Elasticity and Anelasticity of Metals.

Zener, Clarence

doi:10.1021/j150474a017

Cited by 888 publications

(636 citation statements)

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“…Furthermore, it is seen that the level of statistical fluctuations exhibited by the random elasticity tensor is small. This fact can be explained by noticing that (i) the RVE associated with polycrystalline microstructures is generally small (which is here confirmed by the closeness of the upper and lower bounds), and that (ii) the Aluminium single crystal presents a cubic material symmetry (and is relatively close to isotropy, since the Zener anisotropy index [40]…”

Section: Identification Of the Probabilistic Modelsupporting

confidence: 57%

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

Guilleminot

Noshadravan

Soize

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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In this paper, we address the construction of a prior stochastic model for nonGaussian deterministically-bounded positive-definite matrix-valued random fields in the context of mesoscale modeling of heterogeneous elastic microstructures. We first introduce the micromechanical framework and recall, in particular, Huet's Partition Theorem. Based on the latter, we discuss the nature of hierarchical bounds and define, under some given assumptions, deterministic bounds for the apparent elasticity tensor. Having recourse to the Maximum Entropy Principle under the constraints defined by the available information, we then introduce two random matrix models. It is shown that an alternative formulation of the boundedness constraints further allows constructing a probabilistic model for deterministically-bounded positive-definite matrix-valued random fields. Such a construction is presented and relies on a class of random fields previously defined. We finally exemplify the overall methodology considering an experimental database obtained from EBSD measurements and provide a simple numerical application.Key words: Micromechanics; Heterogeneous materials; Apparent elasticity tensor; Mesoscale modeling; Random field; Non-Gaussian. $ J. Guilleminot, A. Noshadravan, R. Ghanem and C. Soize, A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures,

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Section: Identification Of the Probabilistic Modelsupporting

confidence: 57%

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

Guilleminot

Noshadravan

Soize

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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“…This movement is seen to be the direction of motion of partial dislocations in the {lll}Y and is equiva1ent ,to the system {110} <l.io>y in the bee structure. Zener ( 27 ) shmred that in the bee structure the motion of atoms along this direction offers negligible resistance if the a:torns are packed as hard spheres.…”

Section: Ucrl-18868mentioning

confidence: 99%

The martensite phases in 304 stainless steel

Mangonon¹,

Thomas²

1970

Metall Trans

416

165

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A detailed analysis of martensite transformations in 18/8 (3b4) stainless steel,.utilizing transmission electron microscopy and diffraction in conjunction with X-ray and magnetization techniques, has established that the sequence of transformation is y ~ E ~ a. E is a thermodynamically stable hcp phase whose formation is greatly enhanced as a result of plastic deformation. Comparison with the E ~a transformation in pure Fe-Mn alloys lends further support to the above sequence and suggests that a transforma-.tion line between E and a in Fe-Cr:-Ni alloys can be expected. In the 304 stainless steel used in this investigation, formation of a was induced only by plastic deformation and subsequent to formation of E. Nucleation of. a occurs heterogeneously at intersections of E-bands or where E-bands abutt twin or grain boundari~s (which represent unilaterally compressed regions) .. From electron diffraction, the Nishiyama relationship between y and a phases appears to predominate at the start of the transformation, but then changes ·to that of Kurdjumov-Sachs. Based on these observations, a sequence of atom· movements from the hcp structure to the bee structure is proposed which has the basic geometric features of the martensitic transformation.

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“…This is in contrast to the appearance of isolated absorption peaks that are, for instance, commonly found in metals (e.g. Zener, 1948. Outside the absorption band, Q is predicted to be proportional to ω −1 at the low-frequency end, and to ω at the high-frequency end.…”

Section: Description Of Seismic Wave Attenuation Basic Observables Amentioning

confidence: 59%

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

Trampert

Fichtner

2013

Physics and Chemistry of the Deep Earth

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Elasticity and Anelasticity of Metals.

Cited by 888 publications

References 0 publications

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

The martensite phases in 304 stainless steel

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

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