Page 262 - Biaxial Multiaxial Fatigue and Fracture

246 M. END0

K,, = 0.650a0d=

where a0 is the remote applied stress. Thereafter Murakami and Endo [5] employed the Vickers
hardness value as the representative material parameter and showed that the threshold level for
small surface cracks or defects could be expressed by the following equation for uniaxial
loading at the stress ratio, R, of -1 :
AK~,, = 3.3x10-3(~v+120)(Jarea)1/3 (2)

In addition, they found that the fatigue limit could also be expressed as a function of 6
by:

1.43(HY + 120)
6, = (3)

where AK,,, , the threshold SIF range, is in MPaG, aw,the fatigue limit stress amplitude, is in
MPa, HV, the Vickers hardness, is in kgf/mmz, and 6 is in pm. Equations (2) and (3) were
derived on the basis of LEFM considerations. More recently a justification for the exponents of
1/3 in Eq.(2) and -1/6 in Eq.(3) was provided by McEvily et al. [25] in a modified LEFM
analysis which also considered the role of crack closure in the wake of a newly formed crack.
The prediction error involved in the use of Eqs (2) and (3) is generally less than 10 percent for
values of 6 less than 1000 pm, and for a wide range of HV [5,6].
Murakami and co-workers [26-281 further extended Eq.(3) to include the location of the
defect, i.e., whether it was at the surface or sub-surface, and also to include the effect of mean
stress. The generalized expression they developed for the fatigue strength is:

C(W+120) I-R =
ow = (4)
(Jarea)"6 [TI

where the value of C depends on the location of the defect being 1.43 at the surface, 1.41 at a
subsurface layer just below the free surface, and 1.56 for an interior defect. The value of the
exponent a was related to the Vickers hardness by a = 0.226 + HV x 1 O4 . Equations (2)-(4) are
useful for practical applications in that they require no fatigue testing in making predictions.
The & parameter model has been applied to deal with many uniaxial fatigue problems
including the effects of small holes, small cracks, surface scratches, surface finish, non-metallic
inclusions, corrosion pits, carbides in tool steels, second-phases in aluminum alloys, graphite
nodules and casting defects in cast irons, inhomogeneities in super clean bearing steels,
gigacycle fatigue, etc. They are summarized in detail in the literature [6,7].

Criterion for multiaxial fatigue failure of defect-containing specimens

The author has previously shown [17,23,24] that, in in-phase combined axial and torsional
fatigue loading tests, the fatigue limit for specimens containing small defects is determined by
the threshold condition for propagation of a small crack emanating from a defect. The materials
investigated were an annealed 0.37 % carbon steel [17,23] and nodular cast irons [23,24].