In this article we review the nature and mechanics of damage induced in ceramics by spherical indenters, from the classical studies of Hertz over a century ago to the present day. Basic descriptions of continuum elastic and elastic-plastic contact stress fields are first given. Two distinct modes of damage are then identified: Hertzian cone cracks, in relatively hard, homogeneous materials, such as glasses, single crystals, fine-grain ceramics (tensile, brittle mode); and diffuse subsurface damage zones, in relatively tough ceramics with heterogeneous microstructures (shear, quasi-plastic mode). Ceramographic evidence is presented for the two damage types in a broad range of materials, illustrating how an effective brittle-ductile transition can be engineered by coarsening and weakening the grain structure. Continuum analyses for cone fracture and quasi plasticity, using Griffith-Irwin fracture mechanics and yield theory, respectively, are surveyed. Recent micromechanical models of the quasi-plastic mode are also considered, in terms of grain-localized shear faults with extensile wing cracks. The effect of contact-induced damage on the ensuing strength properties of both brittle and quasi-plastic ceramics is examined. Whereas cone cracking causes abrupt losses in strength, the effect of quasi-plastic damage is more gradual-so that more heterogeneous ceramics are more damage tolerant. On the other hand, quasi-plastic ceramics are subject to accelerated strength losses in extreme cyclic conditions (contact fatigue), because of coalescence of attendant microcracks, with implications concerning wear resistance and machinability. Extension of Hertzian contact testing to novel layer structures with hard, brittle outer layers and soft, tough underlayers, designed to impart high toughness while preserving wear resistance, is described.

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Indentation of Ceramics with Spheres: A Century after Hertz

Despite its ubiquitous presence in the built environment, concrete's molecular-level properties are only recently being explored using experimental and simulation studies. Increasing societal concerns about concrete's environmental footprint have provided strong motivation to develop new concrete with greater specific stiffness or strength (for structures with less material). Herein, a combinatorial approach is described to optimize properties of cement hydrates. The method entails screening a computationally generated database of atomic structures of calcium-silicate-hydrate, the binding phase of concrete, against a set of three defect attributes: calcium-to-silicon ratio as compositional index and two correlation distances describing medium-range silicon-oxygen and calcium-oxygen environments. Although structural and mechanical properties correlate well with calcium-to-silicon ratio, the cross-correlation between all three defect attributes reveals an indentation modulus-to-hardness ratio extremum, analogous to identifying optimum network connectivity in glass rheology. We also comment on implications of the present findings for a novel route to optimize the nanoscale mechanical properties of cement hydrate.

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Combinatorial molecular optimization of cement hydrates

Estuarine organisms are exposed to periodic strong fluctuations in seawater pH driven by biological carbon dioxide (CO2) production, which may in the future be further exacerbated by the ocean acidification associated with the global rise in CO2. Calcium carbonate-producing marine spe- cies such as mollusks are expected to be vulnerable to acidification of estuarine waters, since ele- vated CO2 concentration and lower pH lead to a decrease in the degree of saturation of water with respect to calcium carbonate, potentially affecting biomineralization. Our study demonstrates that the increase in CO2 partial pressure (pCO2) in seawater and associated decrease in pH within the environmentally relevant range for estuaries have negative effects on physiology, rates of shell depo- sition and mechanical properties of the shells of eastern oysters Crassostrea virginica (Gmelin). High CO2 levels (pH ~7.5, pCO2 ~3500 µatm) caused significant increases in juvenile mortality rates and inhibited both shell and soft-body growth compared to the control conditions (pH ~8.2, pCO2 ~380 µatm). Furthermore, elevated CO2 concentrations resulted in higher standard metabolic rates in oyster juveniles, likely due to the higher energy cost of homeostasis. The high CO2 conditions also led to changes in the ultrastructure and mechanical properties of shells, including increased thickness of the calcite laths within the hypostracum and reduced hardness and fracture toughness of the shells, indicating that elevated CO2 levels have negative effects on the biomineralization process. These data strongly suggest that the rise in CO2 can impact physiology and biomineralization in marine calcifiers such as eastern oysters, threatening their survival and potentially leading to profound eco- logical and economic impacts in estuarine ecosystems.

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Elevated level of carbon dioxide affects metabolism and shell formation in oysters Crassostrea virginica

The considerable variation in shape, size, structure and properties of the enamel cap covering mammalian teeth is a topic of great evolutionary interest. No existing theories explain how such variations might be fit for the purpose of breaking food particles down. Borrowing from engineering materials science, we use principles of fracture and deformation of solids to provide a quantitative account of how mammalian enamel may be adapted to diet. Particular attention is paid to mammals that feed on 'hard objects' such as seeds and dry fruits, the outer casings of which appear to have evolved structures with properties similar to those of enamel. These foods are important in the diets of some primates, and have been heavily implicated as a key factor in the evolutionary history of the hominin clade. As a tissue with intrinsic weakness yet exceptional durability, enamel could be especially useful as a dietary indicator for extinct taxa.

Dental enamel as a dietary indicator in mammals.

SUMMARY Rising levels of atmospheric CO 2 lead to acidification of the ocean and alter seawater carbonate chemistry, which can negatively impact calcifying organisms, including mollusks. In estuaries, exposure to elevated CO 2 levels often co-occurs with other stressors, such as reduced salinity, which enhances the acidification trend, affects ion and acid–base regulation of estuarine calcifiers and modifies their response to ocean acidification. We studied the interactive effects of salinity and partial pressure of CO 2 ( P CO2 ) on biomineralization and energy homeostasis in juveniles of the eastern oyster, Crassostrea virginica , a common estuarine bivalve. Juveniles were exposed for 11 weeks to one of two environmentally relevant salinities (30 or 15 PSU) either at current atmospheric P CO2 (∼400 μatm, normocapnia) or P CO2 projected by moderate IPCC scenarios for the year 2100 (∼700–800 μatm, hypercapnia). Exposure of the juvenile oysters to elevated P CO2 and/or low salinity led to a significant increase in mortality, reduction of tissue energy stores (glycogen and lipid) and negative soft tissue growth, indicating energy deficiency. Interestingly, tissue ATP levels were not affected by exposure to changing salinity and P CO2 , suggesting that juvenile oysters maintain their cellular energy status at the expense of lipid and glycogen stores. At the same time, no compensatory upregulation of carbonic anhydrase activity was found under the conditions of low salinity and high P CO2 . Metabolic profiling using magnetic resonance spectroscopy revealed altered metabolite status following low salinity exposure; specifically, acetate levels were lower in hypercapnic than in normocapnic individuals at low salinity. Combined exposure to hypercapnia and low salinity negatively affected mechanical properties of shells of the juveniles, resulting in reduced hardness and fracture resistance. Thus, our data suggest that the combined effects of elevated P CO2 and fluctuating salinity may jeopardize the survival of eastern oysters because of weakening of their shells and increased energy consumption.

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Interactive effects of salinity and elevated CO2 levels on juvenile eastern oysters, Crassostrea virginica.

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this flrst part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elasticlplastic indentation frac- ture mechanics. It is thereby asserted that the key to the radial crack response lies In the residual component of the contact fkld. This residual term has important implications concerning the crack evolution, including the possibility of postindentation slow growth under environment-sensitive conditions. Frac- tographic observations of cracks in selected "reference" mater- Ys are used to determine the magnitude of this effect and to investigate other potential complications associated with de- partures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely hpie in procedure and economic in its use of material.

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A. H. Heuer

Papers

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements