time. The load on the unloading curve, at which the residual AE terminates, is called "AE-stop".

If we examine the load versus displacement and load versus time curves in Fig. 22 (a) and (b), we see the maximum AE occurred in the post peak load regime. We denote this point as AEmax. We denote the point at unloading as Fu. We see that there is very little AE at the beginning of the reloading, where the curve has a relatively large curvature compared to the one that follows. The is accompanied by pronounced AE. The former curvature is obviously due to the crack tip non- linearity. The load at which the pronounced AE appears is called the AE-start.

In Series 1 tests, the period of AE silence described earlier is not apparent and F(iAE) and F(AE) are poorly defined. This was because the loading rate was twice as high as for Series 2 tests and the plotting scale on the CMOD axis was too large to pick out the F(iAE) and F(AE) points. Note that Series 1 tests were trial tests.

The above defined parameters were measured for all the tests and presented in tables (Yi 1987). The following observations were made:

In Series 2 tests, the ratio of F( iAE) to the peak load, F(iAE)/Fmax , varies between 21% and 30% with a statistical value of 26 +- 5% (5 data). The ratio of F(AE) to peak load, F(AE)/Fmax, varies between 45% and 63% with a statistical value of 55 +- 7% (7 data). The F(AEmax)/Fmax ratio varies from 66% to 53%. The ratio, AE-stop/Fu, varies between 84% and 92% with a statistical value of 90 +- 3% (7 data) in Series 1 and 2 tests. The AE-start/Fu ratio is 56% in Spec. 1-5 test and 57% in Spec. 1- 7 test. In Series 2 tests, reloading was stopped prior to the occurrence of any AE.

The ratio F( iAE) /Fmax varied between 21% and 32% with a statistical value of 28 +- 6% (5 data points). This value agrees with the one in the Kallax gabbro specimens of Series 2. The ratio, F(AEmax)/Fmax, is 70% for Specimen 3-5. This agrees with the ones in the Series 2 Kallax gabbro specimens. The ratio, AE-stop/Fu, is 96% and 94% respectively for Specimen 3-2 and 3-4. These values are slightly higher than for specimens of Kallax gabbro. This means that AE stopped all most immediately at unloading in marble specimens.

In the Series 3 tests on marble specimens, the substantial AE point F(AE) as defined for Series 2 tests on gabbro specimens was not well defined in all the specimens. The magnitude of the AE count rate in the marble specimens was 1/10 of that in gabbro specimens.

Barker (4) demonstrated that a crack front in the short rod specimen of fused quartz has convex curvature toward the crack mouth (specimen front face), and the magnitude of the curvature decreases as the crack grows. However, in his compliance calibration, the crack front was approximated by a straight line that is between the top and the base of the curvature. Our crack measurement method was not sufficiently accurate to make a conclusion in this aspect.

Results from the study of specimen size effects of fracture toughness were presented by Yi et al. (5) and Yi (3). The level I fracture toughness is a function of peak load and specimen geometry. The Kallax gabbro used for the present study of crack growth is slightly different from that used for the study of size effects. For the present study, the level I fracture toughness for Kallax gabbro and Bjorka marble was 3.25 +- 0.22 (gabbro block no. 1), 2.63 +- 0.13 (gabbro block no. 2), and 1.30 +- 0.20 (MN m^-1.5), respectively. In other words, Kallax gabbro is more than twice as tough as Bjorka marble. The corresponding Young’s modulus values are: 107 +- 5 (6 data), 81 +- 4 (6 data), and 33 +- 3 (5 data) MPa, respectively. Clearly, the marble is a much softer material than the gabbro.

Yi used an aluminum specimen to calibrate the evaluation method for Young’s modulus (3). Afterwards, a Kallax gabbro specimen was tested and the obtained Young’s modulus was 81.2 GPa. Alm obtained a Young’s modulus of 98.9 GPa for Kallax gabbro using three point bend specimens and by uniaxial compression (6). Alm also obtained a uniaxial compressive strength of 279MPa and tensile strength of 18.8 MPa for the Kallax gabbro.

Ouchterlony and Sun obtained a fracture toughnes of 1.87 +- 0.15 MN m^-1.5 and Young’s modulus of 86 GPa for Ekeberg marble (7). Although this marble is similar to Bjorka marble in mineral composition, but its grain size is only half that of Bjorka marble.

The magnitude of the AE count rate in the gabbro specimens was ten times that in marble specimens. This means that a tougher rock emits a higher AE count rate, which agrees with corresponding results for steel alloys (8).

For Kallax gabbro, the fluorescent penetrant proved to be an ideal dye for identifying a fresh crack. Injected while a crack is open, it penetrated to the very crack tip, which renders the measurable crack length to contain most, if not all of the damage zone (micro-cracking zone). For Bjorka marble, the fluorescent penetrant permeated through the grain boundaries and even the grains themselves.

The small AE signals remaining immediately after unloading, as indicated by AE-stop, could be due to the fracture process zone that is not like an open, traction free crack. AE stopped all most immediately at unloading in marble specimens. It was also noted by Yi that the unloading curve for Bjorka marble was more non-linear than for Kallax gabbro (3).

The fracture process zone in Kallax gabbro is likely different from that in Bjorka marble. The former is likely more brittle or less ductile than the latter.

The maximum AE occurs in the post peak load regime at a load level of about 55% of the peak load, which is roughly at Stage 4 on the load versus displacement curve (Fig. 4). This could indicate that the fracture process zone length increased after the peak load was reached. This could imply that the fracture process zone becomes important only in the post peak regime, but not in the pre-peak regime that is mostly elastic.

A crack in Kallax gabbro is formed by crack propagation, micro-cracking, bifurcation and looping. Bifurcation means that there is no more than two branches at any point on the crack, and looping means that the two branches grow to meet at a point ahead. The fact that no more than two branches occur at any point may be a direct result of the simple tensile loading conditions in which two equal and opposing loads were applied. The crust of the earth is subject to firstly, such two simple east-west forces due to the self-rotation around its north-south axis, and secondly, the slight pulling force in the north from outside the solar system. The combination of the two forces have caused all the continents of the world to slowly drift towards the north pole, causing frictions between the continents. The observed crack growth patterns help explain why the Pacific and Atlantic oceans as well as the main valleys and rivers in America, such as the Mississippi River and the Rocky Mountain Divide, are orientated roughly in the north-south direction. A dominant traction free crack is present in the first segment of a crack. The segment behind the crack front is composed of inter-locking cracks and micro-cracks (damage zone). This last segment probably accounts for the Fracture Process Zone.

If a crack in Kallax gabbro were compared to a river, the crack mouth would be like the river mouth at the sea. The two have similar features of looping and bifurcation.

Crack propagation and rock damage are very important areas of research in rock mechanics and earthquake research. The fact that the fracture process zone becomes significant in the post peak regime and that it is closely associated with acoustic emission has important implications in mine rockburst prevention and prediction as well as earthquake engineering. The pattern of crack growth found in this work can be applied to rock blasting, treatment of rock slabs as construction material, rock crushing in mineral processing and road construction, and manufacturing of rock drilling machinery, etc..

The main conclusions are:

(1) For Kallax gabbro, the low viscosity fluorescent dye proved to be an ideal dye in identifying a fresh crack. Injected while the crack was open, it reached the entire crack and the very crack tip. The measured crack length contained nearly all the damage zone with interlocking micro-cracks. A crack is formed by crack propagation, bifurcation and looping. The interlocking fracture process zone length is about 10 mm.

(2) For Bjorka marble, the fluorescent dye permeated through the grain boundaries and even the grains themselves.

(3) The acoustic emission count rate for the specimens of Kallax gabbro was about 10 times that of Bjorka marble. The fracture toughness of gabbro is 2 to 3 times that of marble, and the Young’s modulus of gabbro is about 3 times that of marble. Thus, a tougher rock emits higher acoustic emission count rate.

(4) For both Kallax gabbro and Bjorka marble, the maximum acoustic emission count rate occurred in the post peak load regime. This implies that the fracture process zone and the acoustic emission become important only in the post peak load regime, but not in the pre-peak regime that is mostly elastic. If applied to earthquake prediction, this implies that the seismic waves are emitted immediately after the peak stresses at the source are reached.

Acknowledgements:The research work was completed at the Department of Mining and Underground Construction, Lulea University, Sweden. Berit Alm, Josef Forslund, Ulf Mattila, Bergstrom Kjell and others provided assistance in the laboratory. Olofsson Goran provided secretarial assistance. Peter Digby helped with the English language for the Licentiate thesis.

[1] Labuz J.F., Shah S.P. and Dowding C.H., "Experimental Analysis of Crack Propagation in Granite". Int. J. Rock Mech. Mining Sci., Vol. 22, No.2, pp. 85-98 (1985).

[2] Yi X., "Fracture Process Zone (FPZ) in Short Rod Specimens of Kallax Gabbro". In Chinese Journal of Rock Mechanics and Engineering. Academic Periodicals and Books Press. 8(3), 210-218 (1989).

[3] Yi X., Fracture Toughness and Crack Growth in Short Rod Specimens of Rocks. Licentiate Thesis, 1987:06L,139p (1987) (Lulea University, Sweden).

[4] Barker L. M., "Canpliance Calibration of a Family of Short Rod And Short Bar Fracture Toughness specimens". Eng. Fracture Mech., Vol. 17, No.4, pp. 289-312 (1983).

[5] Yi X., Sun Z., Ouchterlony F. and Stephansson O., Technical Note: fracture toughness of Kallax gabbro and specimen size effect. In Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 28, No. 2/3, pp. 219-223 (1991).

[6] Alm O., "Results from Mechanical Testing of Six Different Rock Materials". Report EM 1983:05, pp. 24 and 29 (1983) (Lu1ea University of Technology).

[7] Ouchter1ony F. and Sun Z., "New Methods of Measuring Fracture Toughness on Rock Cores". First Int. Symposium on Rock Fragmentation by Blasting, Editor: Holmberg R. and Rustan A., Lu1ea, August 22-26, pp. 199-233 (1983).

[8] James L.S. and George A.H., "Investigation of Acoustic Emission during Fracture Toughness Testing of O1evron Notched specimens". O1evron Notched specimens, AS'IM STP 855, pp. 205-233 (1984).