RD-E: 2603 Forming

Failure criteria defined with failure model /FAIL/FLD.

In Radioss it is possible to simulate failure with a failure model. FLD failure models are most commonly used for forming, which describe material failure in strain space. Here, one shell element and circular plate model are used to demonstrate the failure behavior with FLD failure model.

Options and Keywords Used

Johnson-Cook failure model (/FAIL/JOHNSON)
Forming Limit Diagram failure model (/FAIL/FLD)
Imposed velocities (/IMPVEL)
Material LAW2 (/MAT/LAW2 (PLAS_JOHNS))
Rigid sphere (/RWALL)

Input Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this example are available in:

/radioss/example/26_Ruptured_plate

Model Description

FLD Failure Model (Forming Limit Diagram)

This failure model uses the generic forming limit diagram (FLD), defined for the given material. The curve is expressed in the area of principal strains (major and minor strains).

The above FLD diagram shows:

In uniaxial test (by $\frac{d ε_{m i n o r}}{d ε_{m a j o r}} = - v = - 0.33$ $\frac{d ε_{m i n o r}}{d ε_{m a j o r}} = - v = - 0.33$ ) once point P1 (-0.0374,0.1133) is reached, the element fails
In eqibiaxial test (by $\frac{d ε_{m i n o r}}{d ε_{m a j o r}} = 1$ $\frac{d ε_{m i n o r}}{d ε_{m a j o r}} = 1$ ) once point P2(0.26,0.26) is reached, the element fails

The damage will print either with /ANIM/SHELL/DAMA or /ANIM/SHELL/FLDF in the Engine file. Both define damage as:(1)

D = \frac{ε_{m a j o r}}{ε_{\lim}}

$D = \frac{ε_{m a j o r}}{ε_{\lim}}$

It compares the current

ε_{m a j o r}

$ε_{m a j o r}$ with

ε_{\lim}

$ε_{\lim}$ , which is from the FLD curve by the same

ε_{m i n o r}

$ε_{m i n o r}$ .

Figure 3.

Only with /ANIM/SHELL/FLDF and I_{fail_sh}=4 is it possible to compute just the damage and not delete the element. It used to have a better vision of dangerous zones.

Results

Use the above FLD curve in the plate example and failure printed in animation with /ANIM/SHELL/FLDF and /ANIM/SHELL/DAMA like:

/ANIM/SHELL/FLDZ can also be used to print the failure zone.

FLDZ=6: Failure; $ε_{m a j o r} > ε_{\lim}$ $ε_{m a j o r} > ε_{\lim}$
FLDZ=5: Marginal; $ε_{\lim} > ε_{m a j o r} > ε_{m \arg i n a l}$ $ε_{\lim} > ε_{m a j o r} > ε_{m \arg i n a l}$
FLDZ=4: Safe; $ε_{m \arg i n a l} > ε_{m a j o r} > | ε_{m i n o r} |$ $ε_{m \arg i n a l} > ε_{m a j o r} > | ε_{m i n o r} |$
FLDZ=3: Compression; $- ε_{m i n o r} > ε_{m a j o r} > - ε_{m i n o r} \cdot \frac{R_{a n i}}{1 + R_{a n i}}$ $- ε_{m i n o r} > ε_{m a j o r} > - ε_{m i n o r} \cdot \frac{R_{a n i}}{1 + R_{a n i}}$
FLDZ=2: High wrinkle; $- ε_{m i n o r} \cdot \frac{R_{a n i}}{1 + R_{a n i}} > ε_{m a j o r}$ $- ε_{m i n o r} \cdot \frac{R_{a n i}}{1 + R_{a n i}} > ε_{m a j o r}$
FLDZ=1: Loose metal; $ε_{m a j o r}^{2} + ε_{m i n o r}^{2} > F a c t o r_L o o s e m e t a l^{2}$ $ε_{m a j o r}^{2} + ε_{m i n o r}^{2} > F a c t o r_L o o s e m e t a l^{2}$

Conclusion

Failure model /FAIL/FLD used principal strain ratio to describe the material failure behavior which is suitable to describe material failure in forming.