Conditions are considered for the initiation and growth of fatigue cracks in stress concentration zones,
together with the conditions for crack edge opening during propagation. Calculation methods are
presented: the limits to unrestricted fatigue resistance as regards crack formation and failure with
allowance for the skewness in the nominal stress cycle; and working lives of specimens on the basis of the
conditions for crack initiation and propagation.
The specimens with stress concentrators are simple models for real structures; testing and failure analysis for such
specimens give details of the initiation and growth of fatigue cracks in inhomogeneous stress fields.
I have considered  the fatigue failure in smooth specimens for constant bending stress gradients. In the case of an
equilibrium semielliptical crack of depth a in elastic bending, the following expression has been derived for the stress inten-
sity coefficient (SIC):
in which σ
is the nominal stress amplitude and G is the relative gradient of the nominal stresses at the surface (of the plate).
In a specimen with a stress concentrator, the stresses may be higher by an order of magnitude than in the bending
of a smooth laboratory specimen. Then the product Ga is comparable with one and (1) is inapplicable.
I now consider a method of refining the estimate of stress gradient effects in the concentration zone.
For a linear crack of depth l at the edge of a half-plane with a constant stress gradient, one has the following rela-
tion for the SIC:
If there is substantial nonlinearity in the normal stresses at the edges of the crack, that equation gives a large error. We take (2) as
an approximation basis and replace in it the maximum value of the relative gradient G at the surface of the notch by the mean over
the depth of the crack G
Numerical data for a crack at the edge of an elliptical hole show that in order to approximate the SIC one can use
the following simple expression:
in which a
is the depth of the initial crack.
KGal=− π112 1 06
.[.tanh ( )] ,
=−π112 1 06.(.).
KGll=−π112 1 06.(.).
σ (. ) ,1018
Chemical and Petroleum Engineering, Vol. 42, Nos. 9–10, 2006
FINE-CRACK MECHANICS IN ESTIMATING
FATIGUE RESISTANCE WITH STRESS
G. M. Khazhinskii
MATERIALS SCIENCE AND CORROSION PROTECTION
VNIIneftemash OAO, Moscow. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 10, pp. 39–43,
2006 Springer Science+Business Media, Inc.