Crack tip stress intensity factor of the double slip plane crack model: Short cracks and short short-cracks

Abstract

The crack tip stress intensity factorK1 for a short crack is determined using the double slip plane (DSP) crack model. It is shown thatK1 for a stationary crack is larger than the nominal stress intensity factorK. This result differs from the case of the stationary DSP long crack for whichK1 =K. The physical cause whyK1 >K is the fall off with distance of the dislocation shielding/antishielding factor I. at a rate faster than an inverse square root dependence when the distance from a dislocation to a crack tip is of the order of or larger than the crack half widtha. The value ofL for a dislocation situated at an arbitrary position about a crack is derived in this paper. (The Rice-Thomson expressions forL are valid only if a dislocation is very close to a crack tip.) The short short-crack is also analysed using the DSP crack model. (A short short-crack crack is defined to be a short crack whose plastic zone behind the crack tip extends to the center of the crack.) The value of K1 for the short short-crack is a constant and is larger than K. Finally, it is shown that if the crack length is smaller than a critical value that is inversely proportional to the yield stress and is proportional to the critical stress intensity factor Kcb of a Griffith crack that K1 must be smaller than K,t, regardless of how closely the applied stress approaches the yield stress. These results imply that fatigue crack growth of short cracks in the DSP crack model occurs at a faster rate than for long cracks when the conventional cyclic stress intensity factor is above the threshold value and that short cracks can grow under cyclic stress intensity factors smaller than the threshold value.