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Novel Constitutive Equation for Predicting Dynamic Recrystallization During Hot Working Considering the Efficiency of Power Dissipation

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Abstract

The efficiency of power dissipation (η) in a dynamic material model has been conventionally used for qualitative predictions to estimate the hot working conditions at which dynamic recrystallization (DRX) is dominant. However, predicting the quantitative value of the DRX fraction (XDRX) from η remains a challenge. In this paper, a constitutive equation is proposed to quantitatively predict XDRX using η. The proposed equation for describing XDRX is derived from the reaction rate equation using the assumption that the DRX rate depends on η. The proposed equation is verified via hot compression tests of equiaxed Ti–6Al–4V ELI alloys (Ti-64) in the (α + β) region. The predicted and experimental XDRX values are found to be generally consistent with one another, exhibiting an average absolute error of 0.05. Furthermore, the proposed equation provides the same level of prediction accuracy as the conventional Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. Therefore, the proposed equation can be used to quantitatively predict XDRX following hot compression tests of equiaxed Ti-64. Moreover, compared with the JMAK equation, the proposed equation is expressed in fewer parameters and constant terms. It is, thus, expected to facilitate the quantitative prediction of XDRX.

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Abbreviations

T :

Temperature

\(\dot{\varepsilon }\) :

Strain rate

ε :

Strain

σ :

Stress

d DRX :

DRX grain size

D 1 :

Material constant

D 2 :

Material constant

Z :

Zener–Hollomon parameter

R :

Gas constant

Q :

Apparent activation energy for hot deformation

X DRX :

Fraction of dynamic recrystallization

β d :

Rate coefficient in the JMAK equation

k d :

Avrami exponent

ε c :

Critical strain at which DRX initiates

ε p :

Peak strain in σ–ε curves

n 1 :

Material constant

n 2 :

Material constant

ε 0 .5 :

ε when XDRX = 0.5

n 3 :

Material constant

n 4 :

Material constant

n 5 :

Material constant

Q 1 :

Material constant

d 0 :

Initial grain size before deformation

η :

Efficiency of power dissipation

P :

Power dissipated during hot working

G :

Power dissipated for the temperature increase due to plastic deformation

J :

Power dissipated during microstructural evolution

m :

Strain rate sensitivity exponent

K :

Material constant

J max :

Maximum value of J

η′:

Modified efficiency of power dissipation

X Precipitation :

Fraction of precipitation

t :

Time

R 1 :

Radius of a particle

D :

Diffusion coefficient of the solute atoms

N :

Number of participating particles per unit volume

C :

Concentration of a chemical substance

k :

Rate coefficient

μ s :

Shear modulus

b :

Magnitude of the Burgers vector

ρ recrystallized :

Average dislocation density of recrystallized grains

ρ un -recrystallized :

Average dislocation density of un-recrystallized grains

ε com :

True compressive strain

ΔT :

Temperature variation due to the work performed on the sample

η e :

Fraction of the mechanical work that is transformed into heat

c p :

Heat capacity of the material

ρ :

Density of the sample

W :

Energy per unit volume that is input into the sample

A :

Constant

ε e ff :

Effective strain

\({\dot{\varepsilon }}_{\mathrm{eff}}\) :

Effective strain rate

θ :

Misorientation angle

c 1 :

Constant

c 2 :

Constant

X DRX_PRE :

XDRX predicted using constitutive equation

X DRX_EXP :

XDRX obtained via experimentation

AAE :

Average absolute error

i :

ith data obtained by varying the compression conditions and observation locations

I :

Total number of data points

μ :

Chemical potential

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Authors and Affiliations

  1. Numazu Technical Support Center, Industrial Research Institute of Shizuoka Prefecture, 3981-1 Ohoka, Numazu, Shizuoka, 410-0022, Japan

    Sosuke Korenaga & Masakazu Honda

  2. Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Kenta Yamanaka & Akihiko Chiba

Authors
  1. Sosuke Korenaga
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  2. Masakazu Honda
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  3. Kenta Yamanaka
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  4. Akihiko Chiba
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Correspondence to Sosuke Korenaga.

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Korenaga, S., Honda, M., Yamanaka, K. et al. Novel Constitutive Equation for Predicting Dynamic Recrystallization During Hot Working Considering the Efficiency of Power Dissipation. Metall Mater Trans A 53, 2163–2173 (2022). https://doi.org/10.1007/s11661-022-06658-6

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