In order to evaluate the mechanical behaviour around a growing fatigue
crack tip for plane stress of mode I, the asymptotic governing equati
ons and their boundary conditions are formulated by the light of damag
e mechanics. A series of examples are studied numerically to obtain th
e orders of stress, strain and damage, the distributions of the stress
and damage field, and the contour of the process zone determined by a
threshold condition for damage evolution. It is found that the stress
has no (or very weak) singularity while the strain is less singular t
han it is under traditional K-dominance, The conventional boundary con
dition of a crack is substituted with the traction free requirement on
V-notch surfaces. A Paris typed equation of crack growth is also deri
ved as a result of present model.