Research ArticleGEOLOGY

Size effects resolve discrepancies in 40 years of work on low-temperature plasticity in olivine

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Science Advances  13 Sep 2017:
Vol. 3, no. 9, e1701338
DOI: 10.1126/sciadv.1701338
  • Fig. 1 Examples of Berkovich and spherical indents.

    (A) Secondary electron image of a Berkovich indent. (B) Forescattered electron image of a spherical indent. (C and D) Maps of the GND densities associated with each indent as measured by HR-EBSD (25). The activation of plastic deformation mechanisms is shown by the elevated densities of GNDs around the residual indents. Radial fractures emanating from the indents result in artificially high GND densities in the immediate vicinity of these cracks. Regions of each map outside the plastic zone of the indents reveal the minimum resolvable dislocation density by HR-EBSD, which varies for each map based on the analytical conditions and crystal orientation.

  • Fig. 2 Summary of spherical indentation results.

    (A) Sample hardness-strain curves from tests with a 3-μm-radius indenter. The dashed black line is a linear fit to the hardness data after pop-in for the single crystal. This fit is projected back to the elastic portion of the data to calculate the yield hardness. (B) Inverse pole figure (IPF) representing the average hardness at yield calculated for each crystal orientation tested via spherical indentation. Each marker for a single-crystal sample represents the average of 16 tests. Each marker for the polycrystalline sample represents a single indentation test on one grain of the sample. (C) IPF illustrating the measured Young’s modulus for the same orientations as in (B). The background is colored by the theoretical Young’s modulus from Abramson et al. (28).

  • Fig. 3 Size effects observed by spherical and Berkovich indentation.

    (A) Spherical indentation size effect for four different orientations of olivine as a function of contact radius at yield. Data for a fifth orientation (shown in purple) are also plotted but were only measured with a single indenter tip. Plotted values of yield hardness are averages over 12 to 16 tests. (B) Berkovich indentation size effect for a single orientation of olivine, as illustrated in the inset. Markers for non-CSM (continuous stiffness measurement) tests are averages of 6 to 10 tests.

  • Fig. 4 Comparison between observed size effects in our indentation tests and previously published low-temperature plasticity flow laws extrapolated to room temperature.

    Yield stresses from flow laws are calculated for a strain rate of 0.01 s−1 and a confining pressure of 3 GPa to approximately match the strain rate and confining pressure of indentation tests. Data from Druiventak et al. (11) are not from a flow law but are approximate yield stresses from experiments obtained at room temperature and confining pressures of 2.0 to 2.5 GPa. These yield stresses likely reflect plasticity before any brittle deformation. Flow laws from past indentation studies (6, 16), as well as indentation data from this study, are plotted using contact radius as the length scale, whereas flow laws based on tests on polycrystalline samples (813, 18) are plotted using grain size. The predicted yield stress from Idrissi et al. (17), in which dislocation velocity was measured to calibrate a flow law, is assumed to be independent of scale. The predicted yield stress from Kranjc et al. (16) has been rescaled following the method used by Evans and Goetze (6) to calculate the constraint factor (the original data point is plotted as an open pentagon). This rescaling has been performed so that all estimates from indentation experiments using sharp tips are processed in the same manner. The dark gray band represents the approximate size effect observed in all data, with the hatched gray field indicating even larger yield stresses when the dislocation source density is low. Relevant geological length scales are indicated (38, 39, 4145). The predicted stress from Demouchy et al. (14) is not included because their flow law is calibrated using the maximum stress observed in experiments rather than the yield stress.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1701338/DC1

    Supplementary Materials and Methods

    fig. S1. EBSD map of the 120-indent array on PI-1488.

    fig. S2. Zero-point correction for spherical indentation.

    fig. S3. Creation of new surface crack due to stress release from FIB milling.

    fig. S4. Four groups of hardness-strain curves proceeding to different total strains on sample OP4-2.

    fig. S5. EBSD map of a portion of PI-1488, colored by GND density.

    table S1. Summary of deepest spherical indentation tests.

    table S2. Summary of non-CSM Berkovich indentation tests.

    References (5059)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials and Methods
    • fig. S1. EBSD map of the 120-indent array on PI-1488.
    • fig. S2. Zero-point correction for spherical indentation.
    • fig. S3. Creation of new surface crack due to stress release from FIB milling.
    • fig. S4. Four groups of hardness-strain curves proceeding to different total strains on sample OP4-2.
    • fig. S5. EBSD map of a portion of PI-1488, colored by GND density.
    • Legends for tables S1 and S2
    • References (50–59)

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    Other Supplementary Material for this manuscript includes the following:

    • table S1 (Microsoft Excel format). Summary of deepest spherical indentation tests.
    • table S2 (Microsoft Excel format). Summary of non-CSM Berkovich indentation tests.

    Files in this Data Supplement: