Failure criteria defined with ductile failure model.
In Radioss, it is possible to simulate failure with a
failure model. Johnson-Cook failure model is the most commonly used, which uses
exponent function to describe the material failure behavior.
/FAIL/TAB1 is the most sophisticated failure model to
describe with simple curve input, which is more convenient.
/FAIL/BIQUAD can describe with intuitive parameter input. Equivalent failure for these three failure models are discussed
with one shell element and circular plate model.
Options and Keywords Used
Johnson-Cook failure model (/FAIL/JOHNSON) with
parameters
Tabulated
failure model (/FAIL/TAB1) with curve input
Simplified nonlinear strain based failure (/FAIL/BIQUAD) with parameter input
The elasto-plastic behavior of the material is defined using the Johnson-Cook law
(/MAT/LAW2 (PLAS_JOHNS)), with damage (maximum plastic
strain, ). The failure model /FAIL/JOHNSON is independent from
the material law and the hardening model.
The Johnson-Cook failure model is defined using /FAIL/JOHNSON in
the input deck. The model uses accumulative damage to compute
failure.
Where,
Current damage and is in range of .
The element is in failure, if . This can be output to the animation
file by defining /ANIM/SHELL/DAMA in the Engine.
Increment of plastic strain during the loading.
In /FAIL/JOHNSON, the failure strain, is computed as:
Where,
Stress triaxiality (or normalized mean stress) .
, and
The first three parameters for Johnson-Cook failure model.
The strain rate and thermo-plastic effects are not taken into account in this
example. Thus, only three parameters are required (, and ).
The failure plastic strain in /MAT/LAW2 is not taken into account.
In addition to the Johnson-Cook failure model, the maximum stress and the
failure plastic strain are activated.
Two failure approaches are also investigated:
Shell element is deleted, if damage for one layer
(Ifail_sh =
1).
The layer stress tensor is set to zero and the shell element is deleted, if
damage for all layers
(Ifail_sh = 2).
The four simulations performed are:
Ifail_sh =
1
Ifail_sh =
2
/FAIL
+
,
/FAIL
Only
/FAIL
+
,
/FAIL
Only
Johnson-Cook failure model
= 0.11
= 0.08
= -1.5
= 0.151
= 0.09
= 0.08
= -1.5
= 0.11
= 0.08
= -1.5
= 0.151
= 0.09
= 0.08
= -1.5
Figure 1 shows curve with = 0.11, = 0.08 and = -1.5 in the Johnson-Cook failure
model.
Where, curve describes the material failure. Above this
curve, the material failed, below this curve, the material is safe (not failed).Figure 1.
For example, with a one shell element, from above curve,
failure strain by (for uniaxial tension). In results it shows element
failed once reach the smallest failure strain either defined with in LAW2 or in /FAIL/JOHNSON.Figure 2.
Ductile Failure Models
In /FAIL/TAB1 and /FAIL/BIQUAD it is also
possible to have equivalent , as in /FAIL/JOHNSON.
Curve input for in /FAIL/TAB1 failure model is
possible, which is very continent. Directly input curve (created from above Johnson-Cook failure) in
table1_ID of /FAIL/TAB1, and then the same
failure, as in /FAIL/JOHNSON observed with
/FAIL/TAB1.Figure 3.
/FAIL/TAB1 Example:
In the
/FAIL/BIQUAD failure model, it is also possible
to describe with intuitive input parameter
c1, c2, c3,
c4 and c5 as:
Parameter
Description
c1
Failure strain at uniaxial compression test, where
c2
Failure strain at pure shear test, where
c3
Failure strain at uniaxial tension test, where
c4
Failure strain at plainstrain tension test, where
c5
Failure strain at biaxial tension test, where
The parameter c1, c2,
c3, c4 and
c5 are from curve (created from above Johnson-Cook
failure) in /FAIL/BIQUAD, and then the same failure
as in /FAIL/JOHNSON, observed with
/FAIL/BIQUAD.Figure 4.
/FAIL/BIQUAD Example:
The same results show in
/FAIL/JOHNSON, /FAIL/TAB1 and
/FAIL/BIQUAD, with the equivalent failure curve.Figure 5. Figure 6.
In /FAIL/BIQUAD actually use parabolic
function to reproduce the failure curve cording to input
c1, c2, c3,
c4 and c5. In fact, the for /FAIL/BIQUAD used
in Radioss may slightly different than
Johnson-Cook failure model or TAB1 model. As in this example, in /FAIL/BIQUAD is
printed in start output *0000.out file.Figure 7.
Use the above a, b, c, d, e, f coefficient from start
output file in below parabolic functions from
/FAIL/BIQUAD, the is:
Figure 8.
At point c1, c2,
c3, c4 and
c5 are the same; but outside these points, there
are some differences. In the simple one element example (uniaxial test),
it does not involve other stress state during simulation. Therefore, it
shows no difference between these three failure models.
Results
The influence of in material law and in failure model:
Model Setup
Failure Strain
= 0.151 in
LAW2
/FAIL/JOHNSON (with )
By 0.151 ( in LAW2)
= 0.165 in
LAW2
/FAIL/JOHNSON (with )
By 0.1585 (failure defined in
/FAIL/JOHNSON, where
)
= 0 (no failure strain) in
LAW2
/FAIL/JOHNSON (with )
By 0.1585 (failure defined in
/FAIL/JOHNSON, where )
In the plate model test with above plane shows different damage behavior. The element
failed with:
Ifail_sh =1: if strain
in one integration point reached the criteria
Ifail_sh =2: if strain
in all integration point reached the criteria
It shows less failure in plate with
Ifail_sh =2, than in
Ifail_sh =1.
Table 1. Johnson Failure
Ifail
_sh=1 in LAW2
Ifail
_sh=1
Ifail
_sh=2 in LAW2
Ifail
_sh=2
Influence
Use the above equivalent failure model (from above one
element model). Here you can also observe the same failure behavior with these
equivalent failure models.
Table 2. Plate Results with Different Failure Models
Johnson Failure
Ifail_sh=1
TAB1 Failure
Ifail_sh=1
BIQUAD Failure
P_thickfail=1/N
For /FAIL/JOHNSON and
/FAIL/TAB1 the option
Ifail_sh in these models is
to control the element delete criteria. In this plate model,
Ifail_sh=1 means the
element is deleted once damage criteria is reached in just one integration point.
In /FAIL/BIQUAD the equivalent option
Pthickfail is to control the
element deletion. It defines element deletion criteria with percentage of through
thickness integration points. In this plate example, 5 integration points are
defined through thickness (N=5 in /PROP/SHELL). Set
Pthickfail=1/5, which means
element deleted if one of the 5 integration points reaches the damage
criteria.
Conclusion
Failure model Johnson-Cook, TAB1 and BIQUAD (which
use failure curve) are studied here with one shell
element and also circular plate.
Failure could be defined in material model
and in failure model at same time. Compare different combinations of failure
definition in LAW2 and in Johnson-Cook failure model, it shows the element damaged
once first reach any criteria defined in material model or failure
model.
Equivalent failure criteria could be generated with Johnson-Cook, TAB1
and BIQUAD, but for BIQUAD there might be a slight difference since it uses two
parabolic functions.
Pthickfail
in /FAIL/BIQUAD is similar to
Ifail_sh, but is more flexible
since it uses a percentage of thickness to define element deletion criteria.