Page 263 - Biaxial Multiaxial Fatigue and Fracture

The Multiaxial Fatigue Strength of Specimens Containing Small Defects 241

Figure 2 shows typical examples of non-propagating cracks observed in those materials at the
fatigue limit. The direction of a non-propagating crack is approximately normal to the principal
stress, 01, regardless of combined stress ratio, 7/0. Under a stress slightly higher than the
fatigue limit, a crack which propagated in a direction normal to q resulted in the failure of the
specimen. Based upon such observations, the fatigue limit problem for specimens containing
small surface defects when subjected to combined stress loading was considered to be
equivalent to a fatigue threshold problem for a small mode I crack emanating from defects in
the biaxial stress field of the maximum principal stress, 01, normal to the crack and the
minimum principal stress, 02, parallel to the crack.
Consider an mi-symmetric surface defect containing a mode I crack under the remote biaxial
stresses, o, and a,, as shown in Fig. 3. The mode I SIF, ZC1, at the crack tip is given by the

2,
50 pm

31.7"

Axial direction
(a) 0.37% carbon steel; u h = 100 pm, u, = (b) FCD700 nodular cast iron; smooth
175 MPa, 7, = 87.5 MPa [17]. specimen, c, = 7, = 160 MPa [24].

Fig. 2. Small non-propagating cracks emanating from a defect observed at fatigue limit
under combined loading.

t t

+ +
Y
Lx A B
Fig. 3. A three-dimensional defect leading to a crack subjected to biaxial stress.