Page 140 - Biaxial Multiaxial Fatigue and Fracture

The Irtpuence of Static Mean Stresses Applied Normal to the Maximum Shear Planes in ... 125

where Aymax is the largest shear strain range,onmax is the maximum stress normal to the
shear plane and ay is the yield stress of the material.

Second Modified Kandil, Brown and Miller parameter [16]

where Aen is the normal strain range and on, is the mean stress perpendicular to the maximum
shear strain amplitude.

A static tensile mean stress normal to one of the planes of maximum shear strain amplitude in
a tension torsion machine has been shown by a number of investigators to reduce torsional
fatigue strength [17, 181. However, there is only a very small amount of data to document an
increase of fatigue strength in shear due to static compressive stresses normal to the two planes
of maximum shear stress range (if the compressive stress is applied to only one maximum shear
plane, failures continue to occur on the other maximum shear plane at the same shear stress
range). Sines and Ohgi [I91 in an extensive 1981 review of fatigue under combined stresses
show only three data points to support their conclusion that static compressive stresses normal to
the planes of maximum shear are beneficial. Two of these points come from a reanalysis of tests
on notched specimens by Seeger [20] in which the notch constrained cracks from growing on the
second maximum shear plane. Other evidence of the beneficial effect of compressive normal
stresses on shear fatigue that we have uncovered consists of crack growth experiments by Smith
and Smith [21] who reported that a compressive normal stress decreased shear crack growth
rates, and work by Bums and Parry [22] who showed that a superimposed hydrostatic pressure
which introduced compressive stresses on the planes of maximum alternating shear increased
fatigue strength.
Although it was assumed by Sines [6] and subsequent authors [23, 241 that for a given fatigue
life, there is a linear relationship between the maximum alternating shear stress and the static
mean stress normal to the planes of maximum alternating shear for both tensile and compressive
normal stresses, there is little data to support linearity in the compressive region. Recent work
by Bonnen [25] and Varvani-Farahani [26] which relates the effect of tensile mean stress to
crack face interference suggests that, once a tensile mean stress opens the crack so that there is
no longer interference, higher tensile mean stresses will not cause a further reduction in fatigue
strength. Both authors obtained interference free crack growth by combining the application of
periodic Mode I overloads with an alternating shear stress. Bonnen verified that the crack faces
were growing free of interference with each other by performing two tests with different
overloads for a given shear stress amplitude. For the second test, the Mode I overload was
increased to almost double the overstrain level of the first test. The equivalent fatigue life of the
second test was the same as the first result and, consequently, crack face interaction was assumed
to be at the lowest possible level. Varvani-Farahani measured biaxial crack opening stress with
the confocal scanning laser microscope (CSLM). Biaxial specimens were internally pressurized
to separate the crack faces, and .increasing magnitudes of internal pressure were applied until the
crack depth remained constant. His CSLM imaging revealed that, with the application of the
Mode I overstrains (yield stress magnitude), the shear cracks were fully open at zero internal oil
pressure. Theresearch completed by Bonnen and Varvani-Farahani is summarized in Fig. 1, where