Differences

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

--- doc:user:elements:volumes:rupturecritere [2016/10/09 00:29] – [IFRuptureCriterion] 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 31: / Line 43: @@
 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''//
  $C = \int_0^{\overline{\varepsilon}^p} \frac{\sigma_1}{\overline{\sigma}}  d\overline{\varepsilon}^p$
-//Brozzo criterion//
+//Brozzo criterion : ''BROZZO''//
  $C = \int_0^{\overline{\varepsilon}^p} \frac{2\sigma_1}{3(\sigma_1-p)}  d\overline{\varepsilon}^p$
-//Ayada criterion//
+//Ayada criterion : ''AYADA'' //
  $C = \int_0^{\overline{\varepsilon}^p} \frac{p}{\overline{\sigma}}  d\overline{\varepsilon}^p$
-//Rice and Tracey criterion//
+//Rice and Tracey criterion : ''RICE''//
  $C = \int_0^{\overline{\varepsilon}^p} \exp\left(\frac{3}{2} \frac{p}{\overline{\sigma}}\right)  d\overline{\varepsilon}^p$
-//Parameters//
+**Parameters**
 ^          Name      ^  Metafor Code  ^ Dependency         ^
 |Criterion  |  ''RUPT_OP_LAW''  |          -         |
@@ Line 186: / 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 =====
@@ Line 200: / Line 266: @@
 [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.]]