9.8.5. Appendix 9.5: Mechanical Properties

The elastic and thermal expansion properties for metal fuel [9-22] [9-28], SS316, D9, HT9 and 15-15Ti cladding [8-17] [9-29], with temperature defined in Kelvin, are

Elastic Modulus (Pa)

(9.8-20)\[\begin{split} E = \begin{cases} \left( 56 + 0.1158 \left( 865 - T \right) \right) 10^{9} & \text{phase = } \alpha + \delta \\ \left( 56 + 0.2158 \left( 865 - T \right) \right) 10^{9} & \text{phase = } \beta + \gamma \text{ or } \gamma \\ \end{cases}\end{split}\]

(9.8-21)\[\begin{split} E = \begin{cases} E_c(T_f) \times 6.894757 \times 10^{9} & \text{Clad = SS316 or 15-15Ti } \\ \left( 2.137E+05 - 102.74 \left(T - 273.15\right) \right) 10^{6} & \text{Clad = D9 } \\ \left( 2.137E+05 - 102.74 \left(T - 273.15\right) \right) 10^{6} & \text{Clad = HT9 } \\ \end{cases}\end{split}\]

where \(T\) is the temperature in Kelvin, \(T_f\) is the temperature in Fahrenheit, and \(E_c(T_f)\) is defined in Eq. (8.7-22).

Poisson’s Ratio (-)

(9.8-22)\[\begin{split} \nu = \begin{cases} 0.3 & \text{phase = } \alpha + \delta \\ 0.3 & \text{phase = } \beta + \gamma \text{ or } \gamma \\ \end{cases}\end{split}\]

(9.8-23)\[\begin{split} \nu = \begin{cases} 0.3 & \text{Clad = SS316 } \\ 0.3 & \text{Clad = D9 } \\ 0.3 & \text{Clad = HT9 } \\ 0.3 & \text{Clad = 15-15Ti } \\ \end{cases}\end{split}\]

Thermal Expansion Coefficient (\(m/\Delta m\))

The composition-dependent thermal expansion coefficient for metallic fuel is determined by interpolating between alloy/component data in the Metallic Fuels Handbook [9-22].

The cladding thermal expansion strain is with temperature defined in Kelvin, and \(T_0=293.15\) K, is

(9.8-24)\[\begin{split} \alpha \left(T - T_0 \right) = \begin{cases} \alpha_m(T_f) \left(T_f - 70 \right) 10^{-6} & \text{Clad = SS316 or 15-15Ti} \\ \left(-0.4247 + 1.282\times10^{-3} T \right. \\ \left. + 7.362\times10^{-7} T^2 - 2.069\times10^{-10} T^3 \right)10^{-2} & \text{Clad = D9 } \\ \left(-0.2191 + 5.678\times10^{-4} T \right. \\ \left. + 8.111\times10^{-7} T^2 - 2.576\times10^{-10} T^3 \right)10^{-2} & \text{Clad = HT9 } \\ \end{cases}\end{split}\]

where \(T\) is the temperature in Kelvin, \(T_f\) is the temperature in Fahrenheit, \(T_0 = 293.15\) is a reference temperature in Kelvin, and \(\alpha_m(T_f)\) is defined in Eq. (8.7-21).

Fuel Pore Sintering Yield Stress

Experimental data, although limited, shows evidence of pore sintering due to the softness of metallic fuel at elevated temperatures [9‑24]. Prior to eutectic formation, any fuel expansion, caused by thermal expansion or fission product swelling, is balanced by pore sintering and fuel clad mechanical interaction. This balance is also evident in high-level experiments such as TREAT M-Series [9‑25] and Whole Pin Furnace tests [9‑26].

In order to account for the impact of pore sintering at elevated temperatures, a pore yield strength model, which is a function of creep rate and pore compressibility factor, is developed based on a reference data point in Ref. [9‑24] and expert judgement. The selected reference point for pore yield strength is given in Table 9.8.13.

Table 9.8.13 Selected reference point for pore sintering yield stress

Reference Parameters	Reference Values
Temperature	973.15 K
Hydrostatic Stress	2.5 MPa
Pore Compressibility factor	C/6
C - Fitting Factor	6

Given temperature, hydrostatic stress, and fuel porosity, the model computes the pore compressibility factor (\(\alpha_{p}\)), then solves the following equation to compute the pore yield strength(\(\sigma_{f})\):

(9.8-25)\[ \epsilon_{f}(\sigma_{f})\alpha_{pf} = \epsilon_{ref}(\sigma_{ref})\alpha_{pref}\]

where \(\epsilon_{f}\) is the fuel equivalent creep rate (1/s) given the current temperature and hydrostatic stress, \(\alpha_{pf}\) is the current fuel porosity compressibility factor (See Eq. (9.2-94)), \(\epsilon_{ref}\) is the equivalent creep rate (1/s) computed using the parameters in Table 1, \(\alpha_{pref}\) is the pore compressibility factor given in Table 1, and\(\ \sigma_{f}\) and \(\sigma_{ref}\) are the fuel pore yield strength (MPa) and reference stress (MPa), respectively. The assumed upper limits for pore yield strength are for porous fuel with more than 10% fuel porosity and low porosity fuel with less than 10% fuel porosity are 50 MPa and 80 MPa, respectively.

Yield Strength (Pa)

The cladding yield strength is defined in Section 8.7.10. The yield strength for SS316 is utilized for all four cladding types.

Ultimate Tensile Strength (Pa)

The cladding ultimate tensile strength is defined in Section 8.7.9. The ultimate tensile strength for SS316 is utilized for all four cladding types.