Page 124 - Biaxial Multiaxial Fatigue and Fracture

Long-Life Multiaxial Fatigue of a Nodular Graphite Cast Iron I09

AW = AW1 +Awn (4)

Failure is expected to occur on the material plane having the maximum VSE quantity.
Depending on material, temperature, and loading, one of the VSE parameters will dominate.
For materials that fail primarily along tensile planes, the quantity AW is computed by first
identifying the plane on which AWI is maximized and then adding the shear work on that same
plane. Both AW1 and AWu are virtual quantities whose physical meaning is related but not
equal to the elastic strain energy and plastic hysteresis energy. For this reason the model is not
defined for out-of-phase or non-proportional loading.
Murakami and associates have observed that the fatigue limit for many materials is not
equal to the stress for crack initiation but the threshold stress for propagating a crack that
emanates from a defect 119-211. The defects may be small cracks, scratches, inclusions, or
porosity. Many of these flaws are irregularly shaped, and it has been proposed to use the
&& as a measure of the flaw size.
In torsion, the shear stress around a hole is zero, and cracks nucleate in tension at 45" to the
applied shear stresses. Propagation of such cracks will be controlled by the Mode I stress
intensity. Crack driving force near a notch is greater in the case of torsion as compared
touniaxial tension. For example, the stress concentration factor for a center hole is 3 in
uniaxial loading and 4 in torsion suggesting that torsion fatigue strength would be 75% of the
tensile fatigue strength.
Figure 2 shows that the Mode I stress intensity factor is higher in torsion (h = 02 / 01 = -I)
than in tension (A = 0) for a crack originating at the edge of a hole. The fatigue limit for tension
must be decreased by the ratio of the stress intensity factors to obtain the estimate of the torsion
curve. Using fracture mechanics arguments it has been estimated that the fatigue strength in
torsion is 0.8-0.83 of the fatigue strength in tension for materials dominated by Mode I failure
from small pores and defects 121-231. The Murakami model defines fatigue limit values in
tension and torsion as
I .43(HV+I 20)
ofl =
1

I .15( HV+l20)
zfl=0.80fl =
1
(&)6

where HV is the Vickers hardness and & is determined by projecting the defect onto the
plane of maximum tensile stress. So far this parameter has been defined for the cases of tension
only and torsion only, but similar facture mechanics arguments can be used for other
proportional stress ratios as well.
Nodular cast irons are an example of materials that normally fail in cyclic loading in a
brittle fashion. Failure in this case is often initiated from shrinkage pores or other casting
defects. Even when the applied loading is predominantly torsion, damage in nodular iron is
observed to occur along maximum principal stress planes rather than shear planes as small
cracks nucleate and propagate from naturally occurring inclusions and shrinkage pores [ 12- 151.