Page 167 - Biaxial Multiaxial Fatigue and Fracture

152 J; LIU AND H. ZNNER

In addition, the characteristic strength values for alternating axial loading aw, pulsating
axial loading d&hr alternating torsional loading ZW, and pulsating torsional loading Zsch are
necessary. For the pulsating torsional strength, the following value is assumed:

EFFECT OF MEAN STRESS

If the time functions of the stress components of a plane stress state are synchronous, the
following analytical equation can be deduced for the calculation of the equivalent stress
amplitude from Eqs (2) to (6):

and for the equivalent mean stresses from Eqs (8) and (9):

The coefficients Aij depend only on the ratio of the stress amplitudes a,, aya, and zVa. The
coefficients are indicated in Table 1. For the case of an alternating normal stress and an
alternating shear stress (cyclic bending and torsion, for instance), the failure condition (Eq.
(1 0)) yields the well-known elliptical equation for ductile materials: