laws:cazacutn
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laws:cazacutn [2022/03/16 09:57] carlos |
laws:cazacutn [2022/10/14 15:52] (current) carlos |
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| Where: | Where: | ||
| * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress: | * $\bar{\Sigma}_{CPB06}$ is the CPB06 yield stress: | ||
| - | \[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{J=1}{\Sigma}} \big(|\Sigma_{J}| - k\Sigma_{J}\big)^a \Big] ^{\frac{1}{a}}\] | + | \[\bar{\Sigma}_{CPB06}=\tilde{m}\Big[ \overset{3}{\underset{i=1}{\Sigma}} \big(|\Sigma_{i}| - k\Sigma_{i}\big)^a \Big] ^{\frac{1}{a}}\] |
| * $\sigma_{y}$ is the current yield stress of the material: | * $\sigma_{y}$ is the current yield stress of the material: | ||
| \[\sigma_{y} = \sigma_{0} + S_{R}\big[1-exp\big(-C_{R}\bar{\epsilon}^{p}\big)\big]\] | \[\sigma_{y} = \sigma_{0} + S_{R}\big[1-exp\big(-C_{R}\bar{\epsilon}^{p}\big)\big]\] | ||
| * STF is the stress transformation function, containing all the damage-related variables: | * STF is the stress transformation function, containing all the damage-related variables: | ||
| - | \[STF=2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2} - 1\] | + | \[STF= 1 - 2fq_{1}cosh\Big[\frac{3q_{2}\big(\sigma_{m} - X_{m}\big)}{h\sigma_{y}}\Big] - q_{3}f^{2}\] |
| + | The corrected stress ($\hat{\sigma}$) and backstress ($\hat{X}$) are respectively calculated as: | ||
| + | \[\hat{\sigma} = L_{ijmn}T_{mnkl}\sigma_{kl}\] | ||
| + | \[\hat{X}= L_{ijmn}T_{mnkl}X_{kl}\] | ||
| + | |||
| + | |||
| + | The backstress tensor is calculated using the Armstrong-Frederick model: | ||
| + | |||
| + | \[dX = S_{x}[C_{x}d{\epsilon^p}-Xd\bar{\epsilon}^p]\] | ||
| ==== Files ==== | ==== Files ==== | ||
| Prepro: LCAZACUTN.F \\ | Prepro: LCAZACUTN.F \\ | ||
| Lagamine: CAZACUTN.F \\ | Lagamine: CAZACUTN.F \\ | ||
| - | Thomason-Zhang coalescence onset criterion: THZCOAL.F | + | Coalescence onset criterion: COALCITERIA.F |
| ==== Subroutines ==== | ==== Subroutines ==== | ||
| - | ^ Files ^ Contained subroutines ^ Description ^ | + | ^ Files ^ Contained subroutines ^ Description ^ |
| - | | LCAZACUTN.F | LCAZACUTN |Main Prepro LCAZACUTN subroutine | | + | | LCAZACUTN.F | LCAZACUTN |Main Prepro LCAZACUTN subroutine | |
| - | | CAZACUTN.F | CAZACUTN |Main Lagamine CAZACUTN subroutine | | + | | CAZACUTN.F | CAZACUTN |Main Lagamine CAZACUTN subroutine | |
| - | | ::: | CAZACUTNFUN |Calculation of CAZACUTN yield locus | | + | | ::: | CAZACUTNFUN |Calculation of CAZACUTN yield locus | |
| - | | THZCOAL.F | THOMASON_ZHANG |Calculation of coalescence criterion| | + | | COALCRITERIA.F | THOMASON_ZHANG |Calculation of [[https://www.sciencedirect.com/science/article/pii/S0013794400000552|ThZ coalescence criterion]]| |
| + | | ::: | LSP_2006 |Calculation of [[https://www.sciencedirect.com/science/article/pii/S0013794405003048|LSP06 coalescence criterion]]| | ||
| ===== Availability ===== | ===== Availability ===== | ||
| Line 66: | Line 75: | ||
| |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | ||
| ==== Integer parameters ==== | ==== Integer parameters ==== | ||
| - | ^ Line 1 (1I5) ^^ | + | ^ Line 1 (3I5) ^^ |
| - | |MAXIT|Maximal number of iterations during stress integration| | + | |MAXIT |Maximal number of iterations during stress integration | |
| + | |IDAMAGE|Active damage mechanism(s) identifier, //param(35, ilaw)// | | ||
| + | |IDELEM |DELEM section identifier, | | ||
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| ^ Line 1 (6G10.0) ^^ | ^ Line 1 (6G10.0) ^^ | ||
| Line 76: | Line 87: | ||
| |$\nu_{13}$|:::| | |$\nu_{13}$|:::| | ||
| |$\nu_{23}$|:::| | |$\nu_{23}$|:::| | ||
| - | ^Line 2 (1G10.0)^^ | + | ^Line 2 (1G10.0) ^^ |
| - | |A|degree of homogeneity, //param(16, ilaw) //| | + | |$a$ |degree of homogeneity, //param(16, ilaw) // | |
| - | ^Line 3 (1G10.0)^^ | + | ^Line 3 (1G10.0) ^^ |
| - | |k| Asymmetry parameter, //param(17, ilaw) //| | + | |k | Asymmetry parameter, //param(17, ilaw) // | |
| - | ^Line 4 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 4 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{11}$| // param(18,ilaw) //| | + | |$C_{11}$| // param(18,ilaw) // | |
| - | |$C_{12}$| // param(19,ilaw) //| | + | |$C_{12}$| // param(19,ilaw) // | |
| - | |$C_{13}$| // param(20,ilaw) //| | + | |$C_{13}$| // param(20,ilaw) // | |
| - | ^Line 5 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 5 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{22}$| // param(21,ilaw) //| | + | |$C_{22}$| // param(21,ilaw) // | |
| - | |$C_{23}$| // param(22,ilaw) //| | + | |$C_{23}$| // param(22,ilaw) // | |
| - | |$C_{33}$| // param(23,ilaw) //| | + | |$C_{33}$| // param(23,ilaw) // | |
| - | ^Line 6 (3G10.0) Components of orthotropic constants tensor^^ | + | ^Line 6 (3G10.0) Components of orthotropic constants tensor ^^ |
| - | |$C_{44}$| // param(24,ilaw) //| | + | |$C_{44}$| // param(24,ilaw) // | |
| - | |$C_{55}$| // param(25,ilaw) //| | + | |$C_{55}$| // param(25,ilaw) // | |
| - | |$C_{66}$| // param(26,ilaw) //| | + | |$C_{66}$| // param(26,ilaw) // | |
| - | ^Line 7 (4G10.0, 1I5) Damage control parameters^^ | + | ^Line 7 (3G10.0) Isotropic hardening law parameters ^^ |
| - | |$f_{0}$| Initial porosity ratio, // VARIN(21,ilaw) //| | + | |$\sigma_{0}$ | Initial Yield stress [MPa], //param(27, ilaw)// | |
| - | |$q_{1}$| Tvergaard&Needleman parameter, // param(27,ilaw) //| | + | |$S_{R}$ | Saturation rate [MPa], //param(28, ilaw)// | |
| - | |$q_{2}$| Tvergaard&Needleman parameter, // param(28,ilaw) //| | + | |$C_{R}$ | Saturation value [-], //param(29, ilaw)// | |
| - | |$q_{3}$| Tvergaard&Needleman parameter, // param(29,ilaw) //| | + | ^Line 8 (2G10.0) Kinematic hardening parameters ^^ |
| - | |IDAMAGE| Active damage mechanism ID, // param(39,ilaw) //| | + | |$S_{X}$ | Saturation rate [-], //param(30, ilaw)// | |
| + | |$C_{X}$ | Saturation value [MPa], //param(31, ilaw)// | | ||
| + | ^Line 9 (4G10.0) Standard initial damage control parameters ^^ | ||
| + | |$f_{0}$| Initial porosity ratio, // VARIN(5,ilaw) // | | ||
| + | |$q_{1}$| Tvergaard&Needleman parameter, // param(32,ilaw) // | | ||
| + | |$q_{2}$| Tvergaard&Needleman parameter, // param(33,ilaw) // | | ||
| + | |$q_{3}$| Tvergaard&Needleman parameter, // param(34,ilaw) // | | ||
| |**SELECT CASE (IDAMAGE)** |||| | |**SELECT CASE (IDAMAGE)** |||| | ||
| ^ |**CASE (0)**: //No damage increment is calculated// ||| | ^ |**CASE (0)**: //No damage increment is calculated// ||| | ||
| - | | |^Line 8 (3G10.0) Isotropic hardening law parameters ^^ | ||
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | ||
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | ||
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | ||
| - | | |^Line 9 (2G10.0) Kinematic hardening parameters ^^ | ||
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | ||
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | ||
| | |||| | | |||| | ||
| ^ |**CASE (1)**: //Growth is the only active damage mechanism// ||| | ^ |**CASE (1)**: //Growth is the only active damage mechanism// ||| | ||
| - | | |^Line 8 (3G10.0) Isotropic hardening law parameters ^^ | ||
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | ||
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | ||
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | ||
| - | | |^Line 9 (2G10.0) Kinematic hardening parameters ^^ | ||
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | ||
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | ||
| | |||| | | |||| | ||
| - | ^ |**CASE (2)**: //Growth and nucleation of voids are considered// ||| | + | ^ |**CASE (2)**: //Growth and nucleation of voids are active// ||| |
| - | | |^Line 8 (3G10.0) Nucleation model parameters ^^ | + | | |^Line 10 (3G10.0) Nucleation model parameters ^^ |
| - | | ||$F_{N}$ | Total nucleated porosity ratio, //param(40, ilaw)// | | + | |::: ||$F_{N}$ | Total nucleated porosity ratio, //param(36, ilaw)// | |
| - | | ||$S_{N}$ | Standard deviation, //param(40, ilaw)// | | + | |::: ||$S_{N}$ | Standard deviation, //param(37, ilaw)// | |
| - | | ||$\epsilon_{N}$ | Standard mean, //param(40, ilaw)// | | + | |::: ||$\epsilon_{N}$ | Standard mean, //param(38, ilaw)// | |
| - | | |^Line 9 (3G10.0) Isotropic hardening law parameters ^^ | + | |
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | + | |
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | + | |
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | + | |
| - | | |^Line 10 (2G10.0) Kinematic hardening parameters ^^ | + | |
| - | | ||$S_{X}$ | Saturation rate [-], //param(33, ilaw)// | | + | |
| - | | ||$C_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | + | |
| | |||| | | |||| | ||
| ^ |**CASE (3)**: //Growth, nucleation and coalescence are active// ||| | ^ |**CASE (3)**: //Growth, nucleation and coalescence are active// ||| | ||
| - | | |^Line 8 (3G10.0) Nucleation model parameters ^^ | + | | |^Line 10 (3G10.0) Nucleation model parameters ^^ |
| - | | ||$F_{N}$ | Total nucleated porosity ratio, //param(40, ilaw)// | | + | |::: ||$F_{N}$ | Total nucleated porosity ratio, //param(36, ilaw)// | |
| - | | ||$S_{N}$ | Standard deviation, //param(41, ilaw)// | | + | |::: ||$S_{N}$ | Standard deviation, //param(37, ilaw)// | |
| - | | ||$\epsilon_{N}$ | Standard mean, //param(42, ilaw)// | | + | |::: ||$\epsilon_{N}$ | Standard mean, //param(38, ilaw)// | |
| - | | |^Line 9 (3G10.0) Coalescence model parameters ^^ | + | |::: |^Line 11 (3G10.0) Coalescence model parameters ^^ |
| - | | ||$f_{U}$ | Ultimate porosity ratio, //param(43, ilaw)// | | + | |::: ||$f_{U}$ | Ultimate porosity ratio, //param(39, ilaw)// | |
| - | | ||$f_{F}$ | Fracture porosity ratio, //param(44, ilaw)// | | + | |::: ||$f_{F}$ | Fracture porosity ratio, //param(40, ilaw)// | |
| - | | ||$f_{cr}$ | Critical porosity ratio for onset of coalescence, //param(45, ilaw)// | | + | |::: ||$f_{cr}$ | Critical porosity ratio for coalescence onset, //VARIN(19,ilaw) [If 0, Thomason criterion is applied]// | |
| - | | |^Line 10 (3G10.0) Isotropic hardening law parameters ^^ | + | |
| - | | ||$\sigma_{0}$ | Initial Yield stress [MPa], //param(30, ilaw)// | | + | |
| - | | ||$S_{R}$ | Saturation rate [MPa], //param(31, ilaw)// | | + | |
| - | | ||$C_{R}$ | Saturation value [-], //param(32, ilaw)// | | + | |
| - | | |^Line 11 (2G10.0) Kinematic hardening parameters ^^ | + | |
| - | | ||$C_{X}$ | Saturation rate [-], //param(33, ilaw)// | | + | |
| - | | ||$S_{X}$ | Saturation value [MPa], //param(34, ilaw)// | | + | |
| - | | |||| | + | |
| + | ... If the previous was the $n^{th}$ line... | ||
| + | ^ |IF **IDELEM = 1** THEN ||| | ||
| + | | |^Line $(n+1)^{th}$ (2G10.0) DELEM control parameters ^^ | ||
| + | | ||FDELEM | Porosity ratio at which element starts being deleted, //param(42, ilaw)// | | ||
| + | |::: ||TDELEM | Time for deleting the element (linear interpolation), //param(43, ilaw)// | | ||
laws/cazacutn.1647421045.txt.gz · Last modified: 2022/03/16 09:57 by carlos
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