Page 165 - Biaxial Multiaxial Fatigue and Fracture

1 Lru AND H. ZENNER

t'

Y

Fig. 2. Integration domain of the SIH and stress components in the intersection plane ~cp

The stress amplitudes zwl? and owl? each cutting plane are calculated from the time
in
function of the stress components. For loading cases with sinusoidal time functions and same
frequencies of stress components explicit equations for zwl? and crw can be derived in
dependence on the phase shift [24].
The exponents p1 and p2 can be chosen between 2 and infinity. If very large values are
selected for the exponents, the equivalent stress comesponds to the maximal stress over all the
cutting planes according to the maximum norm of the algebra. In order to simplify the
calculation, the exponents are selected as p ,=p2=2. The equivalent stress amplitude is
calculated by combination of the two equivalent stress amplitudes of the shear stress and
normal stress (see Eqs (2) and (3)):

The coefficients a and b are determined from the boundary conditions for pure alternating
tension-compression and pure alternating torsion:

From the conditions a>O and b>o, the ranges of validity for the hypothesis SM are defined
by the fatigue limit ratio: