/FAIL/BIQUAD

A perturbation of the failure limit for each element can be activated using /PERTURB/FAIL/BIQUAD. This failure criteria is developed in a partnership with Christian Cremer from Ford.

Format

Definition

Comments

1. This failure criterion is defined using failure plastic strain versus stress triaxiality (state of stress). This allows for the different plastic failure strains that materials exhibit depending on loading condition. The curve is described by 2 parabolic functions that intersect at the triaxiality value of $\frac{1}{3}$ which is uniaxial tension.

   
   
   

   The parameters for the 2 parabolic failure strain curves versus the state of stress (stress triaxiality) are calculated iteratively by Radioss during the initialization phase using the input c1-c5 values. The calculated parabolic failure curve parameters a, b, c, d, e and f, can be reviewed in the Starter output file.

   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.

   This failure criterion is usable for all elasto-plastic material models with shells and solids.

2. By default, values different than 0 need to be entered for c1 to c5. 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 ( $c1=c2=c4=c5=0.0$ ). 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 to 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.
3. The plastic strain at failure from physical tests can be input as c1 – c5.
4. If failure strain data is not available then the material flag, M-Flag, can be used to select predefined failure values for some material.
   If M-Flag > 0, the entered c1, c2, c4 and c5 values will not be used and instead will be calculated using the predefined ratio values from:

   • $c1=r1\cdot c3$
   • $c2=r2\cdot c3$
   • $c3=c3$
   • $c4=r4\cdot c3$
   • $c5=r5\cdot c3$
   If c3 =0 and M-Flag ≠ 0, c3 values will also be used :

   M-Flag	Roughly Corresponds to Material	c3 (Default)	r1	r2	r4	r5
   1	Mild steel	0.60	3.5	1.6	0.6	1.5
   2	HSS steel	0.50	4.3	1.4	0.6	1.6
   3	UHSS steel	0.12	5.2	3.1	0.8	3.5
   4	Aluminum AA5182	0.30	5.0	1.0	0.4	0.8
   5	Aluminum AA6082-T6	0.17	7.8	3.5	0.6	2.8
   6	Plastic PA6GF30	0.10	3.6	0.6	0.5	0.6
   7	Plastic PP T40	0.11	10.0	2.7	0.6	0.7
   99	Self-defined values (optional line)	0.60	Optional input	Optional input	Optional input	Optional input

   *Neither Altair nor the authors assume any responsibility for the validity, accuracy or any results obtained from these values. You must verify your own values by reasonable test results. Usage is only recommended for early design exploration.

   • If c3 > 0, the selected material behavior is scaled by c3 and the r1 to r5 predefined ratio values.
   • If the M-Flag=99, failure strain ratios r1, r2, r4 and r5 must be input in a following additional line.
5. Damage is accumulated linearly and can be post-processed in the animation files using the output request /ANIM/SHELL/DAMA/ALL or /ANIM/BRICK/DAMA/111. For shells elements when an integration point reaches $D=1$ , the integration point stress tensor is set to zero. Shell elements are deleted based on the value of P_thick_fail.

   If P_thick_fail is blank or set to 0, the value of P_thick_fail from the shell property is used. If P_thick_fail > 0, any P_thick_fail value defined in the shell properties are ignored and the value entered in this failure model is used.

   For values of P_thick_fail > 0, the element fails and is deleted when the ratio of through thickness failed integration points equals or exceeds P_thick_fail.

   In solid elements, the element is deleted when any integration point reaches $D=1$ .

6. If /PERTURB/FAIL/BIQUAD is used, M-Flag > 0 must be used, and the scatter will be applied to the c3 value only. The resulting c1, c2, c4, and c5 values will be calculated using the failure strain ratios thus applying the perturbation noise to the entire failure strain curve.

   
   
   

7. Special features are activated by this flag:

   S-Flag= 1: failure curves created. Comment 1.

   S-Flag= 2: Ensures value c4 as global minimum. To achieve this, the second equation is split into 2 separate quadratic sub-functions where the minimum value of the curves is at c4.

   Where, ${\sigma }^{*}=\frac{1}{\sqrt{3}}$ .

   S-Flag=3: Same as S-Flag= 2 plus a simplified localized necking criterion. The localized necking criterion is based on the Marciniak-Kuczynski analysis. It uses two additional quadratic functions that define a curve that represents the start of localized necking between stress triaxiality $\frac{1}{3}$ and $\frac{2}{3}$ . The minimum value of this curve is defined by the user in the Inst_start field and occurs at plane strain tension ${\sigma }^{*}=\frac{1}{\sqrt{3}}$ . Using this curve, a second localized necking damage value is calculated, and failure only occurs when all integration points reach $D=1$ .

   The Inst_start value can be estimated as the (true plastic) strain at maximum stress, from the uniaxial tension test.

8. 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 option).
9. If non-local regularization is used (with /NONLOCAL/MAT), the element size scaling factor is not used. If a scaling function is still defined (fct_ID_el > 0), the parameters are scaled using LE_MAX parameter of the non-local card (either specified directly by you or computed from the Rlen parameter value).
10. By default, a failure criterion approach with stress computation is used for /FAIL/BIQUAD. This means that damage evolution has no effect on the stress computation until the element deletion triggered by D = 1 occurs. It is possible to soften the stress during damage evolution. Therefore, the flag ICOUP must be set to a value not equal to zero in order to activate the stress/damage coupling. For this purpose the following stress softening equation (similarly to /FAIL/TAB2) is introduced:
    $$\sigma ={\sigma }_{eff}\left(1-{\left(\frac{D-D_{crit}}{1-D_{crit}}\right)}^{EXP}\right)$$
    Where,

    $\sigma$

    Damage stress tensor

    ${\sigma }_{eff}$

    Undamaged effective stress tensor

    $D_{crit}$

    Critical damage value that triggers stress softening

    $EXP$

    Exponent parameter

    Two different approaches can be used:

    • If ICOUP = 1 (for solids and shells), the critical damage parameter DCRIT is directly input by the user. By default, DCRIT = 0.0 which means that damage variable has an influence on stress computation from the beginning of plasticity. However, one may want to delay this stress softening effect to a higher value of damage variable (0 < D < 1). The exponent parameter EXP can be used to control the shape of the stress softening so that it is nonlinear when EXP is different from 1 (default value).

      
      
      

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    • If ICOUP = 2 (for shells with S-Flag = 3 only), the instability damage variable computed from the instability curve (defined with Inst_start) is used to deduce the DCRIT value.

      
      
      

      Indeed, in this case the instability curve represents the criterion that must be reached to trigger stress softening, implying the beginning of the strain localization and then the necking observed especially at high stress triaxiality.

      Note: The instability curves only have an effect between simple tension and biaxial tension stress triaxiality. When the instability criterion is reached, the instantaneous value of the damage variable D is saved in the value DCRIT, which becomes an element history variable and not a constant value.

      In this case, the DCRIT value defined in the input card is ignored. This allows the necking in shells to be triggered by generating a stress softening similar to /FAIL/TAB2. The exponent parameter still can be used with ICOUP = 2.