Table1.
Sample sizes and geometries used by other researchers.
Figure 1.
Miniature SE(B) sample preparation from a human femur.
Figure 2.
Outline of the “Whitening Front Tracking” algorithm.
Figure 3.
Time-lapsed snapshots of the fracture toughness experiment on an SE(B) sample also presented in video S2.
(left) Force – Displacement curve; (middle) damage localization on the calculated difference image; (right) Calculated whitening front propagation –top-most white localiser pixel pointed by the white arrow on damage localization picture– red X represents point of failure.
Figure 4.
Crack- and Whitening Front- propagation relationship.
(top left) Schematic representation of crack- and whitening front- propagation for three arbitrary time – displacement points (t1,2,3,v1,2,3). (top right) whitening front- and crack propagation relationship. Intra-observer variability is visualised on the plot by error bars indicating the standard deviation across the five repetitions. Note that both crack tip and whitening front are propagating in sync with the whitening front being constantly ∼400 µm ahead of the crack tip. (bottom) Gamma corrected frames of a rat tibia sample showing the crack tip (black arrow) and the whitening front (white arrow) propagation during three points bending for the displacement points v1, v2 and v3. Double arrowed lines represent the distance of the crack tip and the whitening front from the pre-notch.
Figure 5.
SRµCT imaging of a partially failed bone specimen.
(top left) Three-point bending test videography. Comparison between the start- and end-frame of a three point bending test of a miniature human bone sample. In the end-frame, note the development of the two distinct whitening zones one close to the notch and the other close to the osteon. Also note the “absence” of visible crack with the use this optical setup; (top right) Schematic representation of the SRµCT ROI; (bottom) SRµCT analysis of the same sample. The higher resolution of SRµCT revealed a “clear” crack at the surface of the specimen and areas of extensive micro-cracking and diffuse damage formation in the bulk. These areas coincide spatially with the whitening areas shown in the end-frame of the videography.
Figure 6.
(left) strain distribution on a three-point bending notched beams with notch-lengths of a0 = 0, 0.075, 0.15 and 0.3 mm; (top-left) variation of the specimen’s stiffness, i.e. slope of load – displacement curve, for different notch-lengths; (bottom-left) relationship between the measured modulus, Eao = n, of a notched sample value and the notch-length.
Figure 7.
Evolution of damage zone (whitening) during the three-points bending test of an SE(B) specimens.
(top) Gamma-corrected and false-coloured frames of a human cortical bone sample showing the sample at the beginning of the test (first frame), at the appearance (second frame) and the propagation (third frame) of the whitening front during three point bending at different time – displacement points. Sample width (W) is 930 µm and the pre-notch (a0) is 450 µm. t0,v0 correspond to point where load and displacement equals 0, t1… t2…. (bottom) Schematic representation of the damage zone formed when bridging and microcracking initiate in front of the crack tip as a result of local stress and strain concentration. The “whitening effect” is deemed to be the result of increased light reflection on the surfaces of the newly formed micro-cracks within this damage zone.
Figure 8.
Initiation of the whitening effect at the initial notch.
(top left) Load – displacement curve of a human sample under three point bending. The green line corresponds to the point when the whitening effect is first detected. Top right and bottom right images show the raw and the difference image of this point. Initiation of the whitening effect is localized at the difference image. Note that the whitening effect appears on the surface of the sample when the Load-displacement curve diverges from linearity (red line) and enters the plastic deformation area.
Figure 9.
Representative “crack” resistance curves of three human bone samples expressed in terms of J and Keff.
Figure 10.
Schematic representation of the three possible cracking orientation of bone.
In the “breaking” configuration, the notch is oriented perpendicularly to the long axis of the osteons, breaking through them during the propagation. This is the most energy consuming mode resulting in a steeply rising fracture resistance curves as shown by Koester et al. [11]. In the “splitting” configuration, the notch is oriented parallel to the long axis of the osteons, splitting them apart during propagation. In this mode the crack is mainly thought to be following the osteonal cement lines and very small amount of crack deflection is taking place. This results in significantly lower “crack” resistance behaviour in comparison to the “breaking” mode [11]. Finally in the “separating” configuration the notch is oriented perpendicularly to the osteons long axis, as in the “breaking” mode but this time, because of the anti-plane orientation, the crack is thought to be mainly propagating around the osteons following the cement lines instead of breaking thorough them. This results in resistance behaviour between the two “extreme” modes closer to the “splitting” one.