Atomistic mechanisms governing elastic limit and incipient plasticity in crystals (original) (raw)

Atomistic processes of dislocation generation and plastic deformation during nanoindentation

To enable plastic deformation during nanoindentation of an initially defect-free crystal, it is necessary first to produce dislocations. While it is now widely accepted that the nucleation of the first dislocations occurs at the start of the pop-in event frequently observed in experiments, it is unclear how these initial dislocations multiply during the early stages of plastic deformation and produce pop-in displacements that are typically much larger than the magnitude of the Burgers vector. This uncertainty about the complex interplay between dislocation multiplication and strain hardening during nanoindentation makes a direct correlation between force–displacement curves and macroscopic material properties difficult. In this paper, we study the early phase of plastic deformation during nanoinden-tation with the help of large-scale molecular dynamics simulations. A skeletonization method to simplify defect structures in atomistic simulations enables the direct observation and quantitative analysis of dislocation nucleation and multiplication processes occurring in the bulk as well as at the surface.

Non-linear deformation mechanisms during nanoindentation

Acta Materialia, 1998

ÐExperiments involving the indentation of single crystals of both tungsten and an iron alloy show that the observed yield phenomena can be predicted using a superdislocation model driven by the change in shear stress between the elastically and fully plastic loading conditions. A low density of dislocation multiplication sites is required to support elastic loading which approaches applied shear stresses on the order of the theoretical shear strength of the material. Oxide ®lm thickness and crystal orientation are examined as parameters in controlling the yield phenomena. A model based on activation of dislocation multiplication sources is suggested to explain the initiation of the yield point during indentation and the overall load±depth relationship during indentation.

An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events

Journal of Applied Mechanics, 2006

Small volume deformation can produce two types of plastic instability events. The first involves dislocation nucleation as a dislocation by dislocation event and occurs in nanoparticles or bulk single crystals deformed by atomic force microscopy or small nanoindenter forces. For the second instability event, this involves larger scale nanocontacts into single crystals or their films wherein multiple dislocations cooperate to form a large displacement excursion or load drop. With dislocation work, surface work, and stored elastic energy, one can account for the energy expended in both single and multiple dislocation events. This leads to an energy balance criterion which can model both the displacement excursion and load drop in either constant load or fixed displacement experiments. Nanoindentation of Fe-3% Si (100) crystals with various oxide film thicknesses supports the proposed approach.

Discrete and continuous deformation during nanoindentation of thin films

Acta Materialia, 2000

ÐThis paper describes nanoindentation experiments on thin ®lms of polycrystalline Al of known texture and dierent thicknesses, and of single crystal Al of dierent crystallographic orientations. Both single-crystalline and polycrystalline ®lms, 400±1000 nm in thickness, are found to exhibit multiple bursts of indenter penetration displacement, h, at approximately constant indentation loads, P. Recent results from the nanoindentation studies of Suresh et al. (Suresh, S., Nieh T.-G. and Choi, B.W., Scripta mater., 1999, 41, 951) along with new microscopy observations of thin ®lms of polycrystalline Cu on Si substrates are also examined in an attempt to extract some general trends on the discrete and continuous deformation processes. The onset of the ®rst displacement burst, which is essentially independent of ®lm thickness, appears to occur when the computed maximum shear stress at the indenter tip approaches the theoretical shear strength of the metal ®lms for all the cases examined. It is reasoned that these displacement bursts are triggered by the nucleation of dislocations in the thin ®lms. A simple model to estimate the size of the prismatic dislocation loops is presented along with observations of deformation using transmission electron microscopy and atomic force microscopy. It is demonstrated that the response of the nanoindented ®lm is composed of purely elastic behavior with intermittent microplasticity. The overall plastic response of the metal ®lms, as determined from nanoindentation, is shown to scale with ®lm thickness, in qualitative agreement with the trends seen in wafer curvature or X-ray diraction measurements.

Dislocation nucleation in the initial stage during nanoindentation

Philosophical Magazine, 2003

The microstructure origin of the elastic-plastic response of a Cu substrate during nanoindentation is studied using molecular dynamics simulation. The elastic response is found to deviate from the Hertzian solution observed experimentally. The departure can be traced to the small tip radius used in the simulation. Further penetration sees the development of an inhomogeneous microstructure. Even at the same strain rate, different parts of the contact surface deform via different mechanisms: some elastically, some via the dislocation bow-out and some via the nucleation and growth of Shockley partials that sometimes interact to form stair-rod locks. The resultant effect produces the observed quasi-elastic behaviour on the load-displacement curve, characterized by interspersed minor yields. The present computer simulation shows in some detail the corresponding dislocation structure development. The stair-rod lock formation is found to provide a more satisfactory explanation to the experimentally observed time-delayed occurrence of pop-in below the spontaneous pop-in load. } 1. Introduction As the nanoscale counterpart of the traditional microhardness tests, nanoindentation can provide much more fundamental insight into the mechanical properties of

Atomistic simulations of incipient plasticity under Al (111) nanoindentation

Mechanics of materials, 2005

Atomistic simulations are performed for the study of defect nucleation and evolution in Al single crystal under nanoindentation. Methodologies employed include the molecular dynamics and molecular mechanics simulations with embedded-atom potentials. Simulated is the indenting process on Al(1 1 1) surface with the spherical tip of indenter. Using the visualization technique of centrosymmetry parameters, homogeneous nucleations and early evolutions of dislocations are investigated for deepening our understanding of incipient plasticity at the atomic scale. We have shown that the nucleation sites of initial dislocation loops vary with the empirical potentials chosen for the simulation. Identifications are also made for the continuously changing structures of dislocation locks underneath the indenter tip and for the glide of prismatic partial dislocation loops far away from the contact surface.

Nanoscale elastic–plastic deformation and stress distributions of the

The nanoscale elastic–plastic characteristics of the C plane of sapphire single crystal were studied by ultra-low nanoindentation loads with a Berkovich indenter within the indentation depth less than 60 nm. The smaller the loading rate is, the greater the corresponding critical pop-in loads and the width of pop-in extension become. It is shown that hardness obviously exhibits the indentation size effect (ISE), which is 46.7 ± 15 GPa at the ISE region and is equal to 27.5 ± 2 GPa at the non-ISE region. The indentation modulus of the C plane decreases with increasing the indentation depth and equals 420.6 ± 20 GPa at the steady-state when the indentation depth exceeds 60 nm. Based on the Schmidt law, Hertzian contact theory and crystallography, the possibilities of activation of primary slip systems indented on the C surface and the distributions of critical resolved shear stresses on the slip plane were analyzed.

Interfaces in size-dependent crystal plasticity

Plasticity in heterogeneous materials with small domains is governed by the interactions and reactions of dislocations and interfaces. These include reactions of existing dislocations, as well as the nucleation of dislocations at an interface. The rational for interface dominated plasticity is simple: dislocations glide through the single crystal domain with relative ease, but pile-up at interfaces, so that interface reactions become a critical step in continuing plastic deformation. While the details of dislocation reactions at interfaces take place at the atomic scale, and the behavior of dislocations in bulk is most accurately modeled by discrete dislocation dynamics, both of these models are much too expensive and impractical for analyzing the resulting bulk behavior. The need for a continuum framework for describing the plasticity across crystal interfaces, including the ubiquitous size effects, is acute. Recently developed size-dependent crystal plasticity theory [Mesarovic et al. 2010 J. Mech. Phys. Solids 58, 311-29] employs the representation of the singular part of dislocation pile-up boundary layers as superdislocation boundary layers, or equivalently, as jumps in slip at the boundary, but internal to the crystal. These boundary superdislocations exist on two sides of an interface and react or combine to lower the total energy under certain conditions. Using this theory, we obtain solutions to simple problems of single-slip and double-slip shear of sandwiched thin film. Then, we compare the results with available discrete dislocation simulations.