Sines method

Both Crossland [Cro56] and Sines [Sin55], [Sin59] published their works throughout the fifties of the last century. Their criteria are very much alike, utilizing the amplitude of second invariant of stress tensor deviator (which corresponds to the von Mises stress) as the basis. Another term is added to the equation in order to cope with the mean stress effect – Sines prefers the mean value of first invariant of stress tensor (i.e. hydrostatic stress):

The coefficients aC and bC can be set through evaluation of the formulas at fatigue limits in torsion and tension:

Note that the criterion is based on three fatigue limits. This is caused by the fact that application of the fatigue limit in reversed push-pull does not generate a real solution and the fatigue limit in repeated tension has to be used.

The method is implemented into PragTic in the formulation referred by Papadopoulos et al. [PDG97]. The amplitude of the J2 term is set from a diameter of the minimum circumscribed hypersphere over the local load path converted to the Ilyushin's deviatoric space.

Crossland's and Sines' formulas can be seen used as sample criteria, but the Crossland’s one is more successful (see [BPL03], [CS01], [PDG97], FatLim Database). The Sines formula provides one of the worst overall results in the FatLim Database.

Mark	Unit	PragTic variable	Meaning
J2	[MPa]		second invariant of stress tensor deviator
	[MPa]	TENS-1, BEND-1	fatigue limit in fully reversed axial loading
	[MPa]		mean value of hydrostatic stress during load history
	[MPa]	TORS-1	fatigue limit in fully reversed torsion

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

E	[MPa]	tensile modulus
NU	[-]	Poisson’s ratio
TENS-1	[MPa]	fatigue limit in fully reversed push-pull (or plane bending)
TORS-1	[MPa]	fatigue limit in fully reversed torsion

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