Dislocation dynamics simulations of plasticity at small scales

As metallic structures and devices are being created on a dimension comparable to the length scales of the underlying dislocation microstructures, the mechanical properties of them change drastically. Since such small structures are increasingly common in modern technologies, there is an emergent need to understand the critical roles of elasticity, plasticity, and fracture in small structures. Dislocation dynamics (DD) simulations, in which the dislocations are the simulated entities, offer a way to extend length scales beyond those of atomistic simulations and the results from DD simulations can be directly compared with the micromechanical tests. The primary objective of this research is to use 3-D DD simulations to study the plastic deformation of nano- and micro-scale materials and understand the correlation between dislocation motion, interactions and the mechanical response. Specifically, to identify what critical events (i.e., dislocation multiplication, cross-slip, storage, nucleation, junction and dipole formation, pinning etc.) determine the deformation response and how these change from bulk behavior as the system decreases in size and correlate and improve our current knowledge of bulk plasticity with the knowledge gained from the direct observations of small-scale plasticity. Our simulation results on single crystal micropillars and polycrystalline thin films can march the experiment results well and capture the essential features in small-scale plasticity. Furthermore, several simple and accurate models have been developed following our simulation results and can reasonably predict the plastic behavior of small scale materials

Crystal plasticity analysis of deformation behavior of nanocrystalline nickel

Nanocrystalline (NC) metals with grain sizes \u3c100 nm have attracted a lot of attention in the materials science field for more than a few decades because of their ultra-high strength and hardness. Various experimental and computational studies indicate that dislocation-mediated plasticity prevails in NC metals when the grain size is larger than ~10 nm. Recent molecular dynamics (MD) simulations have found that dislocation-mediated plasticity in NC fcc metals is predominantly determined by dislocation propagation rather than nucleation and nucleation is the rate-limiting process. However, most of the earlier micromechanics models for NC metals have ignored this key feature. In this study, we have developed a statistical model to analyze the distribution of the critical resolved shear stresses (CRSS) associated with propagating a dislocation, from its grain boundary source, across the grain, t propagate, of a given size. We have incorporated this CRSS distribution into a 3D crystal plasticity model to study the stress–strain response of NC Nickel. The influences of grain size, dominant texture, and GB interactions are all considered in this study. From our study, we find that the distribution of t propagate is very asymmetric and follows the generalized extreme value distribution. By considering the distribution of t propagate, the simulation results from the crystal plasticity model can capture the key experiment trends observed for the strength of NC Ni: the strength increases with decreasing grain size following the Hall–Petch relationship. In addition, our simulation results predict a strong connection between the grain size and heterogeneity of plastic deformation in NC Ni

Coupled Crystal Orientation-Size Effects on the Strength of Nano Crystals

We study the combined effects of grain size and texture on the strength of nanocrystalline copper (Cu) and nickel (Ni) using a crystal-plasticity based mechanics model. Within the model, slip occurs in discrete slip events exclusively by individual dislocations emitted statistically from the grain boundaries. We show that a Hall-Petch relationship emerges in both initially texture and non-textured materials and our values are in agreement with experimental measurements from numerous studies. We find that the Hall-Petch slope increases with texture strength, indicating that preferred orientations intensify the enhancements in strength that accompany grain size reductions. These findings reveal that texture is too influential to be neglected when analyzing and engineering grain size effects for increasing nanomaterial strength

Homogenization of Plastic Deformation in Heterogeneous Lamella Structures

It has been shown that unlike its constituent nanocrystalline (NC) phase, a heterogeneous lamella (HL) composite comprising NC and coarse-grain layers exhibits greatly improved ductility. To understand the origin of this enhancement, we present a 3D discrete dislocation, crystal plasticity finite element model to study the development of strains across this microstructure. Here we show that the HL structure homogenizes the plastic strains in the NC layer, weakening the effect of strain concentrations. These findings can provide valuable insight into the effects of material length scales on material instabilities, which is needed to design heterogeneous structures with superior properties

Repeated Loading Model for Elastic-Plastic Contact of Geomaterial

A new nonlinear hysteretic model with considering the loading, unloading, and reloading processes is developed based on Drucker—Prager yield criterion and finite-element analysis. This model can be used for multiple repeated elastic—plastic normal direction contact problems between two identical spherical geomaterials. After examining the influence of material properties, strain hardening, and loading histories, we found that the hysteretic phenomena (represented by residual displacement and plastic work) become weak after the first cycle, and the subsequent cycles step into elastic shakedown state eventually. A critical number of cycles can be used to estimate the state of ratchetting, plastic shakedown, as well as elastic shakedown. It also found that the subsequent curves will be stiffer than the previous ones, especially when the yield strength is high and ratchetting effect is not strong. This new model can be used for a wide range of geomaterials under different loading levels, and it can also be extended to describe the constitutive behavior of spheres under earthquake as well as aftershocks

Nanograin Size Effects on the Strength of Biphase Nanolayered Composites

In this work, we employ atomic-scale simulations to uncover the interface-driven deformation mechanisms in biphase nanolayered composites. Two internal boundaries persist in these materials, the interlayer crystalline boundaries and intralayer biphase interfaces, and both have nanoscale dimensions. These internal surfaces are known to control the activation and motion of dislocations, and despite the fact that most of these materials bear both types of interfaces. From our calculations, we find that the first defect event, signifying yield, is controlled by the intralayer spacing (grain size, d), and not the intralayer biphase spacing (layer thickness, h). The interplay of two internal sizes leads to a very broad transition region from grain boundary sliding dominated flow, where the material is weak and insensitive to changes in h, to grain boundary dislocation emission and glide dominated flow, where the material is strong and sensitive to changes in h. Such a rich set of states and size effects are not seen in idealized materials with one of these internal surfaces removed. These findings provide some insight into how changes in h and d resulting from different synthesis processes can affect the strength of nanolayered materials

Plastic response by dislocation glide in solid helium under dc strain rate loading

We develop a model for the gliding of dislocations and plasticity in solid He-4. This model takes into account the Peierls barrier, multiplication and interaction of dislocations, as well as classical thermally and mechanically activated processes leading to dislocation glide. We specifically examine the dc stress-strain curve and how it is affected by temperature, strain rate, and dislocation density. As a function of temperature and shear strain, we observe plastic deformation and discuss how this may be related to the experimental observation of elastic anomalies in solid hcp He-4 that have been discussed in connection with the possibility of supersolidity or giant plasticity. Our theory gives several predictions for the dc stress strain curves, for example, the yield point and the change in the work-hardening rate and plastic dissipation peak, that can be compared directly to constant strain rate experiments and thus provide bounds on model parameters.Comment: 10 pages, 8 figures; minor revisions of accepted versio

Dislocation induced anomalous softening of solid helium

The classical motion of gliding dislocation lines in slip planes of crystalline solid helium leads to plastic deformation even at temperatures far below the Debye temperature and can affect elastic properties. In this work we argue that the gliding of dislocations and plasticity may be the origin of many observed elastic anomalies in solid He-4, which have been argued to be connected to supersolidity. We present a dislocation motion model that describes the stress-strain $\tau$-$\epsilon$ curves and work hardening rate $d\tau/d\epsilon$ of a shear experiment performed at constant strain rate $\dot{\epsilon}$ in solid helium. The calculated $d\tau/d\epsilon$ exhibits strong softening with increasing temperature due to the motion of dislocations, which mimics anomalous softening of the elastic shear modulus $\mu$. In the same temperature region the motion of dislocations causes dissipation with a prominent peak.Comment: 15 double-spaced pages, 4 figures; revised model parameters to account for low experimental yield stress, otherwise unchange

Dynamic Phases, Pinning, and Pattern Formation for Driven Dislocation Assemblies

We examine driven dislocation assemblies and show that they can exhibit a set of dynamical phases remarkably similar to those of driven systems with quenched disorder such as vortices in superconductors, magnetic domain walls, and charge density wave materials. These phases include pinned-jammed, fluctuating, and dynamically ordered states, and each produces distinct dislocation patterns as well as specific features in the noise fluctuations and transport properties. Our work suggests that many of the results established for systems with quenched disorder undergoing plastic depinning transitions can be applied to dislocation systems, providing a new approach for understanding pattern formation and dynamics in these systems

A Simple Model for Elastic-Plastic Contact of Granular Geomaterials

We propose a simple elastic-plastic contact model by considering the interaction of two spheres in the normal direction, for use in discrete element method (DEM) simulations of geomaterials. This model has been developed by using the finite element method (FEM) and nonlinear fitting methods, in the form of power-law relation of the dimensionless normal force and displacement. Only four parameters are needed for each loading-unloading contact process between two spheres, which are relevant to material properties evaluated by FEM simulations. Within the given range of material properties, those four parameters can be quickly accessed by interpolating the data appended or by regression functions supplied. Instead of the Von Mises (V-M) yield criterion, the Drucker-Prager (D-P) criterion is used to describe the yield behavior of contacting spheres in this model. The D-P criterion takes the effects of confining pressure, the intermediate principal stress, and strain rate into consideration; thus, this model can be used for DEM simulation of geomaterials as well as other granular materials with pressure sensitivity