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Trace: • "Fluid" materials • Luc PAPELEUX • Marco Lucio CERQUAGLIA • 2D Taylor-Couette flow • Failure criteria
doc:user:elements:volumes:rupturecritere

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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:
 $$ $$
- C = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}+ K = \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: by canales
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