An explicit is solved by calculating results in small time increments or time steps. The size of the time step depends
on many factors but is automatically calculated by Radioss.
The /FAIL/BIQUAD, /FAIL/JOHNSON, and /FAIL/TAB1 failure models define material failure by relating the plastic strain at failure to the stress state in the material.
The Johnson-Cook failure model is often used to describe the ductile failure of metals. It uses a Johnson-Cook equation
to define failure strain as a function of stress triaxiality.
In Radioss, /FAIL/BIQUAD is the most user-friendly failure model for ductile materials. It uses a simplified, nonlinear strain-based
failure criteria with linear damage accumulation.
In Radioss, /FAIL/TAB1 is the most sophisticated failure model for ductile material. The plastic failure strain can be defined as
a function of: stress triaxiality, strain rate, Lode angle, element size, temperature, and instability strain.
Composite materials consist of two or more materials combined each other. Most composites consist
of two materials, binder (matrix) and reinforcement. Reinforcements come in three forms, particulate,
discontinuous fiber, and continuous fiber.
Optimization in Radioss was introduced in version 13.0. It is implemented by invoking the optimization capabilities of
OptiStruct and simultaneously using the Radioss solver for analysis.
The /FAIL/BIQUAD, /FAIL/JOHNSON, and /FAIL/TAB1 failure models define material failure by relating the plastic strain at failure to the stress state in the material.
In Radioss, /FAIL/BIQUAD is the most user-friendly failure model for ductile materials. It uses a simplified, nonlinear strain-based
failure criteria with linear damage accumulation.
In Radioss, /FAIL/BIQUAD is the most
user-friendly failure model for ductile materials. It uses a simplified, nonlinear
strain-based failure criteria with linear damage accumulation.
The failure strain is described by two parabolic functions calculated using curve
fitting from up to 5 user input failure strains.
By default, /FAIL/BIQUAD
(S-Flag=1) uses two parabolic curves to
describe the plastic failure strain , as a function of stress triaxiality . The two parabolic curves use:(1)
(2)
Where,
, , , , , and
Parabolic coefficients
Stress triaxiality
and
Plastic failure strain
The parabolic coefficients , , , , , and are computed by Radioss
using a curve fit based on the plastic failure strain
c1-c5 input values. If the calculated
parabolic failure strain curves have negative failure strain values, these negative
values will be replaced by a failure strain of 1E-6 which results in a very high
damage accumulation and brittle behavior. The results of the curve fit are in the
Starter *0000.out
file.
The c1–c5 plastic failure strains definitions
are:
c1
Plastic failure strain in uniaxial compression
c2
Plastic failure strain in shear
c3
Plastic failure strain in uniaxial tension
c4
Plastic failure strain in plane strain tension
c5
Plastic failure strain in biaxial tension
M-Flag Input Options
Depending on the M-Flag input option, there are three different
ways to define the c1-c5 values.
M-Flag=0, User-defined Test Data
For
this case, you must enter c1-c5
which represents the plastic failure strain for the 5 different stress
states. Ideally this data would be obtained from test or the material
supplier.
M-Flag=1-7, Predefined
Material Data
If failure strain data is not available, you can pick from 7
predefined materials. Figure Figure 2 shows the plastic strain at failure
curves for the 7 materials.
Note: The predefined values are supplied for
early design exploration and it is your responsibility to verify
that their material has the same properties.
M-Flag=99, Plastic Failure Strain Ratio
Input, r1-r5
The last input method
is to enter the plastic failure strain in uniaxial tension,
c3, and plastic failure strain ratios for the
other four stress states. These ratios are defined as:
r1
Failure plastic strain ratio, Uniaxial Compression
(c1) to Uniaxial Tension
(c3), so
r2
Failure plastic strain ratio, Pure Shear
(c2) to Uniaxial Tension
(c3), so
r4
Failure plastic strain ratio, Plane Strain Tension
(c4) to Uniaxial Tension
(c3), so
r5
Failure plastic strain ratio, Biaxial Tension
(c5) to Uniaxial Tension
(c3), so
Using this method, it is easy to change the failure curve by
adjusting the single plastic failure strain in uniaxial tension value,
c3.
Default Behavior
By
default, the values different than 0 for c1 to
c5 need to be entered. However, specific default behaviors
exists, in case failure information are missing.
In case the material failure behavior is unknown, c1 to
c5 are set to 0.0 and the mild steel behavior
(M-Flag=1) is used.
If only the tensile failure value is known, c3 is defined (). The mild steel behavior is used and scaled
by the user- defined c3 value.
In case the material behavior is known, M-Flag is defined
and c3 can be used to adjust the failure model according
the expected tensile failure. The selected material behavior is scaled by
the user-defined c3 value.
For all other cases, all c1 to c5 are
intended to be defined and default value of 0.0 is used.
Element Failure Treatment
A cumulative damage method is used to sum the amount of plastic strain that has
occurred at each integration point in the element using:(3)
Where,
Damage
The change in plastic strain of the integration point
Plastic failure strain for the current stress triaxiality
In shell elements after an integration point reaches , the integration point’s stress tensor is set to
zero. The element fails and is deleted when the percentage of through thickness
failed integration points equals P_thickfail. In solid elements,
the element is deleted when any integration point reaches .
Plane Strain as Global Minimum
The S-Flag=2 option can be used to force the
global minimum of the plastic failure strain curve to occur at the plane strain
stress triaxiality location, c4. This is accomplished by
splitting the second equation into 2 separate quadratic sub-functions.
Modeling Material Instability (Localized Necking)
In materials such as sheet metal, thickness thinning and diffuse necking may appear
during tensile loading of the material. This is called localized
necking and normally occurs in the stress triaxiality range of :
In /FAIL/BIQUAD it is possible to simulate this localized necking
using the option, S-Flag=3 and
Inst_start. This option uses the same plastic failure strain
curve as S-Flag=2 and adds two additional
quadratic functions that define a curve that represents the start of localized
necking between stress triaxiality and . The minimum value of this curve is a user-defined
value in the Inst_start field and occurs at plane strain tension . Using this localized necking curve, a second
localized necking damage value is calculated and failure due to necking only occurs
when all integration points reach . The localized necking criteria is based on the
Marciniak-Kuczynski analysis. 1
When using S-Flag=1 or 2, the
damage accumulation begins once the plastic strain reaches in failure curve (red in
Figure 6).
If S-Flag=3is used to describe the localized necking, damage
accumulation begins once the plastic strain reaches in the localized necking curve
(blue curve in Figure 6). For localized necking, the element is
deleted when all integration points reach damage, , whereas element deletion not due to localized
necking is defined by P_thickfail.
Perturbation of the Failure Limit
Due to a materials imperfection or production process, a material’s failure strain
may not be exactly the same everywhere and thus very small perturbations of failure
limit may exist. When using M-Flag>0 with
/PERTURB/FAIL/BIQUAD, a statistical distribution of the
failure limit is applied to each element assigned the failure model. This is
accomplished by calculating the normal or random distribution of a failure scale
factor which is applied to /FAIL/BIQUAD, c3.
The two different distributions methods are shown in Figure 7 and Figure 8.
/FAIL/BQUAD uses small perturbations of c3
generated by /PERTURB/FAIL/BIQUAD to scale the entire failure
curve using the strain ratio values for the predefined materials or user-defined
ratios, r1, r2, r4 and
r5, depending on the value of M-Flag.
Reference
1 Pack,
Keunhwan, and Dirk Mohr. "Combined necking & fracture model to predict ductile
failure with shell finite elements." Engineering Fracture Mechanics 182
(2017): 32-51