Discrete dislocation dynamics

Abstract In crystalline metals, dislocations movement, nucleation, and interaction with one another and free surfaces govern the material behavior. One can study the size effects in crystalline metals using the discrete dislocation dynamics (DDD) simulation which directly includes dislocations as discrete line defects. Accordingly, the dislocations motion can be obtained by integration of equations of motion which include their interactions with other dislocations. Historically, similar to many other computational material science methods, DDD has been introduced in a 2-dimensional framework where dislocations are simplified as straight lines with infinite length. The next generation of DDD model commonly known as 2.5-dimensional have been introduced in which some of the general 3-dimensional dislocation patterns including dynamic dislocation sources and obstacles and dislocation junction formation are incorporated in the 2-diemnsional model. Although simplified DDD simulation methods can provide valuable insight into many aspects of dislocations mechanisms, a true DDD simulation should be used to handle 3-dimensional dislocation mechanisms. Accordingly, 3-dimensional DDD models have been introduced in which dislocation loops can be discretized as a set of connected straight lines, which can be defined as pure edge or screw dislocations or mixed edge and screw dislocations, or curved splines. Different 3-dimensional DDD codes have been developed to capture the 3D mechanisms of dislocations. The theory of DDD simulation have been described in previous works (see, e.g., Zbib, 2012 ; Sills et al., 2016 ). In this chapter, the focus is on the application of DDD to capture size effect in crystalline metals. First, the investigation of size effects in crystalline metals using DDD simulation is extensively addressed here during micropillar compression test. In the last sections, the size effects during other experiments of microbending and nanoindentation are also briefly presented.