This study explores the interaction between crack initiation and nanomechanical properties in the crack-tip fracture process zone of Carrara marble. Specimens with preexisting cracks were loaded in a uniaxial testing machine until the process zone appeared at the tips of the preexisting cracks. ESEM analysis reveals an increase in microcrack density in the process zone with increased loading of the specimen. Nanoindentation testing comprised of lines and grids of single nanoindentations located both near and far from the process zone shows a decrease in both indentation modulus and indentation hardness near grain boundaries in intact material, and with closeness to the process zone. Ultimately, the study confirms that the crack-tip process zone manifests itself as an area of reduced indentation hardness and indentation modulus in marble.
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Appendix 1: Surface preparation for nanoindentation
Surface preparation is vital for nanoindentation. An ideal surface is smooth and flat and models the infinite half-space assumed in Eqs. 1 and 2. A non-ideal surface is “rough” or contains raised and depressed regions on the surface. The properties derived from nanoindentation on a non-ideal surface exhibit greater spread with surface roughness . Polishing, or rubbing the sample surface with abrasives in stages of decreasing abrasive size, reduces roughness and thereby produces more accurate nanoindentation results. Each nanoindentation specimen in the current investigation underwent a five-stage polishing procedure before nanoindentation testing [5, 23] (Table 6).
The Asylum Research MFP-3D Atomic Force Microscope© was used to verify the adequacy of this polishing procedure. Following statistical corrections for surface sloping and large-scale surface waviness, the final roughness, R q, was determined from (via Mountains SPM Image Analysis Software; Fig. 25):
where n is the number of pixels along the edge of the AFM scan (Fig. 25; each micrometer contains a number of pixels set by the scan resolution) and z ij is the height at a position (i, j) above or below a mean reference plane . The scans in this investigation had a resolution of 40 pixels by 40 pixels and a size of 50 μm by 50 μm. Essentially, the roughness value represents the average distance from a reference level near the sample surface to the highest peaks or the deepest valleys on the surface. Figure 25c depicts the topographical information from a single scan; the dark line through the middle represents the reference level. Roughness is formulated with respect to distances from this datum. This yielded a final roughness of R q = 9.32 nm.
Surface roughness should be less than five times the depth of nanoindentation . In this investigation, the surface roughness of 9.32 nm is far less than five times the depth of nanoindentation −250 nm. Thus, the surface preparation employed in this investigation is sufficient.
Appendix 2: Nanoindentation parameter selection
The selection of two nanoindentation parameters—load applied by the nanoindenter and spacing between indentations—affects the accuracy of nanoindentation results. If the load is too high or spacing too small, indentation-induced fractures may extend from one indentation to the next and influence the derived mechanical properties.
The appropriateness of the nanoindentation parameters was verified with ESEM. An investigation was conducted to see whether indentation-induced fracture occurred for the indentation parameters used in the study. Two types of indentations were conducted—typical indentations with parameters used through the current study and “exaggerated” indentations with a much higher (by a factor of 80) indentation load (see Fig. 26 and Table 7). It was found that no indentation-induced fracture was apparent for typical indentations. It was also found that the “exaggerated” indentations induced fracture extending only 17.2 μm, or nearly twice the typical indentation spacing. It is thus assumed that the typical indentation load of 2.85 mN avoids indentation-induced fracture and a spacing of 8 μm prevents indentations from running into any potential fracture.
Appendix 3: Nanoindentation box plots
A box plot (Fig. 27) provides a first-order means of data analysis for this investigation because it presents a concise summary of the spread and typical values of each nanoindentation test (where a single test consists of over 300 individual nanoindentations). Although box plots may assume various forms and present various statistical parameters, for the data in this investigation, the bottom and top of the whiskers correspond to the mean nanoindentation value (either modulus or hardness), respectively, minus and plus one standard deviation. The central value corresponds to the median value, and the bottom and top of the box correspond to the 25th and 75th percentile of the data. Median is used since it expresses the typical value from many nanoindentations without being susceptible to outlier values, in the way that mean is susceptible. Note that for normally distributed data sets, approximately 25 % of the data can be found between the mean and the 25th or 75th percentile. The closeness of the ends of the box (25th/75th percentile) to the ends of the whiskers (average ±1SD) indicates the spread of the data. Data sets with little spread will have larger boxes, and smaller distances from box to whiskers; data sets with more spread will have larger boxes, and greater distances from box to whiskers. The box plot thus presents a concise summary of the spread and typical values of the data from each nanoindentation test series.
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Brooks, Z., Ulm, F.J. & Einstein, H.H. Environmental scanning electron microscopy (ESEM) and nanoindentation investigation of the crack tip process zone in marble. Acta Geotech. 8, 223–245 (2013). https://doi.org/10.1007/s11440-013-0213-z
- Carrara marble
- Environmental scanning electron microscopy (ESEM)
- Fracture process zone