/FAIL/ALTER
Block Format Keyword An advanced nonlinear stressbased failure criteria for glass applications such as a windshield.
The failure stress is described by parameters defining microcracks and crack propagation speed. With the XFEM approach, the stress is set to zero perpendicular to the crack direction.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/FAIL/ALTER/mat_ID/unit_ID  
Exp_n  V0  Vc  Ncycles  Irate  Iside  mode  
Cr_foil  Cr_air  Cr_core  Cr_edge  grsh4N  grsh3N  
K_{IC}  K_{TH}  Rlen  T_{delay}  Iout  
Kres1  Kres2  
Eta1  Beta1  Tau1  Area_ref  
Eta2  Beta2  Tau2  
Sig0  P_scale  P_switch 
(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  Unit Identifier. (Integer, maximum 10 digits) 

Exp_n  Crack growth exponent for subcritical
crack growth. Default = 16.0 (Real) 

V0  Crack growth velocity
${V}_{0}$
for subcritical crack growth at
K_{IC}. Default = 0.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
Vc  Maximum crack propagation velocity
glass. Default = 0.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
Ncycles  Stress filtering period in cycles. Only
used when Irate=0. 2
(Integer) 

Irate  Stress rate filtering method.
(Integer) 

Iside  Strain rate dependency option.


mode  Flag to switch failure propagation
models between neighbor elements.
(Integer) 

Cr_foil  Crack depth at bottom surface. Default = 0.0 (Real) 
$\left[\text{m}\right]$ 
Cr_air  Crack depth at top surface. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
Cr_core  Crack depth in between bottom and
surface integration points. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
Cr_edge  Crack depth at the edge elements of
windshield. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
grsh4N  (Optional) Group identifier for 4 node
edge shell elements. Default = 0 (Integer) 

grsh3N  (Optional) Group identifier for 3 node
edge shell elements. Default = 0 (Integer) 

K_{IC}  Fracture toughness. Default = 0.0 (Real) 
$\left[Pa\sqrt{m}\right]$ 
K_{TH}  Fatique threshold. Default = 0.0 (Real) 
$\left[Pa\sqrt{m}\right]$ 
Rlen  Reference length. Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
T_{delay}  Relaxation time before removing
elements. Default = 0.0 (Real) 
$\left[\text{s}\right]$ 
Iout  Activate exhaustive failure flag in
Engine output file.
(Integer) 

Kres1  Residual tensile stress scale factor in
first crack direction. Default = 0.0 (Real) 

Kres2  Residual tensile stress scale factor in
second crack direction. Default = 0.0 (Real) 

Eta1  Distribution parameters
${\eta}_{1}$
on bottom surface. 10
(Real) 
$\left[\text{Pa}\right]$ 
Beta1  Distribution parameters
${\beta}_{1}$
on bottom surface. 10 (Real) 

Tau1  Distribution parameters
${\tau}_{1}$
on bottom surface. 10 (Real) 
$\left[\text{Pa}\right]$ 
Area_ref  Reference element surface
area. (Real) 
$\left[{\text{m}}^{2}\right]$ 
Eta2  Distribution parameters
${\eta}_{2}$
on top surface. 10 (Real) 
$\left[\text{Pa}\right]$ 
Beta2  Distribution parameters
${\beta}_{2}$
on top surface. 10 (Real) 

Tau2  Distribution parameters
${\tau}_{2}$
on top surface. 10 (Real) 
$\left[\text{Pa}\right]$ 
Sig0  Initial stress at glass
surface. (Real) 
$\left[\text{Pa}\right]$ 
P_scale  Limits the definition interval of
selected distribution function. (Real, between 0.0 and 1.0) 

P_switch  Distribution function interval:


fail_ID  Failure criteria
identifier. 9 (Integer, maximum 10 digits) 
Example (Glass)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
# MUNIT LUNIT TUNIT
Mg mm s
#12345678910
/MAT/LAW36/72200103/1
Glass with linear hardening
# RHO_I
2.50E9
# E NU Eps_p_max Eps_t Eps_m
70000.0 0.23 0 0 0
# N_funct F_smooth C_hard F_cut Eps_f
1 1 0 1650 0
# fct_IDp Fscale fct_IDE EInf CE
0 0 0 0 0
# fct_ID1 fct_ID2 fct_ID3 fct_ID4 fct_ID5
722001021
# Fscale_1 Fscale_2 Fscale_3 Fscale_4 Fscale_5
1000
# Eps_dot_1 Eps_dot_2 Eps_dot_3 Eps_dot_4 Eps_dot_5
0
#12345678910
/FAIL/ALTER/72200103/1
# EXP_N V0 VC NCYCLES IRATE ISIDE MODE
16.0 6.0 1520000 6 0 0 1
# CR_FOIL CR_AIR CR_CORE CR_EDGE GRSH4N GRSH3N
0.00040 0.00100 0.00500 0 0 0
# KIC KTH RLEN TDEL Iout
23.717 7.9057 1.0 0 0
# KRES1 KRES2
0 0
# ETA1 BETA1 TAU1 AREA_REF
0 0 0 0
# ETA2 BETA2 TAU2
0 0 0
# SIG0 P_SCALE P_SWITCH
0 0 0
#12345678910
/FUNCT/722001021
Function for glass
# X Y
0.0 500.0
1.0 550.0
#12345678910
#enddata
Comments
 This failure criteria is using the maximum stress as failure criterion. It is computed based on the strength of the material determined by initial cracks and the crack propagation velocity. Depending on mode switch flag, different failure propagation models between neighbor elements may be used.
 When
Irate=0, an exponential moving average filter is
used, and the filtered stress is:
(1) $${\sigma}_{f}\left(t\right)=\alpha \sigma \left(t\right)+\left(1\alpha \right)\sigma \left(t\text{\Delta}t\right)$$Where, ${\sigma}_{f}=\text{filteredstress}$
 $\alpha =\frac{2}{{N}_{cycles}+1}$
 This failure model is compatible only with underintegrated shell elements (I_{shell} =24 and I_{sh3n} =2 are recommended) and not compatible fully integrated shells. Also, although there is no restriction of the shell property that can be used, it is only compatible with one layer shell models.
 The elements defined in the groups grsh4N and grsh3N should be along the edge of the windshield and will receive specific failure weakening.
 This failure model is applied to shell elements that sandwich a polyvinyl butyral (PVB) solid element layer using coincident nodes. The entire assembly models a windshield.
 The shell elements using this failure model should be oriented so their normals point away the from the middle PVB.
 The shell elements should have an offset applied to correctly model bending. This can be done using /PROP/TYPE51 I_{pos}=4.
 The fracture limit depends on the location and the fracture state of surrounding elements. ^{1}
 The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL and /PERTURB/FAIL/BIQUAD. 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 .sta file with /STATE/BRICK/FAIL for brick and with /STATE/SHELL/FAIL for shell).
 Ch. Brokmann extension ^{2} defines additional fracture criteria for external glass
surfaces only. It introduces initial stress on the glass surface, due to mechanical or
chemical treatment. Statistical evaluation of micro flaws in the glass surface allows to
define a probability of fracture using lefttruncated Weibull stochastic distribution:
with $i$ = 1,2 for bottom and top surface
(2) $$P(\sigma )=1\mathrm{exp}\left[{{\displaystyle \left(\frac{{\tau}_{i}}{{\eta}_{i}}\right)}}^{{\beta}_{i}}{{\displaystyle \left(\frac{\sigma}{{\eta}_{i}}\right)}}^{{\beta}_{i}}\right]$$Truncation point $\tau =0$ yields the wellknown twoparameter Weibull distribution. The Brokmann model calculates the randomly oriented initial flaws in the glass and distributes them over all finite elements with different lengths and geometry. Crack growth may be expressed by the following differential equation:(3) $$da={V}_{0}.{{\displaystyle \left(\frac{Y\sigma \sqrt{\pi a}}{{{\displaystyle K}}_{IC}}\right)}}^{Exp\_n}dt$$Where, $Y$ is a flaw geometry factor obtained using Weibull distribution.
Integral of Equation 3 will yield actual crack size, strongly dependent on stress rate. Actual stress intensity factors can be calculated and used in the fracture criteria.
The interest of Brokmann’s model is that depending on the distribution parameters and failure stress value, it is possible to estimate the stochastic probability of failure.After running a sufficient number of simulations with random initialization of glass flaws return a possibility to estimate a probability to reach a given value of the head injury criterion (HIC).  Flag Irate is automatically set to 0 when Ch. Brokmann criterion is used. It is then necessary to define the number of cycles for the stress filtering interval using exponential average.