Averaging of elastic constants for polycrystals

Blaschke, Daniel N.

doi:10.1063/1.4993443

Title: Averaging of elastic constants for polycrystals

Abstract

Many materials of interest are polycrystals, i.e., aggregates of single crystals. Randomly distributed orientations of single crystals lead to macroscopically isotropic properties. Here in this paper, we briefly review strategies of calculating effective isotropic second and third order elastic constants from the single crystal ones. Our main emphasis is on single crystals of cubic symmetry. Specifically, the averaging of third order elastic constants has not been particularly successful in the past, and discrepancies have often been attributed to texturing of polycrystals as well as to uncertainties in the measurement of elastic constants of both poly and single crystals. While this may well be true, we also point out here shortcomings in the theoretical averaging framework.

Authors:

Blaschke, Daniel N. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Fri Oct 13 00:00:00 EDT 2017

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1407891

Alternate Identifier(s):: OSTI ID: 1399293

Report Number(s):: LA-UR-17-24288
Journal ID: ISSN 0021-8979; TRN: US1703059

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Applied Physics

Additional Journal Information:: Journal Volume: 122; Journal Issue: 14; Journal ID: ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

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                    Blaschke, Daniel N. Averaging of elastic constants for polycrystals.  United States: N. p., 2017. 
Web.  doi:10.1063/1.4993443.

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                    Blaschke, Daniel N. Averaging of elastic constants for polycrystals.  United States.  https://doi.org/10.1063/1.4993443

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                    Blaschke, Daniel N. Fri .  
"Averaging of elastic constants for polycrystals".  United States.  https://doi.org/10.1063/1.4993443.  https://www.osti.gov/servlets/purl/1407891.

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@article{osti_1407891,

  title        = {Averaging of elastic constants for polycrystals},

  author       = {Blaschke, Daniel N.},

  abstractNote = {Many materials of interest are polycrystals, i.e., aggregates of single crystals. Randomly distributed orientations of single crystals lead to macroscopically isotropic properties. Here in this paper, we briefly review strategies of calculating effective isotropic second and third order elastic constants from the single crystal ones. Our main emphasis is on single crystals of cubic symmetry. Specifically, the averaging of third order elastic constants has not been particularly successful in the past, and discrepancies have often been attributed to texturing of polycrystals as well as to uncertainties in the measurement of elastic constants of both poly and single crystals. While this may well be true, we also point out here shortcomings in the theoretical averaging framework.},

  doi          = {10.1063/1.4993443},

  journal      = {Journal of Applied Physics},

  number       = 14,

  volume       = 122,

  place        = {United States},

  year         = {Fri Oct 13 00:00:00 EDT 2017},

  month        = {Fri Oct 13 00:00:00 EDT 2017}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

Properties of dislocation drag from phonon wind at ambient conditions
text, January 2019

Blaschke, Daniel N.
arXiv
DOI: 10.48550/arxiv.1902.02451

Fourth-order elastic moduli of polycrystals
journal, October 2019

Krasilnikov, O. M.; Vekilov, Yu. Kh.
Physical Review B, Vol. 100, Issue 13
DOI: 10.1103/physrevb.100.134107

Dislocation drag from phonon wind in an isotropic crystal at large velocities
journal, December 2019

Blaschke, Daniel N.; Mottola, Emil; Preston, Dean L.
Philosophical Magazine, Vol. 100, Issue 5
DOI: 10.1080/14786435.2019.1696484

Properties of Dislocation Drag from Phonon Wind at Ambient Conditions
journal, March 2019

Blaschke, Daniel
Materials, Vol. 12, Issue 6
DOI: 10.3390/ma12060948

Properties of dislocation drag from phonon wind at ambient conditions
text, January 2019

Blaschke, Daniel N.
arXiv
DOI: 10.48550/arxiv.1902.02451

Dynamical spin phenomena generated by longitudinal elastic waves traversing ${CoFe}_{2} O_{4}$ films and heterostructures
journal, December 2019

Azovtsev, Andrei V.; Pertsev, Nikolay A.
Physical Review B, Vol. 100, Issue 22
DOI: 10.1103/physrevb.100.224405

Mesomechanical Modeling and Numerical Simulation of the Diffraction Elastic Constants for Ti6Al4V Polycrystalline Alloy
journal, October 2018

Chen, Qiang; Liu, Li; Zhu, Changjun
Metals, Vol. 8, Issue 10
DOI: 10.3390/met8100822

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Similar Records

Title: Averaging of elastic constants for polycrystals

Abstract

Citation Formats

Elastic anisotropy and yield surface estimates of polycrystals journal, August 2009

Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . journal, January 1929

Anharmonicity in Noble Metals; Higher Order Elastic Constants journal, April 1966

Die experimentelle Ermittlung der elastischen Konstanten höherer Ordnung journal, December 1960

Finite Deformations of an Elastic Solid journal, April 1937

Second- and third-order elastic coefficients in polycrystalline aluminum alloy AMg6 journal, November 2015

Calculation of nonlinear effective elastic constants of polycrystalline materials journal, January 1996

Elastic anisotropy and yield surface estimates of polycrystals journal, August 2009

Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect journal, February 1961

Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls journal, August 1958

The Elastic Behaviour of a Crystalline Aggregate journal, May 1952

The third-order elastic constants of quasi-isotropic materials journal, August 1968

Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper journal, January 1889

A variational approach to the theory of the elastic behaviour of polycrystals journal, October 1962

A variational approach to the theory of the elastic behaviour of polycrystals journal, October 1962

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals journal, June 2015

Texture and anisotropy journal, July 2004

Note on a variational approach to the theory of composite elastic materials journal, April 1961

Finite deformations of an elastic solid journal, May 1952

The determination of the elastic field of an ellipsoidal inclusion, and related problems journal, August 1957

Micromechanics of defects in solids book, January 1982

Thermodynamics of Crystals journal, November 1972

On the third order elastic constants of polycrystalline media and their relationships to the single crystal constants journal, September 1968

On the determination of the fourth‐order elastic constants journal, September 1977

New estimates of the third-order elastic constants for isotropic aggregates of cubic crystals journal, April 1997

Third-Order Constants of a Cubic Quasi-Isotropic Solid journal, June 1990

Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik) book, January 1966

Third-Order Elastic Constants and the Velocity of Small Amplitude Elastic Waves in Homogeneously Stressed Media journal, March 1964

On the determination of the fourth‐order elastic constants journal, September 1977

Relation between Third‐Order Elastic Constants of Single Crystals and Polycrystals journal, July 1968

On some variational principles in anisotropic and nonhomogeneous elasticity journal, October 1962

Theoretical multiple-scattering calculation of nonlinear elastic constants of disordered solids journal, February 1992

Micromechanics of Defects in Solids journal, June 1983

Linear and volume compressibilities and isothermal third‐order elastic constants journal, September 1984

Third‐Order Elastic Constants of Polycrystalline Media journal, March 1968

Symmetry of Mixed Third‐Order Elastic Constants journal, January 1967

Relation between Isothermal and Mixed Third‐Order Elastic Constants journal, January 1967

Third-Order Elastic Constants of Aluminum journal, November 1968

Thermodynamic Definition of Higher Order Elastic Coefficients journal, March 1964

Note on a variational approach to the theory of composite elastic materials journal, April 1961

Elastic Stiffness Coefficients of Single‐Crystal Iron from Room Temperature to 500°C journal, July 1968

Third‐Order Elastic Constants of Single‐Crystal and Polycrystalline Columbium journal, June 1968

The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals journal, September 1954

Properties of dislocation drag from phonon wind at ambient conditions text, January 2019

Fourth-order elastic moduli of polycrystals journal, October 2019

Dislocation drag from phonon wind in an isotropic crystal at large velocities journal, December 2019

Properties of Dislocation Drag from Phonon Wind at Ambient Conditions journal, March 2019

Properties of dislocation drag from phonon wind at ambient conditions text, January 2019

Dynamical spin phenomena generated by longitudinal elastic waves traversing CoFe 2 O 4 films and heterostructures journal, December 2019

Mesomechanical Modeling and Numerical Simulation of the Diffraction Elastic Constants for Ti6Al4V Polycrystalline Alloy journal, October 2018

Elastic anisotropy and yield surface estimates of polycrystals
journal, August 2009

Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle .
journal, January 1929

Anharmonicity in Noble Metals; Higher Order Elastic Constants
journal, April 1966

Die experimentelle Ermittlung der elastischen Konstanten höherer Ordnung
journal, December 1960

Finite Deformations of an Elastic Solid
journal, April 1937

Second- and third-order elastic coefficients in polycrystalline aluminum alloy AMg6
journal, November 2015

Calculation of nonlinear effective elastic constants of polycrystalline materials
journal, January 1996

Elastic anisotropy and yield surface estimates of polycrystals
journal, August 2009

Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect
journal, February 1961

Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls
journal, August 1958

The Elastic Behaviour of a Crystalline Aggregate
journal, May 1952

The third-order elastic constants of quasi-isotropic materials
journal, August 1968

Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper
journal, January 1889

A variational approach to the theory of the elastic behaviour of polycrystals
journal, October 1962

A variational approach to the theory of the elastic behaviour of polycrystals
journal, October 1962

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals
journal, June 2015

Texture and anisotropy
journal, July 2004

Note on a variational approach to the theory of composite elastic materials
journal, April 1961

Finite deformations of an elastic solid
journal, May 1952

The determination of the elastic field of an ellipsoidal inclusion, and related problems
journal, August 1957

Micromechanics of defects in solids
book, January 1982

Thermodynamics of Crystals
journal, November 1972

On the third order elastic constants of polycrystalline media and their relationships to the single crystal constants
journal, September 1968

On the determination of the fourth‐order elastic constants
journal, September 1977

New estimates of the third-order elastic constants for isotropic aggregates of cubic crystals
journal, April 1997

Third-Order Constants of a Cubic Quasi-Isotropic Solid
journal, June 1990

Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik)
book, January 1966

Third-Order Elastic Constants and the Velocity of Small Amplitude Elastic Waves in Homogeneously Stressed Media
journal, March 1964

On the determination of the fourth‐order elastic constants
journal, September 1977

Relation between Third‐Order Elastic Constants of Single Crystals and Polycrystals
journal, July 1968

On some variational principles in anisotropic and nonhomogeneous elasticity
journal, October 1962

Theoretical multiple-scattering calculation of nonlinear elastic constants of disordered solids
journal, February 1992

Micromechanics of Defects in Solids
journal, June 1983

Linear and volume compressibilities and isothermal third‐order elastic constants
journal, September 1984

Third‐Order Elastic Constants of Polycrystalline Media
journal, March 1968

Symmetry of Mixed Third‐Order Elastic Constants
journal, January 1967

Relation between Isothermal and Mixed Third‐Order Elastic Constants
journal, January 1967

Third-Order Elastic Constants of Aluminum
journal, November 1968

Thermodynamic Definition of Higher Order Elastic Coefficients
journal, March 1964

Note on a variational approach to the theory of composite elastic materials
journal, April 1961

Elastic Stiffness Coefficients of Single‐Crystal Iron from Room Temperature to 500°C
journal, July 1968

Third‐Order Elastic Constants of Single‐Crystal and Polycrystalline Columbium
journal, June 1968

The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals
journal, September 1954

Properties of dislocation drag from phonon wind at ambient conditions
text, January 2019

Fourth-order elastic moduli of polycrystals
journal, October 2019

Dislocation drag from phonon wind in an isotropic crystal at large velocities
journal, December 2019

Properties of Dislocation Drag from Phonon Wind at Ambient Conditions
journal, March 2019

Properties of dislocation drag from phonon wind at ambient conditions
text, January 2019

Dynamical spin phenomena generated by longitudinal elastic waves traversing ${CoFe}_{2} O_{4}$ films and heterostructures
journal, December 2019

Mesomechanical Modeling and Numerical Simulation of the Diffraction Elastic Constants for Ti6Al4V Polycrystalline Alloy
journal, October 2018