Energetics of Dislocation Nucleation under a Nanoindenter
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Energetics of Dislocation Nucleation under a Nanoindenter Chuanli Zhang and Guanshui Xu Department of Mechanical Engineering University of California, Riverside, CA92521 ABSTRACT Dislocation nucleation under an idealized nanoindenter is analyzed based on the PeierlsNabarro dislocation model. The variational boundary integral method is used to obtain the dislocation profiles that correspond to the shear displacements between the adjacent atomic layers along the slip plane. The critical condition for dislocation nucleation at absolute zero and the activation energies required to thermally activate dislocations from their stable to unstable saddle point configurations are determined. By treating the surface as part of an infinite crack embedded in the infinite medium, a rather straightforward approach is adopted to account for the surface effect. The emission of multiple dislocations from the surface of a film-substrate system is also studied. The size effects of the indenter width and film thickness are characterized by the typical load-displacement relation. INTRODUCTION Nanoindentation has recently emerged as one of the most powerful techniques for probing mechanical behavior of materials at the nanometer scale [1-4]. Using an atomic or interfacial force microscope, a typical nanoindentation experiment measures the load-displacement relation by pushing a diamond indenter on the surface of a solid [5-7]. For crystalline materials, at the earliest stage of indentation, the load-displacement curve matches the prediction based on Hertz's theory of elastic contact [8]. As the load increases, the curve then exhibits abrupt bursts in displacement. This discontinuous form of plasticity continues to occur until the indenter is pushed far enough into the material to eventually result in the smooth continuous form of plasticity. Numerous nanoindentation experiments have revealed that the onset of discontinuous plastic deformation is associated with dislocation nucleation under high stress induced by indenters [3, 5, 9, 10]. The mechanism of dislocation nucleation under nanoindentation has been studied by various methods including continuum dislocation theory, quasicontinuum method, and atomic simulations [11-15]. Parallel to these efforts, we here analyze the energetic of dislocation nucleation under nanoindentation based on the Peierls-Nabarro dislocation model which has been recently advanced for the analysis of dislocation nucleation in perfect crystals [16], from cracks [17, 18, 20, 21], and at free surfaces [19]. Compared to continuum elastic dislocation theory, this model eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core in the dislocation nucleation process. The incorporation of atomic information into continuum approach further allows for effective determination of the unstable saddle point configuration of the embryonic dislocation and its associated activation energy for thermally assisted dislocation nucleation at the finite temperature. Compared to
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