### Abstract

The yield stress of metals increases in proportion to the square root of dislocation density; this relationship is known as the Bailey-Hirsch relation. The increase in yield stress Δσ is expressed as a function of the shear modulus G, the Burgers vector of dislocation b, and dislocation density ρ using the equation: Δσ=αGb√ρ. Here, α denotes the dislocation strengthening coefficient. Research using transmission electron micrographs has revealed a linear relationship between √ρ and Δσ. Various values from 0.77 to 1.4 were reported for α in cold-worked iron, but the equation Δσ≒1.8×10-8 √ρ (α=0.9) has been established as applying to a variety of situations. On the other hand, the micro-strain ϵ has been measured via the Williamson-Hall method for two kinds of cold-worked iron: 0.001%C steel and 0.0056%C steel, with grain sizes of 120 μm and 50 μm, respectively. Plastic strain was induced by cold rolling up to a thickness reduction of 90%. The work hardening behavior is significantly different between these two steels but it was found that Δσ can be calculated for both using the equation Δσ[GPa] = 220×ϵ. From these results, the conversion equation; ρ[m
^{-2}
] ≒ 1.5×10
^{20}
ϵ2 was introduced to relate ϵ and ρ. As a result, it was confirmed that the Bailey-Hirsch relation can be treated as a common standard for understanding of dislocation density, regardless of the measurement methods employed.

Original language | English |
---|---|

Pages (from-to) | 522-527 |

Number of pages | 6 |

Journal | Zairyo/Journal of the Society of Materials Science, Japan |

Volume | 66 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2017 |

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### All Science Journal Classification (ASJC) codes

- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Zairyo/Journal of the Society of Materials Science, Japan*,

*66*(7), 522-527. https://doi.org/10.2472/jsms.66.522

**Evaluation of dislocation density in cold-worked iron as measured via X-ray diffractometry.** / Akama, Daichi; Tsuchiyama, Toshihiro; Takaki, Setsuo.

Research output: Contribution to journal › Article

*Zairyo/Journal of the Society of Materials Science, Japan*, vol. 66, no. 7, pp. 522-527. https://doi.org/10.2472/jsms.66.522

}

TY - JOUR

T1 - Evaluation of dislocation density in cold-worked iron as measured via X-ray diffractometry

AU - Akama, Daichi

AU - Tsuchiyama, Toshihiro

AU - Takaki, Setsuo

PY - 2017/7

Y1 - 2017/7

N2 - The yield stress of metals increases in proportion to the square root of dislocation density; this relationship is known as the Bailey-Hirsch relation. The increase in yield stress Δσ is expressed as a function of the shear modulus G, the Burgers vector of dislocation b, and dislocation density ρ using the equation: Δσ=αGb√ρ. Here, α denotes the dislocation strengthening coefficient. Research using transmission electron micrographs has revealed a linear relationship between √ρ and Δσ. Various values from 0.77 to 1.4 were reported for α in cold-worked iron, but the equation Δσ≒1.8×10-8 √ρ (α=0.9) has been established as applying to a variety of situations. On the other hand, the micro-strain ϵ has been measured via the Williamson-Hall method for two kinds of cold-worked iron: 0.001%C steel and 0.0056%C steel, with grain sizes of 120 μm and 50 μm, respectively. Plastic strain was induced by cold rolling up to a thickness reduction of 90%. The work hardening behavior is significantly different between these two steels but it was found that Δσ can be calculated for both using the equation Δσ[GPa] = 220×ϵ. From these results, the conversion equation; ρ[m -2 ] ≒ 1.5×10 20 ϵ2 was introduced to relate ϵ and ρ. As a result, it was confirmed that the Bailey-Hirsch relation can be treated as a common standard for understanding of dislocation density, regardless of the measurement methods employed.

AB - The yield stress of metals increases in proportion to the square root of dislocation density; this relationship is known as the Bailey-Hirsch relation. The increase in yield stress Δσ is expressed as a function of the shear modulus G, the Burgers vector of dislocation b, and dislocation density ρ using the equation: Δσ=αGb√ρ. Here, α denotes the dislocation strengthening coefficient. Research using transmission electron micrographs has revealed a linear relationship between √ρ and Δσ. Various values from 0.77 to 1.4 were reported for α in cold-worked iron, but the equation Δσ≒1.8×10-8 √ρ (α=0.9) has been established as applying to a variety of situations. On the other hand, the micro-strain ϵ has been measured via the Williamson-Hall method for two kinds of cold-worked iron: 0.001%C steel and 0.0056%C steel, with grain sizes of 120 μm and 50 μm, respectively. Plastic strain was induced by cold rolling up to a thickness reduction of 90%. The work hardening behavior is significantly different between these two steels but it was found that Δσ can be calculated for both using the equation Δσ[GPa] = 220×ϵ. From these results, the conversion equation; ρ[m -2 ] ≒ 1.5×10 20 ϵ2 was introduced to relate ϵ and ρ. As a result, it was confirmed that the Bailey-Hirsch relation can be treated as a common standard for understanding of dislocation density, regardless of the measurement methods employed.

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U2 - 10.2472/jsms.66.522

DO - 10.2472/jsms.66.522

M3 - Article

AN - SCOPUS:85025452721

VL - 66

SP - 522

EP - 527

JO - Zairyo/Journal of the Society of Materials Science, Japan

JF - Zairyo/Journal of the Society of Materials Science, Japan

SN - 0514-5163

IS - 7

ER -