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Title: Elastic strain energy of deformation twinning in tetragonal crystals

Abstract

The aspect of elastic strain for a deformation twin with a pure shear strain is studied through Eshelby's inclusion theory. Beta-Sn, TiO[sub 2], and TiAl of tetragonal structures are considered. As the aspect ratio of a twin approaches zero, its elastic strain energy vanishes since the stress components coupled with the twin shear strain vanish, suggesting that the twin habit plane cannot be determined solely from the shear energy viewpoint, for any twin mode would provide a vanishingly small strain energy for a thin twin. The application of Johnson and Cahn's shape bifurcation theory predicts that the transition from a circular to an elliptic shape would occur when the linear dimension of a lenticular twin is only in the order of 10 nm, indicating that most twins with a substantial aspect ratio should be influenced by growth kinetics. Under an applied stress. The extreme condition of the free energy change usually occurs when the resolved shear stress becomes extreme in the direction of the twin shear strain, thus following the relationship of Schmid's law. The analysis of the matrix stress field immediately outside a twin plate shows a biomodal stress distribution around the lateral tip of the lenticular plate. Themore » locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. As the twin aspect ratio approaches zero, however, the two exterior stress concentrations merge together at the lateral tip of the lenticular plate, yielding a maximum stress value in the order of [mu]g, where [mu] and g are shear modulus and twin shear strain, respectively.« less

Authors:
 [1];  [2]
  1. Michigan Technological Univ., Houghton, MI (United States). Dept. of Metallurgical and Materials Engineering
  2. Oak Ridge National Lab., TN (United States). Metals and Ceramics Div.
Publication Date:
OSTI Identifier:
6989591
DOE Contract Number:  
AC05-84OR21400
Resource Type:
Journal Article
Journal Name:
Metallurgical Transactions, A (Physical Metallurgy and Materials Science); (United States)
Additional Journal Information:
Journal Volume: 21A; Journal ID: ISSN 0360-2133
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ALUMINIUM ALLOYS; DEFORMATION; TWINNING; TIN; TITANIUM ALLOYS; TITANIUM OXIDES; ELASTICITY; INTERMETALLIC COMPOUNDS; TETRAGONAL LATTICES; ALLOYS; CHALCOGENIDES; CRYSTAL LATTICES; CRYSTAL STRUCTURE; ELEMENTS; MECHANICAL PROPERTIES; METALS; OXIDES; OXYGEN COMPOUNDS; TENSILE PROPERTIES; TITANIUM COMPOUNDS; TRANSITION ELEMENT COMPOUNDS; 360102* - Metals & Alloys- Structure & Phase Studies; 360103 - Metals & Alloys- Mechanical Properties; 360202 - Ceramics, Cermets, & Refractories- Structure & Phase Studies; 360203 - Ceramics, Cermets, & Refractories- Mechanical Properties

Citation Formats

Lee, J K, and Yoo, M H. Elastic strain energy of deformation twinning in tetragonal crystals. United States: N. p., 1990. Web. doi:10.1007/BF02646997.
Lee, J K, & Yoo, M H. Elastic strain energy of deformation twinning in tetragonal crystals. United States. https://doi.org/10.1007/BF02646997
Lee, J K, and Yoo, M H. 1990. "Elastic strain energy of deformation twinning in tetragonal crystals". United States. https://doi.org/10.1007/BF02646997.
@article{osti_6989591,
title = {Elastic strain energy of deformation twinning in tetragonal crystals},
author = {Lee, J K and Yoo, M H},
abstractNote = {The aspect of elastic strain for a deformation twin with a pure shear strain is studied through Eshelby's inclusion theory. Beta-Sn, TiO[sub 2], and TiAl of tetragonal structures are considered. As the aspect ratio of a twin approaches zero, its elastic strain energy vanishes since the stress components coupled with the twin shear strain vanish, suggesting that the twin habit plane cannot be determined solely from the shear energy viewpoint, for any twin mode would provide a vanishingly small strain energy for a thin twin. The application of Johnson and Cahn's shape bifurcation theory predicts that the transition from a circular to an elliptic shape would occur when the linear dimension of a lenticular twin is only in the order of 10 nm, indicating that most twins with a substantial aspect ratio should be influenced by growth kinetics. Under an applied stress. The extreme condition of the free energy change usually occurs when the resolved shear stress becomes extreme in the direction of the twin shear strain, thus following the relationship of Schmid's law. The analysis of the matrix stress field immediately outside a twin plate shows a biomodal stress distribution around the lateral tip of the lenticular plate. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. As the twin aspect ratio approaches zero, however, the two exterior stress concentrations merge together at the lateral tip of the lenticular plate, yielding a maximum stress value in the order of [mu]g, where [mu] and g are shear modulus and twin shear strain, respectively.},
doi = {10.1007/BF02646997},
url = {https://www.osti.gov/biblio/6989591}, journal = {Metallurgical Transactions, A (Physical Metallurgy and Materials Science); (United States)},
issn = {0360-2133},
number = ,
volume = 21A,
place = {United States},
year = {Sat Sep 01 00:00:00 EDT 1990},
month = {Sat Sep 01 00:00:00 EDT 1990}
}