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Trace: • Réunion 12 Janvier 2015 • X-ALE-FEM
doc:user:elements:volumes:rupturecritere

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doc:user:elements:volumes:rupturecritere [2015/07/14 10:24] – [References] 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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 for a criterion based on a critical value of the equivalent plastic strain. for a criterion based on a critical value of the equivalent plastic strain.
  
 +===== OneParameterRuptureCriterion =====
 +
 +=== Description ===
 +
 +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 (dimensional Value) : ''COCKROFT2''//
 +$$ C = \int_0^{\overline{\varepsilon}^p} \sigma_1  d\overline{\varepsilon}^p$$
 +//Cockroft and Latham criterion (adimensional value) : ''COCKROFT''//
 +$$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
 +//Brozzo criterion : ''BROZZO''//
 +$$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)}  d\overline{\varepsilon}^p$$
 +//Ayada criterion : ''AYADA'' //
 +$$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
 +//Rice and Tracey criterion : ''RICE''//
 +$$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right)  d\overline{\varepsilon}^p$$
 +
 +**Parameters**
 +
 +^          Name      ^  Metafor Code  ^ Dependency         ^
 +|Criterion  |  ''RUPT_OP_LAW''  |          -         |
 ===== BaoRuptureCriterion ===== ===== BaoRuptureCriterion =====
  
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 === Description === === Description ===
  
-The element is broken if the variable //C//, defined below, reaches a critical value:+Lemaitre criterion [[doc:user:elements:volumes:rupturecritere#References|[4]]]. The element is broken if the variable //C//, defined below, reaches a critical value:
  
 $$ $$
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 === Description === === Description ===
  
-The element is broken if //W//, whose evolution law is defined below, reaches 1.+Goijaerts criterion [[doc:user:elements:volumes:rupturecritere#References|[5]]]. The element is broken if //W//, whose evolution law is defined below, reaches 1.
  
 $$ $$
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 === Description === === Description ===
  
-Element failure is detected differently whether the element is globally under tension of compression. It is broken if:+Maximum Principal Strain criterion [[doc:user:elements:volumes:rupturecritere#References|[6]]]. Element failure is detected differently whether the element is globally under tension of compression. It is broken if:
  
 $ \| \epsilon_{I} \|> $ ''RUPT_MPSTRAIN_TL'' if $ \epsilon_{I}\ $ + $ \epsilon_{II}\ $ + $ \epsilon_{III}\ $ > 0 $ \| \epsilon_{I} \|> $ ''RUPT_MPSTRAIN_TL'' if $ \epsilon_{I}\ $ + $ \epsilon_{II}\ $ + $ \epsilon_{III}\ $ > 0
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 |$A $  |  ''RUPT_MPSTRAIN_CL''  |          -         | |$A $  |  ''RUPT_MPSTRAIN_CL''  |          -         |
 |$B $  |  ''RUPT_MPSTRAIN_TL''  |          -         |  |$B $  |  ''RUPT_MPSTRAIN_TL''  |          -         | 
 +
 +===== BaiRuptureCriterion =====
 +
 +=== Description ===
 +
 +Bai and Wierzbicki rupture criterion [[doc:user:elements:volumes:rupturecritere#References|[7]]]. The element is broken if the variable C, defined below, reaches a critical value:
 +$$
 + C = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}
 +$$
 +where $\overline{\varepsilon}^p_f (\eta,\overline{\theta})$ is defined as:
 +$$\overline{\varepsilon}^p_f (\eta,\overline{\theta}) = \left[ \frac{1}{2}\left( D_1e^{-D_2\eta}+D_5e^{-D_6\eta} \right)-D_3e^{-D_4\eta} \right]\overline{\theta}^2 + \frac{1}{2}\left( D_1e^{- D_2\eta}-D_5e^{-D_6\eta} \right)\overline{\theta}+D_3e^{-D_4\eta}$$
 +
 +=== Parameters === 
 +^          Name      ^  Metafor Code  ^ Dependency         ^
 +|$D_1$  |  ''RUPT_BAI_D1''  |          -         |
 +|$D_2$  |  ''RUPT_BAI_D2''  |          -         |
 +|$D_3$  |  ''RUPT_BAI_D3''  |          -         |
 +|$D_4$  |  ''RUPT_BAI_D4''  |          -         |
 +|$D_5$  |  ''RUPT_BAI_D5''  |          -         |
 +|$D_6$  |  ''RUPT_BAI_D6''  |          -         |
 +|$\eta_{cutoff}$  |  ''RUPT_BAI_CUTOFF''  |          -         |
 +
 +
 +===== LouRuptureCriterion =====
 +
 +=== Description ===
 +
 +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:
 +$$
 + K = \int_0^{\overline{\varepsilon}^p}\dfrac{d\overline{\varepsilon}^{p}}{\overline{\varepsilon}^p_f (\eta,\overline{\theta})}
 +$$
 +where $\overline{\varepsilon}^p_f$ is defined as:
 +$$
 +\overline{\varepsilon}^p_f = D_3\left( \frac{2}{\sqrt{L^2+3}} \right)^{-D_1} \left( \left\langle \frac{1}{1+C}
 +\left[ \eta+\frac{3-L}{3\sqrt{L^2+3}}+C \right] \right\rangle \right)^{-D_2}
 +$$
 +
 +with,
 +$$
 +L = \frac{3 \tan\left( \theta \right) - \sqrt{3}}{\tan \left( \theta \right) + \sqrt{3}}
 +$$
 +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 === 
 +^          Name      ^  Metafor Code  ^ Dependency         ^
 +|$D_1$  |  ''RUPT_LOU_D1''  |          -         |
 +|$D_2$  |  ''RUPT_LOU_D2''  |          -         |
 +|$D_3$  |  ''RUPT_LOU_D3''  |          -         |
 +|$C$    |  ''RUPT_LOU_C''  |          -         |
 +
  
 ===== References ===== ===== References =====
  
-[1] Bao Y, Wierzbicki T. On fracture locus in the equivalent strain and stress triaxiality space. //International Journal of Mechanical Sciences// 2004;46:81-98.+[1] [[http://www.sciencedirect.com/science/article/pii/S0020740304000360|Bao Y, Wierzbicki T. On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sciences 2004;46:81-98.]] 
 + 
 +[2] [[http://www.sciencedirect.com/science/article/pii/0022509676900247|Hancock JW, Mackenzie AC. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. Journal of the Mechanics and Physics of Solids 1976;24:147-160.]] 
 + 
 +[3] [[http://wbldb.lievers.net/10134084.html|Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: 7th International Symposium on Ballistics. The Hague: The Netherlands, 1983; 541-547.]] 
 + 
 +[4] [[http://www.springer.com/us/book/9783662027615|Lemaitre J. A Course on Damage Mechanics. Springer-Verlag Berlin Heidelberg, 1992.]] 
 + 
 +[5] [[http://manufacturingscience.asmedigitalcollection.asme.org/article.aspx?articleid=1437060|Goijaerts AM, Govaert LE, Baaijens FPT. Prediction of ductile fracture in metal blanking. Journal of Manufacturing Science and Engineering 2000;122:476-483.]] 
 + 
 +[6]
  
-[2] Hancock JW, Mackenzie AC. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. //Journal of the Mechanics and Physics of Solids// 1976;24:147-160. 
  
-[3] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: //7th International Symposium on Ballistics//. The Hague: The Netherlands, 1983; 541-547.+[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.]]
  
-{{ :doc:user:references:theta.jpg?200 |}} 
  
-[[doc:user:references]]+[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.]]
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