Liu & Zenner method

The basic formula is very complicated:

Four different fatigue limits f-1, f0, t-1 and t0 are needed for setup of all necessary material constants:

The dependency of the criterion on four material parameters was criticized by Papadopoulos in [PDG97] and led him to exclusion of the criteria from his comparison. Zenner et al. opposed his objections in [ZSL00] with a reference to common methods used for the derivation of fatigue limits in repeated loading from their fully reversed counterparts.

NOTIFICATION: Determination of the value of fatigue limit in repeated axial loading can be done in different ways – [ZSL00] e.g. uses another known value (mean stress sensitivity). There are many other different approaches how to get the fatigue limit in repeated axial loading, while no general formula can be used – see [Ppg05] for information.

Knowledge of fatigue limit in repeated torsion is even more rare. I do not know any more comprehensive analysis of its determination. Thus, if the value is not set in PragTic (input zero as the TORS0 parameter), the following formula given in [ZSL00] is used automatically:

The authors [ZSL00] claim the criterion to be valid within the bounds:

The only really significant source of validity of this criterion is the FatLim Database, data provided by Zenner et al. in [ZSL00] are unclear.

Nomenclature:

Mark	Unit	PragTic variable	Meaning
	[MPa]		shear stress amplitude on an examined plane
	[MPa]		mean shear stress on an examined plane
	[MPa]	TENS-1, BEND-1	fatigue limit in fully reversed axial loading
	[MPa]	TENS0, BEND0	fatigue limit in fully repeated axial loading
	[-]		ratio of fatigue limits ()
	[MPa]		amplitude of normal stress on the plane examined
	[MPa]		mean (average value of maximum and minimum values) normal stress on the plane examined
	[MPa]	TORS-1	fatigue limit in fully reversed torsion
	[MPa]	TORS0	fatigue limit in repeated torsion

Methods & Options & Variables of Calculation – Edit

Decomposition

- Whole load path

Elasto-plasticity

- No – currently no option implemented

Solution option

- Searched planes <0~BS algorithm, 1~globe analogy, 2~random>

- Number of scanned planes

- Only every x-th data-point taken from load history

- Evaluate envelope curve only <1~yes, 0~no>

Solution variable

- Minimum damage – this option is not active for this high-cycle fatigue method

Material parameters

E	[MPa]	tensile modulus
NU	[-]	Poisson’s ratio
TENS0	[MPa]	fatigue limit in repeated tension (or plane bending)
TENS-1	[MPa]	fatigue limit in fully reversed push-pull (or plane bending)
TORS-1	[MPa]	fatigue limit in fully reversed torsion
TORS	[MPa]	fatigue limit in fully repeated torsion (see the text above, if not available)

Result detail variables

Damage fatigue index is computed, not the damage as a reciprocal value to number of cycles or repetitions

FDD1 MAXDP maximum of damage parameter

FDD2 NCX x-coordinate of the normal line vector of the plane with MAXDP

FDD3 NCY y-coordinate of the normal line vector of the plane with MAXDP

FDD4 NCZ z-coordinate of the normal line vector of the plane with MAXDP

FDD5 ALFA angle between the normal lines to the critical plane and to the free surface

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