Models and sets the failure of Zircaloy-4 cladding due to burst in a LOCA event

Description

FailureCladding is the model for Zircaloy-4 cladding failure due to burst during a LOCA accident. For modeling failure due to burst of Zircaloy-4 claddings during LOCA accidents, the Bison code offers three different options:

• An overstress criterion, which assumes that the time of burst is reached when the local hoop stress equals a limiting burst stress (Erbacher et al., 1982): (1) where (MPa) is the hoop stress and (MPa) is the burst stress.

• A plastic instability criterion, which considers cladding burst at the attainment of a limiting value for the effective plastic strain rate: (2) where is the effective plastic (creep + plasticity) strain rate and is the limiting value. Following Marcello et al. (2014), we choose h s.

• A combination of the above criteria, which establishes that cladding burst occurs when either condition Eq. 1 or Eq. 2 is fulfilled.

The calculation of the burst stress follows the work of Erbacher et al. (1982). Based on experimental evidence, the burst stress is considered to depend on the temperature and oxygen concentration in the cladding, and is represented by Erbacher et al. (1982): (3) (MPa) and (K) are constants determined experimentally, and (-) is the oxygen weight fraction in the cladding. An oxygen weight fraction at fabrication, = 1.2 10, is considered (Erbacher et al., 1982). The current oxygen weight fraction is computed based on the oxygen mass gain from the oxidation model (ZryOxidation) as (4) where (m) is the cladding outer radius, = 6550 kgm the density of the cladding metal, (m) the cladding inner radius, g (kgm) the oxygen mass (ZryOxidation), and with S (m) being the oxide layer thickness (ZryOxidation) and R=1.56 the Pilling-Bedworth ratio for Zr.

The values for the parameters and are given in Table 1. In the mixed phase () region, linear interpolations of and are made between the values for pure and middle of (-) phase, and between - and pure phase (Erbacher et al., 1982). The volume fractions of each phase are calculated by the phase transformation model described in ZrPhase.

Table 1: Material parameters used to calculate the burst stress of Zircaloy-4 (Erbacher et al., 1982)

Phasea (MPa)b (K)
830
3000
2300

As the overstress criterion may lead to unsafe predictions in low-stress situations (Marcello et al., 2014), the combined criterion (see Eq. 1 and Eq. 2) is recommended.

Example Input Syntax


[./failure_criterion]
boundary = right #3
criterion = 2
hoop_stress = hoop_stress
eff_strain_rate_creep = creep_rate
temperature = temp
fract_beta_phase = fract_beta_phase
[../]

Input Parameters

• comparedless_equalOptions for variable _compared_ to criteria: greater_than greater_equal less_equal less_than

Default:less_equal

C++ Type:MooseEnum

Description:Options for variable _compared_ to criteria: greater_than greater_equal less_equal less_than

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• function_criteriaFunction name providing criteria value.

C++ Type:FunctionName

Description:Function name providing criteria value.

C++ Type:std::vector

• fract_oxygen_gainWeight fraction of gained oxygen in the cladding

C++ Type:std::vector

Description:Weight fraction of gained oxygen in the cladding

• fract_beta_phaseVolume fraction of Zr beta phase

C++ Type:std::vector

Description:Volume fraction of Zr beta phase

• criterion2Failure criteria: 0 = overstress, 1 = plastic instability, 2 = combined 0 and 1

Default:2

C++ Type:short

Description:Failure criteria: 0 = overstress, 1 = plastic instability, 2 = combined 0 and 1

• eff_strain_rate_plastEffective plastic strain rate in cladding (1/s)

C++ Type:std::vector

Description:Effective plastic strain rate in cladding (1/s)

• hoop_stressHoop stress in cladding (Pa)

C++ Type:std::vector

• constant_criteria0Numerical value providing criteria value.

Default:0

C++ Type:double

Description:Numerical value providing criteria value.

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• variable_checkVariable name which is compared to criteria. Example: Var < 0, true=failed

C++ Type:std::vector

Description:Variable name which is compared to criteria. Example: Var < 0, true=failed

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

• eff_strain_rate_creepEffective creep strain rate in cladding (1/s)

C++ Type:std::vector

Description:Effective creep strain rate in cladding (1/s)

Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

References

1. F. J. Erbacher, H. J. Neitzel, H. Rosinger, H. Schmidt, and K. Wiehr. Burst criterion of Zircaloy fuel claddings in a loss-of-coolant accident. In Zirconium in the Nuclear Industry, Fifth Conference, ASTM STP 754, D.G. Franklin Ed., 271â€“283. American Society for Testing and Materials, 1982.[BibTeX]
2. V. Di Marcello, A. Schubert, J. van de Laar, and P. Van Uffelen. The TRANSURANUS mechanical model for large strain analysis. Nuclear Engineering and Design, 276:19â€“29, 2014.[BibTeX]