Estimation of elastic stiffness ratio c12/c44 and anisotropy parameter ai in the steels with bcc structure

Setsuo Takaki, Takuro Masumura, Toshihiro Tsuchiyama

Research output: Contribution to journalArticle

Abstract

In the dislocation characterization by the modified William-son-Hall method, elastic stiffness ratio cl2/c44 and anisotro-py parameter Ai (=2c44/(c11-c12)) are important parameters to determine the contrast factor. In order to determine the values of elastic stiffness cij we need the information of Young's modulus E∗, shear modulus G∗ in poly crystal, and Young's modulus of single crystal; E100, E110 E111. The values of E∗ and G∗ are experimentally obtained by the resonance method. However, it is not so easy to fabricate single crystal, especially for practically used metals in which many alloying elements are contained. Therefore, we need to estimate the values of E100, E110, E111 in some way. In this paper, the following equations were proposed to estimate these values for the steels with bcc structure. E100 = 0.647 x E∗ Eno = 1.079 x £∗ Em = 1.387 x E∗ Hie coefficient in each equation was determined by the average value of Em/E∗ in pure iron. In the steels with bcc structure (E∗=206 GPa), it was confiiined that c12lc44 and A1 are given by the following equations as a fimction of Poisson's ratio v. c12/c44 =-1.466 + 8.887 x v Ai = 2.885-1.602 x v As a result, == 1.11 and .4,^2.42 are applicable for the modified Williamson-Hall method under the condition; v=0.29.

Original languageEnglish
Pages (from-to)935-937
Number of pages3
JournalTetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan
Volume105
Issue number9
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Steel
stiffness
Anisotropy
Elastic moduli
Stiffness
steels
anisotropy
modulus of elasticity
Single crystals
single crystals
Poisson ratio
Alloying elements
estimates
alloying
Iron
Metals
shear
iron
Crystals
coefficients

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Metals and Alloys
  • Materials Chemistry

Cite this

Estimation of elastic stiffness ratio c12/c44 and anisotropy parameter ai in the steels with bcc structure. / Takaki, Setsuo; Masumura, Takuro; Tsuchiyama, Toshihiro.

In: Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan, Vol. 105, No. 9, 01.01.2019, p. 935-937.

Research output: Contribution to journalArticle

@article{070c514594204ec18fe75d9fcb52101d,
title = "Estimation of elastic stiffness ratio c12/c44 and anisotropy parameter ai in the steels with bcc structure",
abstract = "In the dislocation characterization by the modified William-son-Hall method, elastic stiffness ratio cl2/c44 and anisotro-py parameter Ai (=2c44/(c11-c12)) are important parameters to determine the contrast factor. In order to determine the values of elastic stiffness cij we need the information of Young's modulus E∗, shear modulus G∗ in poly crystal, and Young's modulus of single crystal; E100, E110 E111. The values of E∗ and G∗ are experimentally obtained by the resonance method. However, it is not so easy to fabricate single crystal, especially for practically used metals in which many alloying elements are contained. Therefore, we need to estimate the values of E100, E110, E111 in some way. In this paper, the following equations were proposed to estimate these values for the steels with bcc structure. E100 = 0.647 x E∗ Eno = 1.079 x £∗ Em = 1.387 x E∗ Hie coefficient in each equation was determined by the average value of Em/E∗ in pure iron. In the steels with bcc structure (E∗=206 GPa), it was confiiined that c12lc44 and A1 are given by the following equations as a fimction of Poisson's ratio v. c12/c44 =-1.466 + 8.887 x v Ai = 2.885-1.602 x v As a result, == 1.11 and .4,^2.42 are applicable for the modified Williamson-Hall method under the condition; v=0.29.",
author = "Setsuo Takaki and Takuro Masumura and Toshihiro Tsuchiyama",
year = "2019",
month = "1",
day = "1",
doi = "10.2355/tetsutohagane.TETSU-2019-009",
language = "English",
volume = "105",
pages = "935--937",
journal = "Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan",
issn = "0021-1575",
publisher = "一般社団法人 日本鉄鋼協会",
number = "9",

}

TY - JOUR

T1 - Estimation of elastic stiffness ratio c12/c44 and anisotropy parameter ai in the steels with bcc structure

AU - Takaki, Setsuo

AU - Masumura, Takuro

AU - Tsuchiyama, Toshihiro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In the dislocation characterization by the modified William-son-Hall method, elastic stiffness ratio cl2/c44 and anisotro-py parameter Ai (=2c44/(c11-c12)) are important parameters to determine the contrast factor. In order to determine the values of elastic stiffness cij we need the information of Young's modulus E∗, shear modulus G∗ in poly crystal, and Young's modulus of single crystal; E100, E110 E111. The values of E∗ and G∗ are experimentally obtained by the resonance method. However, it is not so easy to fabricate single crystal, especially for practically used metals in which many alloying elements are contained. Therefore, we need to estimate the values of E100, E110, E111 in some way. In this paper, the following equations were proposed to estimate these values for the steels with bcc structure. E100 = 0.647 x E∗ Eno = 1.079 x £∗ Em = 1.387 x E∗ Hie coefficient in each equation was determined by the average value of Em/E∗ in pure iron. In the steels with bcc structure (E∗=206 GPa), it was confiiined that c12lc44 and A1 are given by the following equations as a fimction of Poisson's ratio v. c12/c44 =-1.466 + 8.887 x v Ai = 2.885-1.602 x v As a result, == 1.11 and .4,^2.42 are applicable for the modified Williamson-Hall method under the condition; v=0.29.

AB - In the dislocation characterization by the modified William-son-Hall method, elastic stiffness ratio cl2/c44 and anisotro-py parameter Ai (=2c44/(c11-c12)) are important parameters to determine the contrast factor. In order to determine the values of elastic stiffness cij we need the information of Young's modulus E∗, shear modulus G∗ in poly crystal, and Young's modulus of single crystal; E100, E110 E111. The values of E∗ and G∗ are experimentally obtained by the resonance method. However, it is not so easy to fabricate single crystal, especially for practically used metals in which many alloying elements are contained. Therefore, we need to estimate the values of E100, E110, E111 in some way. In this paper, the following equations were proposed to estimate these values for the steels with bcc structure. E100 = 0.647 x E∗ Eno = 1.079 x £∗ Em = 1.387 x E∗ Hie coefficient in each equation was determined by the average value of Em/E∗ in pure iron. In the steels with bcc structure (E∗=206 GPa), it was confiiined that c12lc44 and A1 are given by the following equations as a fimction of Poisson's ratio v. c12/c44 =-1.466 + 8.887 x v Ai = 2.885-1.602 x v As a result, == 1.11 and .4,^2.42 are applicable for the modified Williamson-Hall method under the condition; v=0.29.

UR - http://www.scopus.com/inward/record.url?scp=85072704306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072704306&partnerID=8YFLogxK

U2 - 10.2355/tetsutohagane.TETSU-2019-009

DO - 10.2355/tetsutohagane.TETSU-2019-009

M3 - Article

AN - SCOPUS:85072704306

VL - 105

SP - 935

EP - 937

JO - Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan

JF - Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan

SN - 0021-1575

IS - 9

ER -