Compute Crystal Plasticity Volumetric Eigenstrain

ComputeCrystalPlasticityVolumetricEigenstrain is designed to accommodate deformations in the crystal lattice due to the presence of voids. This class uses the simplifying assumptions that the voids are perfect spheres and that the population of voids at a single integration point can be described by a single average void radius and an average number density.

The void average characteristics are allowed to both increase and decrease (e.g. from defect coalescence or from porosity reduction) as calculated from a separate material.

Mathematical Overview

The volume change in the lattice produced by the voids is calculated as where is the void radius and is the number density Was (2007). Consistent with the unit system used in the MOOSE crystal plasticity models, these two void characteristics have units of and , respectively.

The equivalent linear strain measure is calculated in the traditional fashion by taking the cubic root of the volume change due to the voids as defined above. The equivalent linear strain increment is defined as the difference between the volume change at two timesteps. where indicates the current timestep and denotes the previous timestep. The linear expansion increment tensor is then calculated by multiplying the equivalent linear strain increment by the Rank-2 identity tensor, (1)

As is described in ComputeMultipleCrystalPlasticityStress, the eigenstrain contribution is accounted for through the multiplicative decomposition of the deformation gradient: (2) where the superscripts , , and denote the elastic, plastic, and volumetric eigenstrain deformation gradients, respectively Meissonnier et al. (2001). The volumetric eigenstrain deformation gradient is calculated as a function of the linear expansion increment tensor, Eq. (1); the linear expansion increment is first rotated to the current configuration.

where is the volumetric eigenstrain deformation gradient from the previous timestep, is the rotation tensor.

Numerical Implementation

For details of the time integration, Jacobian calculation, and elasto-plastic tangent moduli computation, see the discussion in ComputeCrystalPlasticityThermalEigenstrain. These calculations are based on the eigenstrain deformation gradient: replace the thermal deformation gradient, , with the volumetric eigenstrain deformation gradient, , to obtain the expressions relevant for ComputeCrystalPlasticityVolumetricEigenstrain.

commentnote:Base Class Requirement

Any constitutive eigenstrain model developed for use within the ComputeMultipleCrystalPlasticityStress class must inherit from the ComputeCrystalPlasticityEigenstrainBase class.

Example Input File Syntax

[Materials]
  [stress]
    type = ComputeMultipleCrystalPlasticityStress
    crystal_plasticity_models = 'trial_xtalpl'
    eigenstrain_names = void_eigenstrain
    tan_mod_type = exact
    line_search_method = CUT_HALF
    use_line_search = true
    maximum_substep_iteration = 5
  []

  [void_eigenstrain]
    type = ComputeCrystalPlasticityVolumetricEigenstrain
    eigenstrain_name = void_eigenstrain
    deformation_gradient_name = volumetric_deformation_gradient
    mean_spherical_void_radius = void_radius
    spherical_void_number_density = void_density
  []

  [void_density]
    type = ParsedMaterial
    property_name = void_density
    coupled_variables = temperature
    expression = '1.0e8 * (temperature - 600.0)'
  []

  [void_radius]
    type = GenericConstantMaterial
    prop_names = void_radius
    prop_values = '1.0e-6' ##1 nm avg particle radius
  []
[]
(moose/modules/solid_mechanics/test/tests/crystal_plasticity/cp_eigenstrains/volumetric_eigenstrain_increase.i)

Input Parameters

  • deformation_gradient_nameMaterial property name for the deformation gradient tensor computed by this model.

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Material property name for the deformation gradient tensor computed by this model.

  • eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

  • mean_spherical_void_radiusThe material property name for the mean radius value, in mm, for the spherical voids

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The material property name for the mean radius value, in mm, for the spherical voids

  • spherical_void_number_densityThe material property name of the number density of the spherical voids, in 1/mm^3.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The material property name of the number density of the spherical voids, in 1/mm^3.

Required Parameters

  • base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object applies

  • 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 computeQpProperties() 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

    Unit:(no unit assumed)

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

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

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

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

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

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

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • 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

    Unit:(no unit assumed)

    Controllable:No

    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.

Advanced Parameters

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

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

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

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

    Default:none

    C++ Type:std::vector<OutputName>

    Unit:(no unit assumed)

    Controllable:No

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

Outputs Parameters

References

  1. FT Meissonnier, EP Busso, and NP O'Dowd. Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains. International Journal of Plasticity, 17(4):601–640, 2001.[BibTeX]
  2. Gary S. Was. Fundamentals of Radiation Materials Science: Metals and Alloys. Springer-Verlag, Berlin, 2007.[BibTeX]