Creep behavior of nuclear grade 316LN austenitic stainless steel at 873 K and 923 K

Abstract

Creep deformation and rupture behavior of nitrogen-alloyed (0.14 wt.%) nuclear grade 316LN austenitic stainless steel were investigated for the varying stress levels at 873 K and 923 K. The power-law dependency of creep properties such as steady-state creep rate and rupture life on applied stress was observed. For a given applied stress condition, a systematic increase in strain to failure was noticed with increasing temperature from 873 K to 923 K. Irrespective of test temperatures, creep rupture elongation of the steel increased with the increase in rupture lifetime ($t_{r}$) for $t_{r} > 1000$ h. Analysis indicated that the interdependency between creep properties could be well described by the modified Monkman-Grant relationship. The predominance of inter-granular fracture arising from the triple point cracks and/or coalescence of cavities was observed at all the tested conditions for the steel. The enhanced tendency for wedge cracking was noticed for high stress levels at 873 K and 923 K. The evaluated damage tolerance factor $(\lambda ) < 5$ and the calculated ratio between time to reach the Monkman-Grant strain and creep rupture lifetime in the range of 0.69 to 0.80 indicated the accumulation of Monkman-Grant strain for the major fraction of lifetime during creep deformation of 316LN steel.

Appendix

According to the continuum creep mechanics approach (Kachanov 1960; Rabotnov 1969), the damage and creep rates formulation are represented in coupled form as

$$ \dot{\omega } = \frac{\dot{\omega }_{0}}{(1 - \omega )^{\eta }} $$

(7)

$$ \dot{\varepsilon } = \frac{\dot{\varepsilon }_{s}}{(1 - \omega )^{\beta }} $$

(8)

where $\eta$ and $\beta$ are the constants. $\omega$ is the damage variable and $\dot{\omega }_{0}$ is the characteristic damage rate. With the appropriate boundary conditions, the integration of Eq. (7) is written as

$$ \int _{0}^{w} (1 - \omega )^{\eta } d\omega = \int _{0}^{t} \dot{\omega }_{0} dt $$

(9)

Equation (9) yields

$$ \omega = 1 - \left ( 1 - \dot{\omega }_{0}(\eta + 1)t \right )^{1/(\eta + 1)} $$

(10)

When time ($t$) tends to $t_{r}$, the value of damage variable $\omega$ would approach 1. From Eq. (10), $t_{r}$ can be derived as

$$ t_{r} = \frac{1}{\dot{\omega }_{0}(\eta + 1)} $$

(11)

By substituting Eq. (11) into Eq. (10), the damage variable is represented as

$$ \omega = 1 - \left ( 1 - \frac{t}{t_{r}} \right )^{1/(\eta + 1)} $$

(12)

Equation (12) is substituted in Eq. (8) followed by the integration of Eq. (8) with the suitable boundary conditions can be written as

$$ \int _{0}^{\varepsilon } d\varepsilon = \int _{0}^{t} \frac{\dot{\varepsilon }_{s}}{\left ( 1 - \frac{t}{t_{r}} \right )^{\beta /(\eta + 1)}} dt $$

(13)

The integration of Eq. (13) is given as

$$ \varepsilon = \dot{\varepsilon }_{s}(t_{r})^{\beta /(\eta + 1)}\left ( \left ( t_{r} \right )^{\frac{\eta + 1 - \beta }{\eta + 1}} - \left ( t_{r} - t \right )^{\frac{\eta + 1 - \beta }{\eta + 1}} \right )\frac{\eta + 1}{\eta + 1 - \beta } $$

(14)

By applying the condition $t = t_{r}$ and $\epsilon = \epsilon _{f}$, the creep strain equation (Eq. (14)) takes the form in terms of $\lambda$

$$ \varepsilon = \dot{\varepsilon }_{s}(t_{r})^{(\lambda - 1)/(\lambda )}\left ( \left ( t_{r} \right )^{\frac{1}{\lambda }} - \left ( t_{r} - t \right )^{\frac{1}{\lambda }} \right )\lambda $$

(15)

and the damage tolerance factor $\lambda$ is obtained as

$$ \lambda = \frac{\eta + 1}{\eta + 1 - \beta } $$

(16)

The final forms of strain and strain rate relationships are given as

$$ \varepsilon = \varepsilon _{f}\left ( 1 - \left ( 1 - \frac{t}{t_{r}} \right )^{1/\lambda } \right ) $$

(17)

and

$$ \dot{\varepsilon } = \dot{\varepsilon }_{s}\left ( 1 - \frac{t}{t_{f}} \right )^{\frac{1}{\lambda } - 1} $$

(18)

By imposing the condition i.e. time approaches $t$_MGD, strain rate approaches steady-state creep rate, Eq. (18) can be written as

$$ \frac{t_{\mathit{MGD}}}{t_{r}} = 1 - \left ( \frac{\lambda - 1}{\lambda } \right )^{\lambda } $$

(19)

Equations (18) and (19) have been used in the present analysis to describe the creep behavior and the estimation of $f$_CDM value as given by Eq. (6) and Eq. (5), respectively.