# Modified Hayes - Viscoelastic Primary and Viscoplastic Secondary creep

warning:Deprecated Solid Mechanics Material

The functionality of this solid mechanics material is being replaced in the TensorMechanics system by ZryCreepTulkkiHayesHoppeUpdate.

## Description

This model is recommended for cases where cladding experiences multiple load reversals and load drops. It has been established through experiments (McGrath, 1996; Murty, 1999) that primary creep is re-initiated upon sudden load drops and reversals. In case of a viscoelastic material, the primary creep is the recoverable creep. The primary creep strain is approximately described by a function of the form (Tulkki and Ikonen, 2014): (1) where is a constant, is the hoop stress, is the initial state with zero primary creep, is the characteristic time scale of the primary creep and is the time when the change of stress from its initial to final value occurs.

In order to keep a record of the stress history of several sequential stress changes, the internal state of the system is characterized by a single time-dependent 'stress-like' variable, . The time evolution of describes the relaxation of the internal state of the system toward the steady state determined by the externally applied stress and is expressed as: (2) Here, and . The two equations can be written in the form such that there is no dependence on the initial values and and can be integrated into a finite difference form: (3)

(4)

The secondary creep contribution is calculated as per the Hayes and Kassner model introduced above. This contributes to the visco-plastic part.

## Example Input Syntax


block = 1
disp_r = disp_x
disp_z = disp_y
temp = temp
fast_neutron_flux = fast_neutron_flux
a_coef = 3.14e24
n_exponent = 5
activation_energy = 2.7e5
gas_constant = 8.3143
c0_coef = 1.141e-27
c1_exponent = 0.85
c2_exponent = 1.0
youngs_modulus = 8.0e10
poissons_ratio = 0.3
thermal_expansion = 5.0e-6
stress_free_temperature = 573.15
material_type = 1
[../]

## Input Parameters

• constitutive_modelConstitutiveModel to use (optional)

C++ Type:std::string

Description:ConstitutiveModel to use (optional)

• cracking_stress0The stress threshold beyond which cracking occurs. Must be positive.

Default:0

C++ Type:double

Description:The stress threshold beyond which cracking occurs. Must be positive.

• store_stress_olderFalseParameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

Default:False

C++ Type:bool

Description:Parameter which indicates whether the older stress state, required for HHT time integration, needs to be stored

• material_typeElement material Choices are: SRA RXA 0 1

C++ Type:MooseEnum

Description:Element material Choices are: SRA RXA 0 1

• cracking_releaseabruptThe cracking release type. Choices are abrupt (default) and exponential.

Default:abrupt

C++ Type:std::string

Description:The cracking release type. Choices are abrupt (default) and exponential.

• activation_energy270000The activation energy

Default:270000

C++ Type:double

Description:The activation energy

• formulationElement formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

C++ Type:MooseEnum

Description:Element formulation. Choices are: Nonlinear3D NonlinearRZ AxisymmetricRZ SphericalR Linear PlaneStrain NonlinearPlaneStrain

• fast_neutron_fluxThe fast neutron flux

C++ Type:std::vector

Description:The fast neutron flux

• cracking_beta1The coefficient used in the exponetional model.

Default:1

C++ Type:double

Description:The coefficient used in the exponetional model.

• compute_InteractionIntegralFalseWhether to compute the Interaction Integral.

Default:False

C++ Type:bool

Description:Whether to compute the Interaction Integral.

• thermal_expansion_reference_temperatureReference temperature for mean thermal expansion function.

C++ Type:double

Description:Reference temperature for mean thermal expansion function.

• stress_free_temperatureThe stress-free temperature. If not specified, the initial temperature is used.

C++ Type:double

Description:The stress-free temperature. If not specified, the initial temperature is used.

• youngs_modulusYoung's modulus of the material.

C++ Type:double

Description:Young's modulus of the material.

• gas_constant8.3143The universal gas constant

Default:8.3143

C++ Type:double

Description:The universal gas constant

• poissons_ratioPoisson's ratio for the material.

C++ Type:double

Description:Poisson's ratio for the material.

• compute_methodThe method used in the stress calculation.

C++ Type:MooseEnum

Description:The method used in the stress calculation.

• increment_calculationRashidApproxThe algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

Default:RashidApprox

C++ Type:std::string

Description:The algorithm to use when computing the incremental strain and rotation (RashidApprox or Eigen). For use with Nonlinear3D/RZ formulation.

• n_exponent5The exponent in the thermal creep term

Default:5

C++ Type:double

Description:The exponent in the thermal creep term

• strain_zzThe zz strain

C++ Type:std::vector

Description:The zz strain

• volumetric_locking_correctionTrueSet to false to turn off volumetric locking correction

Default:True

C++ Type:bool

Description:Set to false to turn off volumetric locking correction

• output_iteration_infoFalseSet true to output sub-newton iteration information

Default:False

C++ Type:bool

Description:Set true to output sub-newton iteration information

• 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

• youngs_modulus_functionYoung's modulus as a function of temperature.

C++ Type:FunctionName

Description:Young's modulus as a function of temperature.

• active_crack_planesPlanes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

C++ Type:std::vector

Description:Planes on which cracks are allowed (0,1,2 -> x,z,theta in RZ)

• disp_zThe z displacement

C++ Type:std::vector

Description:The z displacement

• disp_yThe y displacement

C++ Type:std::vector

Description:The y displacement

• cracking_residual_stress0The fraction of the cracking stress allowed to be maintained following a crack.

Default:0

C++ Type:double

Description:The fraction of the cracking stress allowed to be maintained following a crack.

• shear_modulusThe shear modulus of the material.

C++ Type:double

Description:The shear modulus of the material.

• c1_exponent0.85The exponent on the irradiation creep fast neutron flux term

Default:0.85

C++ Type:double

Description:The exponent on the irradiation creep fast neutron flux term

• scalar_strain_zzThe zz strain (scalar variable)

C++ Type:std::vector

Description:The zz strain (scalar variable)

• thermal_expansion_function_typeType of thermal expansion function. Choices are: instantaneous mean

C++ Type:MooseEnum

Description:Type of thermal expansion function. Choices are: instantaneous mean

• disp_rThe r displacement

C++ Type:std::vector

Description:The r displacement

• appended_property_nameName appended to material properties to make them unique

C++ Type:std::string

Description:Name appended to material properties to make them unique

Default:9.881e-28

C++ Type:double

• c2_exponent1The exponent on the irradiation creep stress term

Default:1

C++ Type:double

Description:The exponent on the irradiation creep stress term

• bulk_modulusThe bulk modulus for the material.

C++ Type:double

Description:The bulk modulus for the material.

• outputThe reporting postprocessor to use for the max_iterations value.

C++ Type:std::string

Description:The reporting postprocessor to use for the max_iterations value.

• poissons_ratio_functionPoisson's ratio as a function of temperature.

C++ Type:FunctionName

Description:Poisson's ratio as a function of temperature.

• dep_matl_propsNames of material properties this material depends on.

C++ Type:std::vector

Description:Names of material properties this material depends on.

• disp_xThe x displacement

C++ Type:std::vector

Description:The x displacement

• large_strainFalseWhether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

Default:False

C++ Type:bool

Description:Whether to include large strain terms in AxisymmetricRZ, SphericalR, and PlaneStrain formulations.

• model_primary_creepFalseSet true to turn on primary creep model

Default:False

C++ Type:bool

Description:Set true to turn on primary creep model

• initial_stressThe initial stress tensor (xx, yy, zz, xy, yz, zx)

C++ Type:std::vector

Description:The initial stress tensor (xx, yy, zz, xy, yz, zx)

• 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.

• tempCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

• max_its10Maximum number of sub-newton iterations

Default:10

C++ Type:unsigned int

Description:Maximum number of sub-newton iterations

• cracking_neg_fractionThe fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

C++ Type:double

Description:The fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

• thermal_expansion_functionThermal expansion coefficient as a function of temperature.

C++ Type:FunctionName

Description:Thermal expansion coefficient as a function of temperature.

• compute_JIntegralFalseWhether to compute the J Integral.

Default:False

C++ Type:bool

Description:Whether to compute the J Integral.

• a_coef3.14e+24The leading coefficent in the thermal creep term

Default:3.14e+24

C++ Type:double

Description:The leading coefficent in the thermal creep term

• max_cracks3The maximum number of cracks allowed at a material point.

Default:3

C++ Type:unsigned int

Description:The maximum number of cracks allowed at a material point.

• thermal_expansionThe thermal expansion coefficient.

C++ Type:double

Description:The thermal expansion coefficient.

• cracking_stress_functionThe cracking stress as a function of time and location

C++ Type:FunctionName

Description:The cracking stress as a function of time and location

• absolute_tolerance1e-20Absolute convergence tolerance for sub-newtion iteration

Default:1e-20

C++ Type:double

Description:Absolute convergence tolerance for sub-newtion iteration

• relative_tolerance0.0001Relative convergence tolerance for sub-newtion iteration

Default:0.0001

C++ Type:double

Description:Relative convergence tolerance for sub-newtion 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

• lambdaLame's first parameter for the material.

C++ Type:double

Description:Lame's first parameter for the material.

### 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. M. A. McGrath. In-reactor creep behavior of zircaloy-2 under variable loading conditions in ifa-585. Technical Report HWR-471, Halden, March 1996.[BibTeX]
2. K. L. Murty. Creep studies for zircaloy life prediction in water reactors. JOM, 51(10):32–39, 1999.[BibTeX]
3. V. Tulkki and T. Ikonen. Modeling of zircaloy cladding primary creep during load drop and reversal. Journal of Nuclear Materials, 445(1):98–103, 2014.[BibTeX]