/FAIL/TAB1

Block Format Keyword This advanced failure model allows the failure strain to be defined as a function of: stress triaxiality, strain rate, Lode angle, element size, temperature, and instability strain. Damage is accumulated based on user-defined functions.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/FAIL/TAB1/`mat_ID`/`unit_ID`
`I`_{fail_sh}	`I`_{fail_so}			`P_thick`_fail		`P_thin`_fail			`Ixfem`

Card 2 - Damage accumulation parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`D`_crit		`D`_p		`n`		`D`_adv		`fct_ID`_d

Card 3 - Failure strain table dependent on stress triaxiality and Lode angle parameter

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`table1_ID`	`Xscale1`		`Xscale2`		`table2_ID`	`Xscale3`		`Xscale4`

Card 4 - Element size scale function

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_el	`Fscale`_el		`El_ref`		`inst_start`		`Fad_exp`		`Ch_i_f`

Card 5 - Temperature scale function

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`_T	`Fscale`_T

Card 6 - Optional line

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

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`I`_{fail_sh}	Shell failure flag. If `Ixfem` =0: failure - element deleted. 1 If `Ixfem` =1: failure - element cracked. 2 (Integer) = 1 Shell is deleted/cracked, if the damage criterion is satisfied in one integration point or layer. = 2 Shell is deleted/cracked, if the damage criterion is satisfied in all shell layers. For a single layer shell, the stress tensor is set to zero. = 3 Shell is deleted/cracked, if the damage criterion is satisfied in all layers. Stress tensor is not modified in broken layers until the complete element is ruptured.
`I`_{fail_so}	Solid failure flag. = 1 Solid is deleted, if the damage criterion is satisfied in one integration point. = 2 Deviatoric stress components are set to zero for the integration points where criteria is satisfied. (Integer)
`Ixfem`	XFEM flag (for /SHELL and /SH_SANDW properties only). = 0 (Default) Without XFEM. = 1 XFEM formulation. 2 (Integer)
`P_thick`_fail	Percentage of through thickness integration points that must fail before the element is deleted. (shells only). Only used when `I`_{fail_sh}=2 or 3. 2 6 7 (Real)
`P_thin`_fail	Ratio of thickness reduction before failure (shells only and only active for `Ifail_sh` > 1). (Real)
`D`_crit	Critical accumulated damage value (failure criteria). Default = 0.999 (Real)
`D`_p	Damage accumulation parameter. Default = 1.0 (Real)
`n`	Damage accumulation parameter. Default = 1.0 (Real)
`D`_adv	Criterion for the crack advancement (Only active if `Ixfem`=1). (Real, between 0 and 1) Default = 0 means `D`_adv = `D`_crit 4
`fct_ID`_d	Damage function identifier. 5 Default = 0 (Integer)
`table1_ID`	Failure strain table identifier. 3 (Integer)
`Xscale1`	Scale factor for the first variable of table1 (failure strain). Default = 1.0 (Real)	$[Pa]$
`Xscale2`	Scale factor for the second variable table1 (strain rate). Default = 1.0 (Real)	$[\frac{1}{s}]$
`table2_ID`	Instability strain table identifier. 9 (Integer)
`Xscale3`	Scale factor for the first variable of table2 (strain rate). Default = 1.0
`Xscale4`	Scale factor for the second variable of table2 (instability strain). Default = 1.0
`fct_ID`_el	Element size factor function identifier. (Integer)
`Fscale`_el	Element size function scale factor. Default = 1.0 (Real)
`El_ref`	Reference element size. Default = 1.0 (Real)	$[m]$
`inst_start`	Instability strain (Only used if `table2_ID` is not defined). Default = `D`_n (Real)
`Fad_exp`	Fading exponent. 9 > 0 (Default) Fading exponent. (Real) < 0 Fading exponent relative to element size function identifier. (Integer)
`Ch_i_f`	Choice of instability or fracture regularization flag. = 1 (Default) Element length regularization affects the fracture curve. = 2 Element length regularization affects the instability table. = 3 Element length regularization affects both fracture curve and instability table.
`fct_ID`_T	Temperature factor function identifier. (Integer)
`Fscale`_T	Temperature function scale factor. Default = 1.0 (Real)
`fail_ID`	(Optional) Failure criteria identifier. 10 (Integer, maximum 10 digits)

Example (Shell)

In this example diffuse necking are considered using instability strain options (table2_ID and Fad_exp).

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  kg                  mm                  ms
#---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
Steel
#              RHO_I
              7.9E-6                   0
#                  E                  Nu     Iflag
                 210                  .3         0
#                  a                   b                   n           EPS_p_max            SIG_max0
                 .05                 .52                  .1                   0                   0
#                  c           EPS_DOT_0       ICC   Fsmooth               F_cut               Chard
                .022                .001         0         1                   1                   0
#                  m              T_melt              rhoC_p                 T_r
                1.03                1796                3.91                 300
/FAIL/TAB1/1/1
# failure for shell
# Ifail_sh  Ifail_so                             P_THICKFAIL          P_THINFAIL              I_Xfem
         2         1                                       1                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##CARD2  - Damage accumulation parameters
#              DCRIT                   D                   N                Dadv   fct_IDd
                   1                  .1                   1                   0         0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#CARD3  - Failure strain functions for each defined strain rate  (Nrate lines, at least one)
#Table1_ID             Xscale1             Xscale2 Table2_ID             Xscale3             Xscale4
      4711                   1                   1      4712                   1                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#CARD4 - Element size scale function
#FCT_ID_EL           FSCALE_EL              EI_REF          INST_START             FAD_EXP    Ch_i_f
        21                   1                   1                  0                   10         0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#CARD5 - Temperature scale function
# FCT_ID_T            FSCALE_T
        22                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#CARD6 - Function identifier (optional card)
#  Fail_Id
         1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/4711
failure plastic-strain vs triaxiality for material failure
#
         1
#        Triaxiality      Failure_Strain     
                 -1.                0.50                                       
                  1.                0.50                                       
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/4712
failure plastic-strain vs triaxiality for diffuse necking
#
         1
#        Triaxiality      Failure_Strain     
                 -1.                0.30                                        
                  1.                0.30                                        
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/21
Element length regularisation
#                  X                   Y
# relative ele. size        scale factor
                  .1                   1                                        
                 .25                   1                                        
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/22
Temperature scale function
#                  X                   Y
                   0                 1.0                                                            
                1000                 1.0                                                         
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example (Solid)

In this example triaxiality and Lode angle are considered.

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  kg                  mm                  ms
#---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
Steel
#              RHO_I
              7.9E-6                   0
#                  E                  Nu     Iflag
                 210                  .3         0
#                  a                   b                   n           EPS_p_max            SIG_max0
                 .05                 .52                  .1                   0                   0
#                  c           EPS_DOT_0       ICC   Fsmooth               F_cut               Chard
                .022                .001         0         1                   1                   0
#                  m              T_melt              rhoC_p                 T_r
                1.03                1796                3.91                 300
/FAIL/TAB1/1/1
# Ifail_sh  Ifail_so                             P_THICKFAIL          P_THINFAIL              I_Xfem
         1         1                                       1                   0                   0
#              DCRIT                   D                   N                Dadv   fct_IDd
                   1                   1                   1                   0         0
#Table1_ID             Xscale1             Xscale2 Table2_ID             Xscale3             Xscale4
      4711                   1                   1         0                   0                   0
#FCT_ID_EL           FSCALE_EL              EI_REF          INST_START             FAD_EXP    Ch_i_f
        21                   1                   1                   0                   0         0
# FCT_ID_T            FSCALE_T
        22                   1
#  Fail_Id
         1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/4711
curve_list Failure Function vs. strain rates vs Lode angle
#DIMENSION
         3
#   FCT_ID                   strain_rate          Lode_angle
      3000                          1E-4                  -1                                       0
      3001                          1E-4                   0                                       0
      3002                          1E-4                   1                                       0
      3003                             1                  -1                                       0
      3004                             1                   0                                       0
      3005                             1                   1                                       0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3000
fail strain vs triaxiality 
#        triaxiality         fail strain         
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3001
fail strain vs triaxiality
#        triaxiality         fail strain 
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3002
fail strain vs triaxiality
#        triaxiality         fail strain 
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3003
fail strain vs triaxiality
#        triaxiality         fail strain 
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3004
fail strain vs triaxiality
#        triaxiality         fail strain 
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/3005
fail strain vs triaxiality
#        triaxiality         fail strain 
#                  X                   Y
                   0                  .5                                                            
                   1                  .5                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/21
Element length regularisation
#                  X                   Y
# relative ele. size        scale factor
                   0                   1                                                            
                  10                   1                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/22
Temperature scale function
#                  X                   Y
                   0                   1                                                            
                1000                   1                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Using Ixfem=0, failure leads to element or layer deletion. In this case, if I_{fail_sh}=1, then P_thick_fail has to be set to zero for proper working failure criteria.
Using Ixfem=1 (XFEM formulation), failure leads to element crack:
XFEM formulation is only compatible with Belytchko (I_shell=1 or 2), I_shell=3 or 4 and QEPH (I_shell=24) shell elements.
Two XFEM options are available: mono-layer and multi-layer. The XFEM option depends on the property type associated to the failure criterion applied to the material identifier:
1. If /PROP/SHELL (TYPE1) is used, then mono-layer XFEM will be applied.
  In this case, the whole element thickness is considered as a single layer. The failure criterion is calculated in each integration point but only one single crack can appear in this element. This approach is compatible with all shell flag options (I_{fail_sh}=1, 2 or 3), as well as P_Thick_fail values. The crack direction is determined by the principal constraints in the last failed integration point.
2. If /PROP/SH_SANDW (TYPE11) is used, then multi-layer XFEM will be applied.
  In this case, each integration point over thickness is considered as a distinct layer. The failure criterion is calculated separately, and the crack direction may be different for each layer. Crack direction in each layer will independently propagate from one element to another. Multi-layer XFEM is not compatible with I_{fail_sh}=1 and P_thick_fail>0. Their values will be automatically set to I_{fail_sh}=2 and P_thick_fail=0.
Warning: Mono-layer and multi-layer XFEM formulations cannot be mixed in the same model, yet. The choice between them must be made for the whole model.
The plastic failure strain is defined as:(1)
$ε_{f} = X s c a l e 1 \cdot f (σ^{*}, \dot{ε}, ξ) \cdot f a c t o r_{e l} \cdot f a c t o r_{T}$

Where,

$f (σ^{*}, \dot{ε}, ξ)$

Described in table1_ID and is calculated by interpolating between the failure strain versus stress triaxiality functions for strain rate $\dot{ε}$ and Lode angle $ξ$ .

$σ^{*} = \frac{σ_{m}}{σ_{V M}}$

Stress triaxiality

$σ_{m}$

Hydrostatic stress

$σ_{V M}$

von Mises stress

The first function from table1_ID is used for strain rate values from 0 to its corresponding strain rate. For strain rates above the last defined function, the failure strain value is extrapolated using the last two curves and their corresponding strain rates.

It is possible to consider element size in material failure by function fct_ID_el to scale the failure strain depending on the normalized element size with Ch_i_f=1 or 3.(2)
$f a c t o r_{e l} = F s c a l e_{e l} \cdot f_{e l} (\frac{S i z e_{e l}}{E l_r e f})$

Where, $f_{e l} (\frac{S i z e_{e l}}{E l_r e f})$ is the function of fct_ID_el.

Temperature dependency can be considered in material failure by defining a function to scale the failure strain depending on the normalized temperature:(3)
$f a c t o r_{T} = F s c a l e_{T} \cdot f_{T} (T^{*})$

Here, $f_{T} (T^{*})$ is defined using fct_ID_T and Temperature $T^{*}$ is computed as:(4)
$T^{*} = \frac{T - T_{i n i}}{T_{m e l t} - T_{i n i}}$

It is recommended to use /HEAT/MAT to define the thermal parameter for material laws (which support thermo-plasticity).
Two different failures (rupture or crack) are introduced in this failure model. The failure criteria is calculated as:
Element rupture (Ixfem=0):
- Element rupture (deleted), if (5)
  $\sum Δ D > D_{crit}$
  
  $D_{c r i t}$
  
  The only rupture criterion used when Ixfem=0.
Element crack (Ixfem=1):
- Element cracked, if:(6)
  $\sum Δ D > D_{crit}$
  
  in case no failed neighbors for this element. $D_{c r i t}$ is used for new crack initialization.(7)
  $\sum Δ D > D_{adv}$
  
  in case there is failed neighbors for this element, $D_{a d v}$ is used for crack advancement.
  
  Element is deleted, if a second crack arrives to the same element.
Note: $D_{a d v}$ should always be less than $D_{c r i t}$ ( $D_{a d v}$ < $D_{c r i t}$ ). If not, then $D_{a d v}$ is set to $D_{c r i t}$ _crit ( $D_{a d v}$ = $D_{c r i t}$ ).
Damage accumulation is computed in Radioss one of two different ways:
- With parameter input if fct_ID_d = 0:(8)
  $Δ D = \frac{Δ ε_{p}}{ε_{f}} \cdot n \cdot D_{p}^{(1 - \frac{1}{n})}$
  
  Where,
  
  $Δ ε_{p}$
  
  Change in plastic strain of the integration point
  
  $ε_{f}$
  
  Plastic failure strain
  
  D_p and n
  
  Damage parameters
- With curve input if fct_ID_d ≠ 0:(9)
  $Δ D = \frac{Δ ε_{p}}{ε_{f}} \cdot f_{d}$
  
  Where,
  
  $f_{d}$
  
  Damage scale factor as a function of plastic strain defined in fct_ID_d.
  
  $Δ ε_{p}$
  
  Plastic strain increment.
  
  $f_{d}$
  
  Function of fct_ID_d
P_thick_fail is only compatible with shell elements (except, shells with /PROP/TYPE11 (SH_SANDW)) and is only used when I_{fail_sh}=2 or I_{fail_sh}=3. With Ixfem=1, P_thick_fail is only compatible with mono-layer XFEM formulation. 1
When P_thick_fail is used, the shell complete rupture occurs when the thickness of broken layers is greater than the ratio of shell total thickness. Any P_thickfail value defined in the shell properties is ignored and the value entered in this failure model is used instead.
Only adjacent layers that fail consecutively are accounted for the thickness sum (usually from one of external skin to the mid-surface).
The first variable of table1_ID is the plastic failure strain versus stress triaxialit function, the second variable is strain rate and the third is the Lode angle parameter $ξ$ (for solids).
For shell, only 2D tables are available (no dependency of Lode angle).
Instability (diffuse necking):
- Only available for shells
- The fading exponent describes the softening behvior and starts of instability (diffuse necking). The recommended value of Fad_exp is 5 to 10.
  If Fad_exp < 0 and Ch_i_f=2 or 3, then the absolute value of the fading exponent is a function identifier fct_ID_el which defines the fading exponent as a function of element length.
- The start of instability can be described as a function or constant value:
  - table2_ID is a function of instability strain vs. triaxiality where the instability strain defines when diffuse necking starts. Strain rate dependency for diffuse necking could be considered as well using dimension=2 in /TABLE.
  - If table2_ID is not defined, then inst_start is used as constant flat line for instability starting value over the triaxiality.
  - If table2_ID is not defined, then inst_start is used as constant flat line for instability starting value over the triaxiality, where the default value is D_p.
    
    Figure 1.
- The diffuse necking softening is based according to this equation:(10)
  $σ_{r e d u c e d} = σ \cdot (1 - {(\frac{D_{i n s t a b i l i t y} - i n s t_s t a r t}{1 - i n s t_s t a r t})}^{F a d_\exp})$
  
  Where, $D_{i n s t a b i l i t y} = \sum \frac{Δ ε_{p}}{ε_{f}}$ with $ε_{f}$ being the diffuse necking strain.
  
  Currently diffuse necking (material instability) in /FAIL/TAB1 could be used with material laws greater than 28.
The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL. There is no default value. If the line is blank, no value will be output for failure model variables in the /INIBRI/FAIL (written in the .sta file with /STATE/BRICK/FAIL option).