Bone Microdamage and Its Contributions to Fracture - Skeletal Aging and Osteoporosis: Biomechanics and Mechanobiology - page 97

on calculation of work-to-fracture (area under load-deformation curve) or the
modulus of toughness (area under stress-strain curve). However, fracture resis-
tance depends on the presence of preexisting defects (i.e. microdamage) in
addition to the stress or stain applied to bone.
Hence, parallel research introduced a fracture mechanics based approach in
which a controlled crack was induced in the specimen before mechanical testing in
order to study bone's fracture characteristics. The induced sharp pre-crack func-
tions as the dominant flaw from which the crack initiates. Using a pre-cracked
specimen, toughness at initiation and propagation can be measured. Initiation
toughness (critical stress intensity factor [K c ] or strain energy release rate [G c ])
illustrates the inherent toughness of the bone whereas propagation toughness
(slope of crack growth resistance curve) illustrates bone's resistance to the prop-
agation of a crack [ 82 , 83 ]. For instance, compact tension specimens with an
induced chevron notch have been successfully used for investigation of crack
propagation and measurement of bone's fracture resistance [ 62 , 84 ]. The fracture
mechanics approach has been recently been modified for application on small
animal bones in order to measure whole bone toughness [ 82 , 83 ]. Here, pre-
cracked rodent long bones (e.g. femur) are mechanically tested via three-point
bending. To calculate fracture toughness using this method, three-dimensional
images obtained via microcomputed tomography can be utilized to pinpoint the
exact location of the notch made in the bone. A cross-sectional image of the notch
can then be imported into imaging software (e.g. ImageJ) to measure the inner and
outer radii, cortical thickness, and notch angles (initial notch and notch at the
instability region). If we assume that the test specimen can be approximated as an
edge-cracked cylindrical pipe, these measurements as well as the load obtained
during fracture can be incorporated to calculate the fracture toughness using
Eq. ( 1 ):

p

p H k ¼ F b P c S R o

p ð R o R i Þ

ð 1 Þ

where k = fracture toughness, P c = maximum load (maximum load method) or
load at fracture instability (instability method), S = span length, R o = outer
radius of cortical shell, R i = inner radius of cortical shell, R m = mean radius of
cortical shell, H = half-crack angle at crack initiation (maximum load method) or
half crack angle at fracture instability (instability method), t = cortical thickness,
and F b = geometrical factor for an edge-cracked cylindrical pipe. The geometrical
factor is computed by Eqs. ( 2 ) through ( 8 ):

" #

A b þ B b þ C b 2

þ D b

3
þ E b

4

t
2R m

H
p

H
p

H
p

H
p

F b ¼ 1 þ ð 2 Þ

A b ¼ 0 : 65133 0 : 5774n 0 : 3427n 2 0 : 0681n 3 ð 3 Þ

B b ¼ 1 : 879 þ 4 : 795n þ 2 : 343n 2 0 : 6197n 3

ð 4 Þ