Dynamic discrete dislocation plasticity

This chapter concerns with dynamic discrete dislocation plasticity (D3P), a two-dimensional method of discrete dislocation dynamics aimed at the study of plastic relaxation processes in crystalline materials subjected to weak shock loading. Traditionally, the study of plasticity under weak shock loading and high strain rate has been based on direct experimental measurement of the macroscopic response of the material. Using these data, well-known macroscopic constitutive laws and equations of state have been formulated. However, direct simulation of dislocations as the dynamic agents of plastic relaxation in those circumstances remains a challenge. In discrete dislocation dynamics (DDD) methods, in particular the two-dimensional discrete dislocation plasticity (DDP), the dislocations are modeled as discrete discontinuities in an elastic continuum. However, current DDP and DDD methods are unable to adequately simulate plastic relaxation because they treat dislocation motion quasi-statically, thus neglecting the time-dependent nature of the elastic fields and assuming that they instantaneously acquire the shape and magnitude predicted by elastostatics. This chapter reproduces the findings by Gurrutxaga-Lerma et al. (2013), who proved that under shock loading, this assumption leads to models that invariably break causality, introducing numerous artifacts that invalidate quasi-static simulation techniques. This chapter posits that these limitations can only be overcome with a fully time-dependent formulation of the elastic fields of dislocations. In this chapter, following the works of Markenscoff & Clifton (1981) and Gurrutxaga-Lerma et al. (2013), a truly dynamic formulation for the creation, annihilation, and nonuniform motion of straight edge dislocations is derived. These solutions extend the DDP framework to a fully elastodynamic formulation that has been called dynamic discrete dislocation plasticity (D3P). This chapter describes the several changes in paradigm with respect to DDP and DDD methods that D3P introduces, including the retardation effects in dislocation interactions and the effect of the dislocation's past history. The chapter then builds an account of all the methodological aspects of D3P that have to be modified from DDP, including mobility laws, generation rules, etc. Finally, the chapter explores the applications D3P has to the study of plasticity under shock loading.