Page 260 - Biaxial Multiaxial Fatigue and Fracture

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notches of simple shapes, whereas actual inclusions are often of a three-dimensional irregular
shape. In addition, whereas the large crack problem has attracted attention in fatigue studies
since the birth of fracture mechanics, the behavior of small cracks could not be analyzed in a
similar way, for their behavior has been found to be anomalous with respect to large cracks, as
pointed out by Kitagawa and Takahashi [I]. These authors, in the first quantitative
characterization of the fatigue threshold behavior of small cracks, showed that the value of &h
decreased with decreasing crack size. This finding led the development of many subsequent
studies on small or short cracks. Since their initial work a number of models and predictive
methods for the determination of the fatigue strength of defect-containing components have
been proposed, although most of these have dealt only with uniaxial fatigue. These models have
been reviewed in detail by Murakami and Endo [2]. Research has shown [3,4] that the fatigue
strength of metal specimens containing small defects above a critical size is essentially
determined by the fatigue threshold for a small crack emanating from the defect. Based upon
this consideration, Murakami and Endo [4] used linear elastic fracture mechanics (LEFM) to
propose a geometrical parameter, G, which quantifies the effect of a small defect. Using
this parameter they succeeded in deriving a simple equation 151 for predicting the fatigue
strength of metals containing small defects. Subsequently, this model, referred to as the 6
parameter model, has been successfully employed in the analysis of a number of uniaxial
fatigue problems which dealt with small defects and inhomogeneities [6,7].
However, in many applications, engineering components are often subjected to multiaxial
cyclic loading involving combinations of bending and torsion. A number of studies have been
concerned with this topic [8-131, but with the exception of pure torsional fatigue very few
studies have been directed at the study of the behavior of small flaws under multiaxial fatigue
loading conditions despite the importance of small flaws in design considerations. Nisitani and
Kawano [14] performed rotating bending and reversed torsion fatigue tests on 0.36 YO carbon
steel specimens which contained defect-like holes of diameters ranging from 0.3 to 2 mm. They
reported that the ratio of torsional fatigue limit to bending fatigue limit, q5 = rw Icrw, was about
0.75 and attributed the result to the ratio of stress concentrations at the hole edge at fatigue
limits; that is, 30, under bending and 4r, under torsion. (Here s, and uw are the fatigue
strengths of specimens containing small flaws in reversed torsion and tension, respectively.)
Mitchell [ 151 also predicted q5 = 0.75 for specimens having a hole in the similar way. Endo and
Murakami [ 161 drilled superficial holes which simulated defects ranging from 40 to 500 pm in
diameter in 0.46 % carbon steel specimens to investigate the effects of smail defects on the
fatigue strength in reversed torsion and rotating bending fatigue tests. Based upon the
observation of cracking pattern at the holes, they correlated the fatigue strength under torsion
with that under bending by comparing the stress intensity factors (SIFs) of a mode I crack
emanating from a two-dimensional hole. They predicted 4 = -0.8 for specimens containing a
surface hole. In that study, they also observed that there was a critical diameter of a hole below
which the defect was not detrimental to the fatigue strength, and that the critical size under
reversed torsion was much larger than under rotating bending.
In recent papers [17-191, the fbrther application of the && parameter to multiaxial
fatigue problems has been made. Combined axial-torsional fatigue tests were carried out using
annealed 0.37 % carbon steel specimens containing a small hole or a very shallow notch [ 171. It
was concluded that the fatigue strength was related to the threshold condition for propagation of
a mode I crack emanating from a defect, and an empirical method for the prediction of the
fatigue limit of a specimen containing a small defect was proposed [17]. Murakami and
Takahashi [18] analyzed the fatigue threshold behavior of a small surface crack in a torsional