Page 402 - Biaxial Multiaxial Fatigue and Fracture

386 M. FILIPPINI ET AL.

(3)
+6 ( + A&: + A&;)] ' maximized with respect to rime

The terns A€, , Asq have to be calculated as strain differences between two generic instants tl
and r2, e.g. A&, = E, (1, ) - E, (r, ) , AE~ sXy (t, ) - cXy (I, ) etc. The equivalent strain range Asq ,
=
Eq. (3), is calculated by varying tl and rz such as to obtain its maximum value. This criterion
produces a lower equivalent strain for the out-of-phase than for the in-phase loading,
predicting an increase of the fatigue life, in contradiction with the experimental results. The
application of this criterion may lead to unconservative predictions, as shown by Tipton and
Nelson [14].

Criterion of Sonsino and Grubisic

The criterion of Sonsino and Grubisic [I31 assumes that the fatigue damage is caused by the
interaction of shear strains acting on different elementary material planes, called interference
planes. An interference plane is completely defined by the spherical coordinates, 29 and p, of
its unit normal vector n (Fig. 1).

YAF"

Fig. 1. Definition of interference plane: dA represents the free material surface; n is the unit
normal vector of the generic interference plane
According to Sonsino and Gtubisic [13], in order to simplify the calculation procedure the
shear strain is calculated only on the interference planes defined by a constant value of
p = 90°, corresponding to the planes normal to the surface. The shear strain on these planes
can be obtained at each time in the following way:

The shear amplitudes yo (e) are calculated for each plane: