Discrete Dislocation Plasticity Model Research Articles

A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading

In this article, it is demonstrated that current methods of modelling plasticity as the collective motion of discrete dislocations, such as two-dimensional discrete dislocation plasticity (DDP), are unsuitable for the simulation of very high strain rate processes (10 6 s −1 or more) such as plastic relaxation during shock loading. Current DDP models treat dislocations quasi-statically, ignoring the time-dependent nature of the elastic fields of dislocations. It is shown that this assumption introduces unphysical artefacts into the system when simulating plasticity resulting from shock loading. This deficiency can be overcome only by formulating a fully time-dependent elastodynamic description of the elastic fields of discrete dislocations. Building on the work of Markenscoff & Clifton, the fundamental time-dependent solutions for the injection and non-uniform motion of straight edge dislocations are presented. The numerical implementation of these solutions for a single moving dislocation and for two annihilating dislocations in an infinite plane are presented. The application of these solutions in a two-dimensional model of time-dependent plasticity during shock loading is outlined here and will be presented in detail elsewhere.

Discrete dislocation modeling of fracture in plastically anisotropic metals

The intrinsic lattice resistance to dislocation motion, or Peierls stress, depends on the core structure of the dislocation and is one essential feature controlling plastic anisotropy in materials such as HCP Zn, Mg, and Ti. Here, we implement an anisotropic Peierls model as a friction stress within a 2d discrete dislocation (DD) plasticity model and investigate the role of plastic anisotropy on the crack tip stress fields, crack growth, toughening, and microcracking. First, tension tests for a pure single crystal with no obstacles to dislocation motion are carried out to capture the general flow behavior in pure HCP-like materials having slip on basal and pyramidal planes. Then Mode-I crack growth in such a single crystal of the HCP material is analyzed using the 2d-DD model. Results show that the fracture toughness scales inversely with the tensile yield stress, largely independent of the plastic anisotropy, so that increasing Peierls stress on the pyramidal planes gives decreasing resistance to crack growth, consistent with recent experiments on Zn. Analyzing the results within the framework of Stress Gradient Plasticity concepts shows that the equilibrium dislocation dipole spacing serves as an internal material length scale for controlling fracture toughness. Furthermore, the fracture toughness of materials with flow stress controlled by a Peierls stress (this work) and of materials with flow stress controlled by dislocation obstacles (prior literature) is unified through the Stress Gradient Plasticity concept. Finally, the DD simulations show that local stress concentrations exist sporadically along the pyramidal plane(s) that emanate from the current crack tip, suggesting an origin for experimentally observed basal-plane microcracking near the tip of large cracks.

Modelling dislocation transmission across tilt grain boundaries in 2D

A line tension approach is reviewed to model slip transfer across tilt grain boundaries (GBs). It is implemented as a constitutive rule in the already existing two-dimensional discrete dislocation plasticity model of polycrystalline thin films. GBs are treated as obstacles to dislocation motion but with a finite strength. Dislocation transmission across a GB is potentially allowed, provided that three known geometrical criteria are satisfied. If allowed, the motion of the dislocation across the GB is enabled by dynamically creating a GB source near the GB, the stress on which must exceed the boundary strength. To separate transmission effects from other discrete dislocation features of the plastic deformation of thin films, comparisons are carried out by modelling GBs as impenetrable barriers to dislocation motion. It is shown that slip transfer tends to make the film softer if the density of bulk sources is sufficiently low. Since the position of the boundary source lies within the high-stress region of dislocation pile-ups, once activated the transmission process becomes independent of the source strength. In addition, the Bauschinger effect (BE) in thin films has been studied and a decrease of the BE is seen when dislocation transmission across GBs is enabled.

Compliant interfaces: A mechanism for relaxation of dislocation pile-ups in a sheared single crystal

Discrete dislocation plasticity models and strain-gradient plasticity theories are used to investigate the role of interfaces in the elastic–plastic response of a sheared single crystal. The upper and lower faces of a single crystal are bonded to rigid adherends via interfaces of finite thickness. The sandwich system is subjected to simple shear, and the effect of thickness of crystal layer and of interfaces upon the overall response are explored. When the interface has a modulus less than that of the bulk material, both the predicted plastic size effect and the Bauschinger effect are considerably reduced. This is due to the relaxation of the dislocation stress field by the relatively compliant surface layer. On the other hand, when the interface has a modulus equal to that of the bulk material a strong size effect in hardening as well as a significant reverse plasticity are observed in small specimens. These effects are attributed to the energy stored in the elastic fields of the geometrically necessary dislocations (GNDs).

A Discrete Dislocation Plasticity Model of Creep in Polycrystalline Thin Films

A Discrete Dislocation Plasticity Model of Creep in Polycrystalline Thin Films