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Nanoindentation and incipient plasticity

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Nanoindentation and incipient plasticityE.B. Tadmor,a)R. Miller,b)and R. Phillipsc)Division of Engineering, Brown University, Providence, Rhode Island 02912M. OrtizDepartment of Aeronautics, California Institute of Technology, Pasadena, California 91125(Received 19 August 1998; accepted 1 March 1999)This paper presents a large-scale atomic resolution simulation of nanoindentation into athin aluminum film using the recently introduced quasicontinuum method. The purposeof the simulation is to study the initial stages of plastic deformation under the actionof an indenter. Two different crystallographic orientations of the film and two differentindenter geometries (a rectangular prism and a cylinder) are studied. We obtain bothmacroscopic load versus indentation depth curves, as well as microscopic quantities,such as the Peierls stress and density of geometrically necessary dislocations beneath theindenter. In addition, we obtain detailed information regarding the atomistic mechanismsresponsible for the macroscopic curves. A strong dependence on geometry and orientationis observed. Two different microscopic mechanisms are observed to accommodatethe applied loading: (i) nucleation and subsequent propagation into the bulk of edgedislocation dipoles and (ii) deformation twinning.I. INTRODUCTIONAs mechanical systems continue to decrease in sizeand begin to approach atomic length scales, it is becom-ing important to develop experimental and correspond-ing theoretical tools to characterize material propertiesat these scales. One such experimental technique whichhas become popular due to its relative simplicity isnanoindentation. In this procedure an indenter with di-mensions of the order of tens of nanometers is pressedinto the surface of a solid. Nanoindentation has nowbecome a standard technique for evaluating the mechani-cal properties of thin films.1It can also be a useful toolfor studying the onset of plastic flow in small volumes, aphenomenon which can play a significant role in macro-scopic deformation processes such as adhesion, friction,and fracture.2The nanoindentation test is basically an extensionof traditional hardness and microhardness tests to verysmall scales. The classical tests offer a reasonably un-ambiguous measure of the hardness or mean pressurebeneath the indenter for a given load which can thenbe related to the yield strength of the material throughsemiempirical relations.3,4The assumption here is that alarge plastic region forms beneath the indenter which canbe treated approximately through plastic slip line theoriesa)Present address: Faculty of Mechanical Engineering, Technion–Israel Institute of Technology, 32000 Haifa, Israel.b)Present address: Department of Mechanical Engineering, Universityof Saskatchewan, Saskatoon, Saskatchewan, S7N 5A9, Canada.c)Address all correspondence to this author.e-mail: [email protected] more exactly by computation. Empirical correctionsare sometimes necessary to account for effects such asstrain hardening and deviations of the indenter from itsnominal geometry.In nanoindentation this relative clarity is lost. Atthe very small scales and loads common to these ex-periments the deformation is characterized by discretedislocation nucleation events and the subsequent interac-tion of the small numbers of dislocations that have beengenerated.5This is not the large-scale plasticity observedat the macroscopic scale. It is also not clear what roleother mechanisms such as diffusion and block slip2playin this small-scale incipient plasticity. Interpretation isfurther complicated by the fact that the response canbe highly dependent on the indenter geometry and itsorientation relative to the specimen crystallography. Itcan also be strongly influenced by additional factors suchas surface effects,2,6substrate effects,7grain effects,8andpre-existing defect populations.9Interpretation of nanoindentation tests may be facili-tated by a clearer understanding of the processes takingplace during the test. In recent years there have beena number of molecular dynamics (MD) simulations ofnanoindentation2,10–12which have led to greater insightinto the microscopics of nanoindentation. Due to thecomputational intensity of the problem many of thesesimulations were limited to very small model sizes(cubes of only tens of atoms on a side) or very highloading rates, or both. In this work we make use of therecently developed quasicontinuum method13–17whichallows for the modeling of systems with dimensions ofthe order of microns and thus minimizes the possibilityJ. Mater. Res., Vol. 14, No. 6, Jun 1999  1999 Materials Research Society 2233HelpCommentsWelcomeJournal ofMATERIALS RESEARCHE.B. Tadmoret al.:Nanoindentation and incipient plasticityof the contamination of the results by the boundaryconditions arising from the small model size. The issueof loading rate is sidestepped since the simulation iscarried out in quasistatic fashion, by determining a seriesof static equilibrium states, each corresponding to adifferent load. As long as the load increment is keptsufficiently small, the results are independent of theloading steps.In this paper we focus on incipient plasticity, thevery initial stages of plastic activity, in an aluminumthin film subjected to nanoindentation. We investigatethe mechanisms whereby dislocations are nucleated,their subsequent interactions, and the effects of indentergeometry and film crystallography. We find that depend-ing on the crystallography and geometry, completelydifferent microscopic mechanisms are observed withcorrespondingly different macroscopic manifestations.For a description of the technical details of applyingquasicontinuum to study nanoindentation problems, seeRef. 17.II. METHODOLOGYThe quasicontinuum methodology used here is amixed continuum and atomistic method developed tostudy problems in the mechanics of materials wheremultiple scales operate simultaneously. It was originallyintroduced14,15to study single crystal mechanics andlater extended16,17to treat polycrystals and polyphasematerials. The basic idea is that in a crystal undergoingmechanical deformation the majority of the lattice ex-periences a slowly varying deformation on the atomicscale which is well characterized by the continuumapproximation. It is only in the vicinity of defects orin the presence of mechanical manipulations on theorder of the lattice spacing where discrete atomic effectsgenerally become important. There is thus no need


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