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--- doc:user:elements:volumes:rupturecritere [2015/07/14 10:21] – [References] canales
+++ doc:user:elements:volumes:rupturecritere [2022/07/14 14:32] (current) – papeleux
@@ Line 1: / Line 1: @@
-====== Failure criterion ======
+====== Failure criteria ======
 ===== RuptureCriterion =====
@@ Line 6: / Line 6: @@
 === 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 ===
@@ Line 25: / Line 37: @@
 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 =====
@@ Line 113: / Line 146: @@
 === 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:
 $$
@@ Line 134: / Line 167: @@
 === Description ===
-The element is broken if //W//, whose evolution law is defined below, reaches 1.
+Goijaerts criterion [[doc:user:elements:volumes:rupturecritere#References|[5]]]. The element is broken if //W//, whose evolution law is defined below, reaches 1.
 $$
@@ Line 157: / Line 190: @@
 === 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
@@ Line 169: / Line 202: @@
 | $A$   |  ''RUPT_MPSTRAIN_CL''  |          -         |
 | $B$   |  ''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 =====
-[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.
+[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.]]
-[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.
-{{ :doc:user:references:theta.jpg?200 |}}
+[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.]]