Biomimetic Hard Materials - Engineered Biomimicry - page 65

FIGURE 3.6 (a) Schematic of progressive tablet sliding in staggered composites. Load-transfer mechanisms in (b) flat
tablets and (c) wavy tablets ( θ is the dovetail angle).

approaching the theoretical strength of the
material. Interestingly, the size of mineral inclu-
sions in hard biological materials like bone and
tooth is on the same order [36, 37] . This suggests
that nanometer inclusions in these materials
maximize their fracture resistance.
Although in nacre the tablets are in the
micrometer range, their small size still confers
on them high strength. For example, Bekah et al .
[30] found that the aspect ratio must be small
enough so that an assumed edge crack extend-
ing halfway through the tablet is prevented
from propagating further. This condition is
given by:

improving the load transfer in biomimetic
materials.

3.2.5 Size Effects
In staggered composites, the flow of stress is
such that the interfaces are under shear while
mineral inclusions are under tension (tension-
shear chain). Therefore, the mineral inclusions
should resist high levels of tensile stress in order
to prevent brittle fracture. Brittle materials are
sensitive to initial flaws, which, for example,
include organic molecules embedded in the
mineral crystals during the biomineralization
process [34, 35] . These organic molecules are
much softer than the mineral and act as cracks
within the material.
For a cracked brittle inclusion, the condition
for failure is governed by the Griffith criterion:

ρ<0. 56 K IC

(3.7)

τ S √ T ,

where K IC is the mode-I fracture toughness of
the tablets. This expression suggests that by
decreasing the thickness of the tablets, the maxi-
mum allowable aspect ratio in the structure
increases. Increasing the aspect ratio is desirable
because it improves the performance of materi-
als with staggered structure, as indicated by
Eqs. (3.1)-(3.3) .
Bekah et al . [30] also argued that junctions in
the staggered composites act as crack-like
features when the material is loaded in tension.
Thus, decreasing the tablet thickness results in
a decrease in the size of these crack-like fea-
tures and therefore decreases the resulting
stress-intensity factor K I . Computing this

γ S
E M H ,

σ F M = α E M φ , φ = (3.6)

where σ F M is the fracture strength of the mineral,
γ S is the surface energy, h is the thickness of the
mineral tablet, and the parameter α depends on
the geometry of the crack. Based on the Griffith
criterion, Gao et al . [26] showed that the strength
of the inclusions increases when they are made
smaller, because they can only contain small
defects. In theory, inclusions smaller than a
critical size of 30 nm [26] have a strength