/FAIL/ALTER

Block Format Keyword An advanced nonlinear stress-based failure criteria for glass applications such as a windshield.

The failure stress is described by parameters defining micro-cracks and crack propagation speed. With the X-FEM approach, the stress is set to zero perpendicular to the crack direction.

Format

(1)	(3)	(5)	(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
`Kres1`	`Kres2`

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)
`Exp_n`	Crack growth exponent for subcritical crack growth. Default = 16.0 (Real)
`V0`	Crack growth velocity for subcritical crack growth at `K`_IC. Default = 0.0 (Real)	$[\frac{m}{s}]$
`Vc`	Maximum crack propagation velocity glass. Default = 0.0 (Real)	$[\frac{m}{s}]$
`Ncycles`	Stress filtering period in cycles. Only used when `Irate`=0. 2 = 1 (Default) No filtering. (Integer)
`Irate`	Stress rate filtering method. = 0 Exponential moving average using `Ncycles`. = 1 Arithmetic average using the last 50 cycles. (Integer)
`Iside`	Strain rate dependency option. = 0 (Default) Strain rate dependency only on air (outwards oriented) side. = 1 Strain rate dependency on both sides of the shell. (Integer)
`mode`	Flag to switch failure propagation models between neighbor elements. = 0 (Default) No failure info propagation. = 1 xfem failure propagation. = 2 Isotropic frontwave propagation. = 3 Directional propagation through element edges. = 4 Directional propagation through edges and diagnosis. (Integer)
`Cr_foil`	Crack depth at bottom surface. Default = 0.0 (Real)	$[m]$
`Cr_air`	Crack depth at top surface. Default = 1.0 (Real)	$[m]$
`Cr_core`	Crack depth in between bottom and surface integration points. Default = 1.0 (Real)	$[m]$
`Cr_edge`	Crack depth at the edge elements of windshield. Default = 1.0 (Real)	$[m]$
`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)	$[P a \sqrt{m}]$
`K`_TH	Fatique threshold. Default = 0.0 (Real)	$[P a \sqrt{m}]$
`Rlen`	Reference length. Default = 1.0 (Real)	$[m]$
`fail_ID`	Failure criteria identifier. 9 (Integer, maximum 10 digits)
`T`_delay	Relaxation time before removing elements. Default = 0.0 (Real)	$[s]$
`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)

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
#              MUNIT               LUNIT               TUNIT
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW36/72200103/1
Glass with linear hardening
#              RHO_I
             2.50E-9
#                  E                  NU           Eps_p_max               Eps_t               Eps_m
             70000.0                0.23
#  N_funct  F_smooth              C_hard               F_cut               Eps_f
         1         1                                  1650.0
#  fct_IDp              Fscale   fct_IDE                EInf                  CE

#  fct_ID1   fct_ID2   fct_ID3   fct_ID4   fct_ID5
 722001021
#           Fscale_1            Fscale_2            Fscale_3            Fscale_4            Fscale_5
              1000.0
#          Eps_dot_1           Eps_dot_2           Eps_dot_3           Eps_dot_4           Eps_dot_5
                 0.0 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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_edge    grsh4N    grsh3N
             0.00040             0.00100             0.00500         
#               K_Ic                K_Th                Rlen              Tdelay
              23.717              7.9057                 1.0                   0
#              Kres1               Kres2
                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/722001021
Function for glass
#                  X                   Y
                 0.0               500.0
                 1.0               550.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#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)
$σ_{f} (t) = α σ (t) + (1 - α) σ (t - Δ t)$

Where,

$σ_{f} = filtered stress$

$α = \frac{2}{N_{c y c l e s} + 1}$
This failure model is compatible only with under-integrated 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.

Figure 1. Windshield finite element model

Figure 2. Windshield model - entire assembly
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).

¹ Alter, Christian, Stefan Kolling, and Jens Schneider. "An enhanced non–local failure criterion for laminated glass under low velocity impact." International Journal of Impact Engineering 109 (2017): 342-353.