Microscale Testing and Characterization Techniques for Benchmarking Crystal. . .
113
Fig. 9 Plot of sample yield strength vs normalized sample thickness and reference data from
literature. The error bars on each data point represent the maximum potential error of each
measurement
bars for each sample in Fig. 9 represent the maximum potential error for the
measurement. The maximum total error, calculated from the maximum error of
all sources of measurement errors in the experimental design, was found to be
6.6%, corresponding to a stress of 40–50 MPa. This indicates that experimental
error cannot account for the data scatter, and that the scatter in the experimentally
measured yield strengths is an effect of the sampled microstructure. The overall
increase in scatter with decreasing sample size matches the expectation that smaller
samples are dominated by a limited number of grains, and therefore microstructure
plays a more significant role in determining the strength of the sample. By
comparison, larger samples have many grains and the microstructural effects are
averaged out.
Although the scatter matches the predicted variability of yield strength as a
function of sample size, no increase in yield strength was observed at any sample
size as was initially expected. In order to understand this behavior in more detail,
a numerical study was performed, in collaboration with George Weber et al., to
investigate the potential role of grain orientation on the distribution of resolved
shear stresses for polycrystalline samples of variable size [60]. This simple model
was based on Schmid factor analysis and conducted to gain insight into how
finite sampling of grain orientation would affect the measured strength. This is a
qualitative approach, since it ignores grain-to-grain interactions and the complex
nonuniaxial loading states that may arise within individual grains [20].
For this estimate, the gage volume of a tensile sample was modeled with cubic
grains of a uniform size, and the sample was taken to have a square cross-section
and a 5:1 aspect ratio. Each grain within the gage was assigned a random orientation
and its maximum Schmid factor was calculated, defining the corresponding strength
of that grain. The strength of a sample was determined as follows. The individual
113
Fig. 9 Plot of sample yield strength vs normalized sample thickness and reference data from
literature. The error bars on each data point represent the maximum potential error of each
measurement
bars for each sample in Fig. 9 represent the maximum potential error for the
measurement. The maximum total error, calculated from the maximum error of
all sources of measurement errors in the experimental design, was found to be
6.6%, corresponding to a stress of 40–50 MPa. This indicates that experimental
error cannot account for the data scatter, and that the scatter in the experimentally
measured yield strengths is an effect of the sampled microstructure. The overall
increase in scatter with decreasing sample size matches the expectation that smaller
samples are dominated by a limited number of grains, and therefore microstructure
plays a more significant role in determining the strength of the sample. By
comparison, larger samples have many grains and the microstructural effects are
averaged out.
Although the scatter matches the predicted variability of yield strength as a
function of sample size, no increase in yield strength was observed at any sample
size as was initially expected. In order to understand this behavior in more detail,
a numerical study was performed, in collaboration with George Weber et al., to
investigate the potential role of grain orientation on the distribution of resolved
shear stresses for polycrystalline samples of variable size [60]. This simple model
was based on Schmid factor analysis and conducted to gain insight into how
finite sampling of grain orientation would affect the measured strength. This is a
qualitative approach, since it ignores grain-to-grain interactions and the complex
nonuniaxial loading states that may arise within individual grains [20].
For this estimate, the gage volume of a tensile sample was modeled with cubic
grains of a uniform size, and the sample was taken to have a square cross-section
and a 5:1 aspect ratio. Each grain within the gage was assigned a random orientation
and its maximum Schmid factor was calculated, defining the corresponding strength
of that grain. The strength of a sample was determined as follows. The individual