During cyclic deformation of polycrystalline materials, as substantiat
ed by many experimental observations, due to existence of high stress
concentration at the interfaces the preferential site of crack nucleat
ion is intercrystalline. Accordingly, it is assumed that the highly lo
calized cyclic deformation persistent slip band (PBS) occurs along the
grain boundary (GB) which results in intergranular crack initiation.
In the present work with irreversible accumulation of dislocations are
used to characterize PSB by means of double pile-up which are compose
d of vacancy and interstitial dipoles. We shall give the mechanism and
a quantitative remedy of ratcheting of plastic deformation peculiar t
o fatigue deformation. In a manner conceptually analogous to Griffith
theory (1921), the critical number of cycles to failure and hence the
S-N curves for crack initiation is obtained by considering the free en
ergy of the system. The Gibbs free energy change Delta G increases wit
h the fatigue cycle number due to cyclic increment of elastic strain e
nergy which in turn stems from cyclic pile-up of dislocations along th
e slip planes. The Gibbs free energy change attains its maximum value
at a critical cycle number beyond which the state of dislocation dipol
e accumulation becomes energetically unstable. In our theory we postul
ate that this critical state is the onset of crack initiation. We shal
l give a quantitative value for the fatigue limit and analyze the depe
ndence of the S-N curve on several important physical parameters such
as grain size; surface energy; yield strength; width of the PSB; and t
he ratio of the shear modulus of the bicrystalline material.