JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B1, 10.1029/2000JB000058, 2002

3. Experimental Approach

3.1. Fracture of Ice

[11]   The difficulty in directly applying ice mechanics to the problem of ice shelf fracture lies in the need for both theory and experiment to predict failure at the low deviatoric stresses, well below 1 MPa, occurring in ice shelves. Mechanical tests on ice between -5 and -50°C indicate fracture strengths of 1–2 MPa in uniaxial tension, 4–30 MPa in uniaxial compression, and up to 60 MPa in triaxial compression, depending on confining pressure and strain rate [e.g., Hawkes and Mellor, 1972; Schulson, 1990; Murrell et al., 1991]. This enormous strength variation reflects differing failure mechanisms under different stress states, as well as a dependence on ice type. Brittle failure in tension occurs by unstable propagation of a single crack at stresses very close to the crack nucleation stress for previously uncracked ice. Higher strengths are attained in compression because the extension of tensile microcracks in a compressive stress field is stable. In many other brittle solids, such as cast iron, glass, and hard rock, fracture initiates from preexisting cracks, or “Griffith flaws” (see Gandhi and Ashby [1979] for a review). However, for plastic-brittle solids, such as ice at high homologous temperatures and low confining pressure, cracks must nucleate prior to fracture initiation. We therefore contend that brittle features in ice are essentially extensional and cause failure by propagation of nucleated flaws in a favorable stress field. It is necessary to adopt an experimental, fracture mechanics approach, outlined below, in order to reconcile fracture occurring at the low stresses in ice shelves.

[12]   According to Griffith theory [Lawn, 1993], fracture initiates in brittle solids from preexisting sharp cracks or flaws once the local tensile stresses at the tip of the crack are sufficient to overcome interatomic bonding. In the Irwin-Orowan formulation of linear-elastic fracture mechanics a scale-independent stress intensity factor K describes the magnitude of stresses around a crack tip such that K (a)^1/2, where is the remotely applied stress and 2a is the crack length. The precise formulation depends on crack geometry, but initiation of fracture always occurs at a critical value of the stress intensity factor, K_C, that is a material constant and thus an important scale-independent parameter. This critical value can be achieved through an increase in remotely applied stress or an increase in crack length; hence even at very low stresses, a long enough crack will propagate. Once fracture has initiated, dynamic crack propagation can occur in a tensile stress field.

[13]   There are three basic modes of crack deformation. For the analysis of crevasse penetration we are only concerned with purely tensile, mode I, crack opening where the crack will always grow in its own plane. The stress intensity factor for this case is written K_I, and the critical stress intensity, K_IC, is called the fracture toughness. We do not consider subcritical crack growth (see, for instance, Atkinson and Meredith [1989a]), for which K < K_C, as no experimental data exist for ice, even though it is probably important for understanding the dynamics of ice shelf disintegration. At this stage we are only seeking to model what is essentially a static problem.

3.2. Experimental Fracture Mechanics of Ice

[14]   There are two principal, but related, problems in undertaking fracture mechanics tests on ice. The first is the large grain size of natural ice. For truly scale-independent fracture toughness to be measured in the laboratory, satisfying the strict conditions of linear-elastic continuum mechanics, impossibly large test specimens would be needed [Dempsey, 1991]. Second, ice is notably brittle and has very low fracture toughness, much lower than glass [Lawn, 1993]. Early fracture mechanics tests on ice aimed to measure the fracture toughness at the point of unstable crack growth during simple monotonic loading to failure [e.g., Goodman and Tabor, 1978; Liu and Miller, 1979; Nixon, 1988]. However, even for laboratory-grown freshwater ice, these data displayed a large amount of scatter, possibly due to the use of test specimens which were too small [see Dempsey, 1991]. For this reason, much subsequent work has sought to measure the fracture resistance of ice to crack propagation and has looked toward a nonlinear fracture mechanics approach where the specimen size constraints are not so severe. Here the aim is to allow stable crack propagation to occur under increasing crack extension forces before the onset of rapid fracturing. However, truly stable crack propagation has never been observed in ice. Instead, Parsons et al. [1988], DeFranco and Dempsey [1994], Stehn et al. [1994], and Sammonds et al. [1998] have observed quasi-stable, incremental crack growth (sometimes called “stick slip”), in freshwater, saline and sea ice, for a variety of specimen geometries. Stick-slip cracking consists of crack initiation followed by unstable crack growth and crack arrest. This phenomenon may be explained by the large grain size of natural ice, the fact that fracture resistance is lower for crack propagation than crack initiation, and the experimental geometry.

[15]   We have developed fracture mechanics test methods for ice cores using a chevron-notched short-rod specimen loaded in tension and a chevron-notched round-bar specimen loaded in three-point bend (Figure 3) on the basis of the recommendations of the International Society for Rock Mechanics (ISRM), Commission on Testing Methods [1988] [see also Matsuki et al., 1991]. The chevron-notched specimens have been widely used in rock mechanics because specimens are produced from cored material. Crack growth is initially stable so the specimen is self-precracking, and there is no requirement for direct crack length measurement [Atkinson and Meredith, 1989b].

3.3. Experimental Procedure

[16]   Before testing, a right-cylindrical core piece has a notch cut either perpendicular (three-point bend) or parallel (short-rod) to the core axis in the form of a V or chevron (Figure 3). For both three-point bend and short-rod tests the notch opens under tension, causing a crack to initiate from the sharp notch root, increasing in size as it grows in plane toward the broad end of the chevron. The mode I stress intensity factor associated with this notch geometry increases with increasing crack length. However, the stress intensity factor normalized by applied force at first decreases as the crack length increases, reaches a minimum at crack length a_min, and then increases again. This means that crack extension should initially be stable. As a result, a crack can be grown gradually for some distance by a succession of cycles of increasing load, and its position can be deduced from changes in specimen compliance.

[17]   The three-point bend test allows the investigation of fracture perpendicular to the ice core axis. Strict geometrical controls are imposed on the specimen size and notch dimensions in order to ensure plane strain conditions. In particular, the distance between the lower support points is always 3.33D, where D is the specimen diameter. The depth to the tip of the chevron notch is 0.15D [ISRM, 1988]. Three-point bend specimen diameters used in this study were in the range 60–100 mm. During the testing program we found that unstable fracture propagation almost always occurred with the first crack growth increment for the three-point bend tests; stable or stick-slip crack growth could not be achieved. Figure 4a shows typical behavior, where repeated stress cycles did not result in crack growth prior to failure and so the compliance of the specimen was unchanged. For this type of unstable crack propagation we have evaluated the apparent fracture toughness by arbitrarily assuming a degree of crack growth that minimizes K for the test geometry; this occurs when the crack has advanced ~0.15D from the chevron tip [Rist et al., 1996].

[18]   Short-rod testing allows the investigation of fracture parallel to the ice core axis. It utilizes one half of the (broken) three-point bend specimen after testing. The tensile load is transmitted through freely rotating pull-rods and grips, designed to eliminate bending and torsion stresses on the specimen. Specimen deformation is measured by means of displacement transducers spanning the notch mouth. The standard ISRM short-rod test geometry has a specimen length to diameter ratio of L/D = 1.45. For Antarctic ice we found that abrupt failure occurred immediately following crack initiation, without any stable crack growth, as for the three-point bend tests. However, we were able to resolve this problem for the short-rod geometry by increasing specimen length to L/D = 2.0, effectively stiffening the specimen and creating a more compressive stress field into which the crack was forced to grow. In this way, unlimited unstable propagation was prevented, and crack growth progressed by stick-slip. The mechanical analysis for this modified test specimen has been given by Rist et al. [1999]. Short-rod specimen diameters varied from test to test in the range 46–92 mm.

[19]   Typical behavior during loading for the short-rod test is shown in Figure 4b. Changes in the slope of the load versus crack-mouth opening displacement (CMOD) curve, which is predominantly linear at low loads, indicate changes in specimen compliance and hence crack growth. Compliance is measured by cycling the load at a low level before allowing it to rise until crack growth occurs. A crack initiates from the notch root at load F₀, moves rapidly forward, and then stops. This first increment is not normally analyzed since the nature of the small artificial starter crack is unknown. There are four further growth increments represented in Figure 4b at loads F₁to F₄ before the crack grows out of plane. For each increment the crack position is determined from the measured compliance and then the corresponding stress intensity to initiate growth in each case is computed using the stress intensity-crack length relationship given by Rist et al. [1999].

[20]   Testing was conducted using a stiff, 20-t servohydraulic universal load frame, fitted with a large environmental chamber cooled using liquid nitrogen and controlled to within 1°C. Each ice specimen was precisely machined using an adapted metallurgical machine lathe in a cold room at -10°C. The chevron notch was cut using a sharp, thin, chisel-type blade fitted to a modified histological microtome. This notch was sharpened with a razor blade immediately prior to testing in order to facilitate crack initiation. All tests were carried out at -20°C using a fixed nominal displacement rate of 5 × 10^-6 m s^-1, producing stress intensity rates in the range 5–20 kPa m^1/2s^-1, dependent upon specimen size.

Citation: Rist, M. A., P. R. Sammonds, H. Oerter, and C. S. M. Doake, Fracture of Antarctic shelf ice, J. Geophys. Res., 107(B1), 10.1029/2000JB000058, 2002.

Copyright 2002 by the American Geophysical Union.