Combined influences of micro-pillar geometry and substrate constraint on microplastic behavior of compressed single-crystal micro-pillar: Two-dimensional discrete dislocation dynamics modeling

2D discrete dislocation dynamic modeling of compressed micro-pillars attached on a huge base is executed to study the size-dependent microplastic behavior of micro-pillars and the corresponding size effect. In addition to the conventional dimensional parameters of the micro-pillar such as the micro-pillar size and the height-to-width ratio, the micro-pillar taper angle and the dislocation slip plane orientation angle in the micro-pillar are also considered to address the size effect and its rich underlying mechanism. Computational results show that there are at least two operating mechanisms responsible for the plastic behavior of micro-pillars. One is associated with the dislocation free slip-out from the micro-pillar sidewall; the other is related to the dislocation pile-up at the base and the top end of the pillar. The overall mechanism governing the size effect of the micro-pillar rests with multi-factors, including the micro-pillar size, the height-to-width ratio, the micro-pillar taper and the slip plane orientation angle; however, whether the “free slip band” exists or not is the most important denotation. The well-known Schmid law still validates in the slender micro-pillars due to existence of the free slip band, whereas it may fail in the podgier micro-pillars due to absence of the free slip band; as a result, a complicated even “reverse” size effect appears.