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The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks
International Journal of Rock Mechanics & Mining Sciences 56 (2012) 15–26
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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks N. Erarslan n, D.J. Williams Golder Geomechanics Centre, School of Civil Engineering, The University of Queensland, Australia
a r t i c l e i n f o
abstract
Article history: Received 26 August 2011 Received in revised form 9 April 2012 Accepted 24 July 2012 Available online 13 August 2012
This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I fracture toughness response to static and cyclic loading, as a function of the applied load. Both the static and cyclic loading tests were carried out on Cracked Chevron Notched Brazilian Disc (CCNBD) rock specimens. Two different types of cyclic loading were applied: (a) cyclic loading with constant mean level and constant amplitude, termed sinusoidal cyclic loading and (b) cyclic loading with increasing mean level and constant amplitude, termed increasing cyclic loading. The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (KIC) of 46% was obtained for the highest amplitude increasing cyclic loading test. Conversely, for sinusoidal cyclic loading, a maximum reduction of the static KIC of 29% was obtained. Detailed scanning electron microscope (SEM) examinations revealed that both loading methods cause fatigue in the CCNBD specimens. When compared with static rupture, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular fracturing and transgranular fracturing. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Rock fracture toughness Rock fatigue Increasing cyclic loading CCNBD SEM
1. Introduction Techniques for projects including the design and construction of underground openings, supports and rock pillars as well as drilling, blasting and haul roads are based on an understanding of the mechanical behaviour of rocks under various loading conditions. Rock materials are discontinuous at all scales. At the microscale, defects causing stress concentrations include microcracks, grain boundaries, pores and bedding planes, while at the macroscale geologic fractures are referred to as joints (opening) or faults (shearing), based on their genesis. Numerous experimental and theoretical efforts have been devoted to the understanding of crack initiation, propagation and coalescence in brittle materials [1–3]. Under tension, these three processes take place almost simultaneously in brittle rocks. However, the failure process is more complex under compression. Under both kinds of loading, rupture (failure) of the material results primarily from stable and unstable fracture propagation and crack coalescence, rather than directly from fracture initiation. Griffith [1] realised
n Correspondence to: The University of Queensland, School of Civil Engineering, St Lucia, Brisbane, 4072, Australia. Tel.: þ 61733653912. E-mail address: [email protected] (N. Erarslan).
1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmms.2012.07.015
the significance of inherent flaws or microcracks in reducing a material’s strength and in measuring its imperfection. Griffith [1] argued that brittle solids fail by incremental propagation of a multitude of randomly oriented, small pre-existing cracks. Griffith cracks are common in rocks that contain both intragranular (outside; in grain boundary) and intergranular (inside; in grain) microcracks and larger macroscopic or transgranular multiple cracks. Linear Elastic Fracture Mechanics states that a crack will propagate when its stress intensity factor reaches a critical value (KIC). The stress intensity factor depends on fracture displacement modes and crack geometry. A crack can deform in three basic modes: tensile (mode I), shearing (mode II) and tearing (mode III). This classification of fracturing is based on crack surface displacement or crack tip loading [2]. Mixed-mode I–II fracture problems in compression are shown to be more complicated and quite different from those under tension. In this mode, tensile cracks initially grow at an angle with respect to the direction of axial compressive stress then rapidly grow along the axial compressive stress [3–6]. Mechanical behaviour of rock under static loading has been thoroughly investigated. However, rock reaction to cyclic, repetitive stresses resulting from dynamic loads has been generally neglected, with the exception of a few rather limited studies
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[7–11]. Cyclic loading often causes brittle materials such as ceramics and rocks to fail at a stress level lower than their determined strength under monotonic conditions; a phenomenon commonly termed ‘fatigue’. A principal objective of rock-fatigue research, as found in the literature, has been to establish a relationship between the number of cycles (N) and the reduction of applied stress amplitude (S); the S–N curve approach [7–14]. However, most rock-fatigue research has focused on uniaxial compressive strength degradation under cyclic loads [7,10,14,23]. Therefore, information regarding the dynamic tensile properties of rocks is of considerable importance in assessing the stability of rock structures under dynamic loads. This is also important for determining rock breakage and fragmentation under explosive and percussive excavation [15–18]. There is very limited research on the response of the tensile strength of rocks to cyclic loading (as opposed to dynamic loading, such as explosive loads and impact loading). Moreover, relatively little attention has been given to investigating the damage mechanisms of rock fatigue. A novel outcome of this research is the observation of the effect of indirect tensile cyclic loading on the fracture toughness of rocks. One of the most fundamental parameters in fracture mechanics is critical fracture toughness (KIC), which describes the resistance of a material to crack propagation. KIC is an important material property, which corresponds to the critical state of the stress intensity factor required for crack initiation and subsequent propagation. Therefore, assessment of resistance to crack propagation is crucial for understanding the behaviour of structures involving brittle materials.
Poisson’s ratio
UCS (MPa)
BTS (MPa)
required for testing. It was also unnecessary to perform precracking for a CCNBD specimen because it used a chevron notch that self-pre-cracks during testing and leads to stable crack propagation. Another advantage of the CCNBD method over other ISRM methods involves increased precision; there is a higher load capacity and consistent results for each test. In our research, all the CCNBD samples showed high precision in maximum load measurements. In addition, it was possible to measure mode I, mode II and mixed-mode I–II fracture toughness by inclining the notch at different angles with respect to the axis of diametral load. The geometry of a CCNBD specimen is illustrated in Fig. 1. The chevron notch causes crack propagation to start at the tip of the V alignment and to proceed radially outwards in a stable fashion until the point at which the fracture toughness is calculated. All dimensions of the geometry should be converted into dimensionless parameters with respect to the specimen radius and diameter. The suggested standard specimen dimensions are given in the ISRM suggested methods [19]. Other selections of specimen geometrical dimensions are possible, but in order to have a valid test, the two most important selected dimensions: dimensionless final notched crack length (a1) and the dimensionless quantity (aB) must fall within the range outlined in the suggested ISRM methods [19]. The dimensionless initial crack length (a0 ¼ a0/R), dimensionless final notched crack length (a1 ¼a1/R) and dimensionless quantity (aB ¼B/R) are the three basic dimensions for the CCNBD parameters. All specimen geometries used in this research were in the valid ranges indicated by ISRM [19]. The thickness of the notches, t, was 1.5 mm, the thickness of the samples, B, was 26 mm and radius of samples, R, was 26 mm. The initial chevron notch crack length, 2a0, was 16–18 mm and the final chevron notch crack length, 2a1, was 36–37 mm. A circular 40 mm diamond saw was used to cut the required notch. A specially designed jig recommended by the ISRM was used to ensure that the chevron notches were exactly in the centre of the disc. The crack displacement was measured as crack mouth opening displacement (CMOD) across the crack mouth. A clip gauge for measuring the notch opening was attached to the knives. An Instron 2670 series crack opening displacement gauge was used to measure CMOD. The gauge length was 10 mm and maximum travel was 2 mm. The gauge met the requirements set out in American standard ASTM 399 70T.
0.26
190
15
2.2. Static and cyclic tests
0.22
97
2. Experimental procedure and tests 2.1. Sample preparation Most of the tests in the current research were carried out on Brisbane tuff, because it is a host rock of Brisbane’s first motorway tunnel, CLEM7, from which core samples were obtained. Brisbane tuff was chosen for several reasons. Firstly, being an ash deposit, it is a massive rock type with no bedding and it is easy to handle and prepare for testing, minimising time constraints for the research project. Moreover, Brisbane tuff’s massive character gives less test result variability. Finally, it is a targeted rock type in the Brisbane area for its strength and stability parameters in regard to tunnelling and excavation. Brisbane welded tuff is a fine-grained, massive rock of rhyolitic composition with coarser grains imparting a porphyritic texture. Quartz and feldspar phenocrysts 1–3 mm in size are embedded without interlocking in a matrix consisting of polycrystalline silica. Uniaxial compressive strength (UCS) and indirect Brazilian tensile strength (BTS) tests were conducted on the Brisbane tuff specimens to determine the mechanical characterisation of Brisbane tuff (see Table 1). The Cracked Chevron Notched Brazilian Disc (CCNBD) specimens were used in both the static and cyclic tests. The CCNBD method had advantages over other International Society of Rock Mechanics (ISRM) proposed fracture toughness tests in terms of the simplicity of sample preparation and the reduced material Table 1 Mechanical characterisation results for Brisbane tuff. Rock sample
Young’s modulus (GPa)
Brisbane tuff NST-62 25 (average of five repeats) Brisbane tuff NST-35 19 (average of five repeats)
Fig. 1. The CCNBD specimen geometry with recommended test fixture.
8.0
Disc specimens were diametrically loaded parallel to the diametral compressive loading directions with a crack inclination
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Fig. 2. (a) Sinusoidal cyclic loading and (b) increasing cyclic loading.
angle of zero (b ¼01). A load-controlled testing manner was adopted and loading was continued until failure. For compressive loading tests, an Instron 6027 100 kN load cell hydraulic servocontrol testing system with Bluehill software was used and a loading frame, configured separately according to the test type (i.e., static loading or cyclic loading), was used. Load, diametral displacement and crack mouth displacement were continually recorded during the test using a computerised data logger. Static tests were performed by following ISRM instructions [19]. Two different types of cyclic loading were used in this research: cyclic loading with constant mean level and constant amplitude, termed sinusoidal cyclic loading (see Fig. 2a) and cyclic loading with increasing mean level and constant amplitude, termed increasing cyclic loading (see Fig. 2b). Loading amplitudes are constant in both types of cyclic loading. However, the mean level of each cycle increases at a constant rate in increasing cyclic loading tests, whereas the mean level of each cycle is constant in sinusoidal cyclic loading tests. Sinusoidal cyclic loading test series were conducted to obtain an S–N curve, illustrative of the continuous weakening of rock with the increase in N required for failing a specimen loaded to a certain upper peak stress (S). In the literature, the S–N curve concept has been used for fatigue research under uniaxial compressive loading with cylindrical rock samples [10,14,21]. However, the current research is a first in obtaining an S–N curve for fracture toughness degradation because of fatigue under cyclic loads. Ramp type cyclic compressive loading with increasing mean level with 1 Hz frequency was used in the increasing cyclic loading tests. Four different amplitudes with the same mean load were chosen for each increasing cyclic loading test series to investigate the effect of fatigue on the fracture toughness of rocks: 0.45 kN at 10% static ultimate load (SUL), 0.9 kN at 20% SUL, 1.35 kN at 30% SUL and 1.8 kN at 40% SUL (see Fig. 3).
3. Results of tests 3.1. Results of static tests Five CCNBD samples were tested under load-control test conditions. The specimens were placed under the platens with a crack inclination angle of zero (b ¼01) to provide mode I loading conditions. The loading rate was chosen as 9 kN/s to cause failure within 20 s as suggested by the ISRM [19]. The maximum recorded load and the calculated KIC values obtained from both ISRM standard tests are shown in Table 2.
Fig. 3. Various amplitude increasing cyclic loading with same mean values.
Table 2 Mode I fracture toughness values of Brisbane tuff obtained by CCNBD tests. Rock type
Brisbane Brisbane Brisbane Brisbane Brisbane Brisbane Brisbane Average
tuff-1 tuff-2 tuff-3 tuff-4 tuff-5 tuff-6 tuff-7
Pmax (kN)
KIC (CCNBD)
CCNBD
(MPaOm)
5.2 5.1 4.6 5.1 4.1 4.0 3.5 4.5
1.3 1.3 1.2 1.3 1.1 0.9 0.8 1.1
Two of the load–CMOD plots of CCNBD specimens are shown in Fig. 4. The transition point from stable crack propagation to unstable crack propagation can be determined by using load– CMOD plots. Further, it is possible to show that there is a fracture process zone (FPZ) in front of the tip of the chevron notch crack by obtaining the plastic deformation behaviour just before the reaching of failure load. However, it was not possible to get post-peak tensile softening behaviour after failure with all specimens. 3.2. Results of cyclic tests The main purpose of performing two types of cyclic loading was to find the most damaging cyclic loading type using the same amplitudes. It is known that the act of applying a load provides energy for the crack initiation and propagation process in a
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Fig. 4. Load–CMOD plots of CCNBD specimens during monotonic testing. Fig. 5. S–N curve for CCNBD specimens. Table 3 Results of sinusoidal cyclic loading. Smax (as % of static failure load)
Fmax (failure load, kN)
Number of cycles (N) up to failure
93 93 88 88 84 84 84 80 80 75 75 75 75 71 70 70
4.2 4.2 4 4 3.8 3.8 3.8 3.6 3.6 3.4 3.4 3.4 3.4 3.2 3.1 3.1
835 587 13 205 9 149 285 13000 27000 1761 4831 1153 24175 6250 50000a 50550a
a
No failure after that point.
material. By removing the load, the energy supply driving crack propagation is discontinued and the remaining excess energy in the system dissipates through the crack propagation processes. Hence, the points at which the loading and unloading of a cycle stop become important. The first important conclusion drawn from the sinusoidal cyclic tests was that the failure load used in calculations of indirect tensile strength is definitely weakened 30% by repetitive loading. Results are given in Table 3. The S–N curve clearly shows that as the maximum applied diametral load decreases, the life expectancy of a CCNBD specimen increases (see Fig. 5). Because the load range used in tests to determine fracture toughness is very small, the data around high amplitudes is clustered. However, the S–N curve shows that the ultimate load causing failure is reduced by 30% (from 4.5 kN to 3.2 kN) because of rock fatigue. Therefore, it can be concluded that crack propagation resistance (fracture toughness) can be reduced by 29–30% through repetitive loading. This means that a crack can propagate under lower loads than the expected ultimate loads under repetitive loading. The series of diametral compressive increasing cyclic loading tests was performed on 12 CCNBD Brisbane tuff samples. Fracture toughness values of Brisbane tuff under static loading were calculated as 1.12–1.5 MPaOm using the ISRM [19] suggested methods as discussed above. The fracture toughness reduction because of cyclic loading is given in Table 4 by comparing with
static fracture toughness values. The main purpose of this comparison is to show the clear reduction of ultimate failure load that resulted in the reduction of the mode I stress intensity factor because of rock fatigue. It is shown that crack propagation causing failure is possible with lower stress intensity values (KI) at the crack tip than the critical stress intensity value (KIC). This result goes against the classical theory, which predicts that there will be no crack growth as long as KI oKIC. According to the obtained results, the maximum reduction, 46% of static KIC, was obtained with the highest amplitude, 1.99 kN at 40% SUL, of cyclic loading. The mode I fracture toughness value of Brisbane tuff (NST50) was reduced from 1.12 MPaOm to 0.61 MPaOm with the highest amplitude under increasing cyclic loading. This reduction has important implications for the investigation of the effect of cyclic loading on the fracture resistance of cracks in rocks. To date, experimental observations of cyclic loading tests have indicated that dynamic cyclic loading seems to have a greater effect on fracture toughness degradation of rocks than sinusoidal compressive cyclic loading. The reduction of fracture toughness was found to be 29% under sinusoidal loading tests as shown, whereas increasing cyclic loading caused a reduction of fracture toughness at a maximum of 46%. For a clear understanding of the effect of rock fatigue on damage mechanisms, a comparison between static and dynamic cyclic loading tests is shown in Fig. 6 by plotting both results on the same axes. The amplitude of the dynamic cyclic loading used in the test was 0.45 kN at 10% of SUL. As seen in Fig. 8, both failure load values and damage mechanisms are quite different under static and dynamic cyclic loading. The failure load obtained from the average of two static tests was reduced from an average of 4.2 kN to an average of 2.1 kN because of rock fatigue. In both test types, stable and unstable crack propagation stages were clear. However, the resistance of crack propagation to cyclic loading with accumulation of plastic deformation (1 mm) was much greater than the relative value (0.025 mm) under static loading before failure (see Fig. 6). This behaviour shows that the development of a large number of microcracks causing accumulation of irreversible deformation is observed even prior to the appearance of main cracks in a loaded specimen. This phenomenon is similar to the subcritical failure of geomaterials commonly known as subcritical crack propagation. The mechanisms responsible are discussed in detail below. A load–CMOD plot further reveals that there is a tensile softening behaviour with dynamic cyclic loading. Due to the different post-peak behaviour, the behaviour of the damage zone
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Table 4 The fracture toughness reduction due to cyclic loading: a comparison with static fracture toughness values. Sample
Amplitude % SUL
Ultimate load (kN)
Number of cycles (N) up to failure
Mode-I stress intensity factor (KI)a pffiffiffiffiffi (MPa m) [22]
Fracture toughness pffiffiffiffiffi (KIC)b (MPa m)
Reduction of KIC (%)
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
10 10 10
2.39 1.95 2.69 2.34
2453 1829 2261 2181
0.62 0.50 0.69 0.61
0.72 0.60 0.83 0.72
35 45 26 35
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
20 20 20
2.16 2.10 2.24 2.17
1553 1501 1630 1561
0.55 0.53 0.57 0.55
0.67 0.65 0.70 0.67
41 42 38 40
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
30 30 30
2.40 2.5 2.42 2.44
1218 1702 1501 1473
0.62 0.64 0.62 0.63
0.74 0.77 0.75 0.75
34 32 33 33
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
40 40 40
1.86 2.17 1.95 1.99
319 446 136 300
0.48 0.55 0.50 0.51
0.57 0.67 0.60 0.61
50 41 47 46
a
a is assumed at 0.5.
b
Y nmin is assumed at 1.21.
Fig. 6. Comparison of load–CMOD curves of CCNBD specimens tested under static and increasing cyclic loading.
at the tip of the chevron notch inside the sample is also different. This may help to explain the fatigue mechanisms by using the FPZ concept in front of the cracks. In contrast, no tensile softening post-peak behaviour was observed with the static loading tests (see Fig. 6). These findings are significant and helpful in explaining rock fatigue mechanisms. Another important observation was made by examining the crack surfaces of failed specimens after the dynamic cyclic loading tests. There was a clear crushed region including small particles and dust in front of the chevron tip, as shown in Fig. 7b. However, no rock chips (small particles) were observed at the crack surfaces of failed specimens under static loading, as seen in Fig. 7a. High micro- and macrocrack density in front of the chevron tip shows a gradual separation of crack surfaces along the preferential path set up by microcracking. This damaged zone in front of the chevron tip is called the FPZ. The mechanisms of rock fatigue under cyclic loading have been explained in the literature with many more microcracks induced compared to the failure mechanisms under static loading [23,24]. Therefore, observation of the FPZ zone in
front of the chevron notch in CCNBD specimens is a useful means of investigating fatigue mechanisms. Fig. 8 shows the load–CMOD plots with different amplitudes of increasing cyclic loading tests. To avoid bounding and moving of the samples, a 0.5 kN minimum compressive load was applied at the beginning of all tests. The loading–unloading frequency was 1 Hz. As the plastic deformation is very high compared with elastic deformation in the plots, the CMOD axis was plotted as a log scale. A clear tensile softening can be seen in all plots through post-peak behaviour in load–CMOD plots after an accumulated plastic deformation in the samples. This tension-softening behaviour is responsible for the development of the FPZ in front of and around the crack tip. The cohesive crack model is able to describe materials that exhibit strain-softening behaviour [25]. However, it is hard to say whether there is a single crack plane, as defined traditionally under static loading in fracture mechanics, which takes place in front of the chevron tip under cyclic loading. Therefore, ‘damage’ is the preferred term to use in rock-fatigue research, rather than ‘failure plane’ (main crack). It is possible to see quantified damage as the accumulation of permanent strain within each cycle in all load–CMOD plots. From these plots, it was found that clear tensile softening behaviour took place for all post-peak behaviours after an accumulated plastic deformation in the sample. However, the microcracking damage process that causes the tension-softening behaviour under cyclic loading needs to be determined. The cohesive crack model proposed in the literature may not be able to explain the observed tension-softening behaviour under cyclic loading. This is because there are some limitations among cohesive crack formulations, such as the crack tip face closing smoothly (the stress intensity factor KI vanishes at the crack tip in mode I propagation) and the FPZ being of negligible thickness [25]. Conversely, it was not possible to get tensile softening or post-peak behaviour after a plastic deformation with static loading tests. A detailed discussion about possible fatigue damage mechanisms is given below. 3.3. The Mechanisms of rock fatigue damage A typical feature of rock fatigue in experimental tests can be observed by producing a progressive accumulation of permanent
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Fig. 7. Failed specimens and damaged zone in front of the chevron tip (a) under static loading and (b) under cyclic loading.
Fig. 8. Load–CMOD plots of increasing cyclic loading with amplitudes (a) 10% SUL (0.45 kN), (b) 20% SUL (0.9 kN), (c) 30% SUL (1.35 kN) and (d) 40% SUL (1.8 kN).
strain in the specimen, rather than any significant decay in the material’s elastic modulus. Accumulation of plastic deformation is responsible for the fatigue damage; the magnitude and increasing trend of the irreversible deformation influences the cumulative fatigue damage. The displacements along both x and y directions represent CMOD and diametral axial displacement, respectively,
as shown in Figs. 10 and 11 with different amplitudes. Plots of permanent damage show that both the CMOD and diametral axial displacement increase with increasing damage increments but at different rates. Initially, irreversible CMOD deformation develops quickly. This is followed by deformation increasing at a slow constant rate before cumulative deformation begins to accelerate
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rapidly until failure. Conversely, diametral axial displacement–N plots show that the displacement rate increases with an increasing rate up to failure (see Figs. 9 and 10). The opening of crack faces parallel to the applied load and the closure of crack faces perpendicular to the load causes certain changes in the relative lateral and axial deformations, respectively. Behaviour of diametral axial deformation results may show that irreversible damage accumulation in front of the chevron tip is not caused by the closing of pre-existing microcracks aligned parallel to the maximum principal stress. A closer examination of diametral axial displacement and CMOD after the start of nonlinear behaviour in plots shows both diametral axial displacement and CMOD increase with a concave upward rate (see Fig. 11). Continuous irreversible damage occurs slowly up to a certain point because new stress-induced microcracks are taking place. Coalescence of the induced cracks starts after this point, with the rate of cracking increasing in speed, up to failure. The characteristics of the fracture surfaces were examined by means of a JEOL JMS-6460 LA SEM. The JEOL JSM-6460 LA is a tungsten low-vacuum analytical SEM. In this study, all rock fracture images were obtained under low vacuum chamber pressures, that is, 1–50 Pa (with adjustable pressure between 10 Pa and 270 Pa). This allowed certain samples to be observed uncoated and reduced damage to the specimens caused by the
Fig. 10. (a) CMOD and (b) diametral axial displacement versus number of cycles plots: same mean increasing cyclic loading (type II) tests with amplitude 20% SUL (0.9 kN)
Fig. 9. (a) CMOD and (b) diametral axial displacement versus number of cycles plots: same mean increasing cyclic loading (type II) tests with amplitude 10% SUL (0.45 kN).
effects of high vacuum. In this study, the damaged zone in front of the tip of the chevron notch cracks of the tested CCNBD specimens were examined directly with a SEM, without preparation of thin sections. Thin-section specimens were not used in this study to avoid creating extra microcracks during preparation of the specimens. Scanning electron micrographs of fracture surfaces of Brisbane tuff CCNBD specimens tested under cyclic loading are shown in Fig. 12. Two fatigue mechanisms were observed in the cement of Brisbane tuff: (1) grain decohesion in secondary microcrystalline quartz cement intrusions (see Fig. 13) and (2) fatigue striations in primary silica cryptocrystalline cement. Fig. 13 provides a closer look at the cement and feldspar mineral. Some microcrystalline quartz cement intrusions were seen in the primary silica cryptocrystalline cement after petrographic analyses. Fig. 13b shows those microcrystalline quartz cement intrusions. Closer examination of the damaged cement would appear to indicate that a massive amount of loosened microcrystalline quartz minerals resulted from grain decohesion. Further, there is a clear grain boundary crack between the feldspar and cement (see Fig. 13a). Similar to the fatigue damage in the cement, there were two fatigue damage mechanisms seen with grain-related damage: (1) intergranular cracks causing grain decohesion (a primary mechanism) and (2) intragranular cracks (a secondary mechanism). Brisbane tuff is composed mainly of quartz and K-feldspar minerals
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Fig. 11. Diametral axial displacement and CMOD after the start of nonlinear deformation in front of the chevron crack tip.
Fig. 12. Debris and small particles in front of the tip of the chevron notch as a result of cyclic loading.
with small amounts of siderite (Fe-carbonate) and zeolite minerals. Fig. 14 shows the fatigue-induced cracking around the quartz and feldspar minerals. Fatigue-related microcracking around tuff minerals causing grain decohesion as a result of the pulling out of grains by frictional sliding is visible in Fig. 14c and d. Fig. 14b and e are
presented at greater magnification in Fig. 14a. At this scale, intergranular cracking around the grains is apparent. Under closer examination, fine fragments around the grains were observed, which accumulate in the proximity of the grain corners. This is particularly evident in Fig. 14e, from which it can be inferred that
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Fig. 13. Fatigue damage in the cement of Brisbane tuff resulting from decohesion of microscale quartz minerals.
Fig. 14. Grain decohesion and loosened grains (a)–(e) and fatigue striations in damaged grains under high magnification ( 500) at the surface of the fatigue crack (f).
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such powder is the result of fatigue damage, probably due to local abrasion of the sharp corners of the quartz and feldspar grains. SEM imaging revealed that the primary fatigue damage mechanisms in front of a chevron notch crack are grain decohesion and intergranular cracks. Debris and dust are the results of fatigue damage in Brisbane tuff cement and around loosened grains. The fatigue cracks in the cement are restricted around the grains and cannot grow through the grains. Therefore, it can be deduced that those fatigue cracks are stable (subcritical) cracks that coalescence to form macroscale fatigue cracks resulting in failure. Further, each grain after decohesion may behave as an indenter to indent the surface of the weaker cement material under far field cyclic diametral compressive loading. This would explain the mechanisms of the debris material around and in the corners of the loosened grains.
4. Discussion The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static KIC of 46% was obtained for the highest amplitude dynamic cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static KIC of 29% was obtained. These reductions clearly illustrate the dramatic effect of cyclic loading on the fracture resistance of cracks in rocks. This means that crack propagation and damage can take place under lower than expected ultimate loads compared with static loading. The mode I stress intensity factor KI at the crack tip is known to control crack growth. The stress corrosion lower limit is Ko and the fracture toughness is KIC. When KI 4KIC, the crack grows rapidly at approximately the speed of sound, when KI oKo, the crack does not grow and when Ko oKI oKIC, the crack grows at a certain velocity with the stress intensity factor KI. However, this research shows that unstable crack propagation causing failure occurs with lower KIs at the crack tip than the KIC value. This result contradicts the classical theory, which predicts that there will be no crack growth as long as KI oKIC. This phenomenon is known as ‘subcritical crack growth’ [26,27]. Subcritical crack growth is one of the main explanations for the creep damage mechanism in rocks. In some fatigue research, damage accumulation in brittle materials under cyclic loading has been explained by the creep mechanism and stress corrosion [28,23,29]. Despite using different test geometries and loading boundary conditions to those were used in past studies, this study found similar damage behaviour in front of the notched crack in our disc shaped samples as a result of dilatant creep damage behaviour. It was possible to measure the crack growth rate for subcritical crack growth in other studies under controlled stress corrosive environments with edge-cracked specimens. However, it is not possible to measure the crack growth rate in our cyclic loading experiments because of the unknown stress corrosive mechanism and the high-speed unstable crack propagation due to the embedded notch crack in the disc specimens. Further, there was no pre-existing crack for proper monitoring in our three-dimensional sample geometry because chevron notched specimens do not need to be pre-cracked for rock fracture research [19]. Stress corrosion is the most common mechanism associated with subcritical crack growth in rock. However, it is certainly not the only mechanism by which subcritical crack growth occurs. Another mechanism that can be important, in certain circumstances, is fatigue crack growth. In this study, it has been shown that the N to failure decreased when the amplitude of cycles increased. This effect may also be explained by stress corrosion. Stress corrosion and fatigue represent the major mechanisms of subcritical crack growth in rocks [26,23]. Most of the experimental
work on stress corrosion crack growth in rocks and ceramics use methods originally developed for determining fracture toughness in metallic materials. The corrosive environment is water and there is a chemically active environment in those metallic material experiments. However, some mechanisms have been accepted as additional mechanisms of subcritical crack growth, such as cyclic fatigue [23,20]. In this research, it is believed that fatigue cracks (e.g. intergranular cracks) are the dominant mechanisms of subcritical crack propagation. Thus, the main aim here is to discover the possible mechanisms in microcracks causing the corrosive environment. Therefore, direct observation of the FPZ in front of the tip of the main crack in the tested CCNBD specimens using the SEM was found a suitable observation technique for this research. To investigate possible differences between static and fatigue failure, the fracture surfaces of monotonically tested CCNBD specimens were also observed by SEM. Scanning electron micrographs of fracture surfaces of Brisbane tuff CCNBD specimens tested under monotonic loading are shown in Fig. 15. When compared with static rupture, the main differences are: (1) the number of fragments produced is much greater under cyclic loading than under static loading and (2) intergranular cracks are formed due to particle breakage under cyclic loading, whereas smooth and bright cracks along cleavage planes are formed under static loading. Further, the macroscale main crack causing failure is seen in the cement without any dust or debris material under monotonic loading. Typical sparkling cleavage cracks resulted when rupture of the crystals occurred along cleavage planes.
5. Conclusions The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and induced plastic displacement. The maximum reduction of the static KIC of 46% was obtained for the highest amplitude dynamic cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static KIC of 27% was obtained. These reductions clearly illustrate the dramatic effect of cyclic loading on the fracture resistance of cracks in rocks. Damage was quantified as the accumulation of permanent strain in front of the chevron notch crack tip with each cycle of loading, because microfracturing introduces nonlinearity into the theoretically elastic behaviour of the rock. A continuous irreversible accumulation of damage was observed in dynamic cyclic tests conducted at different amplitudes. After the accumulation of irreversible damage and failure of the specimen, clear tensile softening was observed in cyclic loading tests carried out at different amplitudes on vertically aligned chevron notch cracks (mode I). However, no post-peak behaviour was observed in the CCNBD specimens tested under static loading. Considering the shape of the load–CMOD plots, the accumulation of irreversible damage in front of the chevron notch crack under cyclic loading was found to be similar to static fatigue (creep). Further, the subcritical crack mechanisms were verified from rock-fatigue research, with lower ultimate loads causing smaller KI than the KIC due to rock fatigue. The SEM results enable some of the qualitative features of the fatigue damage process in Brisbane tuff to be inferred. This research found that the failure of a CCNBD specimen under cyclic loading is the result of the coalescence of many microcracks, not of the growth of a single macrocrack. SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular fracturing and transgranular fracturing. The main characteristic is particle breakage under cyclic loading, which probably starts at contacts between particles and is accompanied by the production of very
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Fig. 15. Damage in the cement and cleavage cracks under monotonic loading.
small fragments, probably resulting from frictional sliding within the weak matrix. It is believed that point contacts at grain boundaries are regions of stress concentration (i.e. indenters). Transgranular cracks may emanate from these regions and intergranular cracks sometimes pass through the contact points. This stage can be correlated with a steady progression of damage and produces a general ‘loosening’ of the rock, which is a precursor to the formation of intergranular cracks. When compared with static rupture, the main differences are that a much greater number of small particles and debris are created under cyclic loading than under static loading, and that intergranular cracks are formed due to particle breakage under cyclic loading, whereas smooth and bright cracks are formed along cleavage planes under static loading.
Acknowledgements Acknowledgement is made to Leighton Contractors who provided core samples of Brisbane tuff from the CLEM7 Project and to Ted Brown, Les McQueen, Mark Funkhauser and Rob Morphet of Golder Associates Pty Ltd. for their assistance and advice. The work described forms part of the first author’s PhD research carried out within the Golder Geomechanics Centre at The University of Queensland. The first author was supported by an Australian Postgraduate Award/UQRS and the Golder Geomechanics Centre. References [1] Griffith AA. The phenomena of rupture and flow in solids. Philos Trans R Soc Lond 1920;221:163–98. [2] Lajtai EZ. A theoretical and experimental evaluation of the Griffith theory of brittle fracture. Tectonophysics 1971;11:129–56.
[3] Hoek E. Brittle fracture of rocks. In: Stagg KG, Zienkiewicz OC, editors. Rock Mechanics in Engineering Practice. London: Wiley; 1968. [4] Li YP, Chen LZ, Wang YH. Experimental research on pre-cracked marble under compression. Int J Solids Struct 2005;42(9–10):2505–16. [5] Al-Shayea NA. Crack propagation trajectories for rocks under mixed mode I–II fracture. Eng Geol 2005;81(1):84–97. [6] Chang SH, Lee CI, Jeon S. Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Eng Geol 2002;66(1–2):79–97. [7] Attawel PB, Farmer IW. Fatigue behavior of rock. Int J Rock Mech Min 1973;10(1):1–9. [8] Bagde MN, Pedros V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min 2005;42(2): 237–50. [9] Gatelier N, Pellet F, Loret B. Mechanical damage of an anisotropic porous rock in cyclic triaxial tests. Int J Rock Mech Min 2002;39(3):335–54. [10] Haimson BC, Kim CM. Mechanical behaviour of rock under cyclic fatigue. Rock Mech 1971;3:845–63. [11] Tao Z, Mo H. An experimental study and analysis of the behaviour of rock under cyclic loading. Int J Rock Mech Min Sci 1990;27:5. [12] Burdine NT. Rock failure under dynamic failure conditions. Soc Pet Eng J 1963;3(1):1–8. [13] Evans AG, Fuller ER. Crack propagation in ceramic materials under cyclic loading conditions. Metall Trans 1974;5(1):27–9. [14] Haimson BC. Effect of cyclic loading on rock. Dynamic Geotechnical Testing, 654. ASTM STP; 1978 (p. 228–245). [15] Roxborough FF. Cutting rocks with picks. Min Eng 1963;132:445–52. [16] Roxborough FF. Coal ploughing. Colliery Eng 1968;12(16):66–71. [17] Hood M, Alehossein HA. Development in rock cutting technology. Int J Rock Mech Min Sci 2000;37(1–2):297–305. [18] Gottlieb L, Moore PJ. Vibratory cutting of brown coal. Int J Rock Mech Min Sci 1981;18:335–9. [19] ISRM. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disk (CCNBD) specimens. Int J Rock Mech Min Sci 1995;32(1):57–64. [20] Kim K, Mubeen A. Relationship between differential stress intensity factor and crack growth rate in cyclic tension in Westerly granite. Fracture Mechanics Methods for Ceramics, Rocks, and Concrete, 745. ASTM STP; 1981 (p. 157–168). [21] Singh SK. Fatigue and strain hardening behaviour of greywacke from the flagstaff formation, NSW. Eng Geol 1989;26:171–9.
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[22] Shetty DK, Rosenfield AR, Duckworth WH. Fracture toughness of ceramics measured by a chevron notch diametral compression test. J Am Ceram Soc 1985;68(12):C325–7. [23] Costin LS, Holcomb DJ. Time-dependent failure of rock under cyclic loading. Tectonophysics 1981;79(3–4):279–96. [24] Hadley K. The effect of cyclic stress on dilatancy: another look. J Geophys Res 1976;81(14):2471–4. [25] Dugdale DS. Yielding of steel sheets containing slits. J Mech Phys Solids 1960;8(2):100–4.
[26] Atkinson BK. Subcritical crack growth in geological materials. J Geophys Res 1984;89:4077–114. [27] Atkinson C, Smelser RE, Sanchez J. Combined mode fracture via the cracked Brazilian disk test. Int J Fract 1982;18(4):279–91. [28] Celestino TB, Bortolucci AA. Determination of rock fracture toughness under creep and fatigue. In: Proceedings of the 35th US Rock Mechanics Symposium, Reno, 1995, p. 147–52. [29] Evans AG. Fatigue in ceramics. Int J Fract 1980;16(6):485–98.
Contents lists available at SciVerse ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks N. Erarslan n, D.J. Williams Golder Geomechanics Centre, School of Civil Engineering, The University of Queensland, Australia
a r t i c l e i n f o
abstract
Article history: Received 26 August 2011 Received in revised form 9 April 2012 Accepted 24 July 2012 Available online 13 August 2012
This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I fracture toughness response to static and cyclic loading, as a function of the applied load. Both the static and cyclic loading tests were carried out on Cracked Chevron Notched Brazilian Disc (CCNBD) rock specimens. Two different types of cyclic loading were applied: (a) cyclic loading with constant mean level and constant amplitude, termed sinusoidal cyclic loading and (b) cyclic loading with increasing mean level and constant amplitude, termed increasing cyclic loading. The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (KIC) of 46% was obtained for the highest amplitude increasing cyclic loading test. Conversely, for sinusoidal cyclic loading, a maximum reduction of the static KIC of 29% was obtained. Detailed scanning electron microscope (SEM) examinations revealed that both loading methods cause fatigue in the CCNBD specimens. When compared with static rupture, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular fracturing and transgranular fracturing. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Rock fracture toughness Rock fatigue Increasing cyclic loading CCNBD SEM
1. Introduction Techniques for projects including the design and construction of underground openings, supports and rock pillars as well as drilling, blasting and haul roads are based on an understanding of the mechanical behaviour of rocks under various loading conditions. Rock materials are discontinuous at all scales. At the microscale, defects causing stress concentrations include microcracks, grain boundaries, pores and bedding planes, while at the macroscale geologic fractures are referred to as joints (opening) or faults (shearing), based on their genesis. Numerous experimental and theoretical efforts have been devoted to the understanding of crack initiation, propagation and coalescence in brittle materials [1–3]. Under tension, these three processes take place almost simultaneously in brittle rocks. However, the failure process is more complex under compression. Under both kinds of loading, rupture (failure) of the material results primarily from stable and unstable fracture propagation and crack coalescence, rather than directly from fracture initiation. Griffith [1] realised
n Correspondence to: The University of Queensland, School of Civil Engineering, St Lucia, Brisbane, 4072, Australia. Tel.: þ 61733653912. E-mail address: [email protected] (N. Erarslan).
1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmms.2012.07.015
the significance of inherent flaws or microcracks in reducing a material’s strength and in measuring its imperfection. Griffith [1] argued that brittle solids fail by incremental propagation of a multitude of randomly oriented, small pre-existing cracks. Griffith cracks are common in rocks that contain both intragranular (outside; in grain boundary) and intergranular (inside; in grain) microcracks and larger macroscopic or transgranular multiple cracks. Linear Elastic Fracture Mechanics states that a crack will propagate when its stress intensity factor reaches a critical value (KIC). The stress intensity factor depends on fracture displacement modes and crack geometry. A crack can deform in three basic modes: tensile (mode I), shearing (mode II) and tearing (mode III). This classification of fracturing is based on crack surface displacement or crack tip loading [2]. Mixed-mode I–II fracture problems in compression are shown to be more complicated and quite different from those under tension. In this mode, tensile cracks initially grow at an angle with respect to the direction of axial compressive stress then rapidly grow along the axial compressive stress [3–6]. Mechanical behaviour of rock under static loading has been thoroughly investigated. However, rock reaction to cyclic, repetitive stresses resulting from dynamic loads has been generally neglected, with the exception of a few rather limited studies
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[7–11]. Cyclic loading often causes brittle materials such as ceramics and rocks to fail at a stress level lower than their determined strength under monotonic conditions; a phenomenon commonly termed ‘fatigue’. A principal objective of rock-fatigue research, as found in the literature, has been to establish a relationship between the number of cycles (N) and the reduction of applied stress amplitude (S); the S–N curve approach [7–14]. However, most rock-fatigue research has focused on uniaxial compressive strength degradation under cyclic loads [7,10,14,23]. Therefore, information regarding the dynamic tensile properties of rocks is of considerable importance in assessing the stability of rock structures under dynamic loads. This is also important for determining rock breakage and fragmentation under explosive and percussive excavation [15–18]. There is very limited research on the response of the tensile strength of rocks to cyclic loading (as opposed to dynamic loading, such as explosive loads and impact loading). Moreover, relatively little attention has been given to investigating the damage mechanisms of rock fatigue. A novel outcome of this research is the observation of the effect of indirect tensile cyclic loading on the fracture toughness of rocks. One of the most fundamental parameters in fracture mechanics is critical fracture toughness (KIC), which describes the resistance of a material to crack propagation. KIC is an important material property, which corresponds to the critical state of the stress intensity factor required for crack initiation and subsequent propagation. Therefore, assessment of resistance to crack propagation is crucial for understanding the behaviour of structures involving brittle materials.
Poisson’s ratio
UCS (MPa)
BTS (MPa)
required for testing. It was also unnecessary to perform precracking for a CCNBD specimen because it used a chevron notch that self-pre-cracks during testing and leads to stable crack propagation. Another advantage of the CCNBD method over other ISRM methods involves increased precision; there is a higher load capacity and consistent results for each test. In our research, all the CCNBD samples showed high precision in maximum load measurements. In addition, it was possible to measure mode I, mode II and mixed-mode I–II fracture toughness by inclining the notch at different angles with respect to the axis of diametral load. The geometry of a CCNBD specimen is illustrated in Fig. 1. The chevron notch causes crack propagation to start at the tip of the V alignment and to proceed radially outwards in a stable fashion until the point at which the fracture toughness is calculated. All dimensions of the geometry should be converted into dimensionless parameters with respect to the specimen radius and diameter. The suggested standard specimen dimensions are given in the ISRM suggested methods [19]. Other selections of specimen geometrical dimensions are possible, but in order to have a valid test, the two most important selected dimensions: dimensionless final notched crack length (a1) and the dimensionless quantity (aB) must fall within the range outlined in the suggested ISRM methods [19]. The dimensionless initial crack length (a0 ¼ a0/R), dimensionless final notched crack length (a1 ¼a1/R) and dimensionless quantity (aB ¼B/R) are the three basic dimensions for the CCNBD parameters. All specimen geometries used in this research were in the valid ranges indicated by ISRM [19]. The thickness of the notches, t, was 1.5 mm, the thickness of the samples, B, was 26 mm and radius of samples, R, was 26 mm. The initial chevron notch crack length, 2a0, was 16–18 mm and the final chevron notch crack length, 2a1, was 36–37 mm. A circular 40 mm diamond saw was used to cut the required notch. A specially designed jig recommended by the ISRM was used to ensure that the chevron notches were exactly in the centre of the disc. The crack displacement was measured as crack mouth opening displacement (CMOD) across the crack mouth. A clip gauge for measuring the notch opening was attached to the knives. An Instron 2670 series crack opening displacement gauge was used to measure CMOD. The gauge length was 10 mm and maximum travel was 2 mm. The gauge met the requirements set out in American standard ASTM 399 70T.
0.26
190
15
2.2. Static and cyclic tests
0.22
97
2. Experimental procedure and tests 2.1. Sample preparation Most of the tests in the current research were carried out on Brisbane tuff, because it is a host rock of Brisbane’s first motorway tunnel, CLEM7, from which core samples were obtained. Brisbane tuff was chosen for several reasons. Firstly, being an ash deposit, it is a massive rock type with no bedding and it is easy to handle and prepare for testing, minimising time constraints for the research project. Moreover, Brisbane tuff’s massive character gives less test result variability. Finally, it is a targeted rock type in the Brisbane area for its strength and stability parameters in regard to tunnelling and excavation. Brisbane welded tuff is a fine-grained, massive rock of rhyolitic composition with coarser grains imparting a porphyritic texture. Quartz and feldspar phenocrysts 1–3 mm in size are embedded without interlocking in a matrix consisting of polycrystalline silica. Uniaxial compressive strength (UCS) and indirect Brazilian tensile strength (BTS) tests were conducted on the Brisbane tuff specimens to determine the mechanical characterisation of Brisbane tuff (see Table 1). The Cracked Chevron Notched Brazilian Disc (CCNBD) specimens were used in both the static and cyclic tests. The CCNBD method had advantages over other International Society of Rock Mechanics (ISRM) proposed fracture toughness tests in terms of the simplicity of sample preparation and the reduced material Table 1 Mechanical characterisation results for Brisbane tuff. Rock sample
Young’s modulus (GPa)
Brisbane tuff NST-62 25 (average of five repeats) Brisbane tuff NST-35 19 (average of five repeats)
Fig. 1. The CCNBD specimen geometry with recommended test fixture.
8.0
Disc specimens were diametrically loaded parallel to the diametral compressive loading directions with a crack inclination
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Fig. 2. (a) Sinusoidal cyclic loading and (b) increasing cyclic loading.
angle of zero (b ¼01). A load-controlled testing manner was adopted and loading was continued until failure. For compressive loading tests, an Instron 6027 100 kN load cell hydraulic servocontrol testing system with Bluehill software was used and a loading frame, configured separately according to the test type (i.e., static loading or cyclic loading), was used. Load, diametral displacement and crack mouth displacement were continually recorded during the test using a computerised data logger. Static tests were performed by following ISRM instructions [19]. Two different types of cyclic loading were used in this research: cyclic loading with constant mean level and constant amplitude, termed sinusoidal cyclic loading (see Fig. 2a) and cyclic loading with increasing mean level and constant amplitude, termed increasing cyclic loading (see Fig. 2b). Loading amplitudes are constant in both types of cyclic loading. However, the mean level of each cycle increases at a constant rate in increasing cyclic loading tests, whereas the mean level of each cycle is constant in sinusoidal cyclic loading tests. Sinusoidal cyclic loading test series were conducted to obtain an S–N curve, illustrative of the continuous weakening of rock with the increase in N required for failing a specimen loaded to a certain upper peak stress (S). In the literature, the S–N curve concept has been used for fatigue research under uniaxial compressive loading with cylindrical rock samples [10,14,21]. However, the current research is a first in obtaining an S–N curve for fracture toughness degradation because of fatigue under cyclic loads. Ramp type cyclic compressive loading with increasing mean level with 1 Hz frequency was used in the increasing cyclic loading tests. Four different amplitudes with the same mean load were chosen for each increasing cyclic loading test series to investigate the effect of fatigue on the fracture toughness of rocks: 0.45 kN at 10% static ultimate load (SUL), 0.9 kN at 20% SUL, 1.35 kN at 30% SUL and 1.8 kN at 40% SUL (see Fig. 3).
3. Results of tests 3.1. Results of static tests Five CCNBD samples were tested under load-control test conditions. The specimens were placed under the platens with a crack inclination angle of zero (b ¼01) to provide mode I loading conditions. The loading rate was chosen as 9 kN/s to cause failure within 20 s as suggested by the ISRM [19]. The maximum recorded load and the calculated KIC values obtained from both ISRM standard tests are shown in Table 2.
Fig. 3. Various amplitude increasing cyclic loading with same mean values.
Table 2 Mode I fracture toughness values of Brisbane tuff obtained by CCNBD tests. Rock type
Brisbane Brisbane Brisbane Brisbane Brisbane Brisbane Brisbane Average
tuff-1 tuff-2 tuff-3 tuff-4 tuff-5 tuff-6 tuff-7
Pmax (kN)
KIC (CCNBD)
CCNBD
(MPaOm)
5.2 5.1 4.6 5.1 4.1 4.0 3.5 4.5
1.3 1.3 1.2 1.3 1.1 0.9 0.8 1.1
Two of the load–CMOD plots of CCNBD specimens are shown in Fig. 4. The transition point from stable crack propagation to unstable crack propagation can be determined by using load– CMOD plots. Further, it is possible to show that there is a fracture process zone (FPZ) in front of the tip of the chevron notch crack by obtaining the plastic deformation behaviour just before the reaching of failure load. However, it was not possible to get post-peak tensile softening behaviour after failure with all specimens. 3.2. Results of cyclic tests The main purpose of performing two types of cyclic loading was to find the most damaging cyclic loading type using the same amplitudes. It is known that the act of applying a load provides energy for the crack initiation and propagation process in a
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Fig. 4. Load–CMOD plots of CCNBD specimens during monotonic testing. Fig. 5. S–N curve for CCNBD specimens. Table 3 Results of sinusoidal cyclic loading. Smax (as % of static failure load)
Fmax (failure load, kN)
Number of cycles (N) up to failure
93 93 88 88 84 84 84 80 80 75 75 75 75 71 70 70
4.2 4.2 4 4 3.8 3.8 3.8 3.6 3.6 3.4 3.4 3.4 3.4 3.2 3.1 3.1
835 587 13 205 9 149 285 13000 27000 1761 4831 1153 24175 6250 50000a 50550a
a
No failure after that point.
material. By removing the load, the energy supply driving crack propagation is discontinued and the remaining excess energy in the system dissipates through the crack propagation processes. Hence, the points at which the loading and unloading of a cycle stop become important. The first important conclusion drawn from the sinusoidal cyclic tests was that the failure load used in calculations of indirect tensile strength is definitely weakened 30% by repetitive loading. Results are given in Table 3. The S–N curve clearly shows that as the maximum applied diametral load decreases, the life expectancy of a CCNBD specimen increases (see Fig. 5). Because the load range used in tests to determine fracture toughness is very small, the data around high amplitudes is clustered. However, the S–N curve shows that the ultimate load causing failure is reduced by 30% (from 4.5 kN to 3.2 kN) because of rock fatigue. Therefore, it can be concluded that crack propagation resistance (fracture toughness) can be reduced by 29–30% through repetitive loading. This means that a crack can propagate under lower loads than the expected ultimate loads under repetitive loading. The series of diametral compressive increasing cyclic loading tests was performed on 12 CCNBD Brisbane tuff samples. Fracture toughness values of Brisbane tuff under static loading were calculated as 1.12–1.5 MPaOm using the ISRM [19] suggested methods as discussed above. The fracture toughness reduction because of cyclic loading is given in Table 4 by comparing with
static fracture toughness values. The main purpose of this comparison is to show the clear reduction of ultimate failure load that resulted in the reduction of the mode I stress intensity factor because of rock fatigue. It is shown that crack propagation causing failure is possible with lower stress intensity values (KI) at the crack tip than the critical stress intensity value (KIC). This result goes against the classical theory, which predicts that there will be no crack growth as long as KI oKIC. According to the obtained results, the maximum reduction, 46% of static KIC, was obtained with the highest amplitude, 1.99 kN at 40% SUL, of cyclic loading. The mode I fracture toughness value of Brisbane tuff (NST50) was reduced from 1.12 MPaOm to 0.61 MPaOm with the highest amplitude under increasing cyclic loading. This reduction has important implications for the investigation of the effect of cyclic loading on the fracture resistance of cracks in rocks. To date, experimental observations of cyclic loading tests have indicated that dynamic cyclic loading seems to have a greater effect on fracture toughness degradation of rocks than sinusoidal compressive cyclic loading. The reduction of fracture toughness was found to be 29% under sinusoidal loading tests as shown, whereas increasing cyclic loading caused a reduction of fracture toughness at a maximum of 46%. For a clear understanding of the effect of rock fatigue on damage mechanisms, a comparison between static and dynamic cyclic loading tests is shown in Fig. 6 by plotting both results on the same axes. The amplitude of the dynamic cyclic loading used in the test was 0.45 kN at 10% of SUL. As seen in Fig. 8, both failure load values and damage mechanisms are quite different under static and dynamic cyclic loading. The failure load obtained from the average of two static tests was reduced from an average of 4.2 kN to an average of 2.1 kN because of rock fatigue. In both test types, stable and unstable crack propagation stages were clear. However, the resistance of crack propagation to cyclic loading with accumulation of plastic deformation (1 mm) was much greater than the relative value (0.025 mm) under static loading before failure (see Fig. 6). This behaviour shows that the development of a large number of microcracks causing accumulation of irreversible deformation is observed even prior to the appearance of main cracks in a loaded specimen. This phenomenon is similar to the subcritical failure of geomaterials commonly known as subcritical crack propagation. The mechanisms responsible are discussed in detail below. A load–CMOD plot further reveals that there is a tensile softening behaviour with dynamic cyclic loading. Due to the different post-peak behaviour, the behaviour of the damage zone
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Table 4 The fracture toughness reduction due to cyclic loading: a comparison with static fracture toughness values. Sample
Amplitude % SUL
Ultimate load (kN)
Number of cycles (N) up to failure
Mode-I stress intensity factor (KI)a pffiffiffiffiffi (MPa m) [22]
Fracture toughness pffiffiffiffiffi (KIC)b (MPa m)
Reduction of KIC (%)
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
10 10 10
2.39 1.95 2.69 2.34
2453 1829 2261 2181
0.62 0.50 0.69 0.61
0.72 0.60 0.83 0.72
35 45 26 35
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
20 20 20
2.16 2.10 2.24 2.17
1553 1501 1630 1561
0.55 0.53 0.57 0.55
0.67 0.65 0.70 0.67
41 42 38 40
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
30 30 30
2.40 2.5 2.42 2.44
1218 1702 1501 1473
0.62 0.64 0.62 0.63
0.74 0.77 0.75 0.75
34 32 33 33
CCNBD-Rp1 CCNBD-Rp2 CCNBD-Rp3 Average
40 40 40
1.86 2.17 1.95 1.99
319 446 136 300
0.48 0.55 0.50 0.51
0.57 0.67 0.60 0.61
50 41 47 46
a
a is assumed at 0.5.
b
Y nmin is assumed at 1.21.
Fig. 6. Comparison of load–CMOD curves of CCNBD specimens tested under static and increasing cyclic loading.
at the tip of the chevron notch inside the sample is also different. This may help to explain the fatigue mechanisms by using the FPZ concept in front of the cracks. In contrast, no tensile softening post-peak behaviour was observed with the static loading tests (see Fig. 6). These findings are significant and helpful in explaining rock fatigue mechanisms. Another important observation was made by examining the crack surfaces of failed specimens after the dynamic cyclic loading tests. There was a clear crushed region including small particles and dust in front of the chevron tip, as shown in Fig. 7b. However, no rock chips (small particles) were observed at the crack surfaces of failed specimens under static loading, as seen in Fig. 7a. High micro- and macrocrack density in front of the chevron tip shows a gradual separation of crack surfaces along the preferential path set up by microcracking. This damaged zone in front of the chevron tip is called the FPZ. The mechanisms of rock fatigue under cyclic loading have been explained in the literature with many more microcracks induced compared to the failure mechanisms under static loading [23,24]. Therefore, observation of the FPZ zone in
front of the chevron notch in CCNBD specimens is a useful means of investigating fatigue mechanisms. Fig. 8 shows the load–CMOD plots with different amplitudes of increasing cyclic loading tests. To avoid bounding and moving of the samples, a 0.5 kN minimum compressive load was applied at the beginning of all tests. The loading–unloading frequency was 1 Hz. As the plastic deformation is very high compared with elastic deformation in the plots, the CMOD axis was plotted as a log scale. A clear tensile softening can be seen in all plots through post-peak behaviour in load–CMOD plots after an accumulated plastic deformation in the samples. This tension-softening behaviour is responsible for the development of the FPZ in front of and around the crack tip. The cohesive crack model is able to describe materials that exhibit strain-softening behaviour [25]. However, it is hard to say whether there is a single crack plane, as defined traditionally under static loading in fracture mechanics, which takes place in front of the chevron tip under cyclic loading. Therefore, ‘damage’ is the preferred term to use in rock-fatigue research, rather than ‘failure plane’ (main crack). It is possible to see quantified damage as the accumulation of permanent strain within each cycle in all load–CMOD plots. From these plots, it was found that clear tensile softening behaviour took place for all post-peak behaviours after an accumulated plastic deformation in the sample. However, the microcracking damage process that causes the tension-softening behaviour under cyclic loading needs to be determined. The cohesive crack model proposed in the literature may not be able to explain the observed tension-softening behaviour under cyclic loading. This is because there are some limitations among cohesive crack formulations, such as the crack tip face closing smoothly (the stress intensity factor KI vanishes at the crack tip in mode I propagation) and the FPZ being of negligible thickness [25]. Conversely, it was not possible to get tensile softening or post-peak behaviour after a plastic deformation with static loading tests. A detailed discussion about possible fatigue damage mechanisms is given below. 3.3. The Mechanisms of rock fatigue damage A typical feature of rock fatigue in experimental tests can be observed by producing a progressive accumulation of permanent
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Fig. 7. Failed specimens and damaged zone in front of the chevron tip (a) under static loading and (b) under cyclic loading.
Fig. 8. Load–CMOD plots of increasing cyclic loading with amplitudes (a) 10% SUL (0.45 kN), (b) 20% SUL (0.9 kN), (c) 30% SUL (1.35 kN) and (d) 40% SUL (1.8 kN).
strain in the specimen, rather than any significant decay in the material’s elastic modulus. Accumulation of plastic deformation is responsible for the fatigue damage; the magnitude and increasing trend of the irreversible deformation influences the cumulative fatigue damage. The displacements along both x and y directions represent CMOD and diametral axial displacement, respectively,
as shown in Figs. 10 and 11 with different amplitudes. Plots of permanent damage show that both the CMOD and diametral axial displacement increase with increasing damage increments but at different rates. Initially, irreversible CMOD deformation develops quickly. This is followed by deformation increasing at a slow constant rate before cumulative deformation begins to accelerate
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rapidly until failure. Conversely, diametral axial displacement–N plots show that the displacement rate increases with an increasing rate up to failure (see Figs. 9 and 10). The opening of crack faces parallel to the applied load and the closure of crack faces perpendicular to the load causes certain changes in the relative lateral and axial deformations, respectively. Behaviour of diametral axial deformation results may show that irreversible damage accumulation in front of the chevron tip is not caused by the closing of pre-existing microcracks aligned parallel to the maximum principal stress. A closer examination of diametral axial displacement and CMOD after the start of nonlinear behaviour in plots shows both diametral axial displacement and CMOD increase with a concave upward rate (see Fig. 11). Continuous irreversible damage occurs slowly up to a certain point because new stress-induced microcracks are taking place. Coalescence of the induced cracks starts after this point, with the rate of cracking increasing in speed, up to failure. The characteristics of the fracture surfaces were examined by means of a JEOL JMS-6460 LA SEM. The JEOL JSM-6460 LA is a tungsten low-vacuum analytical SEM. In this study, all rock fracture images were obtained under low vacuum chamber pressures, that is, 1–50 Pa (with adjustable pressure between 10 Pa and 270 Pa). This allowed certain samples to be observed uncoated and reduced damage to the specimens caused by the
Fig. 10. (a) CMOD and (b) diametral axial displacement versus number of cycles plots: same mean increasing cyclic loading (type II) tests with amplitude 20% SUL (0.9 kN)
Fig. 9. (a) CMOD and (b) diametral axial displacement versus number of cycles plots: same mean increasing cyclic loading (type II) tests with amplitude 10% SUL (0.45 kN).
effects of high vacuum. In this study, the damaged zone in front of the tip of the chevron notch cracks of the tested CCNBD specimens were examined directly with a SEM, without preparation of thin sections. Thin-section specimens were not used in this study to avoid creating extra microcracks during preparation of the specimens. Scanning electron micrographs of fracture surfaces of Brisbane tuff CCNBD specimens tested under cyclic loading are shown in Fig. 12. Two fatigue mechanisms were observed in the cement of Brisbane tuff: (1) grain decohesion in secondary microcrystalline quartz cement intrusions (see Fig. 13) and (2) fatigue striations in primary silica cryptocrystalline cement. Fig. 13 provides a closer look at the cement and feldspar mineral. Some microcrystalline quartz cement intrusions were seen in the primary silica cryptocrystalline cement after petrographic analyses. Fig. 13b shows those microcrystalline quartz cement intrusions. Closer examination of the damaged cement would appear to indicate that a massive amount of loosened microcrystalline quartz minerals resulted from grain decohesion. Further, there is a clear grain boundary crack between the feldspar and cement (see Fig. 13a). Similar to the fatigue damage in the cement, there were two fatigue damage mechanisms seen with grain-related damage: (1) intergranular cracks causing grain decohesion (a primary mechanism) and (2) intragranular cracks (a secondary mechanism). Brisbane tuff is composed mainly of quartz and K-feldspar minerals
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Fig. 11. Diametral axial displacement and CMOD after the start of nonlinear deformation in front of the chevron crack tip.
Fig. 12. Debris and small particles in front of the tip of the chevron notch as a result of cyclic loading.
with small amounts of siderite (Fe-carbonate) and zeolite minerals. Fig. 14 shows the fatigue-induced cracking around the quartz and feldspar minerals. Fatigue-related microcracking around tuff minerals causing grain decohesion as a result of the pulling out of grains by frictional sliding is visible in Fig. 14c and d. Fig. 14b and e are
presented at greater magnification in Fig. 14a. At this scale, intergranular cracking around the grains is apparent. Under closer examination, fine fragments around the grains were observed, which accumulate in the proximity of the grain corners. This is particularly evident in Fig. 14e, from which it can be inferred that
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Fig. 13. Fatigue damage in the cement of Brisbane tuff resulting from decohesion of microscale quartz minerals.
Fig. 14. Grain decohesion and loosened grains (a)–(e) and fatigue striations in damaged grains under high magnification ( 500) at the surface of the fatigue crack (f).
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such powder is the result of fatigue damage, probably due to local abrasion of the sharp corners of the quartz and feldspar grains. SEM imaging revealed that the primary fatigue damage mechanisms in front of a chevron notch crack are grain decohesion and intergranular cracks. Debris and dust are the results of fatigue damage in Brisbane tuff cement and around loosened grains. The fatigue cracks in the cement are restricted around the grains and cannot grow through the grains. Therefore, it can be deduced that those fatigue cracks are stable (subcritical) cracks that coalescence to form macroscale fatigue cracks resulting in failure. Further, each grain after decohesion may behave as an indenter to indent the surface of the weaker cement material under far field cyclic diametral compressive loading. This would explain the mechanisms of the debris material around and in the corners of the loosened grains.
4. Discussion The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static KIC of 46% was obtained for the highest amplitude dynamic cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static KIC of 29% was obtained. These reductions clearly illustrate the dramatic effect of cyclic loading on the fracture resistance of cracks in rocks. This means that crack propagation and damage can take place under lower than expected ultimate loads compared with static loading. The mode I stress intensity factor KI at the crack tip is known to control crack growth. The stress corrosion lower limit is Ko and the fracture toughness is KIC. When KI 4KIC, the crack grows rapidly at approximately the speed of sound, when KI oKo, the crack does not grow and when Ko oKI oKIC, the crack grows at a certain velocity with the stress intensity factor KI. However, this research shows that unstable crack propagation causing failure occurs with lower KIs at the crack tip than the KIC value. This result contradicts the classical theory, which predicts that there will be no crack growth as long as KI oKIC. This phenomenon is known as ‘subcritical crack growth’ [26,27]. Subcritical crack growth is one of the main explanations for the creep damage mechanism in rocks. In some fatigue research, damage accumulation in brittle materials under cyclic loading has been explained by the creep mechanism and stress corrosion [28,23,29]. Despite using different test geometries and loading boundary conditions to those were used in past studies, this study found similar damage behaviour in front of the notched crack in our disc shaped samples as a result of dilatant creep damage behaviour. It was possible to measure the crack growth rate for subcritical crack growth in other studies under controlled stress corrosive environments with edge-cracked specimens. However, it is not possible to measure the crack growth rate in our cyclic loading experiments because of the unknown stress corrosive mechanism and the high-speed unstable crack propagation due to the embedded notch crack in the disc specimens. Further, there was no pre-existing crack for proper monitoring in our three-dimensional sample geometry because chevron notched specimens do not need to be pre-cracked for rock fracture research [19]. Stress corrosion is the most common mechanism associated with subcritical crack growth in rock. However, it is certainly not the only mechanism by which subcritical crack growth occurs. Another mechanism that can be important, in certain circumstances, is fatigue crack growth. In this study, it has been shown that the N to failure decreased when the amplitude of cycles increased. This effect may also be explained by stress corrosion. Stress corrosion and fatigue represent the major mechanisms of subcritical crack growth in rocks [26,23]. Most of the experimental
work on stress corrosion crack growth in rocks and ceramics use methods originally developed for determining fracture toughness in metallic materials. The corrosive environment is water and there is a chemically active environment in those metallic material experiments. However, some mechanisms have been accepted as additional mechanisms of subcritical crack growth, such as cyclic fatigue [23,20]. In this research, it is believed that fatigue cracks (e.g. intergranular cracks) are the dominant mechanisms of subcritical crack propagation. Thus, the main aim here is to discover the possible mechanisms in microcracks causing the corrosive environment. Therefore, direct observation of the FPZ in front of the tip of the main crack in the tested CCNBD specimens using the SEM was found a suitable observation technique for this research. To investigate possible differences between static and fatigue failure, the fracture surfaces of monotonically tested CCNBD specimens were also observed by SEM. Scanning electron micrographs of fracture surfaces of Brisbane tuff CCNBD specimens tested under monotonic loading are shown in Fig. 15. When compared with static rupture, the main differences are: (1) the number of fragments produced is much greater under cyclic loading than under static loading and (2) intergranular cracks are formed due to particle breakage under cyclic loading, whereas smooth and bright cracks along cleavage planes are formed under static loading. Further, the macroscale main crack causing failure is seen in the cement without any dust or debris material under monotonic loading. Typical sparkling cleavage cracks resulted when rupture of the crystals occurred along cleavage planes.
5. Conclusions The fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and induced plastic displacement. The maximum reduction of the static KIC of 46% was obtained for the highest amplitude dynamic cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static KIC of 27% was obtained. These reductions clearly illustrate the dramatic effect of cyclic loading on the fracture resistance of cracks in rocks. Damage was quantified as the accumulation of permanent strain in front of the chevron notch crack tip with each cycle of loading, because microfracturing introduces nonlinearity into the theoretically elastic behaviour of the rock. A continuous irreversible accumulation of damage was observed in dynamic cyclic tests conducted at different amplitudes. After the accumulation of irreversible damage and failure of the specimen, clear tensile softening was observed in cyclic loading tests carried out at different amplitudes on vertically aligned chevron notch cracks (mode I). However, no post-peak behaviour was observed in the CCNBD specimens tested under static loading. Considering the shape of the load–CMOD plots, the accumulation of irreversible damage in front of the chevron notch crack under cyclic loading was found to be similar to static fatigue (creep). Further, the subcritical crack mechanisms were verified from rock-fatigue research, with lower ultimate loads causing smaller KI than the KIC due to rock fatigue. The SEM results enable some of the qualitative features of the fatigue damage process in Brisbane tuff to be inferred. This research found that the failure of a CCNBD specimen under cyclic loading is the result of the coalescence of many microcracks, not of the growth of a single macrocrack. SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular fracturing and transgranular fracturing. The main characteristic is particle breakage under cyclic loading, which probably starts at contacts between particles and is accompanied by the production of very
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Fig. 15. Damage in the cement and cleavage cracks under monotonic loading.
small fragments, probably resulting from frictional sliding within the weak matrix. It is believed that point contacts at grain boundaries are regions of stress concentration (i.e. indenters). Transgranular cracks may emanate from these regions and intergranular cracks sometimes pass through the contact points. This stage can be correlated with a steady progression of damage and produces a general ‘loosening’ of the rock, which is a precursor to the formation of intergranular cracks. When compared with static rupture, the main differences are that a much greater number of small particles and debris are created under cyclic loading than under static loading, and that intergranular cracks are formed due to particle breakage under cyclic loading, whereas smooth and bright cracks are formed along cleavage planes under static loading.
Acknowledgements Acknowledgement is made to Leighton Contractors who provided core samples of Brisbane tuff from the CLEM7 Project and to Ted Brown, Les McQueen, Mark Funkhauser and Rob Morphet of Golder Associates Pty Ltd. for their assistance and advice. The work described forms part of the first author’s PhD research carried out within the Golder Geomechanics Centre at The University of Queensland. The first author was supported by an Australian Postgraduate Award/UQRS and the Golder Geomechanics Centre. References [1] Griffith AA. The phenomena of rupture and flow in solids. Philos Trans R Soc Lond 1920;221:163–98. [2] Lajtai EZ. A theoretical and experimental evaluation of the Griffith theory of brittle fracture. Tectonophysics 1971;11:129–56.
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