Combined Creep and Instantaneous Plasticity for Zr4

Calculates combined instantaneous plasticity and time-dependent creep

warning:Deprecated Solid Mechanics Material

The functionality of this solid mechanics material is being replaced in the TensorMechanics system:

Description

Material models are also available for combined instantaneous plasticity and time- dependent creep for Zr4 in ThermalIrradiationCreepPlasZr4.

Creep Model

Creep is modeled using the irradiation and thermal creep constitutive equations described in ThermalIrradiationCreepZr4.

Irradiation-induced creep of cladding materials is based on an empirical model developed by Hoppe (1991) that relates the creep rate to the current fast neutron flux and stress. The specific relation implemented is: (1) where is the effective irradiation creep rate (1/s), is the fast neutron flux (n/m-s), is the effective (Mises) stress (MPa), and , , and are material constants. The material constants , , and are shown in Table 1 for different cladding materials. Note that the original Hoppe formulation is given in terms of circumferential stress, whereas the relation implemented in Bison assumes an effective (Mises) stress.

Table 1: Values of the Material Constants , , and for Different Cladding Materials

SRA3.5570.851.0
RXA1.6540.851.0
PRXA2.7140.851.0
ZIRLO2.8460.851.0

where, SRA = stress relief annealed; RXA = recrystallization annealed; PRXA = partially recrystallization annealed; ZIRLO = SRA ZIRLO.

Thermal Creep

Two thermal creep models are available. The Hayes model describes only secondary creep while the Limback model includes both primary and secondary creep.

Secondary thermal creep of zirconium alloys was thoroughly investigated by Hayes and Kassner (2006) and found to be well-described by a traditional power-law creep formulation. The specific equation recommended there and implemented in Bison is (2) where is the effective thermal creep rate (1/s), is the effective (Mises) stress (Pa), Q is the activation energy (J/mol), R is the universal gas constant (J/mol-K), T is the temperature (K), G is the shear modulus (Pa), and A, and n are material constants.

For Zr-4, Moon et al. (2006) recommend a temperature dependent shear modulus given by G = 4.2519 10 - 2.2185 10 T and Hayes and Kassner (2006) specify a creep law power (n) of 5. A value for A is not reported in Hayes and Kassner (2006); however, based on experimental data presented there, an approximate value of A = 3.14 10 (1/s) was computed.

Linear Strain Hardening Plasticity

Time-independent plasticity is modeled assuming J2 plasticity based on a simple linear strain hardening curve. For each stress update, the model first considers only the creep contribution to compute a new stress, which is then compared to the yield strength. If above yield, instantaneous plasticity is applied to reduce the stress onto the yield curve. Iteration is employed to insure stress convergence.

Example Input Syntax

[./lsh]
block = 1
youngs_modulus = 2.4e5
poissons_ratio = .3
yield_stress = 2.4e2
hardening_constant = 1206.
a_coef = 0.0
n_exponent = 5
activation_energy = 0
fast_neutron_flux = fast_neutron_flux
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
[../]

Input Parameters

• yield_stressThe point at which plastic strain begins accumulating

C++ Type:double

Description:The point at which plastic strain begins accumulating

• hardening_constantHardening slope

C++ Type:double

Description:Hardening slope

Required 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.

• absolute_stress_tolerance1Absolute stress convergence tolerance for combined plasticity-creep stress iteration

Default:1

C++ Type:double

Description:Absolute stress convergence tolerance for combined plasticity-creep stress iteration

• 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 irradition creep fast neutron flux term

Default:0.85

C++ Type:double

Description:The exponent on the irradition 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

• 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

• 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:PostprocessorName

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.

• 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

• 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_its30Maximum number of sub-newton iterations

Default:30

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.

Default:9.881e-28

C++ Type:double

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

Default:1e-20

C++ Type:double

Description:Absolute convergence tolerance for sub-newtion iteration

• relative_tolerance1e-05Relative convergence tolerance for sub-newtion iteration

Default:1e-05

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