Page 335 - Vibrational Spectroscopic Imaging for Biomedical Applications

Raman Imaging of Str ess Patterns in Biomaterials 309

where < σ ∗ > = σ ∗ + σ ∗ + σ is the trace of the principal stress tensor,
∗
ij 11 22 33
and Π is the PS coefficient averaged among all the crystallographic
av
directions. In other words, in a randomly oriented polycrystal for
which the Raman probe is significantly larger than individual grains,
a measurement of Raman spectral shift gives direct access to the trace
of the stress tensor. In addition, the tensile or compressive nature of
the stress tensor trace can also be deduced from the positive or nega-
tive sign of the observed frequency shift Δν with respect to an
unstressed state.
Table 10.1 summarizes the stress dependence of vibrational
modes of different biomaterials in terms of their average PS coeffi-
cients Π ; the shown results are from calibration tests conducted
a
under uniaxial load in four point bending configuration on finely
grained polycrystalline hydroxyapatite, alumina, and zirconia mate-
rials. In the above formalism, the numerical values of the PS coeffi-
cients end up being altered with respect to those measured in the
respective single crystals. In addition, the PS coefficients measured in
polycrystals are also affected by the presence of secondary phases.
For this reason, in order to obtain precise estimations of the stress ten-
sor trace, calibrations should be preliminary repeated for each indi-
vidual material.

10.4 Visualization of Microscopic Stress Patterns
in Biomaterials

10.4.1 Micromechanics of Fracture and Crack-Tip Stress
Relaxation Mechanisms
Unlike the majority of synthetic ceramic materials, bone is a tough-
ened solid whose fracture resistance is cumulatively enhanced by
extrinsic mechanisms operating both in the crack wake and ahead of
the crack tip (i.e., crack-face bridging and microcracking, respec-
tively). 27,28 Fracture mechanics studies have provided quantitative
characterizations of the resistance of bone to fracture in terms of criti-
cal stress intensity factor and critical strain energy release rate as
measured at the onset of crack initiation. This approach has been
coupled with characterizations of toughness as a function of crack
length (rising R-curve behavior), which is useful to quantify the
toughening contribution arising from microscopic mechanisms occur-
ring behind the advancing crack front. 15,29 This latter approach has
also allowed scientists to explicitly demonstrate the differences in
crack propagation resistance between cortical bones of different kinds
30
and from different species. The fracture mechanics results obtained
in those studies provide an improved understanding of the mecha-
nisms associated with the failure of cortical bone, and as such repre-
sent a step forward from the perspective of developing a realistic