112
D. W. Eastman et al.
was used in conjunction with a Mitutoyo 10× microscope objective, allowing for a
significantly smaller field of view of 1.05 × 0.77 mm 2 .
For the 20 μm FIB-machined samples, a separate custom-built load frame was
utilized. The frame was displacement-controlled using a piezoelectric actuator,
load was measured with a strain gage-based load cell, and mechanical testing was
performed in situ in a FEI Quanta SEM. The foil that the samples were machined in
was attached to a bulk sample holder that was mounted to an Attocube-controlled xy-z micro-positioning stage that allowed for precise movement and positioning. The
samples were placed into a SiC grip that was 8 mm long and 0.1 mm in diameter
and connected directly to a load cell. Stepped quasi-static tests were conducted
at an average strain rate of 10 −4 ; the samples were loaded at a constant actuator
voltage ramp rate and then held fixed for acquisition of an SEM image. A detailed
description of the in-SEM load frame and testing procedure can be found in [104,
105]. The entire process of performing the mechanical testing and collecting SEM
images was automated using custom LabVIEW scripts. A periodic grid of 250 nm
circular markers, each 200 nm deep with 1 μm spacing, was FIB-milled onto the
surface of the samples after final machining [60]. The grid of markers extended
along the entire length of the sample gage.
Once the load data from a test was collected, the nominal (engineering) stress was
determined from the recorded load and the measured undeformed cross-sectional
area of the sample. Each image had a strain and time stamp and each recorded load
value had a stress and time stamp, enabling the stress-strain response to be obtained
by stitching these two datasets together. To stitch these datasets, the time stamp was
matched every 1 s and the associated stress and strain values were extracted. The
elastic modulus of the sample was determined from the plot of engineering stress
versus strain using the slope of the linear elastic loading of the curve. Alternatively,
the elastic modulus can be measured in the plastic region if unload and reload of the
sample is performed during testing. The yield strength of each sample was defined
by the 0.2% offset.
Figure 9 presents a summary of this yield strength data from the tested samples
as a function of the normalized sample width and thickness. This normalized width
and thickness was calculated by dividing by the average grain size (20 μm) of the
material. Using this parameter gives an idea of the number of grains through the
thickness and width of the sample, and thus the total number of grains within a
sample gage volume.
The largest samples were 500 μm thick (normalized thickness of 25) and their
yield strength is consistent and comparable to bulk values from the literature [51,
106]. As the sample thickness decreases to 300 μm (normalized thickness of 15),
the average yield strength decreases slightly but remains consistent from sample
to sample, varying by less than 3%. Below this size, however, we begin to see
significant variations in sample strength, down to a value of 650 MPa for samples
with a normalized thickness of 1.
Two literature values of the bulk strength are compared with the experimental
data in Fig. 9 [107, 108], and it was found that the variations in the experimental
measurements are much greater, sometimes by an order of magnitude. The error
D. W. Eastman et al.
was used in conjunction with a Mitutoyo 10× microscope objective, allowing for a
significantly smaller field of view of 1.05 × 0.77 mm 2 .
For the 20 μm FIB-machined samples, a separate custom-built load frame was
utilized. The frame was displacement-controlled using a piezoelectric actuator,
load was measured with a strain gage-based load cell, and mechanical testing was
performed in situ in a FEI Quanta SEM. The foil that the samples were machined in
was attached to a bulk sample holder that was mounted to an Attocube-controlled xy-z micro-positioning stage that allowed for precise movement and positioning. The
samples were placed into a SiC grip that was 8 mm long and 0.1 mm in diameter
and connected directly to a load cell. Stepped quasi-static tests were conducted
at an average strain rate of 10 −4 ; the samples were loaded at a constant actuator
voltage ramp rate and then held fixed for acquisition of an SEM image. A detailed
description of the in-SEM load frame and testing procedure can be found in [104,
105]. The entire process of performing the mechanical testing and collecting SEM
images was automated using custom LabVIEW scripts. A periodic grid of 250 nm
circular markers, each 200 nm deep with 1 μm spacing, was FIB-milled onto the
surface of the samples after final machining [60]. The grid of markers extended
along the entire length of the sample gage.
Once the load data from a test was collected, the nominal (engineering) stress was
determined from the recorded load and the measured undeformed cross-sectional
area of the sample. Each image had a strain and time stamp and each recorded load
value had a stress and time stamp, enabling the stress-strain response to be obtained
by stitching these two datasets together. To stitch these datasets, the time stamp was
matched every 1 s and the associated stress and strain values were extracted. The
elastic modulus of the sample was determined from the plot of engineering stress
versus strain using the slope of the linear elastic loading of the curve. Alternatively,
the elastic modulus can be measured in the plastic region if unload and reload of the
sample is performed during testing. The yield strength of each sample was defined
by the 0.2% offset.
Figure 9 presents a summary of this yield strength data from the tested samples
as a function of the normalized sample width and thickness. This normalized width
and thickness was calculated by dividing by the average grain size (20 μm) of the
material. Using this parameter gives an idea of the number of grains through the
thickness and width of the sample, and thus the total number of grains within a
sample gage volume.
The largest samples were 500 μm thick (normalized thickness of 25) and their
yield strength is consistent and comparable to bulk values from the literature [51,
106]. As the sample thickness decreases to 300 μm (normalized thickness of 15),
the average yield strength decreases slightly but remains consistent from sample
to sample, varying by less than 3%. Below this size, however, we begin to see
significant variations in sample strength, down to a value of 650 MPa for samples
with a normalized thickness of 1.
Two literature values of the bulk strength are compared with the experimental
data in Fig. 9 [107, 108], and it was found that the variations in the experimental
measurements are much greater, sometimes by an order of magnitude. The error