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doc:user:elements:volumes:rupturecritere [2016/10/09 00:38] – [MaximumPrincipalStrainRuptureCriterion] canalesdoc:user:elements:volumes:rupturecritere [2022/07/14 14:32] (current) papeleux
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-====== Failure criterion ======+====== Failure criteria ======
  
 ===== RuptureCriterion ===== ===== RuptureCriterion =====
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 === Description === === Description ===
  
-''RuptureCriterion'' manages various failure criteria. Two parameters are common in all laws. First, the critical value //C// of a variable above which the element is broken. Second, the type of failure the element is broken if the criterion is verified on one integration point (''ONEBROKEN''), on all of them (''ALLBROKEN''), or in average (''MEANBROKEN''over the element.+''RuptureCriterion'' manages various failure criteria.  
 + 
 +The critical value //C// (''RUPT_CRIT_VALUE''of a variable above which the element is broken.  
 + 
 +The type of failure (''RUPT_TYPE_CRIT'') are defined in the table below :  
 + 
 + 
 +^          Name      ^ Description       ^  
 +| ''NOBREAK''      |  Compute the criterion, but never break any element 
 +''ONEBROKEN''     Break an element when ONE integration point override the critical value  | 
 +''ALLBROKEN''     Break an element when ALL the integration points override the critical value  | 
 +''MEANBROKEN''   |  Break an element when the averaged value over the integration points override the critical value  | 
  
 === Parameters ===  === Parameters === 
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 Four simple rupture criteria are gathered in one single family. In order to selected one of the criteria the parameter ''RUPT_OP_LAW'' (only parameter in this criterion) need to be defined as: ''COCKROFT'', ''BROZZO'', ''AYADA'' or ''RICE''. Then, the element is broken if the variable C reaches a critical value, which is defined in each case as: Four simple rupture criteria are gathered in one single family. In order to selected one of the criteria the parameter ''RUPT_OP_LAW'' (only parameter in this criterion) need to be defined as: ''COCKROFT'', ''BROZZO'', ''AYADA'' or ''RICE''. Then, the element is broken if the variable C reaches a critical value, which is defined in each case as:
  
-//Cockroft and Latham criterion //+//Cockroft and Latham criterion (dimensional Value) : ''COCKROFT2''// 
 +$$ C = \int_0^{\overline{\varepsilon}^p} \sigma_1  d\overline{\varepsilon}^p$$ 
 +//Cockroft and Latham criterion (adimensional value) : ''COCKROFT''//
 $$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}}  d\overline{\varepsilon}^p$$ $$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
-//Brozzo criterion//+//Brozzo criterion : ''BROZZO''//
 $$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)}  d\overline{\varepsilon}^p$$ $$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)}  d\overline{\varepsilon}^p$$
-//Ayada criterion//+//Ayada criterion : ''AYADA'' //
 $$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}}  d\overline{\varepsilon}^p$$ $$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
-//Rice and Tracey criterion//+//Rice and Tracey criterion : ''RICE''//
 $$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right)  d\overline{\varepsilon}^p$$ $$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right)  d\overline{\varepsilon}^p$$
-//Parameters//+ 
 +**Parameters** 
 ^          Name      ^  Metafor Code  ^ Dependency         ^ ^          Name      ^  Metafor Code  ^ Dependency         ^
 |Criterion  |  ''RUPT_OP_LAW''  |          -         | |Criterion  |  ''RUPT_OP_LAW''  |          -         |
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 === Description === === Description ===
  
-Lou, Yoon and Huh rupture criterion [[doc:user:elements:volumes:rupturecritere#References|[8]]]. The element is broken if the variable C, defined below, reaches a critical value:+Lou, Yoon and Huh rupture criterion [[doc:user:elements:volumes:rupturecritere#References|[8]]]. The element is broken if the variable K, defined below, reaches a critical value:
 $$ $$
- = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}+ = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}
 $$ $$
 where $\overline{\varepsilon}^p_f$ is defined as: where $\overline{\varepsilon}^p_f$ is defined as:
 $$ $$
-\overline{\varepsilon}^p_f = c_3\left( \frac{2}{\sqrt{L^2+3}} \right)^{-c_1} \left( \left\langle \frac{1}{1+C} +\overline{\varepsilon}^p_f = D_3\left( \frac{2}{\sqrt{L^2+3}} \right)^{-D_1} \left( \left\langle \frac{1}{1+C} 
-\left[ \eta+\frac{3-L}{3\sqrt{L^2+3}}+C \right] \right\rangle \right)^{-c_2}+\left[ \eta+\frac{3-L}{3\sqrt{L^2+3}}+C \right] \right\rangle \right)^{-D_2}
 $$ $$
  
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 L = \frac{3 \tan\left( \theta \right) - \sqrt{3}}{\tan \left( \theta \right) + \sqrt{3}} L = \frac{3 \tan\left( \theta \right) - \sqrt{3}}{\tan \left( \theta \right) + \sqrt{3}}
 $$ $$
-where $c_1$, $c_2$ and $c_3$ are material parameters. $L$ corresponds to an alternative definition of the Lode angle and the $\left\langle \bullet \right\rangle$ symbol denotes the MacAuley brackets. +where $D_1$, $D_2$ and $D_3$ are material parameters. $L$ corresponds to an alternative definition of the Lode angle and the $\left\langle \bullet \right\rangle$ symbol denotes the MacAuley brackets. 
  
 === Parameters ===  === Parameters === 
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 [6] [6]
 +
 +
 +[7] [[http://www.sciencedirect.com/science/article/pii/S0749641907001246|Bai I, Wierzbicki T. A new model of metal plasticity and fracture with pressure and Lode dependence. International Journal of Plasticity 2008;24:1071-1096.]]
 +
 +
 +[8] [[http://www.sciencedirect.com/science/article/pii/S0749641913001617|Lou Y, Yoon JW, Huh H. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. International Journal of Plasticity 2014;54:56-80.]]
doc/user/elements/volumes/rupturecritere.1475966324.txt.gz · Last modified: 2016/10/09 00:38 by canales

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