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The Fracture of Water Ice Ih: a Short Overview

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The Fracture of Water Ice Ih: a Short Overview Meteoritics & Planetary Science 41, Nr 10, 1497–1508 (2006) Abstract available online at http://meteoritics.org The fracture of water ice Ih: A short overview Erland M. SCHULSON Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA E-mail: [email protected] (Received 25 October 2005; revision accepted 09 April 2006) Abstract–This paper presents a short overview of the fracture of water ice Ih. Topics include the ductile-to-brittle transition, tensile and compressive strength, compressive failure under multiaxial loading, compressive failure modes, and brittle failure on the geophysical scale (Arctic sea ice cover, Europa’s icy crust). Emphasis is placed on the underlying physical mechanisms. Where appropriate, comment is made on the formation of high-latitude impact craters on Mars. INTRODUCTION (Weeks and Gow 1980). (The terms S2 and S3 are taken from the classification of texture by Michel and Ramseier 1971). Water ice can adopt one of 13 crystalline forms or one of Subsurface Martian ice may be a textured polycrystal as well, least two amorphous states (Petrenko and Whitworth 1999). should it have formed from the directional solidification of Under low pressure and at temperatures above about −120 °C, water. water ice (or simply ice) adopts a hexagonal crystal structure, Whether in the form of a single crystal or a polycrystal, ice denoted Ih, reflected in the shape of snowflakes. Each exhibits two kinds of inelastic behavior. When slowly loaded it molecule within the Ih unit cell is connected to four others flows plastically (i.e., creeps). This is manifested, for instance, (owing to the 104.5° H-O-H bond angle), and each unit cell by strains in excess of unity within alpine glaciers where the contains four molecules. As a result of the molecular bend, deformation rate is equal to or less than about <10−9s−1 and the structure is relatively open as opposed to the closely stresses are of the order of 0.1 MPa and lower. Creep of clean packed structure of hexagonal metals: upon melting it ice, i.e., free from dust and rock, has been studied extensively collapses and this accounts for the density of ice Ih and is well understood (for reviews see Duval et al. 1983; (917 kg m−3 at 0 °C) being lower than the density of water. Weertman 1983; Durham and Stern 2001). Dirty ice is Given the relatively high temperatures near the surface of currently under investigation (Durham et al. 2006). On the Mars (>−120 °C, Armstrong et al. 2005), ice Ih is probably other hand, when rapidly loaded/deformed, but well below the crystalline form of interest in relation to the role of dynamic rates, ice fractures, as evident from the rubble field volatiles in the evolution of impact craters. that forms when a sheet of sea ice is pushed up against an With the exception of snowflakes, ice Ih generally forms engineered structure or from the fracture patterns that develop as a polycrystal, at least on Earth. Glaciers and icebergs, for within the winter sea ice cover on the Arctic Ocean (Marko and instance, form through the pressure-sintering of snow, and Thomson 1977; Kwok 2001; Schulson 2004; Marsan et al. may be characterized as bubbly aggregates of equiaxed grains 2004). Brittle behavior has been less extensively studied. 1–20 mm in diameter. The as-formed aggregates are However, significant progress has been made during the past randomly oriented (i.e., the crystallographic c-axes exhibit no decade or so, and that progress forms the focus of this preferred orientation), but can develop a strong texture discussion. through creep deformation and dynamic recrystallization In relation to Martian features, creep/ductile behavior (Castelnau et al. 1996). In comparison, the ice cover on the appears to govern the evolution of lobate debris aprons and Arctic Ocean forms through unidirectional solidification, and softened craters (Mangold et al. 2002). On the other hand, is comprised of columnar-shaped grains (~2–20 mm in brittle fracture probably governs the initial formation of high- diameter) whose crystallographic c-axes tend to lie within the latitude impact craters and subsequent rim collapse, and plane of the sheet. The c-axes are randomly oriented within almost certainly controls the initiation of polygonal features that plane in most locations within the Arctic Ocean (giving that form through tensile overloads that result from thermal S2 ice), but aligned within the plane (giving S3 ice) in others contraction (Mellon 1997; Mangold 2005). 1497 © The Meteoritical Society, 2006. Printed in USA. 1498 E. M. Schulson To some extent, the present discussion continues where volume fractions, the nature of that transition is probably earlier and more thorough reviews of brittle failure ended different from the transition in ice per se. (Schulson 2001, 2002a). For details beyond the scope of this Ice, incidentally, is unusual in exhibiting brittle behavior overview, we encourage the reader to consult the earlier right up to the melting point, at deformation rates well below reviews. dynamic rates. At root are sluggish dislocation kinetics (e.g., see Ahmad and Whitworth 1988; Shearwood and Whitworth DUCTILE-BRITTLE TRANSITION 1991). Owing to its crystal structure, ice Ih slips preferentially on the basal planes, and this is impeded by the unique To begin, a few comments on the ductile-brittle transition requirement of protonic rearrangement (Glen 1968). may be helpful. This transition is often defined, especially Molecular diffusivity is low as well—about three orders of under monotonically increasing loads, in terms of a critical magnitude lower than atomic diffusivity through metals at an strain rate, and is marked by a pseudo-linear stress-strain equivalent homologous temperature. (The melting −15 curve that ends abruptly with a sudden drop in load at terminal point diffusion coefficient of H2O in ice Ih is around 10 to failure. Under tension, the transition strain rate is of the 10−14 m2/s compared to 10–12 to 10–11 m2/s for elemental order of 10−7 s−1 for warm (−10 °C) polycrystalline metals.) This factor, however, appears to play more the role of aggregates of 1–2 mm grain size; under compression it is suppressing diffusion creep than of impeding dislocation higher and typically falls within the range 10−4 s−1 to 10−3 s−1 mobility. Interestingly, the “degree of brittleness” is rather for granular ice of the same grain size (Schulson 2001). For high, as evident from the relatively low ratio of toughness to S2 columnar ice compressed across the columns, the surface energy. For structural ceramics and rock, this ratio of transition strain rate is essentially the same as it is for granular toughness (~1 J/m2) to surface energy (~0.1 J/m2) is generally ice, but when loaded along the columns it is an order of greater than 30. The implication is that the creation of new magnitude lower (Kuehn and Schulson 1994). For larger surface is the major process underlying the toughness of ice bodies that contain larger stress concentrators or for more (Nixon and Schulson 1987). coarsely grained ice which also contains larger stress The ductile-brittle transition can be understood in terms concentrators, the transition strain rate is lower, scaling of the competition between crack-tip creep and crack roughly as (length of concentrator)−1.5 (Schulson 2001). The propagation (Schulson 1990, 2001). When creep occurs (compressive) transition strain rate decreases with decreasing sufficiently rapidly to relax stresses that concentrate at crack temperature, to the extent that it is about an order of tips, ductile behavior follows. When creep occurs too slowly, magnitude lower at −40 °C than at −10 °C, for both fresh- stress builds up to the point of local rupture and brittle water ice and salt-water ice of typical salinity 4–5‰ (Qi and behavior sets in. The transition cannot be accounted for Schulson 1998). At −80 °C, the transition (compressive) simply in terms of the onset of cracking, for given the occurs at a strain rate of ~10−5 s−1, for finely grained (d = plastically anisotropic nature of the Ih crystal (Duval et al. 1 mm) polycrystals of fresh-water ice (Aragawa and Maeno 1983), cracks form at quite low strain rates within the ductile 1997). In addition to temperature, grain size, and texture, regime, but are stable there. Nor can the transition be other factors are salinity (more below), confinement, and explained in terms of a critical density of deformation preexisting damage: an increase in each raises the critical damage, for ice that is rather slowly compressed (but not so strain rate (Schulson 2001). slowly as to avoid crack nucleation altogether) is riddled with Little is known about the role of hard particles. This gap short cracks that change the optical appearance of the material is unfortunate, given that Martian ice probably contains dust from transparent to snowy white; yet the damaged material and rock. Indeed, the role of second phases in general has not can be shortened by more than 10% without collapsing. Only been well studied. About all that is known with certainty is when cracks begin to propagate does the macroscopic that inclusions of brine and porosity in salt-water ice (~5% by behavior change. For a physically based model that volume) raise the transition strain rate by about an order of incorporates the resistance to creep, to crack growth and to magnitude with respect to fresh-water ice, owing to a brine- frictional sliding across crack faces, as well as grain size and induced increase in the creep rate or, correspondingly, to a confinement, see the earlier discussions (Schulson 1990, reduction in viscosity under a given stress at a given 2001).
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