The Elastic Constants of Anisotropic Materials

Hearmon, R. F. S.

doi:10.1103/revmodphys.18.409

Cited by 518 publications

(220 citation statements)

References 96 publications

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“…This property was studied much earlier when the elastic moduli of single crystals were measured, 61,79 in which anisotropy was noted to be virtually always present, even in cubic materials, cubic structures requiring three independent elastic constants. Directionally negative values, however, largely went unnoticed because n usually averages out positive for the randomized microstructure of polycrystalline materials.…”

Section: Renaissance Through Interdisciplinarity: Ca 1970 To the Prementioning

confidence: 99%

Poisson's ratio over two centuries: challenging hypotheses

2012

Notes Rec.

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This article explores Poisson's ratio, starting with the controversy concerning its magnitude and uniqueness in the context of the molecular and continuum hypotheses competing in the development of elasticity theory in the nineteenth century, moving on to its place in the development of materials science and engineering in the twentieth century, and concluding with its recent re-emergence as a universal metric for the mechanical performance of materials on any length scale. During these episodes France lost its scientific pre-eminence as paradigms switched from mathematical to observational, and accurate experiments became the prerequisite for scientific advance. The emergence of the engineering of metals followed, and subsequently the invention of composites-both somewhat separated from the discovery of quantum mechanics and crystallography, and illustrating the bifurcation of technology and science. Nowadays disciplines are reconnecting in the face of new scientific demands. During the past two centuries, though, the shape versus volume concept embedded in Poisson's ratio has remained invariant, but its application has exploded from its origins in describing the elastic response of solids and liquids, into areas such as materials with negative Poisson's ratio, brittleness, glass formation, and a re-evaluation of traditional materials. Moreover, the two contentious hypotheses have been reconciled in their complementarity within the hierarchical structure of materials and through computational modelling.

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Section: Renaissance Through Interdisciplinarity: Ca 1970 To the Prementioning

confidence: 99%

Poisson's ratio over two centuries: challenging hypotheses

2012

Notes Rec.

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“…The elastic constants, primarily the compliances, of bulk silver have been measured by several sources [30][31][32][33][34][35] -the most recent by Wolfenden et al 35 Using the expressions for calculating the Young's modulus, E, outlined in Nye 36 , Wolfenden's measurements can be presented in terms of directional Young's moduli as shown in Table II. This table illustrates that in bulk silver, the directionally-dependent Young's modulus, E, is greater in the <111> than in the <200> and <220> directions (E<111> > E<110> > E<100>). If the silver nanoparticles behaved like the bulk material, this would mean that the nanoparticles would more likely compress in the {200} direction than the {111} direction.…”

Section: A Elastic Constantsmentioning

confidence: 99%

Structural distortions in 5–10 nm silver nanoparticles under high pressure

et al. 2008

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We present experimental evidence that silver nanoparticles in the size range of 5 -10 nm undergo a reversible structural transformation under hydrostatic pressures up to 10 GPa. We have used xray diffraction with a synchrotron light source to investigate pressure-dependent and size-dependent trends in the crystal structure of silver nanoparticles in a hydrostatic medium compressed in a diamond-anvil cell. Results suggest a reversible linear pressure-dependent rhombohedral distortion which has not been previously observed in bulk silver. We propose a mechanism for this transition that considers the bond-length distribution in idealized multiply twinned icosahedral particles. To further support this hypothesis, we also show that similar measurements of single-crystal platinum nanoparticles reveal no such distortions.

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“…To directly compare these literature values to the reduced modulus recorded here, we calculate the temperature dependent reduced modulus of Al by (5) where E is the Young's modulus, ν is the Poisson's ratio, and subscripts d and s refer to the properties of diamond and the sample material (in this case Al), respectively. For accuracy, we use both a temperature dependent ν s (values for which are also taken from literature [68][69][70][71][72][73] ) and E d, which is equal to 74 (6) where the superscript RT denotes the room temperature modulus of diamond (~150 GPa 53 ) and c is an empirical constant (-1.027 x 10 -4 K -1 ). Because ν d is usually well-approximated as temperature independent, we use 0.07 53 .…”

Section: Aluminummentioning

confidence: 99%

“…The hardness decreases with temperature as expected for a crystalline metal ( Figure 10A) 52 Although hot hardness values for aluminum are reported in literature, corresponding modulus data are apparently not available. However, temperature-dependent elastic properties for >99.9% pure single-crystal Al have been measured by acoustic methods [68][69][70][71][72][73] . To directly compare these literature values to the reduced modulus recorded here, we calculate the temperature dependent reduced modulus of Al by (5) where E is the Young's modulus, ν is the Poisson's ratio, and subscripts d and s refer to the properties of diamond and the sample material (in this case Al), respectively.…”

Section: Aluminummentioning

confidence: 99%

Hot nanoindentation in inert environments

Trenkle

Packard

Schuh

2010

Review of Scientific Instruments

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An instrument capable of performing nanoindentation at temperatures up to 500 o C in inert atmospheres, including partial vacuum and gas near atmospheric pressures, is described.Technical issues associated with the technique (such as drift and noise) and the instrument (such as tip erosion and radiative heating of the transducer) are identified and addressed. Based on these considerations, preferred operation conditions are identified for testing on various materials. As a proof-of-concept demonstration, the hardness and elastic modulus of three materials are measured: fused silica (non-oxidizing), aluminum and copper (both oxidizing). In all cases, the properties match reasonably well with published data acquired by more conventional test methods.2

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The Elastic Constants of Anisotropic Materials

Cited by 518 publications

References 96 publications

Poisson's ratio over two centuries: challenging hypotheses

Poisson's ratio over two centuries: challenging hypotheses

Structural distortions in 5–10 nm silver nanoparticles under high pressure

Hot nanoindentation in inert environments

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