Crack growth for the double slip plane and the modified dsp crack model-II. fatigue crack growth with and without blunting

Abstract

The double slip plane (DSP) crack model was used to obtain crack growth equations for the mode II and III crack under a monotonically increasing stress in the Part I paper. In this paper the growth law under cyclic stress (the Paris fatigue crack growth equation) is found. The success of the analysis depends upon the fact that the DSP crack closely approximates a Bilby-Cottrell-Swinden (BCS) crack when the slip zone is large compared with the slip plane to crack plane spacing. Consequently the dislocation distribution on the slip planes approximates the BCS crack one ahead of the crack tip. The results obtained are: if no work hardening of the slip planes takes place and the crack does not blunt a 2nd power Paris equation is found. If blunting occurs the exponent of the Paris equation is reduced to a 4 3 rd power. Crack advance starts well below the peak stress intensity factor K p is reached. For both the blunting and the nonblunting cases work hardening reduces the value of the Paris exponent. A modified DSP plane is also investigated. In this model the dislocations on the slip behind the crack tip move into the crack and are annihilated. When no blunting occurs a 4th power Paris equation is obtained. When blunting occurs both 4th power and 2nd power Paris equations can be derived. If no work hardening occurs the fatigue crack does not advance. Crack advance starts well below a stress intensity factor of K p when the power exponent is 2 or smaller. The advance starts almost at the level K p for a 4th power equation.