Differences

This shows you the differences between two versions of the page.

--- doc:user:elements:volumes:rupturecritere [2015/07/14 09:57] – [References] canales
+++ doc:user:elements:volumes:rupturecritere [2017/04/05 09:21] – [OneParameterRuptureCriterion] canales
@@ Line 1: / Line 1: @@
-====== Failure criterion ======
+====== Failure criteria ======
 ===== RuptureCriterion =====
@@ Line 25: / Line 25: @@
 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 //
+$$ C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
+//Brozzo criterion//
+$$ C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)}  d\overline{\varepsilon}^p$$
+//Ayada criterion//
+$$ C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}}  d\overline{\varepsilon}^p$$
+//Rice and Tracey criterion//
+$$ C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right)  d\overline{\varepsilon}^p$$
+**Parameters**
+^          Name      ^  Metafor Code  ^ Dependency         ^
+|Criterion  |  ''RUPT_OP_LAW''  |          -         |
 ===== BaoRuptureCriterion =====
@@ Line 113: / Line 132: @@
 === 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:
 $$
@@ Line 134: / Line 153: @@
 === Description ===
-The element is broken if //W//, whose evolution law is defined below, reaches 1.
+Goijaerts criterion [[doc:user:elements:volumes:rupturecritere#References|[5]]]. The element is broken if //W//, whose evolution law is defined below, reaches 1.
 $$
@@ Line 157: / Line 176: @@
 === 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 188: @@
 |$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:elements:volumes:rupturecritere: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.]]