Page 125 - Biaxial Multiaxial Fatigue and Fracture

110 G.B. MARQUIS AND I? IOIRIALAINEN-ROIKONEN

For thick-section nodular iron castings, Mode I fatigue cracks normally initiated from defects
several hundreds microns diameter. A Goodman-type fatigue limit relation for nodular iron has
been developed to correlate torsion and tension data as well as account for mean stress effects
[ 12,131. The following fatigue limit relation can be written:

where A0 is the fatigue limit stress range, om is the mean stress on the plane of maximum
alternating normal stress and AcW is the R = -1 fatigue limit stress range. The term h is added
to distinguish between the uniaxial and torsion load cases based on the difference in small
crack driving force. The critical plane in this case is computed based on the combined effect of
mean stress and alternating normal stress. In the case of torsion loading with mean torque, the
static and mean shear stresses are resolved as alternating and mean tensile stresses.

Fig. 2. Stress intensity factors for cracks emanating from a hole.

It is interesting to note that the critical plane models for materials that fail predominantly
along tensile planes are generally simple extensions of models developed for uniaxial fatigue.
There are no great difficulties in applying these damage parameters to proportional multiaxial
loading cases other than uniaxial tension or pure torsion, but it is not immediately clear how
they can be applied to more general non-proportional loading.
The purpose of the current investigation is to consider the extension of &. (7) to
proportional equi-biaxial (A = 1) fatigue of thick-section nodular iron. As has already been seen
in Fig. 2, the driving force Qf cracks emanating from defects in biaxial tension is significantly
less than that for tension or torsion. With this in mind, it would be expected that the fatigue