Indentation Deformation Mapping

Local creep deformation events were mapped using a line of nano-indentations positioned within a maximum of 250μm from the bending outer-fibers. A minimum of 100 indentations, of 200 nm depth and 1.50μm spacing using a cube-corner diamond tip indenter, were placed using the MTS Nano Indenter XP (MTS, Eden Prairie, MN) using Testworks4 control

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software under displacement control CSM mode. The indentation array, aligned parallel to the bending stress axis served as markers for mapping deformation. Cracking, from indentation, was not observed in penetration depths ≤ 200 nm for this composite. The indentation array was imaged before and after creep using either secondary (Figure 3- 7a) or backscatter electron SEM detectors and high resolution backscatter electron SEM detector, respectively. Four classes of measurements were made, with aid the of binary threshold image analysis, in the crept and un-crept conditions, for determining indentation position and hence local strain calculations: The total strain distribution, grain deformation strains, grain rotation strains, and grain translation strains. The total strain distribution was measured by assessing the horizontal displacement change between each indentation in the crept and un-crept condition, Figure 3- 7a. The grain deformation strains were calculated based on the indentation displacement change, for a single grain while grain translations were calculated from indentation displacement changes between two grains, Figure 3- 7b. Grain rotations were measured from two construction lines

intersecting the indent average center positions, Figure 3- 7c, for indentations within the same grain. The angle between the construction line and the micrograph horizontal was recorded and the corresponding displacement changes from the angular rotation used for the strain

calculation.

3.3. Mechanical Properties

Room temperature mechanical properties were assessed for all composites and monoliths using 4-pt and 3-pt bending fixtures under displacement controlled. Modulus of Rupture (MOR) and KIC Single Edge Notched Beam (SENB) experiments were conducted using screw driven Instron (Instron, Norwood, MA) loading frames controlled by Merlin II software (Instron (1 )). Load application rods and bending fixtures are made of α-SiC (Hexoloy-St.

Gobain Ceramics, Niagra Falls, NY). MOR experiments use a combination of 4-pt and 3-pt

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Figure 3-7: Un-crept state (left) and crept state (right). Vertical dotted and solid lines are indent shape boundaries based on threshold imaging and the average indent shape position, respectively.

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bending with inner and outer spans of 20/40 mm and 40 mm, respectively; SENB experiments used 10/20 mm 4-pt bending and 20 mm 3-pt. bending fixtures. Fracture stresses were calculated using linear elastic beam theory equations of the form

, (3-15)

for three point bending, and four point bending,

(

, (3-16)

under an the maximum load, P, for a bar of width B and height H over an outer span of length Lo

(3-pt.) or the difference between the inner and outer load span, Lo-Li (4-pt.). Experiments were conducted at cross-head displacement rates of 0.10 -0.15 mm/min. Fracture toughness, KIC,was calculated according to (Anderson 2005)

where a/H = 0.2-0.3 for a crack length a and P, Lo, H and B hold the usual significance for three-point bending. Considering four-three-point bending the fracture toughness is represented by (Gogotsi 2004)

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where a/H = 0.4-0.6 for a crack length a. SENB experiments were completed using cross-head displacement rates of 1x10^-4 – 5 x 10^-4 mm/min. Starting notches were cut using a 0.4 mm thick diamond wafering blade and then sharpened using 1μm diamond paste and a razor blade yielding a starting notch radius of 0.070 +/- 0.02 mm. Crack lengths were measured post mortem, using stereomicroscope and image analysis software (Nikon Nis-Elements

Documentation V3.22.00), taking the average and standard deviation of 10 measurements spaced evenly across the fracture face.

Hardness and Elastic modulus were measured using a Nano Indenter XP (Nano Instruments, Inc. Oak Ridge, TN USA) and Testworks4 version 4.06A control software under displacement control CSM mode. Additionally, Elastic modulus was also measured using the Resonant Ultrasound Spectroscopy (RUS) method at Oak Ridge National Labs (Oak Ridge, TN USA). Moduli measurements were conducted on 240 grit ground composite tiles of dimensions 15 x 15 x 4 mm, +/-0.02 mm on each dimension, rectangular parallelepipeds. This shape was chosen for simplifying the relationship between the resonance frequencies and the modulus tensor through Lagrangian minimization techniques (Migliori and Maynard 2005). Nano- indentation mechanical properties were measured using a Berkovich indenter tip for applying uniform indent loads, to sufficient depths, without cracking for hardness and elastic modulus measurement. Each specimen was ground and polished using the procedures outlined in section 3.2.2.1. Using a diamond scribe, cross-marks were placed onto the polished surface for indentation position referencing. Indentation arrays of 2 x 25 or 2 x 15 were used with

indentation spacing of 5 μm in both vertical and horizontal directions sufficiently away from the neighboring indentation. The indentation loading experimental parameters are summarized in Table 3- 3. Elastic modulus was calculated based on the relationship ((Oliver and Pharr 2004)

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Table 3- 3: Nano-indentation experimental parameters.

Parameter Value

Load 1.5 gf

# Load/Unload Cycles 5

Unload % 90%

Surface approach distance 1000 nm Surface approach velocity 10 nm/s Surface approach sensitivity 25%

Peak load holding time 30 sec

Drift rate 0.05 nm/s and displacement and the projected area of elastic contact A. Finally, the Young’s modulus, E, can be determined with knowledge of the material Poisson’s ratio, , and the indenter Elastic modulus and Poisson’s ratio and , respectively. Hardness is measured from the maximum load, Pmax, and the projected indentation area following

, (3-23)

with the projected area as a function of the indenter depth under load, ( .

Both hardness and moduli are reported for the same load displacement curve, unique to the individual indentation. For polycrystalline monoliths and composites there exists a high probability of an indentation falling on a second phase, grain boundary or other defect rather than the grain proper of the phase of interest. Therefore, a selection criterion was implemented combining load-displacement data review, optical microscopy and statistical methods for

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filtering indentations that are assumed as outliers. Metallographic inspection of the indent array allows for numbering and filtering out indents that do not fall within the phase of interest.

Additionally, any indents on or within 0.5 um of a grain boundary were thrown out as they do not represent the grain interior and any indent in contact with a preexisting defect were also discarded. Subsequent inspection of each load-displacement curve for irregularities was completed for each selected indent. For polycrystalline materials, there exists preexisting defects that might reside below the plane of polish and, therefore, require inspection of the load displacement curves for insights to the indentation depth behavior. For example, Figure 3- 8, represents a load and unloading curve for an indent centered within a grain contrasting with the same pair plots for an indent centered over a preexisting defect. Any remaining

indentations, which have passed both metallographic and load-displacement inspection, and appear as outliers are further filtered using Chauvenet criteria for data selection based on the distribution and sample population (Chauvenet 1868). An acceptable scatter, about the mean, can be determined based on the probability of rejection form normal probabilities based on the relationship

, (3-24)

where is a nondimensional maximum deviation, Sx a precision index and dmax the maximum deviation from the mean. Based on this statistical filtering, all remaining outliers, with no apparent explanation, can be discarded leaving only those which approach the true ZrB2

grain hardness.

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Figure 3-8: Nano-indentation load-displacement (top) and indentation collapse due to the presence of a pore (bottom). The hardness-depth calculations (right) indicate collapse contrasting with the observed hardness plateau.