UO Thermal and Irradiation Creep

Calculates the secondary thermal and irradiation creep for UO2 LWR fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

A model for combined secondary thermal creep and irradiation creep of UO fuel is available, with the creep rate modeled as a function of time, temperature, effective stress, density, grain size, fission rate, and oxygen to metal ratio (O/M). The constitutive relation is taken from the MATPRO FCREEP material model (Allison et al., 1993) and given as (1) where is the creep rate (1/s), is the effective (Mises) stress (Pa), is the temperature (K), is the fuel density (percent of theoretical), is the grain size (, is the volumetric fission rate (fissions/-s), are the activation energies (J/mol), and is the universal gas constant (8.3143 J/mol-K).

The first term in Eq. 1 represents diffusional thermal creep and is applicable to low stress and low temperature conditions. The second term in Eq. 1 represents thermal dislocation or power-law creep and is applicable to high stress and high temperature conditions. Note that irradiation creep is included in both the first and third terms, as both are functions of the fission rate (). Irradiation enhances normal diffusional thermal creep (at elevated temperatures) as indicated in the first term. Irradiation creep also occurs at lower temperatures where thermal creep is not active, and is accounted for by the third term in Eq. 1. Material constants for the thermal creep terms are listed in Table 1.

Table 1: Parameters used in the UO Thermal Creep Model (Allison et al., 1993)

ParameterValue

The activation energies for the thermal creep terms (Q and Q) are strongly dependent upon the fuel oxygen to metal ratio and, in MATPRO, are defined using the Arrhenius type relations (2) (3) where the energies are given in J/mole and (4) This function, Eq. 4, is plotted in Figure 1.

Figure 1: The function defining the dependence of the activation energies for thermal creep on the UO oxygen to metal ratio.

Transitional Stress

In MATPRO, a transition stress is defined to govern the transition between the first (low stress) and second (high stress) regions. When the applied stress is larger than the transition stress, the applied stress is used in the power-law relation and the transition stress is used in the linear creep relation. When the applied stress is lower than the transition stress, the applied stress is used in the linear relation and the power-law contribution is zero. Mai et al. (2010) investigated the MATPRO transition approach in comparison to experimental data and concluded that a better fit to the data could be achieved by simply ignoring the transition stress and applying both the low and high stress terms in all cases. This approach has been adopted in Bison.

Low Temperature Irradiation Creep

The low temperature irradiation creep (third term in Eq. 1) requires further discussion. As the equation indicates, the original MATPRO formulation included exponential temperature dependence in this term. After a careful review of the MATPRO documentation and supporting literature, it is clear that this temperature dependency was based on a single experimental study (Brucklacher et al., 1973) involving only a very limited number of experiments. Additionally, this early study specified a relatively narrow applicability range for the correlation (523 < T(K) < 773), which was not enforced in the MATPRO implementation. Several other studies, both early (Brucklacher and Dienst, 1972; Perrin, 1972; Solomon, 1973; Dienst, 1977) and more recent (Sakai et al., 2011; Sakai, 2013; Szoke and Tverberg, 2014) did not observe temperature dependency for low temperature irradiation creep, reporting creep rate variation as a function of only stress and fission rate. The most extensive data for irradiation creep of UO has been generated at the Halden Research Reactor, resulting in the following correlation (Sakai, 2013): (5)

where A = .

Default MATPRO-Halden Creep Model

The default model in Bison, which is referred to as the MATPRO-Halden model, replaces the third term in Eq. 1 with Eq. 5, thus removing temperature dependency. Note that the temperature dependent formulation can still be specified simply by providing the original MATPRO material constants (given in the table below) as input parameters.

Table 2: Irradiation creep material parameters for the original MATPRO model which included temperature dependence

ParameterValue
1/K

The procedure outlined previously for time-independent plasticity was used to implement time-dependent plasticity (creep). Young's modulus, Poisson's ratio, and the coefficient of thermal expansion can each be specified in two ways. The values can be given directly, or computed using MATPRO correlations.

Example Input Syntax


[./creep]
  type = UO2CreepUpdate
  block = 1
  temperature = temp
  fission_rate = fission_rate
  grain_radius = 10.0e-6
  oxygen_to_metal_ratio = 2.0
[../]
(test/tests/tensor_mechanics/uo2_creep/uo2_creep_irradiation.i)

UO2CreepUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:


[./radial_return_stress]
  type = ComputeMultipleInelasticStress
  tangent_operator = elastic
  inelastic_models = 'creep'
  block = 1
[../]
(test/tests/tensor_mechanics/uo2_creep/uo2_creep_irradiation.i)

Input Parameters

  • temperatureCoupled temperature

    C++ Type:std::vector

    Description:Coupled temperature

  • densityInitial fuel density

    C++ Type:double

    Description:Initial fuel density

Required Parameters

  • matpro_thermal_expansionFalseFlag for using MATPRO to compute the thermal expansion coefficient

    Default:False

    C++ Type:bool

    Description:Flag for using MATPRO to compute the thermal expansion coefficient

  • grain_radius1e-05Fuel grain radius (m)

    Default:1e-05

    C++ Type:double

    Description:Fuel grain radius (m)

  • q30Activation energy for irradiation creep, divided by gas constant (1/K)

    Default:0

    C++ Type:double

    Description:Activation energy for irradiation creep, divided by gas constant (1/K)

  • max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step

    Default:0.0001

    C++ Type:double

    Description:The maximum inelastic strain increment allowed in a time step

  • fission_rateCoupled fission rate

    C++ Type:std::vector

    Description:Coupled fission rate

  • base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

    C++ Type:std::string

    Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

  • po2_fraction0Weight fraction of PO2

    Default:0

    C++ Type:double

    Description:Weight fraction of PO2

  • oxygen_to_metal_ratio2Oxygen to metal ratio

    Default:2

    C++ Type:double

    Description:Oxygen to metal ratio

  • max_its30Maximum number of Newton iterations

    Default:30

    C++ Type:unsigned int

    Description:Maximum number of Newton iterations

  • matpro_poissons_ratioFalseFlag for using MATPRO to compute Poisson's ratio

    Default:False

    C++ Type:bool

    Description:Flag for using MATPRO to compute Poisson's ratio

  • matpro_youngs_modulusFalseFlag for using MATPRO to compute Young's modulus

    Default:False

    C++ Type:bool

    Description:Flag for using MATPRO to compute Young's modulus

  • acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

    Default:10

    C++ Type:double

    Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

  • burnupCoupled burnup

    C++ Type:std::vector

    Description:Coupled burnup

  • a77.78e-37Coefficient on irradiation creep term

    Default:7.78e-37

    C++ Type:double

    Description:Coefficient on irradiation creep term

  • absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

    Default:1e-11

    C++ Type:double

    Description:Absolute convergence tolerance for Newton iteration

  • 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

  • burnup_functionBurnup function

    C++ Type:BurnupFunctionName

    Description:Burnup function

  • relative_tolerance1e-08Relative convergence tolerance for Newton iteration

    Default:1e-08

    C++ Type:double

    Description:Relative convergence tolerance for Newton iteration

  • 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

Optional Parameters

  • effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain

    Default:effective_creep_strain

    C++ Type:std::string

    Description:Name of the material property that stores the effective inelastic strain

  • 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

Advanced Parameters

  • internal_solve_output_onon_errorWhen to output internal Newton solve information

    Default:on_error

    C++ Type:MooseEnum

    Description:When to output internal Newton solve information

  • internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.

    Default:False

    C++ Type:bool

    Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.

Debug Parameters

  • 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

Outputs Parameters

Input Files

Child Objects

References

  1. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPRO–A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]
  2. D. Brucklacher and W. Dienst. Creep behavior of ceramic nuclear fuels under neutron irradiation. Journal of Nuclear Materials, 42:285–296, 1972.[BibTeX]
  3. D. Brucklacher, W. Dienst, and F. Thummler. Creep behavior of oxide fuels under neutron irradiation, Paper 251. In Proceedings REAKTORTAGUNG 1973 des Deutschen Atomforums/KTG held in Karlsruhe, 413–416. Apr 10–13, 1973.[BibTeX]
  4. W. Dienst. Irradiation induced creep of ceramic materials. Journal of Nuclear Materials, 65:1–8, 1977.[BibTeX]
  5. A. T. Mai, W. F. Lyon, R. O. Montgomery, and R. S. Dunham. An evaluation of the MATPRO fuel creep model using the FALCON fuel analysis code. Trans. Am. Nucl. Soc., 102:888–889, 2010.[BibTeX]
  6. J. S. Perrin. Effect of irradiation on creep of UO_2-PuO_2. Journal of Nuclear Materials, 42:101–104, 1972.[BibTeX]
  7. K. Sakai. The fuel creep test IFA-701: results after four irradiation cycles. Technical Report HWR-1039, OECD Halden Reactor Project, 2013.[BibTeX]
  8. K. Sakai, H. Hanakawa, and T. Tverberg. Investigation of fission induced creep of UO2 and Cr-doped fuel in IFA-701. Technical Report HWR-1006, OECD Halden Reactor Project, 2011.[BibTeX]
  9. A. A. Solomon. Radiation induced creep of UO_2. Journal of the American Ceramic Society, 56:164–171, 1973.[BibTeX]
  10. R. Szoke and T. Tverberg. Update on in-pile results from the fuel creep test IFA-701. Technical Report HWR-1092, OECD Halden Reactor Project, 2014.[BibTeX]