Page 163 - Biaxial Multiaxial Fatigue and Fracture

148 J. LIU AND H. ZENNER

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90"

0"
0"
-90" -90"
-
ola~ Endurance limit for smooth specimens, steel 34Cr4:
158 MPa 240 MPa
Fig. 1. Coordinate stresses, principal stresses and direction of principal stresses for one cycle.
Influence of variable principal stress direction on the endurance limit.

For calculating the fatigue limit, a number of multiaxial criteria have been developed in the
past. The multiaxial criteria can be subdivided as follows: empirical approach, critical plane
approach, and integral approach.
The empirical theories were derived by extension of the classical criteria or were usually
developed for specific load cases in correspondence with test results [I-81. With the critical
plane approach, the stress components in the critical plane with the maximal value of
equivalent stress are considered as relevant for the damage [9-15].
In the case of the integral approach, the equivalent stress is calculated as an integral of the
stresses over all cutting planes of a volume element, for instance, with the hypothesis of
effective shear stress [16] or the shear stress intensity hypothesis [17]. The hypothesis of
Papadopoulos [ 18,191 is based on the same principle and differs from the shear stress intensity
hypothesis by the consideration of the mean stresses.