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
Evaluation of dislocation density in cold-worked iron as measured via X-ray diffractometry. / Akama, Daichi; Tsuchiyama, Toshihiro; Takaki, Setsuo.
In: Zairyo/Journal of the Society of Materials Science, Japan, Vol. 66, No. 7, 07.2017, p. 522-527.Research output: Contribution to journal › Article
}
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 -