FCC Single and Poly Crystals

Ryder Bolin 1, Hakan Yavas 1,2,3, , Hengxu Song 1,2, Kevin J Hemker 2 and Stefanos Papanikolaou 4 1,2,4* 5 1 Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV 26506; 6 rcbolin@mix.wvu.edu 7 2 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21216; 8 3 Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in 9 Prague, Technika 2, Prague 6, Czech Republic; 10 4 Department of Physics, West Virginia University, Morgantown, WV 26506; 11 * Correspondence: sp0045@mix.wvu.edu 12 13 Abstract: We present a high-throughput nanoindentation study of in-situ bending effects on 14 incipient plastic deformation behavior of polycrystalline and single-crystalline pure aluminum and 15 pure copper at ultra-nano depths (<200nm). We find that hardness displays a statistically inverse 16 dependence on in-plane stress for indentation depths smaller than 10nm, and the dependence 17 disappears for larger indentation depths. In addition, plastic noise in the nanoindentation force and 18 displacement displays statistically robust noise features, independently of applied stresses. Our 19 experimental results suggest the existence of a regime in FCC crystals where ultra-nano hardness is 20 sensitive to residual applied stresses, but plasticity pop-in noise is insensitive to it. 21


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In this paper, we focus on the statistical features of the noise in the nanoindentation force-depth 51 curves at very shallow depths (<200nm). We concentrate our efforts on common FCC metals, in 52 particular single and poly crystalline pure aluminum, and single crystal pure copper. In addition, we 53 explore the effect of in-situ bending stress on nanoindentation at very shallow depths. At shallow 54 depths, plasticity is not primarily controlled by the shape of the indenter tip and the most pronounced 55 evidence of this fact is the well known observation that the post-indentation surface profile is 56 stochastic at these depths and does not exactly follow the indenter tip's shape [30,31]. We study two 57 tips, Berkovich and spherical with radius 5μm, and we find qualitative agreement. In this work, we 58 report on high-throughput indentation measurements on pre-stressed FCC samples and statistically

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Electropolished commercial aluminum polycrystals (99.99% purity, Plasma Materials Inc., 69 US) and commercial aluminum and copper single crystals at orientation (100) (99.99% purity, 70 MTI Corporation., US), of dimensions 2mm x 5mm x 10mm, were used in this study. 71 Custom-made 4-point loading fixtures (see Figure 1(a),(c)) were designed to apply in-plane 72 tension at the sample top central region during nanoindentation, controlling the local strain 73 at the top central surface area through a screw element at the bottom of the fixture. The strain 74 was measured in situ by using commercial strain gauges (see Fig.1c). High-throughput 75 nanoindentations were performed in the center (1mm) 2 surface areas of the samples, with 76 typical distances between nanoindentation sites being 10μm in each direction. Given that 77 nanoindentation depths did not exceed 250nm, the distance between nanoindentation sites 78 may be regarded independent [35]. For the estimation of the applied tension at the 79 nanoindentation sites, independently measured elastic moduli and yield stresses were 80 exported into finite element simulations, performed using the ABAQUS software (see an 81 example in Figure (1)b and also in the Supplementary Material (SM)). Through systematic 82 calculations and testing, tables for strain/stress/plastic-strain mapping were developed for 83 each material (see Tables 1,2 for a particular example of polycrystalline, as well as single-84 crystalline aluminum). The applied strain on the samples extended, in small steps, up to 0.5%, 85 well in the crystal plasticity regime. Clear surface steps (primarily due to dislocation 86 plasticity) formed after 0.2% strain in all the materials tested (example seen in Fig.1d for a 87 single crystal copper sample), naturally influencing the indentation results at small depths. 88 Our main results are focused on small loads/strains which should not be influenced by such 89 steps, but more details on these issues are discussed in the SM. 90 Nanoindentation experiments were performed with an iNano (Nanomechanics Inc., TN) 91 nanoindenter with Berkovich (apex roundness of 20nm) and spherical (5μm) tips, acquired 92 by Microstar Inc.. The details of the materials preparation, bending fixture and 93 nanoindentation protocols are discussed in the SM. 94 In the following, we present our main results on the correlation between hardness and secondary 98 pop-in bursts in FCC polycrystalline pure aluminum, single-crystalline pure aluminum and single 99 crystalline pure copper. Our data is also supported by the SM which provides additional details. In 100 each of the cases, we focused on two main observables: i) the raw force-depth curves and ii) the       Table 1). Samples were electropolished before being loaded and indented.

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In all cases, load-displacement curves show a continuous elastic response followed by multiple 115 measurable displacement bursts (see Figure 2

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Interestingly, the applied tension appears to consistently suppress large events, however the  Table 1

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The sample-averaged force-displacement curves in Figure 6

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The behavior of the CSM hardness for single crystalline Cu is quite consistent with the 181 polycrystalline case. As seen in Figure 5(a), the sample-averaged hardness shows that the applied 182 tension drastically decreases the small-depth hardness by a factor of 30. As shown in Figure 5

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we suggest that the local flow stress during indentation is a function of the local dislocation density: