13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- (10) Where L is the grain size, ks is the Hall-Petch microstructural stress intensity parameter, c* is the specific heat at constant volume, is Poisson’s ratio, xi is the spacing of dislocations in pile-up and v is the terminal dislocation velocity. Using an upper limit for the dislocation velocity of the shear wave speed and with other parameters for steel, a value of T < 3.2 x 103 K was obtained. The over-estimated temperature rise for pile-up collapse was taken to give credence to the mechanism. Experimental results obtained on shear plugging of Ti-6Al-4V alloy material produced regions of sprayed molten metal onto the shear plug walls, consistent with prediction of the pile-up avalanche mechanism. 6. Strain Concentration in Fatigue-Persistent Slip Bands It has long been known that fatigue loading results in roughening of the surface and that the bands in which deformation is carried are of a “persistent” nature [22]. Persistent slip bands (PSBs) have long been a subject intense research but it was not until the development of dislocation theory that some understanding of the fatigue process could be established on a physical basis. This too was a field in which Prof. Cottrell provided initial insight [23], particularly on the formation of slip band intrusions and extrusions. Considerable research has been carried to understand the details of this important phenomenon and a broad outline has emerged in which a unique structure is developed, at least in FCC single phase materials, of which Cu has received by far the most attention. A representative PSB is shown in Fig. 6. It consists of dislocation walls of primary edge character bounded by edge dislocations on the top and bottom surfaces with cyclic deformation being carried by screw dislocations. Controversy exists as to the signs of the dislocations at PSB boundary, the Figure 6. Walls in persistent slip bands (dark regions) and gliding screw segments in the channels between walls [24]. state-of-stress within the PSB’s [25], the nature of intrusions, and the mechanism of crack formation [27]. Complex processes take place on the PSB walls which result in excess vacancy production. Evidence of this is found in the fact that a single PSB produced extrusions on both sides of a single crystal of Cu and also in the fact that at high temperatures the vacancies can migrate to sinks and the PSB’s are actually thinner than at low temperature [28]. These ideas have been used with some success to numerically model crack nucleation at grain boundaries in Ni-base superalloys by accounting for the system energy including importantly the energy in the PSB and taking crack nucleation at an energy extremum. Of course application of the PSB morphology to precipitate systems may require some modification. An actual PSB taken from a fatigued René 95 LCF specimen in shown in Fig. 7 [30]. The morphology is very different from that shown in Fig. 6.
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