Page 139 - Biaxial Multiaxial Fatigue and Fracture

124 R.F! KAUFMAN AND TH. TOPPER

INTRODUCTION
It has been observed that the fatigue resistance of machine parts can be increased by producing
compressive residual stresses at the surface of a component [3-71. The action in fatigue of the
residual stresses in an engineering component should be the same as that of a mean stress in a
test specimen if the stress state in the component is similar to that in the test specimen. Hence,
the fatigue behavior of test specimens subjected to alternating shear stresses and static mean
stresses normal to the maximum shear planes can be used to predict the effect of residual surface
stresses in multiaxial fatigue. Residual stresses induced by surface heat treatments, such as
induction hardening, result in static mean stresses normal to the maximum shear planes.
Therefore, the stress state in the test specimens used during this program of study is similar to
that of engineering components with these residual stresses. The purpose of this paper is to
investigate the effects of static mean stresses normal to both shear planes and compare the effects
with those predicted by current static mean stresses theories and a proposed static mean stress
model.
Current multiaxial fatigue life prediction techniques can be categorized into three cases:
equivalent stredstrain, energy and critical plane approaches. The equivalent stresdstrain
approaches are easy to implement and allow the wealth of uniaxial data to be used in making
multiaxial life predictions. Most energy-based methods utilize the plastic energy of stresdstrain
hysteresis loops as a correlating parameter and are insensitive to static mean stresses applied
normal to the maximum shear planes. The critical plane approaches are based on the mode of
crack initiation. For these approaches, a damage parameter based on a combination of shear
stress/strain and/or normal stress/strain is computed on a number of planes. The plane with the
highest value is taken to be the critical plane [8]. Some of the multiaxial critical plane static
mean stress theories that the author has found to date are the following;
Findley parameter

where rmax is the alternating shear stress, crnis the normal stress on the maximum shear plane
and f is a constant for a given number of cycles to failure [4]. Several other parameters are very
similar to Eq. I [3, 9-13].

Modified Kandil, Brown and Miller parameter

PMKBN* = Ymax + S *En (2)
where ymax is the maximum shear strain and En is the strain normal to the maximum shear
plane. The value of S* is an empirical constant used to condense the experimental data into a
parameter vs fatigue life curve [ 141.
Fatemi and Socie [IS]