Page 166 - Biaxial Multiaxial Fatigue and Fracture

Fatigue Limit of Ductile Metals Under Multiaxial Loading 151

For most ductile materials, the fatigue limit ratio is situated within these limits. For
extending the range of validity for the hypothesis SM, the exponents p 1 and p2 can be selected
to be greater than two; thus, the values between 1 and 2 can also be included.
For the calculation of the equivalent mean stresses, the mean shear stresses are weighted
over the shear stress amplitude, and the mean normal stresses over the normal stress amplitude
in all cutting planes:

Generally the sign of the mean shear stress is of no importance. A positive or negative mean
shear stress has the same effect. Therefor, VI is selected to be exactly equal to 2 for the
equivalent mean shear stress. Thus, for a positive or negative mean shear stress, a positive
equivalent value is always obtained; that is, the mean shear stress still exerts a reducing effect.
For the evaluation of the normal mean stress, the exponent v2 is selected to be equal to unity;
consequently, positive and negative mean normal stresses can be distinguished.
For considering the effect of the mean stresses, the failure condition can be formulated in
different ways. For example, an equivalent mean stress can be obtained by combining the
equivalent mean shear stress and equivalent mean normal stress, CT, = rnovrn,, +
The equivalent stress amplitude, Eq. (4), and the equivalent mean stress can be compared with
the help of a Haigh-diagram.
In the following, the failure condition is formulated directly by a combination of the
equivalent stresses from Eqs (4), (8), and (9):

The coefficients m and n are determined from the fact that the failure condition is fulfilled in
the case of both pulsating tension and pulsating torsion: