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Crossland 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 – while Sines prefers the mean value of first invariant of stress tensor (i.e. hydrostatic stress), Crossland recommends use of its maximum value:
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The coefficients aC and bC can be set through evaluation of the formulas at fatigue limits in torsion and tension:
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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]).
Nomenclature:
|
Mark |
Unit |
PragTic variable |
Meaning |
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J2 |
[MPa] |
second invariant of stress tensor deviator |
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[MPa] |
TENS-1, BEND-1 |
fatigue limit in fully reversed axial loading |
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[MPa] |
maximum value of hydrostatic stress during load history |
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[MPa] |
TORS-1 |
fatigue limit in fully reversed torsion |
Methods & Options & Variables of Calculation – Edit
Decomposition
Elasto-plasticity
- No – currently no option implemented
Solution option
- 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 |
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NU |
[-] |
Poisson’s ratio |
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TENS-1 |
[MPa] |
fatigue limit in fully reversed push-pull (or plane bending) |
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TORS-1 |
[MPa] |
fatigue limit in fully reversed torsion |
Result detail variables
Damage fatigue index is computed, not the damage as a reciprocal value to number of cycles or repetitions
FDD1 AMP_J2 amplitude of the second invariant of stress tensor deviator
FDD2 MAX_HS maximum hydrostatic stress during loading
© PragTic, 2007
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