Page 412 - Biaxial Multiaxial Fatigue and Fracture

3 96 M. FILIPPINI ET AL.

- SONSIWS CRITERION - SAE 1015 NEWCRITERION--SAE 1015

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18 -
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5 12
3

6
4
2
30 -20 -10 0 10 20 30
Loganthmic error index [%] Logarithmic error index [%]
Fig. 10: Logarithmic error index for SAE 1045 steel: Sonsino-Grubisic criterion (left), new
criterion (right)
For the examined materials, the new proposal gives errors between predicted and
experimental fatigue lives that pile up in the classes around 0% with a rather small scatter. It is
observed that, by employing the Sonsino-Grubisic method, the majority of the logarithmic
error values concentrate on the positive side, showing a more conservative prediction. This
could be attributed to the fact that the beneficial effect of the stress gradients is not taken into
account, thus predicting a fatigue life in torsion lower than the experimental one. It is noticed
that the basic material curve used in the new proposal is the axial straidlife curve. An
improved version of the Sonsino criterion, including the effect of stress gradients [20], may be
used instead, where the fatigue life of notched components could be also assessed. Another
source of the slight discrepancy observed in torsion tests might be the anisotropy in the
material, particularly in the case of the SAE 1045 steel [ 181.

COMPARISON BETWEEN CRITERIA
As mentioned previously, the von Mises approach, the Sonsin+Grubisic method and the new
proposal are, in principle, all applicable under in-phase and out-of-phase loading conditions.
However, it is reminded that for two loads with the same strain amplitudes, the one being in-
phase the other being out-of-phase, the von Mises approach produces the same equivalent
strain, leading thus to the same predicted life. This contradicts the experimental findings.
Actually, several experimental results show a fatigue life reduction for the out-of-phase case
due to the variation of the principal strain directions and the interaction of the deformations
acting along different directions. Both the Sonsino-Grubisic criterion and the new proposal are
able to correctly model this behaviour, predicting a higher equivalent strain value and thus a
fatigue life reduction for the out-of-phase case in comparison to the in-phase condition. For
the new criterion the study of the interaction of the deformation in different direction is
extended to all possible material interference planes, obtaining thus an equivalent strain lower
than the value predicted by the Sonsino-Grubisic criterion.
In Fig. 11 a combined axial and shear strain loading is examined. On the left, the equivalent
strains calculated according to the three approaches above are shown for the case where the
axial and shear strains are in-phase. It is noticed that the new proposal leads to the same value
of equivalent strain as the von Mises method. On the right, the axial and shear strains are out-