/FAIL/RTCL
Block Format Keyword The RTCL (RiceTracey–Cockroft–Latham) criterion is a stress triaxialitybased 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 
(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
${\epsilon}_{cal}$
(for a reference mesh size of
${L}_{e}$
if the
regularization is activated for shells). (Real) 

Inst  Flag to activate damage
regularization for shells.
(Integer) 

n  Hardening exponent for shell damage
regularization. (Real) 

fail_ID  (Optional) Failure criteria
identifier. (Integer, maximum 10 digits) 
Example (Aluminum)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat and failure
# MUNIT LUNIT TUNIT
Mg mm s
#12345678910
# 1. MATERIALS:
#12345678910
/MAT/PLAS_JOHNS/1/1
Aluminum
# RHO_I
2.7E9 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
#12345678910
#enddata
#12345678910
Comments
 The factor is computed
according to stress triaxiality as:
(1) $$D=\frac{1}{{\epsilon}_{cr}^{f}}{\displaystyle \underset{0}{\overset{\infty}{\int}}{f}_{RTCL}(\eta )\text{d}{\epsilon}_{p}}$$Where, $\eta $
 Stress triaxiality defined as
$\frac{{\sigma}_{m}}{{\sigma}_{VM}}$
 ${\sigma}_{m}$
 Mean stress
 ${\sigma}_{VM}$
 von Mises equivalent stress
 ${\epsilon}_{p}$
 Cumulated plastic strain.
 ${\epsilon}_{cr}^{f}$
 Plastic strain at failure in simple tension.
 ${f}_{RTCL}$
 A factor whose computation is defined below.
 The factor is computed
according to stress triaxiality
as:
${f}_{RTCL}=\{\begin{array}{ccc}0& \text{if}& \eta <\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.\\ 2\frac{1+\eta \sqrt{1227{\eta}^{2}}}{3\eta +\sqrt{1227{\eta}^{2}}}& \text{if}& \raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.\le \eta <\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.\\ {e}^{\frac{1}{2}}{e}^{\frac{3}{2}\eta}& \text{if}& \eta \ge \raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$3$}\right.\end{array}$
 The plastic strain at
failure ${\epsilon}_{cr}^{f}={\epsilon}_{cal}$
for solid elements.
However, two cases can be encountered for shell elements:
 If $Inst=1$ : ${\epsilon}_{cr}^{f}={\epsilon}_{cal}$
 If
$Inst=2$
:
${\epsilon}_{cr}^{f}=n+({\epsilon}_{cal}n)\frac{{t}_{e}}{{L}_{e}}$
Where,
 $n$
 Hardening exponent (assuming a power type hardening: $A+B{\epsilon}_{p}^{n}$ )
 ${t}_{e}$
 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 ${\epsilon}_{cal}$ is encountered when ${t}_{e}={L}_{e}$ .
 Damage can be postprocessed 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.