Robert F. Cook

Crack resistance by interfacial bridging: Its role in determining strength characteristics

An indentation-strength formulation is presented for nontransforming ceramic materials that show an increasing toughness with crack length (T curve, or R curve) due to the restraining action of interfacial bridges behind the crack tip. By assuming a stress-separation function for the bridges a microstructure-associated stress intensity factor is determined for the penny-like indentation cracks. This stress intensity factor opposes that associated with the applied loading, thereby contributing to an apparent toughening of the material, i.e., the measured toughness in excess of that associated with the intrinsic cohesion of the grain boundaries (intergranular fracture). The incorporation of this additional factor into conventional indentation fracture mechanics allows the strengths of specimens with Vickers flaws to be calculated as a function of indentation load. The resulting formulation is used to analyze earlier indentation-strength data on a range of alumina, glass-ceramic, and barium titanate materials. Numerical deconvolution of these data determines the appropriate T curves. A feature of the analysis is that materials with pronounced T curves have the qualities of flaw tolerance and enhanced crack stability. It is suggested that the indentation-strength methodology, in combination with the bridging model, can be a powerful tool for the development and characterization of structural ceramics, particularly with regard to grain boundary structure.

Fracture toughness measurements of YBa2Cu3Ox single crystals

We report fracture toughness measurements on single crystals of YBa2Cu3Ox, the phase responsible for superconductivity above liquid‐nitrogen temperatures. Indentation crack length measurements on the (010) orthorhombic crystal growth faces revealed the (100) and (001) planes as preferred fracture planes. The toughness of these planes is Kc=1.1±0.3 MPa m1/2, and the hardness H=8.7±2.4 GPa. The observed growth of both radial and lateral cracks in ambient air suggests that these crystals are susceptible to moisture‐enhanced nonequilibrium crack propagation.

Microhardness, toughness, and modulus of Mohs scale minerals

Abstract We report new results of microhardness and depth-sensing indentation (DSI) experiments for the fist nine minerals in the Mohs scale: talc, gypsum, calcite, fluorite, apatite, orthoclase, quartz, topaz, and corundum. The Mohs scale is based on a relative measure of scratch resistance, but because scratching involves both loading and shearing, scratch resistance is not equivalent to hardness as measured by modern loading (indentation) methods; scratch resistance is also related to other material properties (fracture toughness, elastic modulus). To better understand the relationship of hardness to scratch resistance, we systematically determined hardness, fracture toughness, and elastic modulus for Mohs minerals. We measured hardness and toughness using microindentation, and modulus and hardness with DSI (.nanoindentation.) experiments. None of the measured properties increases consistently or linearly with Mohs number for the entire scale.

A practical guide for analysis of nanoindentation data

Mechanical properties of biological materials are increasingly explored via nanoindentation testing. This paper reviews the modes of deformation found during indentation: elastic, plastic, viscous and fracture. A scheme is provided for ascertaining which deformation modes are active during a particular indentation test based on the load-displacement trace. Two behavior maps for indentation are presented, one in the viscous-elastic-plastic space, concerning homogeneous deformation, and one in the plastic versus brittle space, concerning the transition to fracture behavior when the threshold for cracking is exceeded. Best-practice methods for characterizing materials are presented based on which deformation modes are active; the discussion includes both nanoindentation experimental test options and appropriate methods for analyzing the resulting data.

Electrical resistance of metallic contacts on silicon and germanium during indentation

The effects of indentation on the electrical resistance of rectifying gold-chromium contacts on silicon and germanium have been studied using nanoindentation techniques. The DC resistance of circuits consisting of positively and negatively biased contacts with silicon and germanium in the intervening gap was measured while indenting either directly in the gap or on the contacts. Previous experiments showed that a large decrease in resistance occurs when an indentation bridges a gap, which was used to support the notion that a transformation from the semiconducting to the metallic state occurs beneath the indenter. The experimental results reported here, however, show that a large portion of the resistance drop is due to decreases in the resistance of the metal-to-semiconductor interface rather than the bulk semiconductor. Experimental evidence supporting this is presented, and a simple explanation for the physical processes involved is developed which still relies on the concept of an indentation-induced, semiconducting-to-metallic phase transformation.

The effect of grain size on microstructure and stress relaxation in polycrystalline Y 1 Ba 2 Cu 3 O 7−δ

We have used transmission electron microscopy and optical microscopy to examine the effect that grain size and heat treatment have on twinning and microcracking in polycrystalline Y 1 Ba 2 Cu 3 O 7−δ . It is shown that isothermal oxygenation heat treatments produce twin structures consisting of parallel twins, with a characteristic spacing that increases with increasing grain size. Slow cooling through the temperature range where the orthorhombic-to-tetragonal transformation induces twinning, however, produces a structure consisting of a hierarchical arrangement of intersecting twins, the scale of which appears to be independent of grain size. It is also shown that the microcracking induced by anisotropic changes in grain dimensions on cooling or during oxygenation can be suppressed if the grain size of the material is kept below about 1 μm. The results are examined in the light of current models for transformation twinning and microcracking and the models used to access the effect other processing variables such as oxygen content, doping or heat treatment may have on the microstructure of Y 1 Ba 2 Cu 3 O 7−δ .

Stress‐Corrosion Cracking of Low‐Dielectric‐Constant Spin‐On‐Glass Thin Films

Variations in the electrical and mechanical properties of silsesquioxane spin‐on‐glass thin films are examined as a function of curing time and temperature. Particular attention is paid to the trade‐off between producing low‐dielectric‐constant films, suitable for advanced microelectronic interconnection structures, and mechanically stable films, able to withstand semiconductor wafer fabrication processes. Two critical aspects of the mechanical stability of spin‐on glasses are shown to be the positive thermal expansion mismatch with silicon, leading to tensile film stresses, and reactivity with water, leading to susceptibility to stress‐corrosion cracking. An absolute reaction‐rate model is used to predict crack velocity using a deleted‐bond model and fused silica as a basis and is compared with observed steady‐state crack velocities as a function of film thickness and variations in the curing process. An implication is that on curing, the driving force for film fracture, determined by thermal expansion mismatch, increases less rapidly than the fracture resistance, determined by polymerization.

The effect of lateral crack growth on the strength of contact flaws in brittle materials

The effect of lateral cracks on strength controlling contact flaws in brittle materials is examined. Inert strength studies using controlled indentation flaws on a range of ceramic, glass, and single crystal materials reveal significant increases in strength at large contact loads, above the predicted load dependence extrapolated from strength measurements at low indentation loads. The increases are explained by the growth of lateral cracks decohesing the plastic deformation zone associated with the contact from the elastically restraining matrix, thereby reducing the residual stress field driving the strength controlling radial cracks. A strength formulation is developed from indentation fracture mechanics which permits inert strengths to be described over the full range of contact loads. The formulation takes account of the decreased constraint of the plastic deformation zone by lateral crack growth as well as post-contact nonequilibrium growth of the radial cracks. Simple extensions permit the strengths of specimens controlled by impact flaws to be described, as well as those failing under nonequilibrium (fatigue) conditions. The implications for materials evaluation using indentation techniques are discussed and the dangers of unqualified use of strength measurements at large indentation loads pointed out. The work reinforces the conclusion that a full understanding of the residual stress field at dominant contact flaws is necessary to describe the strength of brittle materials.

Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films

The mechanical response of plasma-enhanced chemical vapor deposited SiO2 to thermal cycling is examined by substrate curvature measurement and depth-sensing indentation. Film properties of deposition stress and stress hysteresis that accompanied thermal cycling are elucidated, as well as modulus, hardness, and coefficient of thermal expansion. Thermal cycling is shown to result in major plastic deformation of the film and a switch from a compressive to a tensile state of stress; both athermal and thermal components of the net stress alter in different ways during cycling. A mechanism of hydrogen incorporation and release from as-deposited silanol groups is proposed that accounts for the change in film properties and state of stress.

Elastic moduli of faceted aluminum nitride nanotubes measured by contact resonance atomic force microscopy

A new methodology for determining the radial elastic modulus of a one-dimensional nanostructure laid on a substrate has been developed. The methodology consists of the combination of contact resonance atomic force microscopy (AFM) with finite element analysis, and we illustrate it for the case of faceted AlN nanotubes with triangular cross-sections. By making precision measurements of the resonance frequencies of the AFM cantilever-probe first in air and then in contact with the AlN nanotubes, we determine the contact stiffness at different locations on the nanotubes, i.e. on edges, inner surfaces, and outer facets. From the contact stiffness we have extracted the indentation modulus and found that this modulus depends strongly on the apex angle of the nanotube, varying from 250 to 400 GPa for indentation on the edges of the nanotubes investigated.