/FAIL/RTCL

Block Format Keyword The RTCL (Rice-Tracey–Cockroft–Latham) criterion is a stress triaxiality-based failure model especially adapted to ductile failure.

The theory is based on voiding growth modeling. This failure model can be used for shell and solid elements.

Format


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/FAIL/RTCL/`mat_ID`/`unit_ID`
`EPScal`		`Inst`	`n`

Optional line


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fail_ID`

Definition


Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit identifier. (Integer, maximum 10 digits)
`EPScal`	Calibrated simple tension failure strain $ε_{c a l}$ (for a reference mesh size of $L_{e}$ if the regularization is activated for shells). (Real)
`Inst`	Flag to activate damage regularization for shells. = 0 Default value. = 1 Necking instability regularization is not activated. = 2 (Default) Necking instability regularization is activated. (Integer)
`n`	Hardening exponent for shell damage regularization. (Real)
`fail_ID`	(Optional) Failure criteria identifier. (Integer, maximum 10 digits)

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/PLAS_JOHNS/1/1
Aluminum
#              RHO_I
              2.7E-9                   0
#                  E                  Nu     Iflag
               70000                  .3         0
#                  a                   b                   n           EPS_p_max            SIG_max0
                  90                 200                  .3                   0                   0
#                  c           EPS_DOT_0       ICC   Fsmooth               F_cut               Chard
                   0                   0         0         0                   0                   0
#                  m              T_melt              rhoC_p                 T_r
                   0                   0                   0                   0
/FAIL/RTCL/1/1
#             EPScal      Inst                   n         
                  .2         0                 .67                   
#  fail_ID
         1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

The factor is computed according to stress triaxiality as:
$D = \frac{1}{ε_{c r}^{f}} \int_{0}^{\infty} f_{R T C L} (η) d ε_{p}$
Where,

$η$

Stress triaxiality defined as $\frac{σ_{m}}{σ_{V M}}$

$σ_{m}$

Mean stress

$σ_{V M}$

von Mises equivalent stress

$ε_{p}$

Cumulated plastic strain.

$ε_{c r}^{f}$

Plastic strain at failure in simple tension.

$f_{R T C L}$

A factor whose computation is defined below.
The factor is computed according to stress triaxiality as:
$f_{R T C L} = {\begin{matrix} 0 & if & η < - \frac{1}{3} \\ 2 \frac{1 + η \sqrt{12 - 27 η^{2}}}{3 η + \sqrt{12 - 27 η^{2}}} & if & - \frac{1}{3} \leq η < \frac{1}{3} \\ e^{- \frac{1}{2}} e^{\frac{3}{2} η} & if & η \geq \frac{1}{3} \end{matrix}$
The plastic strain at failure $ε_{c r}^{f} = ε_{c a l}$ for solid elements. However, two cases can be encountered for shell elements:
- If $I n s t = 1$ : $ε_{c r}^{f} = ε_{c a l}$
- If $I n s t = 2$ : $ε_{c r}^{f} = n + (ε_{c a l} - n) \frac{t_{e}}{L_{e}}$
  Where,
  
  $n$
  
  Hardening exponent (assuming a power type hardening: $A + B ε_{p}^{n}$ )
  
  $t_{e}$
  
  Shell initial thickness
  
  $L_{e}$
  
  Square root of the shell area.
  
  This last formula allows necking instability for shells to be considered and to regularize the results.
  Note: The calibrated value $ε_{c a l}$ is encountered when $t_{e} = L_{e}$ .
Damage can be post-processed in the animation files using the output request DAMA. For shell elements, when an integration point reaches D=1, the integration points stress tensor is set to zero. The element fails and is deleted when the ratio of through thickness failed integration points equals P_thick_fail defined in the shell properties. In solid elements, the element is deleted when any integration point reaches D=1.
The fail_ID is used for the failure initialization in the element using the keyword /INISHE/FAIL, /INISH3/FAIL or /INIBRI/FAIL. These values can be written in the .sta file with /STATE/SHELL/FAIL or /STATE/BRICK/FAIL options.