Dang Van Criterion (Factor of Safety)

Used to predict if a component will fail in its entire load history. In certain physical systems, components may be required to last infinitely long.

For example, automobile components which undergo multiaxial cyclic loading at high rotational velocities (like propeller shafts) reach their high cycle fatigue limit within a short operating life. The conventional fatigue result that specifies the minimum fatigue cycles to failure is not applicable in such cases. It is not necessary to quantify the amount of fatigue damage, but just to consider if any fatigue damage will occur during the entire load history of the component. If damage does occur, the component cannot experience infinite life. Fatigue analysis based on the Dang Van criterion is designed for this purpose.

Fatigue crack initiation usually occurs at zones of stress concentration such as geometric discontinuities, fillets, notches and so on. This phenomenon takes place in the microscopic level and is localized to certain regions like grains which have undergone local plastic deformation in characteristic intra-crystalline bands. The Dang Van approach postulates a fatigue criterion using microscopic variables in the apparent stabilization state; this is a state of elastic shakedown if no damage occurs. The main principle of the criterion is that the usual characterization of the fatigue cycle is replaced by the local loading path and so damaging loads can be distinguished.

The general procedure of Dang Van fatigue analysis is:

Evaluate the macroscopic stresses $σ_{i j} (t)$ , for each location at a different point in time.
Split the macroscopic stress $σ_{i j} (t)$ into a hydrostatic part $p (t)$ and a deviatoric part $S_{i j} (t)$ .
Calculate the stabilized microscopic residual stress $d e v p *$ based on the following equation:
(1)
$d e v p^{*} = M i n (M a x (J_{2} (S_{i j} (t) - d e v p)))$

The expression is minimized with respect to $ρ$ and maximized with respect to $t$ .
Calculate the deviatoric part of microscopic stress.
(2)
$s_{i j} (t) = S_{i j} (t) + d e v p^{*}$
Calculate factor of safety (FOS):
(3)
$F O S = M i n (\frac{b}{τ (t) + a p (t)})$
(4)
$τ (t) = 0.5 T r e s c a (s_{i j} (t))$

Where, $b$ and $a$ are material constants.

If FOS is less than 1, the component cannot experience infinite life.

OptiStruct Factor of Safety Setup

Select the FOS tool from the fatigue modules.
The torsion fatigue limit and hydrostatic stress sensitivity values required for an FOS analysis can be assigned in the Assign Material module.
Assign load histories and proceed to evaluate.