A failure model for FeCrAl cladding. Three failure criteria exist including ultimate tensile strength, tresca criterion, and an Idaho National Laboratory developed criterion.

Description

The model FeCrAlCladdingFailure determines whether or not FeCrAl claddings have failed based upon a chosen criterion. There are three options available to choose from in this model:

1. Ultimate Tensile Strength (UTS) Criterion

2. Tresca Criterion

3. Idaho National Laboratory (INL) Criterion

Ultimate Tensile Strength Criterion

For the UTS criterion the hoop stress is compared to the UTS of the material. For FeCrAl alloys the UTS is calculated as a function temperature based upon the data of Yamamoto et al. (2015) as shown in Table 1. Yamamoto et al. (2015)s data only covers temperatures ranging from 300 to 1000 K. Based on research by Yano et al. (2016) on other ferritic and martensitic steels, there are distinct temperature dependent regions (low, mid, high) of the ultimate tensile strength (UTS). In the low temperature region the UTS drops relatively slowly with increasing temperature. In the midrange temperatures there is a rapid decrease in the UTS as temperature increases. The high temperature region results in a slow reduction of the UTS to approximately zero at the melting point. Using these observations on other alloys, an additional data point of a UTS of zero was added to Yamamoto's data at the melting point of FeCrAl alloys (1773 K). The minimum UTS is used if the temperature is outside the temperature bounds presented here. For example if the temperature is 280 K the UTS is taken as 569.475 MPa.

Table 1: Value of FeCrAl Ultimate Tensile Strength as a Function of Temperature

Temperature (K)Ultimate Tensile Strength (MPa)
294.738569.475
551.495543.205
644.048527.023
829.850288.826
1011.9565.373
1773.000.0

Tresca Criterion

In the well known Tresca failure criterion if the maximum shear stress exceeds one half of the yield stress the material is considered failed. According to Boresi and Schmidt (2003) the maximum shear stress is determined from the principal stresses. The maximum shear stress is the largest value of the following three quantities: (1) (2) (3) where , , and are the max, mid, and min prinicipal stresses respesctively.

Idaho National Laboratory Criterion

The INL model for failure of FeCrAl alloys is based upon the experimental work of Massey et al. (2016). It was found that the UTS and Tresca criteria described above do not accurately predict the failure observed in Massey et al. (2016)'s experiments. Therefore, in the absence of other burst data for FeCrAl, it is argued that the data can be used directly to develop a failure criterion.

The developed failure model is a burst stress () that varies as a function of temperature. The experimental data can be visualized as hoop stress as a function of temperature. Using a least squares methodology a best fit to the experimental data is performed to obtain a correlation for burst stress as an exponential function of temperature. Below 796.8 K the UTS is used as the burst stress. Therefore, the combined equation is given by: (4) Further details of the derivation of the above model can be found in Gamble et al. (2017).

Example Input Syntax


[./failure_fecral]
temperature = temp
hoop_stress = hoop_stress
failure_criterion = INL
[../]`
(test/tests/tensor_mechanics/fecral_failure/fecral_failure_inl.i)

Input Parameters

C++ Type:std::vector

Required Parameters

• comparedless_equalOptions for variable _compared_ to criteria: greater_than greater_equal less_equal less_than

Default:less_equal

C++ Type:MooseEnum

Description:Options for variable _compared_ to criteria: greater_than greater_equal less_equal less_than

• 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.

• function_criteriaFunction name providing criteria value.

C++ Type:FunctionName

Description:Function name providing criteria value.

• max_principal_stressMax principal stress (Pa)

C++ Type:std::vector

Description:Max principal stress (Pa)

• hoop_stressHoop stress in cladding (Pa)

C++ Type:std::vector

• constant_criteria0Numerical value providing criteria value.

Default:0

C++ Type:double

Description:Numerical value providing criteria value.

• 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

• variable_checkVariable name which is compared to criteria. Example: Var < 0, true=failed

C++ Type:std::vector

Description:Variable name which is compared to criteria. Example: Var < 0, true=failed

• mid_principal_stressMid principal stress (Pa)

C++ Type:std::vector

Description:Mid principal stress (Pa)

• min_principal_stressMin principal stress (Pa)

C++ Type:std::vector

Description:Min principal stress (Pa)

• 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

• failure_criterionUTSThe criterion selected for failure of the material. Default is Ultimate Tensile Strength.

Default:UTS

C++ Type:MooseEnum

Description:The criterion selected for failure of the material. Default is Ultimate Tensile Strength.

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

References

1. A. P. Boresi and R. J. Schmidt. Advanced Mechanics of Materials, 6th Edition. John Wiley & Sons, Inc., 2003.[BibTeX]
2. K. A. Gamble, T. Barani, D. Pizzocri, J. D. Hales, K. A. Terrani, and G. Pastore. An investigation of FeCrAl cladding behavior under normal operating and loss of coolant conditions. Journal of Nuclear Materials, 491:55â€“66, 2017. URL: http://www.sciencedirect.com/science/article/pii/S0022311516312740, doi:https://doi.org/10.1016/j.jnucmat.2017.04.039.[BibTeX]
3. Caleb P. Massey, Kurt A. Terrani, Sebastien N. Dryepondt, and Bruce A. Pint. Cladding burst behavior of Fe-based alloys under LOCA. Journal of Nuclear Materials, 470():128â€“138, 2016. URL: http://www.sciencedirect.com/science/article/pii/S0022311515303871, doi:http://dx.doi.org/10.1016/j.jnucmat.2015.12.018.[BibTeX]
4. Y. Yamamoto, B.A. Pint, K.A. Terrani, K.G. Field, Y. Yang, and L.L. Snead. Development and property evaluation of nuclear grade wrought FeCrAl fuel cladding for light water reactors. Journal of Nuclear Materials, 467:703â€“716, 2015.[BibTeX]
5. Y. Yano, T. Tanno, Y. Sekio, H. Oka, S. Ohtsuka, T. Uwaba, and T. Kaito. Tensile properties and hardness of two types of 11cr-ferritic/martensitic steel after aging up to 45,000 h. Nuclear Materials and Energy, 000:1–7, 2016.[BibTeX]