Nanomechanics of rhenium wires: Elastic modulus, yield strength and strain hardening
Introduction
Rhenium nanowires (RhNWs) are unique nanoscale materials that exhibit high strength and interesting electric properties. Their hexagonal atomic structures also give them particular mechanical properties [1], which are different from those of face-centered cubic structures such as Au or Ag nanowires. These properties could make them ideal for technological applications in electromechanical sensors, field emission devices, scanning probe microscopes and interconnects [2], [3], [4], [5]. Characterizing the mechanical properties of nanowires is therefore of great importance in view of their future applications.
The mechanical properties of nanomaterials have long been known to change with the amount of probed volume at the micro/nanoscale [6], [7], [8], [9], [10]. The mechanisms that govern small-scale plasticity in metals are generally related to dislocation storage, motion, pinning and nucleation over the submillimeter to nanometer scale [11]. Unlike silicon or germanium nanowires [12], to the best of our knowledge, the elastoplastic properties including the strain-hardening behavior of RhNWs, have not yet been investigated. In an earlier paper [13], the mechanical properties of a hexagonal crystal structure have been evaluated for the first time for monocrystalline RhNWs. Numerical and analytical findings reported yield stress values of around 26 GPa for RhNW, which represents almost 10% of the Young’s modulus value and 100 times higher than the yield stress reported for its bulk counterpart. Discrepancies and errors intrinsic to the experimental data clearly underlined the importance of an advanced numerical model to measure accurately the yield stress of RhNWs. The effects of substrate, stiffness anisotropy and surface state properties of the system were investigated, and it was shown that their influence on the resulting mechanical properties cannot be neglected.
The measurement on free-standing nanowires is always challenging since the mechanical properties determined by standard macroscale materials testing procedures cannot easily be employed for nanomaterials. Several methods have been reported for measuring the mechanical properties of nanowires, including resonance [9], [14], [15] and cantilever bending [16], [13] methods. In this article, we present an in situ atomic force microscopy (AFM) method combined with an inverse finite-element (FE) analysis to determine the mechanical properties of free-standing RhNWs under large strain. The bending modulus and the ultimate stress are measured using a nanobending experiment. Experimental data is then analyzed using FE simulations to calculate the strain-hardening coefficient. The combination of experiment and theoretical simulation yields a complete analytical elastoplastic model for the analysis of the stress–strain behavior.
Section snippets
Nanobending experiments
In our experiments, we use monocrystalline RhNWs, which are synthesized by directional solidification of an eutectic NiAl–Rh alloy and subsequent selective etching of the NiAl matrix [17]. To carry out the nanobending experiment, a rectangular AFM cantilever fixed at one end on a nanomanipulation system was set up inside a chamber of scanning electron microscope (SEM), as reported in detail elsewhere [13]. The AFM tip has been used to apply a lateral force on the wire tip to bend individual
Results
In this study, the elastoplastic parameters of RhNWs were obtained from the analysis of (force–displacement) curves. One example is shown in Fig. 2. This curve is typical for a material exhibiting elastoplastic behavior. The initial linear slope corresponds to the elastic region. A breakdown of the linear load–displacement slope corresponds to the initiation of plastic deformation observed by in situ image analysis. Finally, strain localization on the wire takes place, corresponding to
Modeling
In order to build a constitutive law for the elastoplastic behavior of RhNWs, we analyzed our experimental data using an inverse method, which consists in fitting mechanical properties parameters to sets of experimental results. From classical theories of plasticity, we use the power-law work-hardening model [22], which is considered as a fairly good approximation for metals. In this model, the relationship between the true stress and the true strain can be written as follows:
Acknowledgements
Financial support by the Swiss State Secretariat for Education and Research in the frame of the European Project HYDROMEL (under contract No. 026622-2) is gratefully acknowledged. We thank M. Zaiser at the University of Edinburgh for helpful discussions.
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