Stress measurement with non-indentation Page: 6 of 8
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P= C3/2 cm- res C2 (2)
Eq. (2) was first fitted using non-linear regression to the measured lengths of
cracks at the neutral axis where ;.es is zero. This regression gave a value for X,
assuming K = 0.75 MPa(m)/2 for each of the three glasses. The crack lengths of
indents placed in the compression side of the specimen at three different distances
from the neutral axis were regressed successively using the above obtained x value
and Y = 1.29.5 These regressions gave the estimate for the local stress, ;es .
3. RESULTS AND DISCUSSION
Figure 2 shows the average crack length data for soda-lime glass plotted as
indentation load versus crack length. Error bars are also shown for the cracks
measured at the neutral axis (solid circles). Error bars of similar magnitude for the
other locations are omitted for sake of clarity. In addition, the figure shows the
regression lines (Eq. (2)) for the four different local stress locations. It can be seen
that the crack length derived stresses are within 30% of the actual bending stresses
in the beam. This is reasonable agreement considering that the crack lengths were
obtained from only five cracks at each indentation load / local stress combination.
Similar results were obtained for the fused silica and boro-silicate glasses with
the only exception of one stress level in fused silica glass where the estimate was
50% higher than the local stress. All other estimates for the three glasses were
better than 30%. These results are summarized on Fig. 3 which shows the esti-
mated stress versus the applied (local) stress. The reasonable correlation between
the estimated and applied stress is evident in the figure.
The most important result of this study is that the elastic-plastic indentation
theory relating crack length, load, and local stress is valid for very small cube-
corner indentations. However it should be noted that the indentation constant x is
different for these small indents than for the larger Vickers indents. For example, in
soda-lime glass y is 0.22 for the nano-indents used in study, whereas it is 0.055
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Jakus, K.; Evans, N.D. & Hay, J.C. Stress measurement with non-indentation, report, November 1998; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc702873/m1/6/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.