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 $var element = document.getElementById("moose-equation-34bc2674-a0d7-417a-b5af-ea45a6da3ea5");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ , a gradient interface coefficient $var element = document.getElementById("moose-equation-2ef8e6c8-db4a-4b9d-8439-332393c39ea8");katex.render("\\kappa", element, {displayMode:false,throwOnError:false});$ , and a set of interface pair coefficients $var element = document.getElementById("moose-equation-e50f4a61-4ad0-49fb-bab4-98e27988b0ef");katex.render("\\gamma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ Aagesen et al. (2018). Note that this model is a multi phase / poly crystal model and the indices $var element = document.getElementById("moose-equation-8a8df412-55cc-41b3-8aa1-86eea675320e");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-21f6dba6-be47-4a63-88c3-efbc3f54cdbc");katex.render("\\beta", element, {displayMode:false,throwOnError:false});$ represent phases and $var element = document.getElementById("moose-equation-905d8c33-87db-4aeb-9717-d7fd33da33f9");katex.render("i", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-32cbb8bb-5c19-454a-92ae-9c00c09c96b9");katex.render("j", element, {displayMode:false,throwOnError:false});$ represent grains.

This material class provides the above mentioned parameters and calculates them using the physical parameters of the free energy area density $var element = document.getElementById("moose-equation-f0a1cd5b-1310-4ead-b7a6-258177107635");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ (sigma) for the interface between each pair of phases, and an interface width $var element = document.getElementById("moose-equation-ca384ff1-b811-4da0-a0be-80f444519de0");katex.render("l", element, {displayMode:false,throwOnError:false});$ (width).

To compute the parameters, a reference interface is assigned $var element = document.getElementById("moose-equation-7d6dd1f7-3495-4e2b-aa0c-2237a05dd5b6");katex.render("\\gamma_{\\alpha i \\beta j}=1.5", element, {displayMode:false,throwOnError:false});$ . By default this is the interface with the largest $var element = document.getElementById("moose-equation-9381e2c5-4305-4174-9bee-a047a326e81b");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ (reference_sigma = max), following the parameterization procedure of Moelans (2022). Alternatively the interface with the median $var element = document.getElementById("moose-equation-20b2d83e-1b60-44c6-a30b-32b3c204c459");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ (reference_sigma = median), or the $var element = document.getElementById("moose-equation-48bc0ff0-c737-463e-b8b2-8c000469d0eb");katex.render("\\sigma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ entry with the index sigma_index is chosen (overriding reference_sigma). For this gamma value a set of analytical expressions holds

$var element = document.getElementById("moose-equation-35b556f0-f072-4142-9a80-e7d7c98f5f98");katex.render("\\begin{aligned} \\kappa &= \\frac 34 \\sigma_{\\alpha i \\beta j} l_{\\alpha i \\beta j}\\\\ \\mu &= \\frac{6 \\sigma_{\\alpha i \\beta j}} {l_{\\alpha i \\beta j}}. \\end{aligned}", element, {displayMode:true,throwOnError:false});$

note:Interface widths

Note that the interface width $var element = document.getElementById("moose-equation-3c0ed127-18a9-4ce1-8656-62ca83e16124");katex.render("l", element, {displayMode:false,throwOnError:false});$ (width) is only guaranteed for the reference interface. All other interface widths are a function of their respective interfacial free energies, and interfaces with a lower interfacial free energy are wider. With the default reference_sigma = max the reference interface is therefore the narrowest one.

With $var element = document.getElementById("moose-equation-e2e84d80-7576-42a5-a573-dfcea59a550a");katex.render("\\kappa", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-41058d30-1e31-4a6c-b2c3-413f6bcfd673");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ determined the remaining $var element = document.getElementById("moose-equation-a3a44d5d-f2c4-4705-88a8-1a9650ab2376");katex.render("\\gamma_{\\alpha i \\beta j}", element, {displayMode:false,throwOnError:false});$ can be computed using the fitted relation Moelans (2022)

$var element = document.getElementById("moose-equation-4462cddc-debc-40b4-94e2-83ef613ae3d1");katex.render("\\begin{aligned} g_{\\alpha i \\beta j} &= \\frac{\\sigma_{\\alpha i \\beta j}}{\\sqrt{\\mu\\kappa}} \\\\ \\gamma_{\\alpha i \\beta j} &= \\left( -3.0944 g_{\\alpha i \\beta j}^8 -1.8169 g_{\\alpha i \\beta j}^6 + 10.323 g_{\\alpha i \\beta j}^4 -8.1819 g_{\\alpha i \\beta j}^2 + 2.0033 \\right)^{-1}. \\end{aligned}", element, {displayMode:true,throwOnError:false});$

This fit is valid for $var element = document.getElementById("moose-equation-628aede6-6900-408c-8c41-17b04133d5c8");katex.render("0.53 \\le \\gamma_{\\alpha i \\beta j} \\le 40", element, {displayMode:false,throwOnError:false});$ , i.e. $var element = document.getElementById("moose-equation-077a0356-cc20-4c3c-aac8-e054ac9e0d0a");katex.render("0.098 \\le g_{\\alpha i \\beta j} \\le 0.766", element, {displayMode:false,throwOnError:false});$ , and an error is reported for interfacial free energies outside this range. The earlier fit Moelans (2009)

$var element = document.getElementById("moose-equation-39ffaa09-2cb1-43fb-ad0f-1c53962ddd01");katex.render("\\gamma_{\\alpha i \\beta j} = \\left( -5.288 g_{\\alpha i \\beta j}^8 -0.09364 g_{\\alpha i \\beta j}^6 + 9.965 g_{\\alpha i \\beta j}^4 -8.183 g_{\\alpha i \\beta j}^2 + 2.007 \\right)^{-1}", element, {displayMode:true,throwOnError:false});$

can be selected with interface_fit = moelans2009 to reproduce earlier results. It is accurate for $var element = document.getElementById("moose-equation-02dbd201-d80c-4f69-975b-b0a6b42a2a7a");katex.render("\\gamma_{\\alpha i \\beta j} \\lesssim 5", element, {displayMode:false,throwOnError:false});$ , loses accuracy above that, and diverges near $var element = document.getElementById("moose-equation-9acaddb1-58bb-4cfe-ac7b-deb37e997772");katex.render("\\gamma_{\\alpha i \\beta j} \\approx 34", element, {displayMode:false,throwOnError:false});$ .

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<Real>
Unit:(no unit assumed)
Controllable:No
Description:Interfacial free energies
widthInterfacial width (for the interface with gamma = 1.5)
C++ Type:Real
Unit:(no unit assumed)
Range:width > 0
Controllable:No
Description:Interfacial width (for the interface with gamma = 1.5)

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
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>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object 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
Controllable:No
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 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
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.
gamma_namesInterfacial / grain boundary gamma parameter names (leave empty for gamma0... gammaN)
C++ Type:std::vector<MaterialPropertyName>
Unit:(no unit assumed)
Controllable:No
Description:Interfacial / grain boundary gamma parameter names (leave empty for gamma0... gammaN)
interface_fitmoelans2022Polynomial fits relating gamma to the interfacial free energy and diffuse interface width: 'moelans2022' (N. Moelans, Mater. Des. 217, 110592, 2022, valid for 0.53 <= gamma <= 40) or the earlier 'moelans2009' fits
Default:moelans2022
C++ Type:MooseEnum
Options:moelans2022, moelans2009
Controllable:No
Description:Polynomial fits relating gamma to the interfacial free energy and diffuse interface width: 'moelans2022' (N. Moelans, Mater. Des. 217, 110592, 2022, valid for 0.53 <= gamma <= 40) or the earlier 'moelans2009' fits
kappa_namekappaGradient interface parameter name
Default:kappa
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Gradient interface parameter name

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
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
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
Description:Grain growth bulk energy parameter name
reference_sigmamaxInterface that is assigned gamma = 1.5 and the interfacial width 'width': the one with the largest (max) or the median (median) interfacial free energy
Default:max
C++ Type:MooseEnum
Options:max, median
Controllable:No
Description:Interface that is assigned gamma = 1.5 and the interfacial width 'width': the one with the largest (max) or the median (median) interfacial free energy
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
sigma_indexSigma index to choose gamma = 1.5 for. Omit this to choose it according to reference_sigma.
C++ Type:unsigned int
Controllable:No
Description:Sigma index to choose gamma = 1.5 for. Omit this to choose it according to reference_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
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>
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>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

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
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.

Material Property Retrieval Parameters

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.

BibTeX

@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"
}

RIS

TY  - JOUR
AU  - Aagesen, Larry K.
AU  - Gao, Yipeng
AU  - Schwen, Daniel
AU  - Ahmed, Karim
TI  - Grand-potential-based phase-field model for multiple phases, grains, and chemical components
JO  - Phys. Rev. E
PY  - 2018
VL  - 98
PB  - American Physical Society
DO  - 10.1103/PhysRevE.98.023309
UR  - https://link.aps.org/doi/10.1103/PhysRevE.98.023309
SP  - 023309
ER  -

Plain Text

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.

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

BibTeX

@misc{MoelansWeb,
    author = "Moelans, N.",
    note = "http://nele.studentenweb.org/docs/parameters.m; accessed 13-Nov-2018",
    year = "2009"
}

RIS

TY  - GEN
AU  - Moelans, N.
PY  - 2009
ER  -

Plain Text

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

Nele Moelans. New phase-field model for polycrystalline systems with anisotropic grain boundary properties. Materials & Design, 217:110592, 2022. URL: https://doi.org/10.1016/j.matdes.2022.110592, doi:10.1016/j.matdes.2022.110592.

BibTeX

@article{Moelans2022,
    author = "Moelans, Nele",
    title = "New phase-field model for polycrystalline systems with anisotropic grain boundary properties",
    journal = "Materials \\& Design",
    volume = "217",
    pages = "110592",
    year = "2022",
    doi = "10.1016/j.matdes.2022.110592",
    url = "https://doi.org/10.1016/j.matdes.2022.110592"
}

RIS

TY  - JOUR
AU  - Moelans, Nele
TI  - New phase-field model for polycrystalline systems with anisotropic grain boundary properties
JO  - Materials & Design
PY  - 2022
VL  - 217
DO  - 10.1016/j.matdes.2022.110592
UR  - https://doi.org/10.1016/j.matdes.2022.110592
SP  - 110592
ER  -

Plain Text

Nele Moelans. New phase-field model for polycrystalline systems with anisotropic grain boundary properties. Materials & Design, 217:110592, 2022. URL: https://doi.org/10.1016/j.matdes.2022.110592, doi:10.1016/j.matdes.2022.110592.

Input Parameters
References