An Experimental and Computational Study of the Elastic-Plastic Transition in Thin Films
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An Experimental and Computational Study of the Elastic-Plastic Transition in Thin Films Erica T. Lilleodden1 , Jonathan A. Zimmerman2 , Stephen M. Foiles3 and William D. Nix1 1 Department of Materials Science & Engineering, Stanford University, Stanford, CA 943052205, 2 Sandia National Laboratories, Livermore, CA 94551, 3 Sandia National Laboratories, Albuquerque, NM 87185 ABSTRACT Nanoindentation studies of thin metal films have provided insight into the mechanisms of plasticity in small volumes, showing a strong dependence on the film thickness and grain size. It has been previously shown that an increased dislocation density can be manifested as an increase in the hardness or flow resistance of a material, as described by the Taylor relation [1]. However, when the indentation is confined to very small displacements, the observation can be quite the opposite; an elevated dislocation density can provide an easy mechanism for plasticity at relatively small loads, as contrasted with observations of near-theoretical shear stresses required to initiate dislocation activity in low-dislocation density materials. Experimental observations of the evolution of hardness with displacement show initially soft behavior in small-grained films and initially hard behavior in large-grained films. Furthermore, the small-grained films show immediate hardening, while the large grained films show the ‘softening’ indentation size effect (ISE) associated with strain gradient plasticity. Rationale for such behavior has been based on the availability of dislocation sources at the grain boundary for initiating plasticity. Embedded atom method (EAM) simulations of the initial stages of indentation substantiate this theory; the indentation response varies as expected when the proximity of the indenter to a Σ79 grain boundary is varied. INTRODUCTION Length-scale is fundamentally important to materials science, as evidenced by its relation to microstructure-property relations. For example, the flow stress of a material is known to scale with the square root of the dislocation density, inversely with the square root of the grain size, and, in the case of thin films, inversely with film thickness. However, a single-valued flow stress, considered to be a material property, is typically used in continuum mechanics. This removes any explicit length-scale dependence from the constitutive relations, taking into account only the average microstructure of the material. This is a reasonable approach in cases where the scale of deformation is large relative to the scale of microstructural inhomogeneities. However, as the characteristic length-scale of the deformation field tends toward the characteristic material length-scale, the governing relations between stress and strain may deviate from classical laws. Indeed, anomalous yielding behavior has been commonly observed in nanoindentation studies. Discrete load-displacement response in the early stages of indentation (e.g. several nanometers to tens of nanometers) has been widely observed [e.g. 2, 3, 4],
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