Biomimetic Hard Materials - Engineered Biomimicry - page 63

ratios may result in brittle fracture of the tablets,
which is a detrimental failure mode. This limit
to the aspect ratio of tablets is discussed in
Section 3.2.5 .

3.2.3 Toughness

FIGURE 3.4 Representative volume element of a stag-
gered composite when loaded in tension ( U max represents
the maximum cohesive displacement).

Toughness is the most remarkable property of
hard biological materials [31, 32] . Nacre, as an
example, shows a toughness that is 3,000 times
higher than that of its main constituent (arago-
nite). Several experimental studies have identi-
fied the main toughening mechanisms of these
materials [14, 33] . Recently, it has also been
theoretically demonstrated that the toughness
achieved through the staggered arrangement of
nacre is far greater than the toughness of both
the mineral and organic mortar [26, 29] .
Several powerful mechanisms exist in nacre
to resist crack propagation and increase tough-
ness. Crack deflection, crack bridging, and
viscoplastic-energy dissipation in volumes of
material around cracks (process zone) are the
dominant toughening mechanisms. Bridging
develops as a crack advances and occurs when
mineral tablets are not completely pulled out.
The shear stresses between tablets therefore
apply closure forces to the crack faces. The pro-
cess zone, where the tablets slide onto one
another, consists of two parts: the frontal zone
and the wake. The frontal zone is the area in
front of the crack tip experiencing inelastic
deformation at the interfaces. Once the crack is
advanced through the frontal zone, the stresses
are released and some of the deformation is
recovered, leaving a wake behind the crack tip,
as depicted schematically in Figure 3.5 . The
energy is therefore dissipated through loading
and unloading of inelastic interfaces. The effect
of moisture on this inelastic behavior is also
crucial; increasing the moisture plasticizes the
organic molecules and increases their deform-
ability [9] .
When a crack advances across the direction
of the tablets, as shown in Figure 3.5 , the effect

softer than the mineral tablets ( G i  E m ) [14] .
Equation (3.2) can then be rewritten as [28, 29]

1 − ϕ
ϕ 2

1
E ≈ ϕ E M + 4 1

1 1

G I ,

(3.3)

ρ 2

where φ is the volume fraction of mineral tablets
and ρ = L / T is the tablet aspect ratio. This expres-
sion reveals the effects of microstructural param-
eters on the modulus. Thus, for constant G i , the
elastic modulus of the material converges to φE m
when the mineral volume fraction φ increases to
values near 1. Therefore, for high mineral con-
centrations, the modulus of staggered compos-
ites reaches its theoretical limit associated with
a Voigt (uniform strain) composite.

3.2.2 Strength
Under tensile loading, staggered structures fail
either at the interfaces (tablet pull-out fracture
mode) or through the tablets (brittle fracture).
The latter should be prevented so that the tablets
slide on each other and energy is dissipated
through inelastic deformation at the interfaces.
Assuming tablet pull-out fracture mode and
using a simple shear-tension load-transfer chain,
we see that the strength of the composite σ s can
be written as [30]

1
2 ρτ S ,

(3.4)

σ S =

provided that t i  t . This expression shows that
the strength of the composite is controlled by
the shear strength τ s of the interfaces and the
aspect ratio ρ of tablets. Although strength
increases with the aspect ratio, very high aspect