Dislocation Pile-Ups and Slip Transmission

We begin with a consideration of the relevant phenomenology. Fig. 11.10 shows a number of different possible outcomes of the interaction between an array of 

The advent of transmission electron microscopy opened the doors to the direct observation of processes such as the pile-up of dislocations at a grain boundary and the subsequent commencement of dislocation motion in adjacent grains. The process of slip transmission described above may be seen from the perspective 

11 Points, Lines and Walls Defect Interactions and Material Response 

Our fundamental assertion concerning the geometry of pile-ups is that they reflect the equilibrium spacing of the various dislocations which are participants in such a pile-up. From a discrete viewpoint, what one imagines is an equilibrium between whatever applied stress is present and the mutual interactions of the dislocations. In simple terms, using the geometry depicted schematically in fig. 11.12, we argue that each dislocation satisfies an equilibrium equation of the form 

This equation considers the equilibrium of the Z dislocation. In particular, it is nothing more than a dislocation-by-dislocation statement of Newton s first law of motion, namely, = 0, which says that the total force on the dislocation is zero. The factor A is determined by the elastic moduli and differs depending upon whether we are considering dislocations of edge A = fib/27r l — v)), screw(A = fib/lit) or mixed character. The problem of determining the equilibrium distribution of the dislocations in the pile-up has thus been reduced to one of solving nonlinear equations, with the number of such equations corresponding to the number of free dislocations in the pile-up. For further details see problem 3 at the end of the chapter. 

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