The significance and challenges on determining the size-effect of indentation hardness at nano-scale

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SCIENTIA SINICA Physica, Mechanica & Astronomica
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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48, Issue 9: 094603(2018) https://doi.org/10.1360/SSPMA2018-00206

The significance and challenges on determining the size-effect of indentation hardness at nano-scale

Rong YANG1,2,*, TaiHua ZHANG3, Pan XIAO1,2, Jun WANG1,2, Qun ZHANG1,2,4, Fei SHUANG1,2, FuJiu KE5, YiLong BAI1,2,*
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  • ReceivedMay 29, 2018
  • AcceptedJul 25, 2018
  • PublishedAug 9, 2018
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Abstract

Instrumented indentation is a method that has been widely used to obtain material properties at micro and nano scale, yet creditable indentation size effect at real nano-scale and its mechanism are still unsolved. This paper summarizes our recent work on progresses in experimental and simulation approaches to this problem. By confirming the crystalline orientations and the surface roughness of the sample, obtaining the tip radius of the indenters, as well as considering tip radius in large-scale molecular simulation, the gap between the experiment and simulation results is bridged, and these two results can be cross verified with each other, which leads to a reliable hardness trend over the indentation depth at nano-scale. Two opposite size effects are observed, and their different mechanisms are revealed, as the conventional size effect results from the plastic behavior such as dislocation nucleation and propagation in the sample beneath the indenter, while the initial reverse size effect is due to the combined effect of the indenter roundness and elastic behavior of the material. Systematic investigation on the efficiency and fidelity of MD and MS is carried out, on problem of the dislocation evolution during indentation, the influence of the relaxation time and convergence resolution on the load curve and dislocation patterns are studied, and suggestion on choice of two simulation methods and the relaxation time and convergence resolution are given.


Funded by

国家重大科学研究计划(2012CB937500)

中国科学院战略性先导科技专项B类(XDB22000000)

国家自然科学基金(11727803)


Acknowledgment

感谢北京大学夏蒙棼教授对于相关工作长期以来的支持和指导.


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    Figure 1

    Illustration of indentation parameters with conical indenter.

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    Figure 2

    Comparison between numerical and experimental results of hardness in single crystal Cu, based on available literatures.

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    Figure 3

    (Color online) Specimen specifications. (a) EBSD map for the surface orientation of (100), (110) and (111), no apparent grains and grain boundaries are observed; (b) misorientation profiles of the surface to the presumed orientations, the misorientations are within 1.5°; (c) surface morphology of specimens, scan size of 2?μm′2?μm, the roughness peaks are under 3?nm.

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    Figure 4

    (Color online) Experiment and simulation results of indentation on Cu. (a) Hardness curves of the Cu samples. The hardness goes up then goes down as the indentation depth deceases, the transition occurs in the range of 8?10?nm, and peak value can be observed in this range too. Hardness value is higher for Tip-100, the corresponding depth to the hardness peak is lower than that of Tip-150. The effect of the tip radius abates when the indentation depth is over 100?nm. (b) Displacement “bursts” in the loading curves. They correlate to each drop in hardness curve. (c) Force-depth curves obtained using two indenters with 100 and 150?nm tip radius, respectively. The repeatability of the experiments is good when indentation depth is within 10?nm and over 25?nm. In the range of 8?25?nm, the curves separate due to displacement “bursts” patterns in the curves. The 150?nm tip loading curves are higher compare to these of 100?nm tip. (d) Hardness curves of the Cu. The hardness is lower with larger tip radius. (e) Displacement “bursts” patterns in the loading curves for the case of R=10?nm at 0?K. This is similar to that from the experiments, and each drop of hardness value coincides with a burst in displacement curve. (f) A close look at the loading and unloading curves at shallow depth, and CSP distributions after the indenter is retrieved from the sample at step point e and p. The loading and unloading curves converge with each other before step point e, and CSP map shows the distortion of the lattice is not great and after the indenter is removed, the lattice will recover to origin state; and then a hysteresis loop emerges when loading beyond step point e, indicating the deformation is not reversible. CSP map shown stacking fault and dislocation initiate, and the lattice cannot be restored to its origin state after the indenter retrieves from the sample.

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    Figure 5

    (Color online) (a) Indentation force and (b) accumulated times of force evaluation versus indentation depth obtained in MD and MS simulations. (c) Dislocation distribution obtained in MD and MS simulations at the last loading step.

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    Figure 6

    The regimes when attractive and adhesive force between the sample and the indenter influence the simulation results, and the definition of zero point for force and depth.

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    Figure 7

    (Color online) (a) Experiment and simulation results of hardness of Cu in this paper, along with results from available literatures. (b) Hardness peak value over the tip radius. The results from experiment (black square dots), simulation (black round circles) and analytical (red round dot) seem follow the same trend, a power-law fitting curve (red dotted-line) to the data is plotted in the figure. The simulation and experiment results overlap at R = 100?nm.

  • Table 1   Roughness of the specimen surface. Ra is the average roughness (arithmetic average), Rq is the root-mean-square roughness and Rt is the vertical distance from the deepest valley to the highest peak

    晶向

    Ra (nm)

    Rq (nm)

    Rt (nm)

    (1 0 0)

    0.170

    0.216

    1.98

    (1 1 0)

    0.201

    0.256

    2.10

    (1 1 1)

    0.261

    0.348

    3.19

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