On the effects of dislocation density on micropillar strength
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1185-II05-07
On the effects of dislocation density on micropillar strength A. A. Benzerga Texas A&M University, College Station, TX 77843, USA
ABSTRACT There is an increasing amount of experimental evidence that the plastic behavior of crystals changes at micro- and nano-scales in a way that is not necessarily captured by state-of-the-art plasticity models. In this paper, length scale effects in the plasticity of crystals are analyzed by means of direct numerical simulations that resolve the scale of the carriers of plasticity, i.e., the dislocations. A computationally efficient, atomistically informed dislocation dynamics framework which has the capability of reaching high dislocation densities and large strains at moderately low strain rates in finite volumes is recalled. Using this theoretical framework, a new type of size effect in the hardening of crystals subject to nominally uniform compression is discovered. In light of such findings, behavior transitions in the space of meaningful structural parameters, from foresthardening dominated regime to an exhaustion hardening dominated regime are discussed. Various scalings of the flow stress with crystal size emerge in the simulations, which are compared with recent experimental data on micro- and nano-pillars. INTRODUCTION Over the past few years, various experimental techniques have been developed to interrogate the mechanical response of materials at the scale of their microstructures. Among these, compression pillars have been extensively used [1–4]. In general, a common trend emerges from pillar compression experiments with smaller being harder. However, there are conflicting reports on whether hardening is size-dependent, and if so what is the origin of the apparent hardening? In addition, the strength of the scaling of flow stress with pillar diameter varies from one experimental data set to another. Therefore, there is a need for further analysis of plasticity in small volumes, especially in the absence of gradients in the macroscopic fields. Under such circumstances, state-of-the-art strain-gradient and other nonlocal theories of plasticity do not predict the size dependence evidenced in pillar compression experiments. Since continuum plasticity is currently incapable of providing a rationale for pillar plasticity, recourse to lower resolution analyses is necessary. Fully discrete atomic-level methods, such as molecular dynamics, are incapable of resolving sample sizes ranging from 100 nm to over 10 microns, i.e., the range of pillar diameters considered in the experiments thus far. Alternatively, semi-discrete analyses may be used which are based on dislocation theory, i.e., linear elasticity for long-range dislocation interactions as well as suitably specified atomic-level input. Discrete dislocation dynamics (DD) simulations have recently been reported [5–9] which capture various aspects of plastic behavior in micro- and nano-pillars. Despite this progress, it is fair to say that our understanding of the basic mechanisms and how these relate to macros
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