7.6.15.10.5. Mmp_Model

Syntax

Pore Defect Radius [{of} SpeciesName] = Mmp_Model [Beta0 = beta0 | Beta1 = beta1 | B_Init = b_init | T_Init = t_init | Bulk_Modulus = BULK_MODUlUS | Poisson_Ratio = poisson_ratio | Youngs_Modulus = youngs_modulus]

Scope

Aria Material

Summary

Pore defect radius from MMP model

Description

The pore defect radius $r$ is computed in two stages. First after decomposition ( $r_{decomp}$ ) and then after mechanical displacement ( $r_{displace}$ ). After decomposition, the radius is computed as $r_{decomp} = B_o*\phi^{\frac{1}{3}}$ where $B_o$ is the initial half distance between pores and $\phi$ is the gas volume fraction.

After mechanical displacement, the radius is computed as $r_{displace} = (1+u_{T})r_{decomp}$ where $u_{T}$ is a dilational displacement field from a thermally induced strain. This displacement field is computed as $u_{T} = \frac{1-2\nu}{E} (K \varepsilon_T - P_{r})$ where $\nu$ is Poisson’s ratio, $E$ is Young’s modulus, $K$ is the bulk modulus, $\varepsilon_T$ is a thermally induced strain and $P_{r}$ is the pressure from chemical decomposition, which is computed from the BKW MMP model for pressure.

Note

You should supply two of the three mechanical terms ( $\nu$ , $E$ , and $K$ ). The third quantity will be calculated using $E = 3 K (1 - 2\nu)$ . If you supply all three parameters, they must satisfy this relationship or an error will be thrown.

Lastly, the thermal strain $\varepsilon_T$ is computed as $\varepsilon_T = (\beta_0 + \beta_1 T)(T - T_{o})$ where $T_{o}$ is the initial/reference temperature $\beta_0$ is the volumetric expansion coefficient and $\beta_1$ is a volumetric expansion coefficient multiplier.

Parameter	Value	Default
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
beta0	real	0
beta1	real	0
b_init	real	–
t_init	real	–
BULK_MODUlUS	real	0
poisson_ratio	real	0
youngs_modulus	real	0