Transitional Behavior for Dynamic Recrystallization in Nuclear Grade 316H Stainless Steel during Hot Deformation

Abstract

The dynamic recrystallization (DRX) behaviors and their transformation process during hot deformation with various Zener–Hollomon (Z) values were investigated in nuclear grade 316H stainless steel, and the factors influencing DRX transformation, especially adiabatic heating, were evaluated in depth. During hot deformation, with the increase of the Z value, the degree of flow softening (DFS) showed a tendency to decrease first and then increase gradually. The analysis of the microstructure revealed that at low Z value (not exceeding 3.9 × 10¹⁹ s^–1) deformation conditions, DRX was massively activated and the recrystallization mechanism had a transition from continuous DRX (CDRX) to discontinuous DRX (DDRX) with the increasing Z values, leading to the transition of homogeneous grains to heterogeneous grains. Furthermore, with the reactivation of DRX at high Z value deformation conditions, the discontinuous DRX becomes the primary recrystallization mode. Adiabatic heating plays an important role in facilitating the reactivation of DRX and flow softening during hot deformation with low temperature or high strain rate (high Z values, above 6.1 × 10²¹ s^–1).

Appendix

The process of solving the Q value:

The Arrhenius constitutive model can effectively predict the hot deformation behavior of materials and is often used to describe the relationship between stress, strain rate, and deformation temperature, which can be expressed as the following equations:

$$ \dot{\varepsilon } = A_{1} \sigma^{{n_{1} }} \exp [ - Q/\left( {{\text{R}}T} \right)]\quad (\alpha \sigma < 0.8) $$

(A1)

$$ \dot{\varepsilon } = A_{2} \exp (\beta \sigma )\exp [ - Q/\left( {{\text{R}}T} \right)]\quad (\alpha \sigma > 1.2) $$

(A2)

$$ \dot{\varepsilon } = A\left[ {\sinh \left( {\alpha \sigma } \right)} \right]^{n} \exp [ - Q/\left( {{\text{R}}T} \right)]\quad \left( {{\text{for all }}\sigma } \right) $$

(A3)

where Q is the deformation activation energy (kJ/mol); T is the absolute temperature (K); R is the universal gas constant (8.3145 J mol^–1 K^–1); $\dot{\varepsilon }$ is the strain rate (s^–1); σ is the true stress (MPa); and A, A₁, A₂, α, n₁, n, and β are the material constants, α = β/n₁.

The material constants and Q value were attained by applying Eqs. [A1] through [A3] to the experimental data of peak stress ($\sigma_{p}$) under different deformation temperatures and strain rates. By taking the natural logarithm on both sides of Eqs. [A1] through [A3], the following equations can be obtained:

$$ \text{ln}\, \sigma = \frac{1}{{n_{1} }} {\text{ln}\, \dot{\varepsilon}} - \frac{1}{{n_{1} }}\text{ln}\, A_{1} + \frac{Q}{{n_{1} {{R}}T}} $$

(A4)

$$ \sigma = \frac{1}{\beta } {\text{ln}\, \dot{\varepsilon}} - \frac{1}{\beta }\text{ln}\, A_{2} + \frac{Q}{{\beta {{R}}T}} $$

(A5)

Fig. A1

Evaluation of values of (a) n₁ by plotting ln σ vs ln $\dot{\varepsilon }$, (b) β by plotting $\sigma$ vs ln $\dot{\varepsilon }$, (c) n by plotting ${\text{ln}}\left[ {{\text{sinh}}\left( {\alpha \sigma } \right)} \right]$ vs ln $\dot{\varepsilon }$, and (d) L by plotting ${\text{ln}}\left[ {{\text{sinh}}\left( {\alpha \sigma } \right)} \right]$ vs $1000/T$

For a certain deformation temperature, by substituting the values of the peak stress and strain rate into Eqs. (A4) and (A5), the relationship of ln σ vs ln $\dot{\varepsilon }$ and σ vs ln $\dot{\varepsilon }$ can be obtained, as presented in Figures A1(a) and (b), respectively. By using linear regression for the data points, the values of n₁ and β can be calculated from the reciprocal slope of lines. The mean values of n₁ and β for all deformation temperatures are calculated to be 10.081 and 0.0601, respectively. Hence, the value of α = β/n₁ = 0.00596 can be obtained.

Furthermore, by taking the natural logarithm on both sides of Eq. [A3], [A6] can be obtained:

$$ {\text{ln sinh}}(\alpha \sigma ) = \frac{1}{n}\mathop {\text{ln} \,\dot{\varepsilon }} - \frac{1}{n}\text{ln}\, A + \frac{Q}{{n{{R}}T}} $$

(A6)

Substituting the values of the peak stress and strain rate at given deformation temperatures into Eq. [A6], the relationship of ${\text{ln sin}} h(\alpha \sigma )$ vs ln $\dot{\varepsilon }$ can be obtained, as presented in Figure A1(c). By using linear regression for the data points, the value of n can be obtained from the reciprocal slope of lines, for which the mean value for all deformation temperatures is calculated to be 7.418.

For a certain strain rate, by taking the natural logarithm and partial differentiation in Eq. [A3], the activation energy Q can be expressed as

$$ Q\; = \;Rn\left\{ {\frac{\partial [\ln \;\sinh \;(\alpha \sigma )]}{{\partial (1000/T)}}} \right\}\; = \;RnL $$

(A7)

Substituting the values of peak stress and deformation temperature at a given strain rate into Eq. [A7], the relationship of ${\text{ln sin}} h(\alpha \sigma )$ vs 1000/T can be obtained, as presented in Figure A1(d). By using linear regression for the data points, the value of L can be obtained from the slope of lines, which means the value for all strain rates is calculated to be 8.214. Furthermore, the Q = 506.61 kJ/mol can be obtained by substituting the value of n into Eq. [A7].

In this solution process, although some deviation exists because of the nature of the linear regression method, the Q value is attained by using multiple averaged material constants (β, n₁, n, and L) under different deformation conditions (T, $\dot{\varepsilon }$), and the error range is relatively small. So far, many researchers have investigated the Q_DRX for the hot deformation of ASSs such as 398 kJ/mol in 316 ASS,^[9] 400 kJ/mol in 304 ASS,^[10] 420.68 kJ/mol in 316 LN ASS,^[6] 516.7 kJ/mol in 20Cr-25Ni super ASS,^[26] and 577.85 kJ/mol in 254SMO super ASS.^[27] It can be found that the calculated value of Q_DRX in this nuclear grade 316H ASS is higher than that of the conventional ASS but lower than that of the super ASS whose deformation is more difficult due to high alloying elements,^[22] suggesting that the relatively high alloying elements in ASS result in the higher activation energy.