.Papadopoulos method
Papadopoulos reassumed the Dang Van methodology in the mesoscopic branch, but decided to integer both input variables over all planes [Pap87], [Pap94] and [PDG97]. Such integration is understood as averaging the load manifestation over all planes. The solution is not based on the MCCM or any other methodology for obtaining the shear stress amplitude Ca, but on another integration of resolved shear stress (shear stress path projection) over all possible directions in the current examined plane.
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The integration of the normal component over all planes is expected too, but here the equality is followed up:
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The final form of the Papadopoulos criterion is:
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Coefficients can be set on a basis of two uniaxial tests as:
The criterion leads to a very simple formula for the case of a pure combination of axial and torsion harmonic loadings with phase shift:
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see [PDG97] for its derivation. The influence of phase shift is under defined loading condition zeroed, which Papadopoulos sees as a positive sign of quality of the criterion. The same formula can be obtained by Crossland method in expectation of in-phase loading, whereas both methods differ under non-proportional loading.
The criterion is fully integrated into the PragTic. All the formulas presented previously in this section are usable according to Papadopoulos [PDG97] for hard metals, i.e. metals where κ ratio is:
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Nomenclature:
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Mark |
Unit |
PragTic variable |
Meaning |
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[MPa] |
TENS-1, BEND-1 |
fatigue limit in fully reversed axial loading |
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[-] |
ratio of fatigue limits ( |
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[MPa] |
amplitude of normal stress on the plane examined |
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[MPa] |
maximum hydrostatic stress during loading |
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[MPa] |
resolved shear stress (a projection of shear stress into a given direction) |
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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
- Searched planes <0~BS algorithm, 1~globe analogy, 2~random>
- Number of scanned planes
- Number of scanned directions on each plane
- 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
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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_T_AVG spatial average of the resolved shear stress amplitude
FDD2 MAX_HS xmaximum hydrostatic stress
© PragTic, 2007
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