ISRM Suggested Method for the Determination of Mode II Fracture Toughness
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Fracture is a failure mechanism of brittle materials that is of great importance for the performance of structures. Rapid and violent failures of large-scale geotechnical, mining or civil engineering structures cause significant safety hazards, material damage, and interruption to or even cessation of mining or building activities. Ability to recognise pre-failure rock mass behaviour may result in predicting or averting the potential for geotechnical and geological failures (Szwedzicki 2003). Rock fracture mechanics is one approach to resolve this task.
Rock fracture mechanics can be employed not only to improve safety, but also to enhance the performance and profitability of rock engineering structures. Examples are the geological disposal of radioactive waste, terrestrial sequestration of carbon dioxide to ease prejudicial effects on the environment, efficient underground storage of oil, gas or air, enhanced recovery of hydrocarbons, geothermal energy extraction, and underground constructions at increasing overburden pressure for infrastructure or transport. For these geomechanical applications the stress states are mostly compressive, therefore, shearing is an important failure mechanism in rock materials.
The stress and displacement field around a crack tip during shearing results from the application of uniform shear loadings at infinity. In this so-called Mode II loading in fracture mechanics, the crack faces slide relative to each other and displacements of the crack surfaces are in the crack plane and perpendicular to the crack front. The crack initiation takes place when the crack tip stress intensity factor KII reaches a critical value, called the Mode II plain strain fracture toughness KIIC. The value of KII depends on the external loading, the geometry of the specimen and crack dimension. The fracture toughness KIIC, sometimes called critical stress intensity factor, is a material parameter depending on the type of rock material and its physical boundary conditions, such as confining pressure and temperature.
Whittaker et al. (1992) have presented an overview of different methods for determination of Mode II fracture toughness. Some more recent methods have been proposed by e.g. Chang et al. (2002), Hakami and Stephansson (1990), Ko and Kemeny (2006), Rao et al. (2003). Only Rao et al. (2003) performed experiments on Short Beam Compression specimens with application of confining pressure that is independent of the vertical load, but the method is under discussion as it frequently delivers KIC > KIIC (Whittaker et al. 1992; Watkins and Liu 1985).
The important influence of confining pressure on Mode II fracture toughness can only be determined by methods that can independently apply a normal load to the fracture plane. It has been stated by several researchers that under conditions of overall compression Mode II fracture, propagation is most likely (Melin 1986; Lawn 1993). This was experimentally confirmed by Bobet and Einstein (1998) who demonstrated that macroscopic wing fractures (Mode I) can be suppressed by applying confining pressure, i.e. normal stress. Confining pressure had to be applicable to the specimen to be able to suppress macroscopic tensile fracturing. The Punch-Through Shear with Confining Pressure (PTS/CP) experiment (Backers 2005; Backers et al. 2002a, b, 2004) allows measuring KIIC at different confining pressures. A modified version of PTS/CP test of rectangular samples under biaxial loading was presented by Lee (2007).
In Mode I loading the crack is subjected to a normal stress, the crack surfaces separate symmetrically and the crack front propagates in direction of the crack plane. Three ISRM Suggested Methods for determining Mode I fracture toughness K have been presented (Ouchterlony 1988; Fowell et al. 1995). Fracturing in rock structures commonly occurs under mixed mode I–II loading where crack faces undergo both opening and sliding displacements and where pure Mode I stress and pure Mode II stress intensity are the limiting cases of mixed mode I–II loading. To solve common rock engineering problems with a fracture mechanics approach both fracture toughnesses KIC and KIIC are needed.
The suggested method for KIIC fracture toughness determination makes use of the PTS/CP experiment, where specimens from KIC testing (Chevron Bend test Ouchterlony 1988) can be used to obtain fracture toughness data for both Mode I and Mode II analysis.
It may be discussed if the concept of mode of fracturing is applicable to rock material. Rock is, in general, a multi-component material. Hence, when a fracture propagates through the material, it may not follow a straight trace but is influenced by grain boundaries, cracks, flaws and other discontinuities. From a mathematical point of view, in which the concept of the mode of fracturing was developed, a pure mode of fracture can only be achieved if the fracture propagates in a straight continuous plane within a given homogeneous stress field. Therefore, any deviation of the propagation direction of the fracture within the applied stress field introduces some mixed mode kind of fracturing.
Moreover, the fracture follows the given fabric and the fabric itself will introduce stress fluctuations that superimposes to the applied stress field (Dyskin 1999). In addition, the fracture generated will itself introduce cracks in its surrounding and build up a zone of mixed mode microcracking, the so-called fracture process zone. Hence, for a granular material the differentiation into the mode of fracturing is not possible on the microscale.
From analysis of acoustic emission recording in laboratory experiments it has been clearly shown that at Mode I and Mode II loading conditions, where the macroscopic fracture follows the direction of Mode I and Mode II, respectively, the micromechanical breakdown involves both tensile as well as shear cracking (e.g. Backers et al. 2005; Stanchits et al. 2003). Therefore, neither under pure Mode I nor Mode II loading conditions is the crack propagation pure tensile or pure shear; fracturing in rock material which always involves a mixed mode on the microscale.
In the context of laboratory based fracture toughness testing the mode of fracturing is here understood from a macroscopic point of view, at which the fracture propagation is in the direction of Mode I or Mode II. Further, as fracture toughness depends on boundary conditions, the term material property is not applicable.
The laboratory experiment is intended to directly measure the Mode II (in-plane shear) fracture toughness of rock material. The geometry of the test specimen is designed to use standard core material (NX size or 50 mm diameter) and to deploy the remaining halves from Mode I (tensile) fracture toughness testing by the Chevron Bend method [ISRM Suggested Method (Ouchterlony 1988)]. The experimental set-up allows the Mode II fracture toughness to be measured at different levels of confining pressure. The test is called the PTS/CP experiment.
3 Specimen Preparation
For any specimen preparation treatment appropriate high precision (preferably diamond stud) tools should be used. During specimen preparation, caution has to be taken to limit the micromechanical damage of the specimen. Micromechanical damage may influence the fracture propagation and cause reduced magnitude of fracture toughness. Cautious specimen preparation should involve slow drilling, cutting and grinding operations to limit vibrations and heat generation. If no cooling agent can be used in the process of specimen preparation, special caution has to be taken to limit the temperature increase due to specimen preparation.
- 2.The specimens should be right circular cylinders having a height L to diameter D ratio of 1:1 and a diameter D equal to 50 mm (Fig. 1). The end surfaces should be flat to 0.01 mm and shall not depart from perpendicularity to the longitudinal axis of the specimen by more than 0.5°.
The mantle surface of the specimen cylinder should be smooth, free of abrupt irregularities and straight to within 0.5 mm over the full length of the specimen. Such irregularities might act as stress concentrators.
A circular notch of diameter ID = 0.5D = 25 ± 0.2 mm and depth a = 0.1D = 5 ± 0.2 mm is to be inserted into one end surface of the cylindrical specimen and a circular notch of diameter ID = 0.5D = 25 ± 0.2 mm and depth b = 0.6D = 30 ± 0.2 mm shall be manufactured into the other end surface (Fig. 1). Hence, the intact rock portion is of length IP = L − a − b = 15 mm. The axis of the circular notches has to be aligned with the cylinder axis of the specimen. The sinking of the notches may be performed preferably by a computerised numerical control (CNC) milling machine or alternatively an appropriate hollow drill bit. The width of the notches shall be t = 1.5 ± 0.2 mm. The bottom of the notches should have a small curvature.
The dimensions of the specimen should be measured to the nearest 0.1 mm. The specimen diameter should be measured by averaging two diameters measured at right angles at at-least two levels. The notch depths should be reported by averaging three measurements at angles of 120°. The specimen height should be determined by averaging three measurements at angles of 120°.
The specimen should be stored after specimen preparation for an appropriate time interval at sufficient conditions to achieve the desired moisture condition and history. The conditions of storage, moisture adjustment or drying shall be reported.
The minimum information on each specimen shall include dimensions, specimen preparation routines, special observations made during specimen preparation, moisture content, and macroscopic description of the surface.
4 Experimental Set-Up
- 1.The specimen is placed on top of a bottom support that has a central cut out CO of diameter ID + 2t < CO < ID + 5 mm and depth CD ≈ 0.1D (Fig. 2). The specimen end surface with the notch of length b faces downwards.
A load stamp assembly is placed on top of the specimen that should contain a load piston of diameter LO = ID and shall provide a sealing of the specimen from a possible confining pressure liquid (Fig. 2).
The whole assembly may be covered by a jacket that seals the specimen from the confining pressure medium.
The assembly consisting of specimen, loading devices and jacket is placed into a loading frame of sufficient capacity and equipped with a system to apply a confining pressure that can be independently controlled. The load piston of the system should be travelled into contact with the load stamp of the installed assembly; no axial load should be applied at this stage. Thereafter, the confining pressure system should be filled with confining pressure medium.
No guidelines on how to insert the specimen assembly into the loading frame or confining pressure device are given in detail, as very different systems are available. It must be assured that the workflow can be followed with the used loading equipment.
5 Testing Procedure
The minimum information collected during experiment is the applied confining pressure PC and peak load Fmax. However, it is advisable to continuously record the axial deformation δ (accuracy Δδ = 0.001 mm), the axial load Fax (accuracy ΔFax = 0.05 kN) and the confining pressure (accuracy ΔPC = 0.05 MPa) during the experiment. The rate of data acquisition should be appropriate to detect the maximum load achieved; a rate of four data sets per second (s) may be found sufficient for the suggested axial displacement rate.
- 2.A small pre-load Fpre is applied to the experimental set-up. The pre-load Fpre should be large enough to firmly stabilise the assembly, but sufficiently small as to not introduce any damage to the specimen (Fig. 3a).
The confining pressure PC is applied subsequently (Fig. 3b). The confining pressure will act on the mantle surface and on the top surface of the specimen. On reaching the desired level of confining pressure, PC should be kept constant. A servo-controlled system is recommended.
The axial displacement is increased at a constant rate of dδ = 0.2 mm/min (3.3 × 10−6 m/s) (Fig. 3c) resulting in an increase of the axial load. The other boundary conditions are kept constant.
At peak load a fracture propagates between the notches (Fig. 3d). The experiment may be terminated after driving the test to the post-peak.
The number of specimens per sample tested should be determined by practical considerations, but a minimum of five specimens is recommended. A sample in the sense of experiments consists of all specimens tested at the same boundary conditions.
7 Reporting of Results
Source of specimen as precisely as possible; location and orientation.
Lithological description of the rock type including grain size.
Details of the methods used for specimen preparation, dimensions of the prepared specimen, special observations made during specimen preparation, and macroscopic description of the specimen surface.
Orientation of the loading axis with respect to the specimen anisotropy, bedding planes, etc.
History and environment of test specimen storage or treatment (temperature, drying, saturation, etc.).
Specimen condition at time of test (saturation degree, fluid/gas content, temperature, etc.).
Details of experiment including history, confining pressure, loading rate, etc.
A record of the peak load.
Individual test plots showing confining pressure, axial stress and axial displacement vs. time. If there is major stress drops during loading, the test should be considered invalid.
The calculated value of the Mode II fracture toughness; if known, along with the Mode I fracture toughness and the ratio of KIIC/KIC.
Description of the specimen after testing, especially description of the macroscopic visible fractures. If there are fractures other than the vertical connection of the notches on stopping the test at peak load, the test may be discarded.
The report of a series of samples should contain the following:
The average value of each sample of experiments including a representative measure of the scatter.
A plot showing the Mode II fracture toughness of each sample as a function of confining pressure.
The ratio of KIIC/KIC if the Mode I fracture toughness was determined, e.g. by the Chevron Bend experiment [ISRM Suggested Method (Ouchterlony 1988)].
8 Typical Values
Values for Mode I and Mode II fracture toughness of various rocks
KIIC (low P)
KIIC (high P)
Ävrö granite, medium grained
Aue granite, coarse grained
Mizunami granite, medium grained
Seoul granite, finegrained
Flechtingen sandstone, finegrained
Bentheim sandstone, finegrained
Ruedersdorf limestone, mudstone
9 Notes and Recommendations
The following notes and recommendations shall support and explain the details of the suggested method. For further details on the reported results and information, please refer to the given references.
9.1 Evaluation Procedure
The KIIi at given boundary stresses for different ri are determined and plotted as functions of the distance from the notch tip. For the linear part of that function, a linear regression extrapolates KIIi to the notch tip, i.e. r = 0 and KIIi*.
The Energy Release rate obtained by the J-integral analysis of a limestone sample (PC = 5 MPa, σA = 87.2 MPa) is J ≈ 4 × 104 J/m2 or KIIC ≈ 3.1 MPa m1/2. In comparison, the DET method provides KIIC = 3.3 MPa m1/2. The J-integral method requires that small scale yielding is evident to be able to assume equivalence to KIIC, and additional fracturing in the specimens, as sometimes obtained, limits the evaluation capability of the method.
The advantage of the suggested method to determine KIIC is that only the peak load needs to be recorded. For e.g., a J-integral approach a full load and displacement recording would be necessary.
The given formulation is valid only for the suggested geometry and deviations from the ideal configuration will result in inaccurate values of KIIC. Further, at low confining pressures wing fractures may be introduced in the specimen altering the stress fields. This alteration is not accounted for in the equation.
9.2 Influence of Confining Pressure
The reported shear stress at failure increases non-linearly with confining pressure. As KIIC is linearly linked to the shear stress at failure,1KIIC shows similar behaviour. Due to the observations from microstructural analyses (Backers et al. 2002a), the increase of shear stress and fracture toughness may be interpreted as a bi-linear relation. At low confining pressures the average shear stress between the notches, τav, steeply increases with PC, while at high PC the τav necessary for fracture propagation increases moderately with increase in confining pressure. The transition from steep to shallow slope is around 25–35 MPa. Alternatively, one might consider a square root rise to a maximum value. However, that would imply constant fracture toughness at very high PC and no frictional influence.
From microstructural analyses, it has been reported that at low confining pressures wing fractures, i.e. tensile fractures, are initiated at the bottom notch inner tip at about 30 % of the peak load. The wing fractures are typically not initiated at confining pressures PC > 30 MPa. Also, the signature (shape and crack content) of the fracture process zone changes with the increase of confining pressure up to about 30 MPa, but not above, indicating a change of micromechanism. A discussion of these features can be found in Backers et al. (2002a, b).
9.3 Discussion of Loading History
The PTS/CP experiment has the unique ability to independently apply an external shear load and a normal stress perpendicular to the plane of shear loading. In principle, some other methods do have the possibility to vary the confining pressure, but not independently to an external shear load (i.e. triaxial compression test (Hakami and Stephansson 1990) and compression shear cube test (Jumikis 1979). The very important influence of overall compression (confinement) on Mode II loading induced fracturing (Melin 1986; Lawn 1993) can be adequately studied by the Punch-Through Shear test only.
Due to the geometry and the suggested loading layout of the test, the specimen is not loaded purely isostatically on application of the confining pressure. A shear load is introduced in the plane between the notches. The ratio of confining pressure to shear stress, κ = PC/τ, is constant during application of confining pressure.
After application of confining pressure, the inner cylinder is punched down in displacement control. The ratio of confining pressure to shear stress, κ = PC/τ, will, therefore, decrease on punching down the inner cylinder. It was shown numerically by Melin (1986) that at high ratios of κ Mode II is preferred. Lower ratios will cause preferred initiation of Mode I fracture. When PC is high enough KII will reach KIIC before τ has reached the level at which Mode I is preferred. κ is decreased in the PTS/CP experimental procedure, hence Mode II is preferred if PC is sufficiently high. In other methods (e.g. Rao et al. 2003; Jumikis 1979), Mode II loading is applied by adjusting the loading angle and confining pressure also depends on the loading angle. Hence, κ is governed by the limited loading angle to achieve Mode II loading and then is kept constant with simultaneous increase of shear stress and confining pressure.
9.4 Discussion of Displacement Rate
9.5 Discussion of Geometry
The circular geometry of the PTS/CP experiment is superior to a rectangular geometry in terms of structural stability as is mostly favoured in several Mode II testing methods. The tubular (hollow-cylindrical) layout of the PTS/CP test in the notch regions is able to withstand high confining pressures due to the tangential stresses; no sign of specimen failure is reported up to 120 MPa for limestone (Backers et al. 2004). A geometry with straight notches can be studied at low confining pressures only, as bending stresses introduced by the confining pressure would cause failure.
9.5.1 Influence of Notch Depth
Variation of rock ligament between the notches, IP, illustrates a plateau of τav for a certain range of IP (Fig. 7). Similar results are reported by Yoon et al. (Yoon and Jeon 2003) for Daejeon granite. They report constant KIIC for IP of about 17 to 40 mm. Numerical analyses performed by Watkins (1983) on samples with similar, but cubic geometry give evidence of constant stress intensity factor in Mode II for IP/L ratios of 0.3–0.5 (IP = 15–25 mm in case of PTS/CP geometry) for experimental Mode II fracture toughness determination of mortar without confining pressure.
For small ligament lengths the notches are expected to influence each other by coalescence and interaction of the initial process zones before actual fracture propagation takes place at peak load; a decrease of shear stress necessary for fracture propagation is expected at small IP. The initial fracture process zone was shown by means of acoustic emission to be few millimetres in length (~2–3 mm for Mizunami granite; (Backers 2005; Stanchits et al. 2003). If the process zones of the top and bottom notches interact at low IP, as is suggested by acoustic emission, coalescence/overlap of the fracture process zones should result in a magnified loss of strength. This is only vaguely supported by the shape of the stress versus IP plot at low IP in Fig. 7 for Ruedersdorf limestone and Carrara marble. The elevated average shear stress necessary for fracture growth in Aue granite (Fig. 7) might be explained by the comparably large grains (average is 1 mm, but up to 5 mm are included). At small IP only few grains are located between the notches and hence coalescence might be aggravated by inter- as well as intragranular crack propagation accompanied by interlocking and crack arrest.
9.5.2 Influence of Asymmetric Specimen Geometry
The proposed depth of the notches is non-symmetrical; this is to avoid compressive failure of the upper part of the inner cylinder during axial loading.
To investigate the influence of notch length, tests were performed with a = 30 mm and b = 5 mm, i.e. with the (suggested) specimen turned upside down, and compared to testing of samples with suggested set-up (Fig. 8). No evidence for a noteworthy influence of the notch depth on τav is reported (Backers 2005). During this series of testing, compressive failure of the top of the inner cylinder was frequently observed for specimens with a = 30 mm.
An unsymmetrical shape of the sample, i.e. notch depth a ≠ b, and sample height, L, is shown to have a minor influence on the obtained τav. Hence, the contribution of bending of the unsupported outer ring to the Mode II fracture process is either negligible or non-existing.
9.5.3 Influence of Notch Diameter and Sample Diameter
It should be noted that the Mode II fracture toughness as derived from the PTS/CP experiment may be sensitive to the sample diameter D and notch diameter ID (Backers 2005). It was reported that τav decreases with increasing ID at constant D for one large grained rock type. In addition, from selected experiments it is suggested that an increase of D increases τav at given ID. The effect appears to depend on grain size, but has only been studied at low confining pressure up to PC = 5 MPa.
9.5.4 Influence of Notch Width
9.6 Discussion of Fracture Generation
The fracture generation was studied on a variety of specimens and rock types and under varying boundary conditions. Fracture development and characteristics were described using macroscopic observations, thin section analysis, SEM, and analysis of acoustic emission recordings.
The reported formation of the bottom wing fracture (~30 % peak load) and upper horizontal fracture (~60 % peak load) are not detectable in the stress versus displacement data, hence the energy consumption of those is assumed to be minor.
Increased confining pressure, typically PC > 30 MPa, the wing shaped fractures are not initiated. The negative stress intensity at the level of loading is sufficient to suppress tensile macroscopic fracture. Only the fracture connecting the notches develops at increased confining pressures.
In contrast to the wing shaped fracture, which is usually a very distinct feature highlighting only a single crack line separating mostly grains boundaries, the fracture that develops at peak load shows a wide fracture process zone. In a study of the influence of the confining pressure on the characteristic of the process zone of the shear fracture it was observed that the width of the zone is considerably reduced with increase of confining pressure (Backers et al. 2002a). The applied normal load to the fracture trace alters the local stress redistribution and the fractures initiated in the process zone rotate to align with the main fracture trace. Further, less crack surface is initiated leading to a smaller fracture process zone width. These changes in characteristics were most prominent at PC < 30 MPa. Above this confining pressure the reported changes were minor.
The changes in appearance of the fracture evolution and its characteristics with confining pressure may be related to a change in slope in the shear strength/Mode II fracture toughness vs confining pressure data, c.f. Fig. 5.
Application of confining pressure superimposes a negative2KI and this results in shorter wing fractures that stop before being aligned with the major principle stress. No wing fractures are initiated at the notches in samples subjected to confining pressures >30 MPa. According to Melin (1986) pure macroscopic shear fracture growth occurs if the level of confining pressure is high enough so that all tensile stresses at the fracture tips vanish or even become compressive. The stresses at the bottom notch in PTS/CP testing at higher confining pressures are consequently below a critical level to allow macroscopic wing fracture initiation. Suppression of Mode I fracturing above a certain level of confining pressure was experimentally proven by Bobet and Einstein (1998) and is consistent with the observations for the PTS/CP experiment.
9.7 Influence of Temperature
9.8 Subcritical Crack Growth
The PTS/CP experiment was also employed to determine the subcritical crack growth parameters as defined in Charles‘ law (Backers et al. 2006). The study applied static loading at different fractions of the peak load and measured the time-to-failure. From a weakest link theory (Wilkins 1980, 1987) the subcritical parameters may be derived.
Erik Rybacki, Georg Dresen (both Helmholtz-Centre Potsdam—GFZ German Research Centre for Geosciences, Germany) and Tobias Meier (then Geomecon GmbH) were involved in certain aspects of the development of the testing procedure, the discussion of results, and the review of this contribution. John Napier, John Kemeny, Chulwhan Park, Resat Ulusay and an anonymous reviewer gave valuable comments, which helped improve the manuscript. The early versions of the method were developed in collaboration with Technical University of Berlin, Germany, and Royal Institute of Technology KTH Stockholm, Sweden. The main body of work was conducted at Helmholtz-Centre Potsdam—GFZ German Research Centre for Geosciences, Germany. The work on some aspects as reported in the appendix was carried out partly in the context of a GeoFrames GmbH (now Geomecon GmbH) research and development project supported by the European Union, European Fund for Regional Development, program ‘Investment to Future’, Period 2007–2013. Calvin Seward (Geomecon GmbH) gave the manuscript a final language reading. The contributions of the different individuals and institutions are greatly acknowledged.