Finite Strain Crystal Plasticity Slip Rate Residual

Crystal Plasticity base class: FCC system with power law flow rule implemented

Description

warning

The FiniteStrainCPSlipRateRes model is not actively developed. Use of the ComputeMultipleCrystalPlasticityStress system is recommend instead.

In FiniteStrainCPSlipRateRes the convergence of the crystal plasticity strain and stress response is determined with respect to the slip rate on each slip system of the crystal plasticity model. In contrast, in the material FiniteStrainCrystalPLasticity determines the crystal strain and stress response with response to the residual calculated by the second Piola-Kirchoff stress increment.

Constitutive Model Definition

Constitutive models are used to calculate the plastic slip rate. In this crystal plasticity material the slip rate is modeled as a power law: $(1)var element = document.getElementById("moose-equation-89379980-a54e-4ab5-a3ab-49f003d0e144");katex.render(" \\dot{\\gamma}^{\\alpha} = \\dot{\\gamma}_o \\left| \\frac{\\tau^{\\alpha}}{g^{\\alpha}} \\right|^{1/m} sign \\left( \\tau^{\\alpha} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-38bcc84a-445d-41fd-b863-144151e1c7c1");katex.render("\\dot{\\gamma}_o", element, {displayMode:false,throwOnError:false});$ is a reference slip rate, $var element = document.getElementById("moose-equation-97876798-44b1-446c-a139-e89cf90fe4f1");katex.render("\\tau^{\\alpha}", element, {displayMode:false,throwOnError:false});$ is the applied shear stress on each slip system $var element = document.getElementById("moose-equation-b112d3e0-1bcb-4f55-ab6b-9434da379816");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-8e866e35-0457-450f-a19a-47520434214b");katex.render("g^{\\alpha}", element, {displayMode:false,throwOnError:false});$ is the slip system strength, or resistance to slip, and $var element = document.getElementById("moose-equation-2e65df8e-874e-487e-98d2-64fc7809a624");katex.render("m", element, {displayMode:false,throwOnError:false});$ is the strain rate sensitivity exponent. The strength of each slip system is solved with an iterative process as a function of the slip increment $(2)var element = document.getElementById("moose-equation-86ca2955-9d33-4aa4-b226-0295a6350049");katex.render(" g^{\\alpha} = g_o + \\Delta \\gamma^{\\alpha} q^{\\alpha \\beta} h _o \\left| 1 - \\frac{g^{\\alpha}}{g_{sat}} \\right|^a sign \\left( 1 - \\frac{g^{\\alpha}}{g_{sat}} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-18adb683-9d90-4a77-9646-2455e252ad66");katex.render("q^{\\alpha \\beta}", element, {displayMode:false,throwOnError:false});$ is a hardening coefficient matrix that accounts for the different in self and latent hardening, Eq. (3), $var element = document.getElementById("moose-equation-343abb1f-278e-41f1-906f-49cfc8505643");katex.render("h_o", element, {displayMode:false,throwOnError:false});$ is an initial hardening term, $var element = document.getElementById("moose-equation-2c1040da-cee9-41ed-8eb3-74dc10326b3b");katex.render("g_{sat}", element, {displayMode:false,throwOnError:false});$ is a constant saturated hardening value, and $var element = document.getElementById("moose-equation-bea5acda-1c21-44d9-9d89-76ef87fd5ba8");katex.render("a", element, {displayMode:false,throwOnError:false});$ is the hardening exponent (Kalidindi et al., 1992). The self and latent hardening of the crystal is defined for an FCC system as $(3)var element = document.getElementById("moose-equation-1a412af9-8fcc-44fe-924a-d4a1aae29a6a");katex.render(" q^{\\alpha \\beta} = \\begin{Bmatrix} 1.0 & q & q & q \\\\ q & 1.0 & q & q \\\\ q & q & 1.0 & q \\\\ q & q & q & 1.0 \\end{Bmatrix}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-afb8a2b3-9726-4610-98e9-487effc38d6e");katex.render("q", element, {displayMode:false,throwOnError:false});$ is a constant value of latent hardening among non-coplanar slip systems. In Eq. (3) the slip systems which share the same slip plane normal (e.g. $var element = document.getElementById("moose-equation-14f11a66-7a02-467b-909d-c97cd6775536");katex.render("[\\bar{1}11]", element, {displayMode:false,throwOnError:false});$ ) are coplanar and grouped together with a latent hardening rate of unity (Kalidindi et al., 1992). Each matrix entry in Eq. (3) represents the interaction among two different coplanar slip system groups, that is a total of six slip systems (Kalidindi et al., 1992).

Units Assumed in the Crystal Plasticity Materials

The simulation domain for crystal plasticity models is resolved on the order of individual crystal grains, and, as such, the mesh size is small. Although MOOSE itself is dimension agnostic, the crystal plasticity models are implemented in the mm-MPa-s unit system. This dimension system choice impacts the input files in the following manner:

Mesh dimensions should be constructed in mm
Elastic constant values (e.g. Young's modulus and shear modulus) are entered in MPa
Initial slip system strength values are entered in MPa
Simulation times are given in s
Strain rates and displacement loading rates are given in 1/s and mm/s, respectively

In physically based models, which maybe based on this class, initial densities of crystal defects (e.g. dislocations, point defects) should be given in 1/mm $var element = document.getElementById("moose-equation-c83a666c-8609-4174-bd09-b5f8eb6a5b18");katex.render("^2", element, {displayMode:false,throwOnError:false});$ or 1/mm $var element = document.getElementById("moose-equation-1fd0f896-9c05-47e1-b6a9-e517f439c01f");katex.render("^3", element, {displayMode:false,throwOnError:false});$

Input Parameters

nssNumber of slip systems
C++ Type:int
Controllable:No
Description:Number of slip systems
slip_sys_file_nameName of the file containing the slip system
C++ Type:FileName
Controllable:No
Description:Name of the file containing the slip system

Required Parameters

abs_tol1e-06Constitutive stress residue absolute tolerance
Default:1e-06
C++ Type:double
Controllable:No
Description:Constitutive stress residue absolute tolerance
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
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>
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
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
flowpropsParameters used in slip rate equations
C++ Type:std::vector<double>
Controllable:No
Description:Parameters used in slip rate equations
gen_random_stress_flagFalseFlag to generate random stress to perform time cutback on constitutive failure
Default:False
C++ Type:bool
Controllable:No
Description:Flag to generate random stress to perform time cutback on constitutive failure
gpropsInitial values of slip system resistances
C++ Type:std::vector<double>
Controllable:No
Description:Initial values of slip system resistances
gtol100Constitutive slip system resistance residual tolerance
Default:100
C++ Type:double
Controllable:No
Description:Constitutive slip system resistance residual tolerance
hpropsHardening properties
C++ Type:std::vector<double>
Controllable:No
Description:Hardening properties
input_random_scaling_varFalseFlag to input scaling variable: _Cijkl(0,0,0,0) when false
Default:False
C++ Type:bool
Controllable:No
Description:Flag to input scaling variable: _Cijkl(0,0,0,0) when false
intvar_read_typenoneRead from options for initial value of internal variables: Default from .i file
Default:none
C++ Type:MooseEnum
Options:slip_sys_file, slip_sys_res_file, none
Controllable:No
Description:Read from options for initial value of internal variables: Default from .i file
line_search_maxiter20Line search bisection method maximum number of iteration
Default:20
C++ Type:unsigned int
Controllable:No
Description:Line search bisection method maximum number of iteration
line_search_methodCUT_HALFThe method used in line search
Default:CUT_HALF
C++ Type:MooseEnum
Options:CUT_HALF, BISECTION
Controllable:No
Description:The method used in line search
line_search_tol0.5Line search bisection method tolerance
Default:0.5
C++ Type:double
Controllable:No
Description:Line search bisection method tolerance
maximum_substep_iteration1Maximum number of substep iteration
Default:1
C++ Type:unsigned int
Controllable:No
Description:Maximum number of substep iteration
maxiter100Maximum number of iterations for stress update
Default:100
C++ Type:unsigned int
Controllable:No
Description:Maximum number of iterations for stress update
maxitergss100Maximum number of iterations for slip system resistance update
Default:100
C++ Type:unsigned int
Controllable:No
Description:Maximum number of iterations for slip system resistance update
min_line_search_step_size0.01Minimum line search step size
Default:0.01
C++ Type:double
Controllable:No
Description:Minimum line search step size
num_slip_sys_flowrate_props2Number of flow rate properties for a slip system
Default:2
C++ Type:unsigned int
Controllable:No
Description:Number of flow rate properties for a slip system
num_slip_sys_props0Number of slip system specific properties provided in the file containing slip system normals and directions
Default:0
C++ Type:unsigned int
Controllable:No
Description:Number of slip system specific properties provided in the file containing slip system normals and directions
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
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.
random_scaling_var1e+09Random scaling variable: Large value can cause non-positive definiteness
Default:1e+09
C++ Type:double
Controllable:No
Description:Random scaling variable: Large value can cause non-positive definiteness
random_seed2000Random integer used to generate random stress when constitutive failure occurs
Default:2000
C++ Type:unsigned int
Controllable:No
Description:Random integer used to generate random stress when constitutive failure occurs
read_prop_user_objectThe ElementReadPropertyFile GeneralUserObject to read element specific property values from file
C++ Type:UserObjectName
Controllable:No
Description:The ElementReadPropertyFile GeneralUserObject to read element specific property values from file
rtol1e-06Constitutive stress residue relative tolerance
Default:1e-06
C++ Type:double
Controllable:No
Description:Constitutive stress residue relative tolerance
slip_incr_tol0.02Maximum allowable slip in an increment
Default:0.02
C++ Type:double
Controllable:No
Description:Maximum allowable slip in an increment
slip_sys_flow_prop_file_nameName of the file containing the values of slip rate equation parameters
C++ Type:FileName
Controllable:No
Description:Name of the file containing the values of slip rate equation parameters
slip_sys_hard_prop_file_nameName of the file containing the values of hardness evolution parameters
C++ Type:FileName
Controllable:No
Description:Name of the file containing the values of hardness evolution parameters
slip_sys_res_prop_file_nameName of the file containing the initial values of slip system resistances
C++ Type:FileName
Controllable:No
Description:Name of the file containing the initial values of slip system resistances
tan_mod_typenoneType of tangent moduli for preconditioner: default elastic
Default:none
C++ Type:MooseEnum
Options:exact, none
Controllable:No
Description:Type of tangent moduli for preconditioner: default elastic
use_line_searchFalseUse line search in constitutive update
Default:False
C++ Type:bool
Controllable:No
Description:Use line search in constitutive update

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
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

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

References

Surya R Kalidindi, Curt A Bronkhorst, and Lallit Anand. Crystallographic texture evolution in bulk deformation processing of fcc metals. Journal of the Mechanics and Physics of Solids, 40(3):537–569, 1992.

@article{kalidindi1992,
    author = "Kalidindi, Surya R and Bronkhorst, Curt A and Anand, Lallit",
    title = "Crystallographic texture evolution in bulk deformation processing of FCC metals",
    journal = "Journal of the Mechanics and Physics of Solids",
    volume = "40",
    number = "3",
    pages = "537--569",
    year = "1992",
    publisher = "Elsevier"
}