Page 226 - Biaxial Multiaxial Fatigue and Fracture

210 A. YARVANI-FARA HANI

superimposed on torsional loading has a significant effect on the fatigue life. In 1942 Smith
[3 11 reported experimental results for twenty-seven different materials from which it was
concluded that mean shear stresses have very little effect on fatigue life and endurance limit.
Sines [30] reported his findings and Smith's results by plotting mean stress normalized by
monotonic yield stress versus the amplitude of alternating stress normalized by fatigue limit
(R=-1) values. The relation is linear as long as the maximum stress during a cycle does not
exceed the yield stress of the material [28]. Concerning the effect of mean strain on fatigue life,
Bergmann et al. [32] found almost no effect in the low-cycle fatigue region and very little
effect in the high-cycle fatigue region.
Mean stress effects are included into fatigue parameters in different ways [28]. One
approach was applied earlier by Fatemi and Socie [33] to incorporate mean stress using the
maximum value of normal stress during a cycle to modify the damage parameter. Considering
[ 3
the effect of mean axial stress, a mean stress correction factor I+-+ inserted into Eq (loa)

showed a good correlation of multiaxial fatigue data containing mean stress values for both in-
phase and out-of-phase straining conditions. This correction is based on the mean normal
stress, 6, applied to the critical plane. To take into account the effect of mean axial stress on
the proposed parameter, Eq (loa) is rewritten as:

where the normal mean stress 4 acting on the critical plane is given by:

where and are the maximum and minimum normal stresses, respectively, which are
calculated from the stress Mohr's circles. The mean normal stress correction factor can be
applied for both a," >O and a," <O at which a," >o, the tensile mean normal stress, increases the
fatigue damage and u," ~0, the compressive mean normal stress, decreases the fatigue damage.
Equation (lob) takes into account the effects of compressive and tensile stress ranges on
fatigue damage analysis. This coincides with a numerous fatigue tests and analyses performed
earlier by Topper and his research group [34-381. They have confirmed that the compressive
portion of the stress cycle contributes significantly to the accumulation of fatigue damage, even
when the maximum stress is below the fully reversed fatigue limit.

Proposed fatigue damage parameter for biaxial fatigue tests where the stresses are at different
frequencies
The proposed damage parameter has been further developed to assess the fatigue lives under
in-phase and out-of-phase biaxial constant amplitude fatigue stressing where the stresses are at
different frequencies. In this parameter, the normal and shear stress and strain ranges have been
calculated from the largest stress and strain Mohr's circles corresponding to the most damaging
planes in each cycle. The total damage accumulation in a block loading history has been
calculated from the summation of the normal and shear energies on the basis of cycle-by-cycle