Scale-dependent pop-ins in nanoindentation and scale-free plastic fluctuations in microcompression
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Scale-dependent pop-ins in nanoindentation and scale-free plastic fluctuations in microcompression John Shimanek1, Quentin Rizzardi1, Gregory Sparks1, Peter M. Derlet2, Robert Maaß1,a) 1
Department of Materials Science and Engineering and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 2 Condensed Matter Theory Group, Paul Scherrer Institute, Villigen-PSI 5232, Switzerland a) Address all correspondence to this author. e-mail: [email protected] Received: 2 July 2019; accepted: 3 December 2019
Nanoindentation and microcrystal deformation are two methods that allow probing size effects in crystal plasticity. In many cases of microcrystal deformation, scale-free and potentially universal intermittency of event sizes during plastic flow has been revealed, whereas nanoindentation has been mainly used to assess the stress statistics of the first pop-in. Here, we show that both methods of deformation exhibit fundamentally different event-size statistics obtained from plastic instabilities. Nanoindentation results in scale-dependent intermittent microplasticity best described by Weibull statistics (stress and magnitude of the first pop-in) and lognormal statistics (magnitude of higher-order pop-ins). In contrast, finite-volume microcrystal deformation of the same material exhibits microplastic event-size intermittency of truncated power-law type even when the same plastic volume as in nanoindentation is probed. Furthermore, we successfully test a previously proposed extreme-value statistics model that relates the average first critical stress to the shape and scale parameter of the underlying Weibull distribution.
Introduction Discrete plastic flow is a well-known feature in both bulk deformation and microplasticity [1]. At the macroscopic scale, plastic instabilities during dynamic strain aging of solid solutions [2, 3] or serrated stress–strain behavior of complex multicomponent (high-entropy) alloys [4] and metallic glasses [5] can be observed. Only a small number of reports have revealed the intermittent nature of plastic flow via direct recording of discrete stress–strain curves obtained from pure bulk single crystals [6, 7, 8]. This is quite different at the small scale, where virtually any pure single-crystalline metal exhibits intermittent flow in a uniaxial deformation experiment [1, 9], which in contrast to bulk deformation may be due to the typically used deformation rates that are well below the underlying dislocation avalanche velocity [10]. The general observation of intermittent plastic flow also applies to a large number of nanoindentation studies that focus on incipient plasticity via so-called pop-ins [11, 12, 13, 14, 15, 16]. The main feature distinguishing the pop-ins of nanoindentation from the intermittent plasticity of microcrystal deformation is that the discrete plastic events of the latter are traced along the entire
ª Materials Research Society 2020
strain range, whereas pop-ins become unresolvable for large indentation depths. Co
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