Page 225 - Biaxial Multiaxial Fatigue and Fracture

Critical Plane-Energy Based Approach for Assessment of Biaxial Fatigue Damage where ... 209

where Nf is the number of cycles to failure. In Eq (9) A& and A0 are the range of normal strain
and stress, and Ayand AT are the range of shear strain and stress, respectively.
Tipton [25] found that a good multiaxial fatigue life correlation was obtained for 1045 steel
with a scaling factor C of 0.90. Andrews [26] found that a C factor of 0.30 yielded the best
correlation of multiaxial life data for AIS1 3 16 stainless steel. Chu et al. [ 151 weighted the
shear energy part of their formulation by a factor of C=2 to obtain a good correlation of fatigue
results. Liu's [ 141 and Glinka et al. [ 161 formulations provided an equal weight of normal and
shear energies. The empirical factor (C) suggested by each of the above authors gave a good
fatigue life correlation for a specific material which suggests that the empirical weighting
factor C is material dependent.
In the present study, the proposed model correlates multiaxial fatigue lives by normalizing
the normal and shear energies using the axial and shear material fatigue properties,
respectively, and hence the parameter uses no empirical weighting factor. Both normal and
shear strain energies are weighted by the axial and shear fatigue properties, respectively:

where a;. and if are the axial fatigue strength coefficient and axial fatigue ductility coefficient,
respectively, and if and ir are the shear fatigue strength coefficient and shear fatigue ductility
coefficient, respectively.

Out-ofphase strain hardening

Under out-of-phase loading, the principal stress and strain axes rotate during fatigue loading
(e.g. see [13]) often causing additional cyclic hardening of materials. A change of loading
direction allows more grains to undergo their most favorable orientation for slip, and leads to
more active slip systems in producing dislocation interactions and dislocation tangles to form
dislocation cells. Interactions strongly affect the hardening behavior and as the degree of out-
of-phase increases, the number of active slip systems increases. Socie et al. [27] performed in-
phase and 90" out-of-phase fatigue tests with the same shear strain range on 304 stainless steel.
Even though both loading histories had the same shear strain range, cyclic stabilized stress-
strain hysteresis loops in the 90" out-of-phase tests had stress ranges twice as large as those of
the in-phase tests. They concluded that the higher magnitude of strain and stress ranges in the
out-of-phase tests was due to the effect of an additional strain hardening in the material [28].
During out-of-phase straining the magnitude of the normal strain and stress ranges is larger
than that for in-phase straining with the same applied shear strain ranges per cycle. The
proposed parameter via its stress range term increases with the additional hardening caused by
out-of-phase tests whereas critical plane models that include only strain terms do not change
when there is strain path dependent hardening. To calculate the additional hardening for out-of-
phase fatigue tests, these approaches may be modified by a proportionality factor like the one
proposed by Kanazawa et al. [29].

Mean stress correction
Under multiaxial fatigue loading, mean tensile and compressive stresses have a substantial
effect on fatigue life. Sines [30] showed compressive mean stresses are beneficial to the fatigue
life while tensile mean stresses are detrimental. He also showed that a mean axial tensile stress