GrandPotentialInterface

Calculate Grand Potential interface parameters for a specified interfacial free energy and width

The multiphase Grand Potential model is parameterized using a bulk free energy coefficient $var element = document.getElementById("moose-equation-7d98e246-0839-43f5-a4d5-c4deedc7c450");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , a gradient interface coefficient $var element = document.getElementById("moose-equation-1d46f114-dafe-41c4-b92a-35a21684be42");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and a set of interface pair coefficients $var element = document.getElementById("moose-equation-728b24b8-4124-416d-aafe-a645d38912ff");katex.render("\\gamma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ Aagesen et al. (2018). Note that this model is a multi phase / poly crystal model and the indices $var element = document.getElementById("moose-equation-34801e58-1a50-4326-99e2-6a2999bc5862");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-9ed2b54b-6a89-4c11-9108-b829c12f19bd");katex.render("\\beta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ represent phases and $var element = document.getElementById("moose-equation-2a8230c3-b062-4692-aea9-5716dc3b0ff1");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-6ab1d538-5ee0-4977-93bc-cfcc4c732d39");katex.render("j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ represent grains.

This material class provides the above mentioned parameters and calculates them using the physical parameters of the free energy area density $var element = document.getElementById("moose-equation-ec2e2694-44c6-40aa-ad94-31bcd761266d");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (sigma) for the interface between each pair of phases, and an interface width $var element = document.getElementById("moose-equation-facafb75-6f7a-4c21-a040-3d98a8849be1");katex.render("l", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (width).

To compute the parameters first either the median of all $var element = document.getElementById("moose-equation-f3dd0c34-509d-4292-a8a1-96231afc1a28");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is chosen or, if supplied by the user, the $var element = document.getElementById("moose-equation-5cafaeeb-b62e-4832-a47c-e7fd0645660f");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ entry with the index sigma_index is chosen (overriding the median computation). The chosen $var element = document.getElementById("moose-equation-8796c81b-cec1-40c4-bed2-fb6e3b375110");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is assigned a value $var element = document.getElementById("moose-equation-d8b2a0f6-dc0b-4cd6-af2f-48ba062e2903");katex.render("\\gamma_{\\alpha i \\beta j}=1.5", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . For this gamma value a set of analytical expessions holds

$var element = document.getElementById("moose-equation-cc424269-6890-4360-b889-5b5d748eed75");katex.render("\\begin{aligned} \\kappa &= \\frac 34 \\sigma_{\\alpha i \\beta j} l_{\\alpha i \\beta j}\\\\ \\mu &= \\frac{6 \\sigma_{\\alpha i \\beta j}} {l_{\\alpha i \\beta j}}. \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

note:Interface widths

Note that the interface with $var element = document.getElementById("moose-equation-2420ff4a-2760-415a-abf4-9756c5e54763");katex.render("l", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (width) is only guaranteed for the interface with either the median $var element = document.getElementById("moose-equation-02c6400d-8ea6-4b54-b2cc-a88e2d2fa7f8");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ or - if provided - the index supplied in sigma_index. All other interface widths are a function of their respective interfacial free energies.

With $var element = document.getElementById("moose-equation-14612db8-a863-47ee-9916-461780875aec");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-e08fcfbf-cc90-471c-8bb2-60eafed2b73b");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ determined the remaining $var element = document.getElementById("moose-equation-58f1494b-b46b-4546-bebf-b9a272551b5d");katex.render("\\gamma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ can be computed using the fitted relation Moelans (2009)

$var element = document.getElementById("moose-equation-bc1b3fb8-9ed5-4d73-bd78-b86d183fdf05");katex.render("\\begin{aligned} g_{\\alpha i \\beta j} &= \\frac{\\sigma_{\\alpha i \\beta j}}{\\sqrt{\\mu\\kappa}} \\\\ \\gamma_{\\alpha i \\beta j} &= \\left( -5.288 g_{\\alpha i \\beta j}^8 -0.09364 g_{\\alpha i \\beta j}^6 + 9.965 g_{\\alpha i \\beta j}^4 -8.183 g_{\\alpha i \\beta j}^2 + 2.007 \\right)^{-1}. \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The material propertied provided by this class are directly used by the ACGrGrMulti and ACInterface objects and indirectly used by the GrandPotentialKernelAction.

Input Parameters

sigmaInterfacial free energies
C++ Type:std::vector
Options:
Description:Interfacial free energies
widthInterfacial width (for the interface with gamma = 1.5)
C++ Type:double
Options:
Description:Interfacial width (for the interface with gamma = 1.5)

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Options:
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
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
Options:NONE ELEMENT SUBDOMAIN
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
gamma_namesInterfacial / grain boundary gamma parameter names (leave empty for gamma0... gammaN)
C++ Type:std::vector
Options:
Description:Interfacial / grain boundary gamma parameter names (leave empty for gamma0... gammaN)
kappa_namekappaGradient interface parameter name
Default:kappa
C++ Type:MaterialPropertyName
Options:
Description:Gradient interface parameter name

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
mu_namemuGrain growth bulk energy parameter name
Default:mu
C++ Type:MaterialPropertyName
Options:
Description:Grain growth bulk energy parameter name
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
sigma_indexSigma index to choose gamma = 1.5 for. Omit this to automatically chose the median sigma.
C++ Type:unsigned int
Options:
Description:Sigma index to choose gamma = 1.5 for. Omit this to automatically chose the median sigma.
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
Options:
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
Options:
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
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialInterface.i

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialInterface.i

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

[Materials]
  [./iface]
    # reproduce the parameters from GrandPotentialMultiphase.i
    type = GrandPotentialInterface
    gamma_names = 'gbb gab'
    sigma       = '0.4714  0.6161' # Ratio of 1:1.307 to obtain dihedral angle of 135deg
    width       = 2.8284
  [../]
[]

[VectorPostprocessors]
  [./mat]
    type = MaterialVectorPostprocessor
    material = iface
    elem_ids = 0
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Problem]
  solve = false
[]

[Outputs]
  csv = true
  execute_on = TIMESTEP_END
[]

References

Larry K. Aagesen, Yipeng Gao, Daniel Schwen, and Karim Ahmed. Grand-potential-based phase-field model for multiple phases, grains, and chemical components. Phys. Rev. E, 98:023309, Aug 2018. URL: https://link.aps.org/doi/10.1103/PhysRevE.98.023309, doi:10.1103/PhysRevE.98.023309.

@article{AagesenGP2018,
    author = "Aagesen, Larry K. and Gao, Yipeng and Schwen, Daniel and Ahmed, Karim",
    title = "Grand-potential-based phase-field model for multiple phases, grains, and chemical components",
    journal = "Phys. Rev. E",
    volume = "98",
    issue = "2",
    pages = "023309",
    numpages = "16",
    year = "2018",
    month = "Aug",
    publisher = "American Physical Society",
    doi = "10.1103/PhysRevE.98.023309",
    url = "https://link.aps.org/doi/10.1103/PhysRevE.98.023309"
}

N. Moelans. 2009. http://nele.studentenweb.org/docs/parameters.m; accessed 13-Nov-2018.

Input Parameters
Input Files
References

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